JP3824540B2 - Structure with fold line, fold line forming mold, and fold line forming method - Google Patents

Description

次に図１８９Ａの各要素の展開図を２Ｎ等分（Ｎ；整数）する。この時、螺旋状の折り線になるよう図のように半径方向と角θをなすような角度で展開図上に分割線を描く。図１８９Ａは各展開図を１６等分したものである。分割された小要素を半径方向に積上げ新たに扇形要素を作る。積上げて構成された扇形要素を図１８９Ｂに示し、これは湾曲した形状の扇形要素を表す。この湾曲形状の扇形要素を１６個接合し、接合線を交互に山、谷折り線とすると、螺旋形折り線を持つ放物面形状殻（図１８３参照）が得られる。図１８３の放物面形状殻の頂点を通る中心軸回りに巻取ったものは図１８４、図１８５に示されている。
（実施例３０）
図１９０は本発明の実施例３０の折り線付構造物としての巻取式のテントの斜視図である。
図１９１は前記図１９０の巻取式のテントの折り畳み途中の状態の斜視図である。
図１９２は前記図１９０の状態から更に折り畳んだ状態のテントの斜視図である。
図１９０において、巻取式のテントＨは、山折り線Ｍおよび谷折り線Ｖが等角螺旋（ベルヌーイの螺旋）に沿って形成されており、前記折り線Ｍ，Ｖにより形成された扇形のパーツを、折り線Ｍ，Ｖに沿って折り畳みながら巻き取ることができる。テントＨは伸長状態ではドーム型となり、その外側面の外周部および半径方向の中央部にはそれぞれ円周方向に延びるリング状のフレキシブルチューブＨ１およびＨ２が固着されている。前記テントＨは、前記フレキシブルチューブＨ１，Ｈ２にエアを供給して膨らますことにより、図１９０の伸長状態に保持される。
この実施例３０では、殻を構成する膜厚が大きい時には中央部分で巻き取りが窮屈になる場合があるので、これを避けるため前記図１８９Ａを分割する際、最初８等分し、次にこれを適当に不等分に分割する。
すなわち８等分した後、これを更に中心角比０．４７５：０．５２５で２分割して構成した時の湾曲形状の扇形要素の組８個（１６要素）を交互に接合して構成した曲面は図１９０に示されている。ここで中心角の小さな要素の左方を谷折り、右方を山折りとすると中心軸回りに下方にずれながら巻き取られる。これを図１９１、図１９２に示す。この巻取り法は上述の窮屈度合いを緩和させる利点がある。
これ等のモデルは巻取り／展開可能な大型のテント以外に、パラボラアンテナのパラボラ面を形成するのに利用可能である。
産業上の利用可能性
以上、本発明の実施例を詳述したが、本発明は、前記実施例に限定されるものではなく、特許請求の範囲に記載された本発明の要旨の範囲内で、種々の変更を行うことが可能である。本発明の変更実施例を下記に例示する。
（１）前記実施例１、２では、折り線形成用型は、一対の折り畳み可能な折り線形成部材（ｆｌｅｘｉｂｌｅ金属）を有し、前記一対の折り線形成部材によりシート状部材を挟んだ状態で一対の折り線形成部材を同時に折り畳むことにより、シート状部材に折り線を形成するように構成したが、折り畳み可能な折り線形成部材（ｆｌｅｘｉｂｌｅ金型）は一対ではなく、１枚だけでもよい。折り線形成部材を１枚とした場合には、その一面側にシート状部材を吸着した状態で折り畳めばよい。前記シート状部材を吸着する方法としては、例えば、折り線形成部材のパーツに通気孔を開けておいて、他面側を低圧にすることにより一面側にシート状部材を吸着することが可能となる。
また、磁化した材料製のパーツを使用した折り線形成部材と、柔軟な磁性ラバーシートとの間にシート状部材を挟んだ状態で折り線形成部材を折り畳むことにより折り線を形成することが可能となる。
（２）前記本発明者の研究結果および各実施例の説明から分かるように、本発明は新規な折り畳み可能な折り線により種々の形状の折り線およびパーツを使用可能となったので、多種多様な折り線付の折り畳み可能構造物を得ることが可能である。したがって、本発明は、種々の形状の伸長、収縮可能な宇宙空間構造物を構成することが可能である。Technical field
The present invention relates to a structure with a fold line, a fold line forming mold, and a fold line forming method that can be folded so as to be deformed between a folded state in which the outer shape is reduced and a developed state in which the outer shape is increased. A plate-like, cylindrical or conical wall-shaped structure is divided into polygonal parts (flat plate walls) such as triangles or quadrangles by a large number of folding lines, and the boundary parts of the divided parts (flat plate walls) are folded. The present invention relates to a folding structure with a folding line that can be folded.
The present invention can be applied to a plate-like object with a folding line, and a cylindrical object and a cone-like object with a folding line that can be folded in the axial direction, for example, a rigid plate-like member such as a floor or a bottom wall, The present invention can be used for various containers having a cylindrical wall such as a plastic bottle, an object having a conical wall such as a lamp shade, a space structure, and a building structure.
Background art
Research on the development of folding and unfolding structures has progressed in relation to the study of plastic buckling using the folding method, or the construction of antennas and solar cell structures for deployment in space. did. These studies have also been applied to research aimed at elucidating the growth and motor functions of living organisms, such as the mechanism of folding insect wings and leaves.
Planar folding structures and foldable cylindrical structures having foldable folding lines are conventionally known (see (J01) and (J02) below), but conical folding structures having foldable folding lines are It is not known so far.
As a conventional foldable structure with fold lines, it has been devised mainly for the development of space structures, and the following techniques (J01) and (J02) are known.
(J01) Planar folding structure
As a flat folding structure, Miura ori using folding lines of origami (concept of unfolding space structure [written by Kimisuke Miura, Journal of the Japan Society of Mechanical Engineers, Vol. 90, No. 828, issued in November 1987, P1394] ~ 1400]) is conventionally known. Miura ori divides a planar structure into a large number of parallelograms formed by fold lines, and is a flat plate with an expanded outer shape in the expanded state where the fold lines are extended, and the outer shape is reduced and thickened in the folded state. It becomes a flat plate shape with increased unevenness.
(J02) Cylindrical folding structure
As a conventional cylindrical folding structure, a folding cylinder having a triangular folding line is described in the following document.
(A) The Folding of Triangulated Cylinders, Part I: Geometric Considerations (S.D.Guest, S.Pellegrio, Journal of Applied Mechanics, DECEMBER 1994, Vol.61 / 773-777)
(B) The Folding of Triangulated Cylinders, Part II: The Folding Process (S.D.Guest, S.Pellegrio, Journal of Applied Mechanics, DECEMBER 1994, Vol.61 / 778-783)
(C) The Folding of Triangulated Cylinders, Part III: Experiments (S.D.Guest, S.Pellegrio, Journal of Applied Mechanics, MARCH 1996, Vol. 63 / 77-83)
In the above references (a) to (c) by SDGuest, S. Pellegrio, etc., a cylindrical wall is divided into a large number of triangular plate walls by a large number of folding lines including folding lines formed along a spiral. It is described that a foldable cylindrical wall can be formed by foldably connecting the boundary portions of each triangular flat plate wall. In the above-mentioned document, the length of the side of a triangle that can be folded is shown by numerical calculation. Judging from the length of the side of the triangle indicated by the numerical calculation, the shape of the foldable triangle appears to be a triangle approximate to an isosceles triangle having a base angle of about 30 °.
The cylindrical folding structure described in the documents (a) to (c) becomes a cylinder in the unfolded state where the folding line is extended, and becomes a cylindrical body contracted in the axial direction in the folded state.
(Problems of conventional technology)
In the conventional planar folding structure and the cylindrical folding structure, the condition of the folding line that can be folded is not known. Therefore, the folding line used is used within a range that is empirically known. . That is, the flat plate wall formed by the folding line used is limited to a parallelogram in a planar folding structure, and limited to a triangle in a cylindrical folding structure.
The conventional foldable cylindrical folding structure is premised on having a fold line along the spiral, and the shape of the flat plate wall formed by the fold line has a base angle of about 30 °. This is only a triangle similar to the isosceles triangle.
Even if research on the use of a folding structure such as the planar folding structure and the cylindrical folding structure is conducted within a narrow range that is empirically known, a new fold line of the folding structure can be obtained. It seems that it is not easy to find and find a folded structure using a new fold line.
The present inventor can easily discover a new folding method of a folding structure and invent and use the new folding structure when the conditions of the folding line of the folding structure in which the folding line is formed are clarified. I thought.
Therefore, the present inventor conducted a study (study on a folding method) for finding a folding line condition of a folding structure (folded structure) with a folding line in advance.
In addition, research on a folding structure that can be folded by a conventional folding line is often performed using an origami model using origami, but the folding line that can be folded is complicated. For this reason, it takes time to form a foldable folding line. In particular, it takes time to form a fold line on a sheet that is more rigid than origami.
Therefore, the present inventor has studied a method for easily forming a fold line on a sheet-like member such as paper, metal foil, or plastic sheet.
What has been found in the above-described research on the folding method and the folding line forming method will now be described.
(Research results of folding method and folding line formation method)
As a result of research on a folding method of a folding structure and a folding line forming method of a sheet-like member, the present inventor has found the following.
(A) The plane wall and the pseudo cylindrical wall and conical wall formed by a large number of divided plane walls may be formed by a large number of divided plane walls having a predetermined shape divided by a large number of linear folding lines. it can. In that case, the plane wall, the cylindrical wall, and the conical wall can be folded when the fold line satisfies a predetermined folding condition.
(B) The inventor has clarified all the folding conditions of the planar wall, the cylindrical wall, and the conical wall. According to the folding conditions, the shape of a large number of divided planar walls of a predetermined shape obtained by dividing a planar wall or a cylindrical wall by folding lines is the shape that has been studied in the past (in the case of a parallelogram or a cylindrical wall in the case of a planar wall). Various shapes other than isosceles triangles and isosceles trapezoids are possible.
(C) By folding the plate with the folding line half-folded or completely with the sheet-like member sandwiched between two folding lines with the same folding line, the sheet-like member can be easily folded. It is possible to form.
Next, the details of the research results will be explained.
Here, focusing on clarifying the possibility of folding from a geometric point of view, we will first discuss general folding methods using origami models, and then describe a foldable cylindrical structural model. After that, the folding performance of the cylinder manufactured using the polymer sheet will be described.
In addition, after obtaining geometrical models using collapsible ideas for creating collapsible conical structures that have not been reported so far, these models can be developed by combining equiangular spirals. Analyze that the figure is represented.
(1) Planar folding structure with folding lines
1. Folding method
FIG. 1 is a fold line explanatory view showing a typical example of a fold line that is a folded straight line of origami or a folded structure and a node that is an intersection of a plurality of fold lines.
In FIG. 1, the fold line by mountain fold is represented by a solid line (M1, M2, M3), the valley fold line is represented by a broken line (V1), and the numbers of mountain fold and valley fold lines joining the nodes are NM and NV, respectively. . It is well known that the following equation holds between NM and NV at a node.
│NM-NV│ = 2 (1)
If the total number of folding lines is NT, NT = NM + NV. If, for example, NM−NV = 2 in Equation (1), NT = 2 (1 + NV), and it can be seen that the number of folding lines constituting the node is “even”. The total number of fold lines NT is NT ≧ 4, and NT = 4 is the minimum number of fold lines for constituting a node.
When the X axis is aligned with the mountain fold line (M3) and the mountain folds (M1) and (M2) are performed as shown in FIG. 1, valley fold (V1) occurs. If the angles between the mountain folds (M1) and (M2) and the X axis are α and β, respectively, the angle γ between the fold lines (V1) and (M2) is
γ = α (2)
Given in. Expression (2) is a relational expression of angles when the sheet is completely folded at the fold lines (M1), (M2), (M3), and (V1) in the Y-axis direction.
By this operation, the belt-like paper is folded in half, and the axial direction to the right of the node is bent by 2α (when α <β) or 2β (when α> β).
When α = β, the axial direction is not bent in the Y-axis direction. At this time, if the mountain fold and the valley fold are alternately performed, the belt-like paper is bent zigzag, and if only the mountain fold (or valley fold) is continuously performed, it is easily guessed that it becomes a cylindrical shape.
In this specification, the plane paper is folded in a zigzag manner and folded into a new plane as “planar folding”, and the folding method for producing a cylindrical structure that can be folded in the same direction and folded in the Y-axis direction is “cylindrical”. It is roughly classified as “Ori”.
2 Plane fold
2.1 Miura ori (Prior art)
In order to examine the possibility of structure construction, consider the simplest case of “1-node 4-fold line”.
FIG. 2 is an explanatory view of a so-called “Miura ori” folding structure devised by Miura for the development of a space structure.
In FIG. 2, the fold line of the foldable structure has three horizontal fold lines ((1) to (3)) and three zigzag fold lines (respectively, mountain, valley, mountain fold line, (4) To (6)). The fold lines (1) to (3) are alternately mountain-folded and valley-folded so that the expression (1) is satisfied, and each of the fold lines (4) to (6) is the fold line (1) to (3). “Symmetric” for everything. Therefore, at each node (black dot), the folding condition of Expression (2) is automatically satisfied for an arbitrary angle α in the drawing, and can be completely folded in the Y-axis direction in the drawing.
At this time, it contracts in the X-axis direction depending on the angle α, and the amount of contraction increases as the folding angle α increases. Further, as can be seen from FIG. 2, the horizontal fold line alternately changes from mountain fold to valley fold and from valley fold to mountain fold on the left and right of the node. This characteristic of the 4-fold line method makes it possible to periodically fold flat paper from Y = + ∞ to −∞.
FIG. 3 is a diagram in which the horizontal folding lines shown in FIG.
In FIG. 2, the fold lines (4) to (6) are symmetrical with respect to the horizontal fold lines (1) to (3), but the horizontal folds are zigzag at the same angle as in FIG. 3 is satisfied, the folding condition in the Y-axis direction of Expression (2) is satisfied, and the flat paper in FIG. 3 is completely folded in a new form. It can be seen that if this folding is in a half-folded state, the flat paper can be made three-dimensional, that is, in an “apparent” thickness state, and a high-rigidity and lightweight flat plate can be manufactured.
2.2 Generalization of plane folding
If the horizontal fold lines provided in the zigzag in FIG. 3 are continued in the same direction, the fan or disk can be folded in the radial direction.
FIG. 4 is a diagram illustrating an example of a foldable folding line of a part of a disk (fan-shaped portion) formed by six fan-shaped elements having an apex angle 2Θ.
In FIG. 4, the folding lines (1) to (5) in the circumferential direction are bent by 2Θ. The folding lines (7), (8), (9),... In the radial direction are provided in a zigzag manner within an angle Θ, and the outer sides A, B, C,.
At this time, since the angle β in FIG. 4 is α0 + Θ due to the periodicity of these folding line groups, if the angle α1 formed by the circumferential folding line (1) and the radial folding line is α0−Θ, The folding conditional expression (2) is satisfied. That is, if the angle between the folding line in the radial direction and the folding line in the circumferential direction is selected as α0−Θ, α0−2Θ... As shown in the figure, the folding condition is satisfied at all nodes, and the fan-shaped A development can be drawn that allows the plate to be folded radially.
It is to be noted that, similarly to the fan-shaped plate, it is possible to draw a development view in which the disc can be folded in the radial direction.
FIG. 5 is a diagram in which the horizontal fold line group shown in FIG. 2 is set at an arbitrary inclination. The fold lines (7) to (9) are equal to the fold lines (1) to (6) at all nodes. It is the figure drawn in the angle and symmetry.
As shown in FIG. 5, when the fold lines (7) to (9) are drawn equiangularly and symmetrically with respect to the fold lines (1) to (6), the folding condition is satisfied at each node. It can be folded in the Y-axis direction.
Here, α1 and β1 (initial values) can be freely selected.
FIG. 6 is a diagram showing an example of folding lines taking into account the periodicity of the folding method of FIG.
In FIG. 6, the fold lines (1) to (6) in the horizontal direction indicate a fold line group having minute angles ± θ alternately with the horizontal direction. The zigzag of the vertical fold line groups (7), (8),...
FIG. 7 is a diagram showing an example of the folding method considered by the present inventor, showing plane folding by the 1-node 4-fold line method and the 1-node 6-fold line method.
In FIG. 7, even if the 6-fold line method and the 4-fold line method of symmetrical fold lines are combined with respect to the horizontal fold line, the flat paper can be folded in a zigzag manner, similarly to Miura ori shown in FIG. .
FIG. 8 is a diagram showing folding conditions of one node where six folding lines among the nodes shown in FIG. 7 intersect and six surrounding folding lines (one node six folding lines).
As shown in FIG. 8, there is a combination in which two valley fold lines are inserted at symmetrical positions of four mountain fold lines when one node has six fold lines. This shows the angle relationship that satisfies the folding condition in the folding line method frequently used in this specification.
The mountain fold line is (M1), (M2), (M3), (M4), the valley fold line is (V1), (V2), and the extension line of the fold line (V1) is the X axis. The angles formed by the folding lines (M1) and (V1), (M2) and (V1) are α and β, the angles formed by (M3) and (V2), (M4) and (V2) are γ and δ, If the angle formed by V2) and the X axis is θ, the folding condition is expressed by the following equation (3).
β−α = δ−γ + θ (3)
The fact that the equation (3) is established is proved as follows using the equation (4) described later.
In the case of the 6-fold line method shown in FIG. 8, a condition for folding in the Y-axis direction at the node A is derived. The XY axis is taken as shown in the figure with the node A as the origin. The angles formed by the folding lines (M1), (V1), (M2) and the vertical line (P) to the X axis are p1, p2, p3, the vertical line (Q) and the folding lines (M4), (V2), ( If the angles formed by M3) are q1, q2, and q3, p1 = π / 2-α, p2 = π / 2, p3 = π / 2 + β, q1 = π / 2 + δ + θ, q2 = π / 2 + θ, q3 = π / 2-γ + θ.
Expression (4) is used as a vector pointing in the same direction based on the symmetrical position (points A and B) of the X axis in the region of X <0 by mountain fold (M1), (M2), and valley fold (V1). And an angle of PL = (− α + β + π / 2) after folding.
In the region where X> 0, the vector in the same direction based on the points C and D is folded by mountain folding (M3), (M4), and valley folding (V2), and then QR = (δ−θ−γ + π / 2). Since the points A and C and the points B and D are on the same plane and these vectors point in the same direction, when PL = QR is set, Expression (3) is obtained.
When (V2) and the X axis coincide with each other, θ = 0 is established and the following expression (3 ′) is established.
β−α = δ−γ (3 ′)
In the case of the 6-fold line method, mountain folding (or valley folding) is always performed on both sides of the central node. When this folding method is repeated, the paper is folded in the same direction, and the flat paper is automatically formed into a cylindrical shape. On the other hand, in order to perform planar zigzag folding using the 6-fold line method, it is indispensable to combine this fold line method with the previous 4-fold line method (see FIG. 2) (see FIG. 7).
(2) Cylindrical folding structure with folding lines
It is easily guessed that a cylinder that can be folded in the vertical direction can be manufactured by performing equiangular mountain folding continuously. Hereinafter, it will be considered to produce a foldable cylinder by such an operation.
1. A strip with a cylinder developed
FIG. 9 is a diagram for explaining the conditions under which both ends of the band plate are joined to form a cylinder when the band plate is folded along the fold line, and FIG. 9A shows the angle between the band plate, the fold line, and the fold line. FIG. 9B is a diagram showing a change in the orientation of the reference axis when folded along the fold line shown in FIG. 9A.
Let us consider a case where the band plate is folded in a mountain and valley folds alternately or N-diffracted in the same direction as shown in FIG. 9A (N: even number). The angles formed by the N fold lines (1), (2),... And the X axis are θ1, θ2,..., Θn, and the axial directions after being folded are X1, X2,. By the first folding operation (fold line (1)), the right portion of (1) becomes the back surface.
By this operation, the new axis (X1) forms an angle of 2θ1 = Θ2 with the X0 axis (see FIG. 9B). When the second fold is performed at the fold line (2), the X2 axis forms an angle Θ2 = 2θ1-2θ2 with the reference axis X0. By folding (3), the X3 axis is at an angle of X0 and Θ3 = 2 (θ1−θ2 + θ3). By these series of folding operations, the front and back surfaces appear alternately, and the angle ΘN (when N = even number) formed by the XN axis and the reference axis by N folding operations is expressed by the following equation.
ΘN = 2 [θ1-θ2 + θ3 -...- θN] (4)
When this strip is folded, the condition for joining (closing) the left and right ends of the strip without gap is given by the following equation (5) when n is an integer other than 0.
ΘN / 2π = n (5)
Next, an example in which the left and right ends of the strip folded so as to satisfy the formula (5) are joined without a gap will be described with reference to FIGS.
FIG. 10 is an explanatory diagram of an example in which the formula (5) is satisfied and the folding direction is folded into a regular quadrangle by a folding line in the same direction (either mountain fold or valley fold), and FIG. 10A is in an unfolded state. FIG. 10B is a diagram showing a state during folding, and FIG. 10C is a diagram showing a folded state. FIG. 10B is a diagram showing folding lines (1), (2), (3), and (4).
In FIG. 10A, fold lines (1), (2), (3), (4) folded in the same direction (either mountain fold or valley fold) of the strip extending in the X-axis direction as the reference axis are respectively The angles θ1, θ2, θ3, and θ4 are formed with respect to the X axis, and θ1 = θ3 = 135 ° and θ2 = θ4 = 45 °. That is, the folding lines (1), (2), (3), (4) are formed in a zigzag manner at 45 ° (= π / 4) with respect to the X axis. Further, the X0 axis is the left side of the fold line (1) of the X axis, and the X axis portion on the right side of each fold line (n) when n = 1, 2, 3, 4 is Xn axis (n = 1). To 4).
In FIG. 10C, the angle Θ2 formed by the axis X2 and the axis X0 is Θ2 = 2 (θ1-θ2) = 2 (135 ° −45 °) = 2 × 90 ° = 180 ° = π.
The angle Θ4 formed by the axis X4 and the axis X0 is Θ4 = 2 (θ1−θ2 + θ3−θ4) = 2 (135 ° −45 ° + 135 ° −45 °) = 2π. Therefore, n in the equation (5) is n = (Θ4 / 2π) = 1, and the axis X4 overlaps the axis X0. In this case, both ends of the strip are joined without a gap.
FIG. 11 is an explanatory diagram of an example in which the expression (5) is satisfied and the folding direction is folded into a regular hexagon by a fold line in the same direction (either mountain fold or valley fold), and FIG. 11A is in an unfolded state. Fig. 11B is a diagram showing the folding line (1), (2), (3), (4), (5), (6) of the band plate, Fig. 11B is a diagram showing a state during folding, and Fig. 11C is a folded state. FIG.
In FIG. 11A, fold lines (1) to (6) folded in the same direction of the strip extending in the X-axis direction as the reference axis form angles θ1 to θ6 with respect to the X-axis, respectively, and θ1 = θ3 = θ5. = 150 °, θ2 = θ4 = θ6 = 30 °. That is, the folding lines (1) to (6) are formed in a zigzag manner at 30 ° (= π / 6) with respect to the X axis.
In FIG. 11, the angle Θ6 formed by the axis X6 and the axis X0 is Θ6 = 2 (θ1-θ2 + θ3-θ4 + θ5-θ6) = 2 (150 ° -30 ° + 150 ° -30 ° + 150 ° -30 °) = 2 × 2π. . Therefore, n in the equation (5) is n = (Θ6 / 2π) = 2, and the axis X6 overlaps the axis X0. In this case, both ends of the strip are joined without a gap.
FIG. 12 is an explanatory view of an example in which the above formula (5) is satisfied and the folding direction is folded in a regular octagon by a folding line having the same folding direction, and FIG. 12A is a folding line (1), (2 ),... (8), FIG. 12B is a diagram showing a state during folding, and FIG. 12C is a diagram showing a folded state.
In FIG. 12A, the fold lines (1) to (8) folded in the same direction of the strip extending in the X-axis direction as the reference axis form angles θ1 to θ8 with respect to the X-axis, respectively, and θ1 = θ3 = θ5. = Θ7 = 157.5 °, θ2 = θ4 = θ6 = θ8 = 22.5 °. That is, the folding lines (1) to (8) are formed in a zigzag manner at 22.5 ° (= π / 8) with respect to the X axis.
In FIG. 12, the angle Θ8 formed by the axis X8 and the axis X0 is Θ8 = 2 (θ1-θ2 + θ3-θ4 + θ5-θ6 + θ7-θ8) = 2 (157.5 ° -22.5 ° +... + 157.5 ° -22.5 ° ) = 3 × 2π. Therefore, n in the equation (5) is n = (Θ8 / 2π) = 3, and the axis X8 overlaps the axis X0. In this case, both ends of the strip are joined without a gap.
From the description of FIGS. 10 to 12, when the band plate is folded in the same direction by a fold line having the same folding direction (either mountain fold or valley fold), and folded into a regular N-gon (N is an even number), It can be seen that the folding lines (1), (2),..., (N) having an angle θ = π / N with respect to the reference axis X may be formed in a zigzag manner at equal intervals.
FIG. 13 is an explanatory diagram of an example in which the expression (5) is satisfied and the folding direction is alternately reversed (reversed in the mountain folding direction and the valley folding direction) and folded into a regular hexagon. FIG. 13A is developed. FIGS. 13B to 13F are diagrams showing a state in the middle of folding, and FIG. 13G is a diagram showing a folded state.
In FIG. 13A, fold lines (1), (3),..., (11) indicated by solid lines folded in the same direction (for example, mountain fold direction) of the strip extending in the X-axis direction as the reference axis are respectively on the X-axis. .., Θ11, and θ1 = θ3 =... = Θ11 = 60 °. Further, fold lines (2), (4),..., (12) indicated by dotted lines folded in a direction opposite to the fold lines (1), (3),. The angles θ2, θ4,..., Θ12 are formed with respect to the X axis, respectively, and θ2 = θ4 =.
The imaginary line (13) shown in FIG. 13 is a line that overlaps the fold line (1) when the strip is folded.
In FIG. 13, the angle Θ12 formed by the solid line and the axis X12 and the axis X0 is Θ12 = 2 (θ1-θ2 + θ3-... + Θ11-θ12) = 2 (60 ° -30 ° + 60 ° -... + 60 ° -30 °) = 2 × π. It is. Therefore, n in the equation (5) is n = (Θ12 / 2π) = 1, and the axis X12 overlaps the axis X0. In this case, both ends of the strip are joined without a gap.
2. Cylinder with fold line whose main fold line consists of horizontal fold lines
The upper and lower ends of the strip-shaped paper (FIG. 9A) are considered as horizontal fold lines, and several levels of these are assumed in the Y-axis direction. The parallel horizontal fold line (s) is named the main fold line.
FIGS. 14 to 16 show development views of a model for manufacturing a cylinder that can be folded in the Y-axis direction, in which the main fold line using the 4-fold line method and the 6-fold line method is composed of a group of horizontal fold lines. .
When manufacturing a cylinder that is folded with a regular N-gonal cross-sectional shape by the 1-node 4-fold line method, as is well known (as can be understood from the description of FIGS. 9A and 9B), a belt-like plate is formed by π · (N−2) / When N is bent in the same direction at equal intervals, a regular N-gon can be formed. Note that π · (N−2) / N is the size of the interior angle of a regular N-gon.
FIG. 14 is a typical developed view in the case where the belt-like plate shown in FIG. 9A is bent in the same direction by π · (N−2) / N in the same direction to form a regular N-gon and N = 6. FIG.
Here, in consideration of the fact that it is bent by 2θ at the folding angle θ in the equation (4), six zigzag mountain fold lines (1) to (6) forming an angle π / 6 with the horizontal folding line. Are introduced at regular intervals. At each mountain fold line, a cylindrical structure is produced that is bent by π / 3 and finally folded with a hexagonal cross-sectional shape.
15 is composed of trapezoidal elements with unequal sides by disassembling twice the angle (π / 3) of the mountain fold line and the horizontal fold line in FIG. 14 to α = 2π / 9 and β = π / 9. FIG.
In the case of folding into a regular hexagon, the division of the angle can be arbitrarily selected as long as the total is π / 3.
16 introduces six sets of folding lines obtained by decomposing the mountain fold line in the Y-axis direction of FIG. 14 into a mountain fold line I of α = π / 3 and a valley fold line II of β = π / 6. FIG. 16A is a developed view, FIG. 16B is a diagram showing a half-folded state of a folded cylinder produced when both ends of the developed view of FIG. 16A are joined, and FIG. 16C is a diagram of FIG. 16B. It is the perspective view seen from a different direction of the same thing.
In FIG. 16A, as long as α−β = π / 6, the values of α and β can be freely selected.
FIG. 17 is a diagram in which the points A and B in FIG. 14 are matched, and the mountain fold portion is eliminated from the horizontal fold line, and the diamond pattern ((1) ˜ It is an expanded view of (3)).
At this time, the cross-sectional shape at the horizontal folding line portion is an equilateral triangle, which corresponds to a model of diamond buckling in plastic buckling of a thin cylinder.
FIG. 18 is a development view of a deformed diamond pattern composed of unequal triangular elements.
FIG. 19 is an explanatory view of a pseudo-cylindrical body having a developed view that is symmetrical with respect to a horizontal folding line and that can be folded. FIG. 19A is a developed view, and FIG. 19B is an end view of the developed view of FIG. FIG. 19C is a diagram showing a half-folded state of the folding cylinder manufactured when the two are joined, and FIG. 19C is a diagram showing the same thing as FIG. 19B seen from a different direction. The five types of development shown in FIGS. 14 to 17 are objects with respect to all horizontal folding lines, but the development shown in FIG. 19 can also be folded.
In FIG. 19, the folding condition equation (3) is satisfied at point A because of its symmetry, but the equation (3) also holds at point B.
FIG. 20 is a diagram showing an example of a development view of a fold composed only of fold lines similar to the point B in FIG.
FIG. 21 is a developed view of a foldable cylindrical wall having a plurality of polygonal parts (flat plate walls) formed by folding lines.
The cylindrical wall having the developed view of FIG. 21 can create a foldable cylinder having a plurality of polygonal parts.
3. Cylinder with fold line when main fold line is inclined (spiral type)
Consider the case where the horizontal folding line in FIGS. 14 to 21 is inclined.
In the above-mentioned documents (a) to (c), Guest et al. Consider a cylinder formed by a triangular divided flat plate, whether a cylindrical folding structure can be manufactured, and the above-mentioned for folding this cylinder. The appropriate shape of the triangle was studied by numerical calculation.
FIG. 22 shows a cylindrical structure when the connecting portion of the divided flat plate made of the triangular divided flat plate studied by Guest et al. Is spiral, and the spiral (1) rises one step each time they make a round. Is shown in a developed view by the present inventor. They analyzed the characteristics of the cylindrical folding shown in the development diagram of FIG. 22 using the angles (α, β) between the spirals as variables, but could not show the complete folding conditions. It was.
FIG. 23 is a developed view of a foldable cylindrical structure corresponding to the whole of FIG. 17 inclined by ψ = π / 6, which comprises three diagonal diamond patterns.
FIG. 24 is an explanatory view of a pseudo-cylindrical body having a development view equivalent to FIG. 23, FIG. 24A is a development view, and FIG. 24B is a fold produced when both ends of the development views of FIG. 23 and FIG. It is a figure which shows the cylinder half-folded state.
In the example shown in FIGS. 23 to 24B, when a cylinder is manufactured by joining the left end L and the right end R of the development view, patterns formed by folding lines are continuous.
FIG. 25 is an explanatory view of a pseudo-cylindrical body having a developed view in which FIG. 14 is inclined by π / 6. FIG. 25A is a developed view, and FIG. 25B is manufactured when both ends of the developed view of FIG. It is a figure which shows the half-folded state of a folding cylinder.
FIG. 25A corresponds to a diagram in which FIG. 14 is cut along a straight line GH inclined by π / 6 with the horizontal line, and the cut line is the horizontal lower end.
26 is an explanatory view of a pseudo-cylindrical body having a developed view in which FIG. 15 is inclined by π / 6. FIG. 26A is a developed view, and FIG. 26B is manufactured when both ends of the developed view of FIG. 26A are joined. It is a figure which shows the half-folded state of a folding cylinder.
FIG. 27 is a developed view in which FIG. 16 is inclined by π / 6.
In the example shown in FIGS. 25 to 27, when a cylinder is manufactured by joining the left end L and the right end R of the development view, the pattern formed by the folding line is not generally continuous. Details of the continuity of the development will be described later.
FIG. 28 is the spiral type of FIG. 19 and is obtained by cutting along a straight line connecting points A and D in FIG. The angle (˜0.193π) shown in FIG. 28 indicates the angle formed by the cutting line and the horizontal line. In this case, since the shape of the triangular element is given, the angle of the valley fold line is limited. Become.
29 is an explanatory view of a spiral folding cylinder having a fold line generalized from FIG. 24. FIG. 29A is a developed view, and FIG. 29B is manufactured when both ends of the developed view of FIG. 29A are joined. It is a figure which shows the half-folded state of a folding cylinder.
The folding condition does not depend on the value of β in FIG. 29A (described later).
FIG. 30 is a development view in the case where the six-stage development view of FIG. 29A is changed to three stages, α is 30 °, and the value of β is changed for each stage.
As shown in FIG. 30, the folding condition can be satisfied even if the value of β is set independently for each stage.
FIG. 31 is a development view of a repetitive spiral type obtained by reversing the spiral mountain fold line and valley fold line of FIG. 29A for each stage. This development is also obtained by matching points A and B in FIG.
FIG. 32 is a diagram showing a portion cut by two parallel straight lines AB ′ and C′D in the developed view of the cylindrical body shown in FIG. 21 so that A and B ′ and D and C ′ overlap. It is an expanded view of what becomes a foldable cylindrical body by connecting the left and right end edges of FIG.
The cylindrical wall having the development shown in FIG. 32 can create a foldable cylindrical body having a plurality of polygonal parts.
FIG. 33 is a developed view of a collapsible cylinder having a rectangular element (part) having an arbitrary shape.
In FIG. 33, when a straight line obtained by extending AF is defined as AE, the folding condition is ∠BAE = ∠DAC = α. The value of α can be arbitrarily determined as α = 180 ° / N (N is a positive integer). For example, when N = 8, α = 180 ° / 8 = 22.5 °. Therefore, by setting ∠BAE = ∠DAC = α = 22.5 ° and setting the length of AE to an appropriate arbitrary value, a foldable cylindrical body having parts of arbitrary shapes can be created.
4). Continuity of folding lines in spiral development
As described above, when the left and right ends of the spiral development view are joined, the continuity of the folding line is not always satisfied at both ends of the development view. When development views are given by trapezoidal elements as in FIGS. 25 to 27, continuity can be maintained by appropriately selecting the upper base length Lu of the trapezoid in FIG.
FIG. 34 is an explanatory view of a method for maintaining continuity when both ends of the developed view are joined.
In FIG. 34, N trapezoidal elements are drawn in the direction of the main folding line (angle ψ) with the origin O as the base point, and a point A is determined. When the height of the trapezoid is h, the length OA = N {(h / tan θ) + Lu} in the case of a regular N square. Draw m (even) elements below the Nth large-diameter element, and define point B as shown. In order for the developed view to be continuous for an arbitrary ψ, it is necessary that the point B is on the X axis. Since AB = mh, the following equation (6) is obtained from tan ψ = AB / OA.
Lu = {2N-m · tanψ / tanθ} h / tanψ (6)
That is, when Lu is appropriately determined by the expression (6), the continuity of the left and right ends of the developed view in these cases is obtained.
5). Verification of folding condition of cylinder with folding line
It will be verified by a typical example whether or not the condition (see formula (5)) for closing in the circumferential direction is satisfied when the cylinder having the folding line described above is folded.
In the cylinder given in FIG. 25, the folding line of the lowermost band plate portion (small width D) in this development view is considered. Here, there are 18 fold lines, and fold lines having the same inclination appear repeatedly for every six lines from the left side, so they are composed of three sets of six fold lines. Using equation (4), the rotation angle of the axis line by these folding lines is ψ = (= π / 6) as the inclination angle,
ΘN = 2 {(α + ψ) −ψ + ψ−ψ + (α + ψ) −ψ} × 3 = 12 (7)
It becomes. Since α = π / 6, ΘN = 2π in equation (4) is satisfied and equation (5) is satisfied, so that it is understood that the closing condition is satisfied after folding.
In the case of FIG. 29A, when the rotation angle by the folding line of the six parallelogram parts at the bottom end is considered, the following expression is obtained.
ΘT = 2 {(α + β) −β} × 6 = 12α (8)
When α = π / 6 is used, ΘT = 2π is satisfied and the closing condition (see equation (5)) is satisfied. As can be seen from equation (8), it can be seen that ΘT does not depend on the β value.
That is, in the models of FIGS. 29 to 31, the condition for folding into a regular N-gon shape is α = π / N, and the angle β in the figure can be freely selected.
In the spiral model of FIGS. 23 to 31 described above, except for FIG. 28 (considering hexagonal folding), the inclination angles ψ of the valley fold lines are all π / N. However, as seen in the example of FIG. 25, the inclination angle ψ of the main fold line is not limited to π / N as long as the left and right continuity of the developed view can be satisfied.
6). Production of foldable pseudo cylinder
The inventor examined the folding characteristics in the axial direction with a pseudo-cylinder made of a polypropylene sheet having a thickness of 0.2 mm, and confirmed that this was possible in accordance with the development described above. When the helical folding model shown in FIGS. 25 and 27 is pushed by a material testing machine, the upper part of the cylinder is folded while rotating while the lower part is stopped.
The results of observing the progress of the folding showed that the proposed model was able to fold well and that the load required for complete folding was very low, 20-40N. (Cylinder diameter before folding; about 100 mm).
7). Summary of research on cylinders with fold lines
In the above description, N = 6 (partially N = 3, 8) is taken as an example, and the developed view is divided into triangular elements, trapezoidal elements, or arbitrarily shaped quadrangular shapes, and a method of manufacturing a pseudo-cylinder folded in a regular N-gonal shape. Explained. Except for the case where the main fold line, which is difficult to satisfy the continuity of the left and right ends of the developed view, is composed of an odd number of trapezoidal elements, the folding angle at one node is (N-2) / N · By setting π, a folded structure can be manufactured for any N value (N ≧ 3, integer).
Further, if the angle of the fold line is selected so as to satisfy the expression (5) and the length of the fold line is appropriately selected, it is possible to manufacture a folded structure that is not a regular N-gonal shape.
In the case where the cylinder is manufactured with a thin polymer sheet, it seems that it is easy to form the cylinder into a shape as shown in FIGS. 16B and 24B. Therefore, it is considered that a container such as a foldable PET bottle can be manufactured by performing molding in such a shape.
When the valley fold line has a spiral shape, the expansion and contraction in the axial direction is generally easier than that of the horizontal type. This should be taken into account when improving the folding structure.
(3) Conical folding structure with folding lines
1. Basic equation for folding
When the conical walls constituting the foldable conical folding structure with folding lines are one-contact six-fold lines and one-node four-fold lines, the angular relationship between the folding lines for folding at this node is shown in FIGS. 37.
FIG. 35 is a diagram showing an angular relationship between folding lines that satisfy folding conditions when a valley folding line is inserted symmetrically in the case of a 1-node 6 folding line, and the folding conditions in the case of FIGS. It is explanatory drawing.
When the line formed by the inserted valley fold line is θ and the angles α to δ are determined as shown in FIG. 35, the following expression (3) is established.
β−α = δ−γ + θ (3)
FIG. 36 is a diagram showing an angular relationship between folding lines that satisfy the folding condition when valley folding lines (V1) and (V2) are alternately inserted between mountain folding lines (M1), (M2), and (M3). FIG. 56B is an explanatory diagram of folding conditions in the case of FIGS. 56B and 57 described later.
In FIG. 36, the angles formed by the X axis, which is an extension of the mountain fold line (M4), and (M1) and (M3) are α^*, Β^*And the angle between each fold line is θ₁~ Θ₄And The XY axes with the node O as the origin are taken as shown in FIG.
The condition for folding in the Y-axis direction at the node O is derived in the same manner as described above. In the region of X <0, the vector pointing in the same direction at the symmetric position (points B and C) of the X axis is the angle π (= Q after folding by mountain folding (M4).₂) And turn in the opposite direction.
Next, consider vectors of points D and E in the region of X> 0. The angle formed by the perpendicular (Q) to the X axis and the folding lines (M1), (V1), (M2), (V2), (M3) is represented by q as shown in FIG.₁~ Q₅Then,
q₁= Π / 2 + α^*,
q₂= Π / 2 + α^*−θ₁,
q₃= Π / 2 + α^*− (Θ₁+ Θ₂),
q₄= Π / 2-β^*+ Θ₄,
q₅= Π / 2-β^*
It becomes. The angle Q between these vectors due to this folding₂Is given by the following equation (9).
Q₂/ 2
= Q₁-Q₂+ Q₃-Q₄+ Q₅
= Π / 2 + α^*− (Θ₂+ Θ₄) (9)
After folding, points B and D are on the same plane, and the vector at this point is in the same direction.₂Value and Q of negative area₁= Π is equal,
α^*= Θ₂+ Θ₄
Get.
α^*+ Β^*= Θ₁+ ... + θ₄
Using
β^*= Θ₁+ Θ₃
Therefore, the folding condition in this case is expressed by the following formula (10).
α^*= Θ₂+ Θ₄, Β^*= Θ₁+ Θ₃    ...... (10)
FIG. 37 shows the case of a 1-node 4-fold line. The folding conditional expression is obtained by the same procedure as above.
Q₂/ 2 = q₁-Q₂+ Q₃= Π / 2 + α-γ
So,
Q₂= Q₁= Π
And put
α = γ.
That is, when the mountain fold lines (M1) to (M3) are given, valley folds (V1) occur at the position of the γ value equal to the angle α formed by the X axis that is an extension line of (M3) and (M1).
2. Conical wall with fold line whose main fold line is parallel to the outer side of the development
FIG. 38 is an enlarged view of the main part of the development view when the development view in the cone whose main fold line is parallel to the outer side of the development view is composed of N isosceles triangles having the apex angle 2Θ.
The valley fold line (broken line) in FIG. 38 is called a main fold line. The vertex is 0, the points on the outer side are A, B, C, and D, a straight line that forms an angle α with the outer side is drawn from these points, and the intersections are E, F, and G, respectively.
A line that forms an angle α with the line segments EF and FG is drawn from the points E, F, and G in the same manner as above, and the intersections thereof are denoted as H and I. By this drawing, the developed view is divided by two types of isosceles triangular elements. O, H, B and O, I, C form a straight line due to symmetry, and a symmetrical diamond pattern is obtained on the left and right of the straight line OF. The straight line OF is perpendicular to the outer side BC. The folding line constituting the node F corresponds to that of FIG.
In FIG. 35, δ is set to α and γ is set to β in consideration of symmetry at the node F, with ∠CFG = ∠BFE = β. Since the angle formed by the valley fold line EF and FG is 2Θ, if θ = 2Θ is set, equation (10) becomes
β−α = Θ (11)
It becomes. Since ΔOFE and ΔOFG are isosceles triangles (basic angle π / 2Θ) having an apex angle 2Θ, when 式 HFI = γ ¥ t * ¥ t, the following equation (12) is obtained.
γ^*+ 2α = π-2Θ (12)
When folded at the node F, the angle between the valley fold lines EF and FG is γ^*-2α. If it is folded in a regular N-gon shape, the angle formed by the valley fold line is (N−2) / N · π, so the following equation (13) is established.
γ^*-2α = (N-2) / N · π (13)
The α and β values satisfying the folding condition are given by the following equation (14) from the equations (11) to (13).
α = π / 2N−Θ / 2, β = α + Θ = π / 2N + Θ / 2 (14)
Considering the case of N = 3 and 2Θ = π / 6, α = π / 8 and β = 5π / 24 are obtained from the equation (14).
39 is an explanatory view of a pseudo-cone wall having a development view of a pseudo-cone wall with a folding line obtained using the value obtained by the equation (14), FIG. 39A is a development view, and FIG. 39B is a development view of FIG. 39A. It is a perspective view of the half-folded state of the conical wall with a fold line which has.
FIG. 40 is an enlarged view of a main part of a developed view of a conical wall with a folding line when it is divided into unequal triangular elements by folding lines.
In FIG. 40, the points on the outer side are A, B, C, D, etc., the line segment forming the angle α with the outer side at each point is drawn on the upper right side, and the line segment forming the angle δ is drawn on the upper left side. Is E, F, G (∠BOF = θ^*). From these points, straight lines are drawn with the line segments EF and FG at an angle α in the upper left direction and at an angle δ in the upper right direction, and their intersections are designated as H and I.
The points O, H, B and O, I, C form a straight line. Asymmetric diamond patterns are obtained on the left and right of the straight line OF. Let ∠BFE = β, ∠CFG = γ, and let J be the intersection of EF and BC. ΔOBC and ΔOCD, ΔOEF and ΔOFG are isosceles triangles each having an apex angle 2Θ, and ∠DCJ = ∠GFJ = 2Θ, and ∠OFJ = ∠OCJ is obtained.
That is, the points O, F, C, and J are on the same circle, and ∠CJF = ∠FOC = 2Θ−θ^*It becomes. Paying attention to ΔBFJ, the following equation is obtained.
β-α = 2Θ-θ^*    ...... (15)
∠CFJ = γ−2Θ obtained from the angular relationship around the point F is obtained from δ = ∠CFJ + (2Θ−θ^*), The following equation (16) is obtained.
δ−γ = −θ^*    ...... (16)
Θ in equation (16)^*Is substituted into the equation (15), and considering that the angle between the valley fold lines EF and FG is 2Θ, the following folding condition equation (17 ′) is satisfied.
β−α = δ−γ + 2Θ (17 ′)
As before, ＝ HFI = γ^*The angle between the valley fold lines EF and FG when folded at the node F is γ.^*− (Α + δ). Considering the folding of a regular N-gon, this value and (N−2) / N · π are equally placed, and γ obtained from the geometric relationship^*When + (α + δ) = π−2Θ is used, the following folding conditional expression (17) is obtained.
(Α + δ) = π / N−Θ (17)
When α and δ satisfying Expression (17) are selected, a foldable development view including unequal triangular elements is obtained.
FIG. 41 is a development view of a conical wall with fold lines when it is divided into unequal triangular elements by fold lines, where N = 3, 2Θ = π / 9, α = π / 9, and δ = π / 6. Fig.^*= About 0.0688π).
FIG. 42 is a developed view of a conical wall with fold lines when it is divided into inequilateral triangular elements by a fold line having an angle α in the upper right direction and an angle δ in the upper left direction at the point F in FIG. , Δ values are the same as those in FIG.
A development view that can be folded is obtained even if the angle α is set to the upper right and the angle δ is set to the upper left at the point F in FIG. The rectangle obtained here is a lazy parallelogram, and the points F, 1,...^*Rotate with. The folding conditions at the nodes are established as in FIG.
FIG. 43 is an enlarged view of a main part of a developed view of a conical wall with a folding line when divided by a trapezoidal element instead of the division by the isosceles triangular element of FIG.
In FIG. 43, two straight lines (AC, BD) that form an angle α with AB from points A, B on the outer side are drawn symmetrically with respect to the straight line OI, and the apex angle φ^*Points C and D are determined so that
∠DCE = Γ^*And ∠DCE = ∠DCO + ∠OCE, ∠DCO = π / 2−φ^*/ 2, ∠OCE = (π / 2-Θ) -α^*Is represented by the following equation (18).
Γ^*= Π- (φ^*/ 2 + Θ + α) (18)
Since the line segment CF is a valley fold line, the angle between the folded mountain fold DC and the valley fold CF is Γ by folding at the node C.^*-Α, and this value can be expressed by the following equation (19) using the above equation (18).
Γ^*−α = π− (φ^*/ 2 + Θ + 2α) (19)
Considering the case of folding with a regular N-gon, (Γ^*−α) and {(N−2) / N} · π are equalized to obtain the following equation (20-1).
α = π / N− (φ^*/ 2 + Θ) / 2 (20-1)
∠HCF = Θ + φ^*Since AB and CD are parallel, ∠ACH = α, and β = ∠ACF is expressed by the following equation (20-2).
β = α + φ^*/ 2 + Θ
= Π / N + (φ^*/ 2 + Θ) (20-2)
At point C, since ∠ACH = ∠ECF = α, the folding conditional expression (17) is satisfied.
44 shows a conical wall with a folding line that is divided into an isosceles trapezoid by a folding line and folded into a regular N pyramid, N = 6, φ in FIG.^*FIG. 44A is a development view, and FIG. 44B is a half-fold view of the cone wall with a folding line having the development view of FIG. 44A. It is a perspective view of the state made into.
3. Conical wall with fold line in which the main fold line is a spiral
2. In Section, we explained the development where the valley fold line is parallel to the bottom when the cone is formed. Here, the folding in the case where the valley fold line as the main fold line becomes a spiral shape will be considered.
FIG. 45 is a developed view of a conical wall with folding lines composed of N isosceles triangular elements (vertical angle 2Θ), and only one of them is written as a curved belt-like portion.
Here, it is assumed that mountain folds and valley folds are periodically introduced, and the angles between the fold lines and the outer sides AB,... Are ζ and η (0 ≦ (ζ, η) ≦ π / 2).
When this strip is bent along these folding lines, it is bent in the circumferential direction by φ = 2 (ζ−η) N. Originally, this band plate was bent at an angle ψ = 2NΘ, and after folding, it is necessary that φ + ψ = 2π be established in order to join both ends of the band plate without gaps. This corresponds to the folding condition in the circumferential direction, and this condition is expressed by the following equation (21).
φ + ψ = 2 (ζ−η + Θ) N = 2π (21)
FIG. 46 is a developed view of a conical wall with a fold line having a simple, spiral developed view of three isosceles triangular elements. FIG. 47 is a top view when the developed view of FIG. 46 is folded.
In FIG. 46, three radiation lines ((1) to (3)) and a line group ((4), (5)...) Parallel to the outer side are mountain fold lines. The valley fold line forms the corner α with the outer edge. Considering that the angles β to δ in FIG. 46 are isosceles triangular elements (vertical angle 2Θ), the following equation is established.
β = π / 2 + Θ−α
γ = π / 2 + Θ + α
δ = π / 2−Θ−α
The valley fold line forming the spiral bends by 2Θ every time it passes through one triangular element. By substituting α˜δ with θ = 2Θ in the folding conditional expression (17), it can be seen that the expression (17) holds for an arbitrary α.
The α value is obtained under the condition of closing in the circumferential direction after folding. When folding in a regular N-gon shape, ζ = α, η = π / 2-Θ is used in equation (21), and the following equation (22) Is obtained.
α = {(N−2) / 2N} · π (22)
In FIG. 47, the three spirals (1) to (3) coming out from the points A, F and G are composed of the radial mountain fold lines shown in FIG.
Although this model gives a typical spiral pattern, it is folded without gaps to the center of FIG. 46, so that it is difficult to put it to practical use as a folding method for thin plates and films having a thickness.
48 is an explanatory diagram of a practical model obtained by modifying the model described with reference to FIGS. 45 and 46, FIG. 48A is an explanatory diagram of a deformation method, and FIG. 48B is an enlarged view of a main part of FIG. 48A.
In FIG. 48A, the points C and D are arranged at an angle 2θ around the center O on the circumference.^*And rotate to points E and F respectively. And ∠CAE = ∠DBF = ... = ψ^*Put it.
By this operation, congruent rectangles ABFE, BGHF... Are periodically drawn on the same circumference.
In FIG. 48B, the valley fold line is AF, and the angles α to δ and p, q are given as shown.
∠OAB = ∠OBA = π / 2-Θ
Taking into account, the following equation is obtained.
p = π / 2−Θ + ψ^*, Β = π / 2 + Θ−γ−ψ^*,
δ = π / 2−Θ− (γ + ψ^*) (23)
∠ACE = π / 2 + θ^*Therefore, paying attention to ΔAEC, ∠AEC = π / 2−θ^*−ψ^*Get. Considering that ΔOCE and ΔOEF are isosceles triangles, using ∠AEF = q = 2π− (∠OEC + ∠OEF + ∠AEC) obtained from the angular relationship around point E, the following equation (24) is obtained.
q = π / 2 + 2θ^*+ Ψ^*+ Θ, α = γ−20^*    (24)
FIG. 49 is a view showing a state in which the figure ABGHFE formed by the fold line in FIG. 48A is sequentially folded along the fold lines AF and BF. FIG. FIG. 49B is a diagram showing a state after further mountain-folding at B′F (original line segment BF) in the state of FIG. 49A.
When each point is determined as shown in FIG. 49B, ∠AFB ′ = β and ∠FB′H ″ = δ. By the valley fold AF and the mountain fold BF in one block, these two blocks become the straight line AF in FIG. 49B. And B'H "can be bent. Assuming that this angle is ψ as shown in the figure, ψ = π− (β + δ). Β + δ = π−2 (γ + ψ obtained from equation (23)^*), The following equation (25) is obtained.
ψ = 2 (γ + ψ^*) (25)
Considering folding in a regular N-gon shape, one of the inner angles is (N−2) π / N.
(Γ + ψ^*) = (N−2) π / 2N (26)
Get.
FIG. 50 is a diagram showing a portion corresponding to the first-stage strip shown in FIG. 48A and a portion corresponding to the second-stage strip.
In FIG. 50, it is possible to newly draw the second stage using the points E, F, and H as the base points in the same procedure as that shown in FIG. The rectangular group in the second stage is similar to those in the first stage.
Next, taking the point F in FIG. 50 as an example, the folding condition is examined. From Equations (23) and (24), β−α = π / 2 + Θ−ψ^*+ 2θ^*-2γ and δ-γ = π / 2-Θ-ψ^*-2γ is obtained. That is, the following formula (27) is obtained.
β−α = δ−γ + 2 (Θ + θ^*) (27)
The angle between the valley fold lines (1) and (2) in FIG. 50 is 2Θ due to periodicity, and the angle between the fold lines (2) and (3) is 2θ as well.^*It is. That is, (1) and (3) are 2 (Θ + θ^*(27) shows that the folding conditional expression is satisfied at the node F.
51 shows a conical wall with a folding line having the folding lines shown in FIGS. 48 to 50, where N = 6 and γ + ψ.^*= Π / 3, ψ^*FIG. 51A is a developed view, and FIG. 51B is a developed view of FIG. 51. FIG. 51A is a developed view of a pseudo-conical wall having a developed view (2Θ = π / 18) when γ = π / 6 and γ = π / 6 It is a perspective view of the state which folded the conical wall with a fold line in half.
FIG. 52 shows a conical wall with fold lines having the fold lines shown in FIGS. 48 to 50, where N = 6 and γ + ψ.^*= Π / 3, ψ^*FIG. 4 is a development view (2Θ = π / 6) when = π / 4 and γ = π / 12.
FIG. 53 is a development diagram of FIG.^*It is an expanded view when the value of is increased.
In FIG. 53, in the case of a conical wall, ψ^*+ Γ = 60 °. ψ^*Ψ under + γ = 60 °^*And γ are divided. Ψ for each stage^*And can be arbitrarily divided into values of γ. In an equiangular spiral, the scale becomes smaller toward the center, so to avoid it, ψ^*Is made smaller.
FIG. 54 is a development view in which the same cone wall as the folding cone wall having the development view of FIG. 53 is formed.
54 is a developed view of a conical wall having the same shape as FIG. FIG. 54 is easier to join on both side edges than FIG.
FIG. 55 is a diagram in the case where the second-stage valley fold line in FIG. 50 is taken in the opposite direction to that of the first stage at an angle γ.
If the intersection of this valley fold line and OA (O; center) is K, ∠KEO is ψ^*The newly obtained rectangle EFIK is similar to that of the first stage. The state of the fold line at the point F corresponds to FIG. If the mountain fold line (M4) in FIG. 36 is made to correspond to the mountain fold line FH, θ in FIG.₁~ Θ₄Is θ₁= Δ, θ₂= Γ, θ₃= Α, θ₄= Β.
Since the line segments FH and FE in FIG. 55 form an angle 2Θ, α in FIG.^*And β^*Is shown in FIG.
α^*= Δ + γ + 2Θ, β^*= Α + β-2Θ (28-1)
It becomes.
Using equations (23) and (24), α in the above equation^*, Β^*Is
α^*= Π / 2-ψ^*+ Θ = β + γ
β^*= Π / 2-ψ^*-Θ-2θ^*= Α + δ (28-2)
It becomes. Θ₁= Δ, θ₂= Γ, θ₃= Α, θ₄When β is used, Expression (10) is obtained, and the folding condition is satisfied.
Thus, when a valley fold line is drawn in the reverse direction for each stage, a repetitive folding structure with a spiral pattern is created.
56 is an explanatory view of a pseudo cone having a development view in which FIG. 51 is repetitively spiraled, FIG. 56A is a development view, and FIG. 56B is a half-fold view of a cone wall with a folding line having the development view of FIG. FIG.
FIG. 57 shows 2Θ = π / 6, ψ^*It is a development view (N = 6) of a repetitive spiral type obtained as = π / 6 and γ = π / 6.
4). Analytical study using conformal spirals
The two kinds of patterns formed by the folding lines in the development view described above are similar and become smaller toward the center.
58 is an explanatory view of a developed view of a foldable conical wall having a fold line along an equiangular spiral, FIG. 58A is an overall explanatory view, and FIG. 58B is an enlarged view of a main part of FIG. 58A.
The developed views shown in FIG. 39A and FIG. 42 are generally expressed in the form shown in FIG. 58A, where the angle at which one pattern is stretched with respect to the center O is 2Θ, as in the previous geometrical treatment. The This FIG. 58A is drawn as follows. First, line segments (1) and (2) are drawn in the upper right direction so as to make an angle ψ with the radiations OA and OI from the center O starting from the points A and I.
Next, line segments (4) and (5) are drawn in the upper left direction from points A and M so as to form an angle φ with the radiations OA and OM (φ and φ values are α and δ in FIGS. 40 and 42, and ψ = π / 2-Θ-α, φ = π / 2-Θ-δ). If the intersections of (1) and (5), (2) and (4) are F and B, respectively, the points B and F are on concentric circles.
Similarly, when the above operation is performed at points B and F, points C, J, and G are determined, and points D, K, and H are sequentially determined. That is, a sequence of points F, G, H... Taken in the upper right direction from the point A always forms an angle ψ with the radial direction, and a sequence of points A, B, C, D, E forms an angle φ with the radial direction. It is drawn as follows. Point A. If the line connecting F, G, and H is a new curve (1), and the line connecting points A, B, C, and D is a new curve (4), these two curves are equiangular with the radial direction. However, it becomes a line toward the center.
That is, each of these points is on an equiangular helix coming from the center O. In FIG. 58A, (1), (2), and (3) are counterclockwise spirals, and (4), (5), and (6) are clockwise spirals.
As shown in FIG. 58A, when the angle formed by the line segments AB, BC,... With respect to the center angle is 2Θ ′, the angle formed by the line segments AF, FG, GH is 2 (Θ−Θ ′). The folding condition is examined using the enlarged views (FIG. 58B) of the two rectangles on the left and right of the point F. These rectangles are congruent, and the line segments BF and FG form an angle 2Θ. The angular relationship between ψ, φ and α to δ is as shown in the figure. Since ΔOBF in FIG. 58A is an isosceles triangle having an apex angle 2Θ, α + φ = π / 2-Θ and δ + ψ = π / 2-Θ are obtained.
α + δ = π− (φ + ψ) −2Θ (29)
Get. From the internal angle relationship of ΔABF or ΔMFN,
β + γ = π− (φ + ψ) (30)
Get. From the equations (23) and (24), the following equation is established.
β−α = δ−γ + 2Θ (31)
Considering that the line segments BF and FN form an angle 2Θ, the above equation (3) is established.
That is, it is understood that the folding condition is automatically satisfied when the folding line is drawn with an equiangular spiral.
FIG. 42 corresponds to when φ = ψ is FIG. 39A and φ ≠ ψ. Radius R of points B and F₁Is the radius of the development₀Is given by the following equation using the sine law.
R₁/ R₀= Sin {2 (Θ−Θ ′) + ψ} = p (32)
The radius of the second stage point (C, F, G...) And the third stage point (D, K, H...) From the outer periphery is sequentially p.², P³Given by ...
FIG. 59 is an explanatory view of a developed view of a conical wall with a folding line when the spiral of FIG. 58 is reversed.
In FIG. 59, as in FIG. 58, the radial direction and the angle ψ are taken upward from the point A, and the angle φ is taken upward. Let these be (1) and (2), respectively. Draw (3) from point J to (1), and (4) from point K to (2). The intersection of (1) and (4) is the point C, and the intersection of (2) and (3) Is point B. At this time, the angle spanned by the line segment BC is 2Θ.
Next, line segments BD and CD are drawn in the opposite directions at the same angles ψ and φ from points B and C, respectively. The intersection point D comes on the radius OA. When this is repeated, zigzag folding lines ACDFGI..., ABDEGH. Since ΔOBC is an isosceles triangle with apex angle 2Θ,
∠DBC = δ = π / 2−Θ−φ, ∠DCB = απ / 2−Θ−ψ (33)
Is obtained. Using the external angle relationship between ΔOBA and ΔOAC, the following equation (34) is derived.
∠CBA = γ = π / 2 + Θ− (φ + 2Θ−θ^*),
∠BCA = β = π / 2 + Θ− (ψ + θ^*) (34)
Expressions (15) and (16) are obtained from Expressions (33) and (34), and folding conditions at all nodes are established.
FIG. 41 corresponds to this case, and FIG. 39 can also be expressed in this form.
FIG. 60 is an explanatory diagram of how to draw the developed view of FIG. 44A.
In FIG. 60, line segments (1) and (2) are drawn from points A and G at the same angle φ, and line segments OB and OH taken symmetrically with respect to a perpendicular line drawn from point O to the base AG of ΔOAG. Let the intersections be B and H.
Φ is taken in the opposite direction from points B and H, and the intersections with OA and OG are C and I, respectively. By such an operation, zigzag folding lines ABCDE ... and GHLJK ... are obtained. The folding conditions at each node are clarified in the description of FIG.
51A can be easily understood from the description of FIG. 50 that it is an equiangular spiral.
FIG. 61 is an explanatory view of a pseudo cone having a development view in which the above FIG. 44 is an equiangular spiral shape, FIG. 61A is a development view, and FIG. 61B is a half-folded view of the cone wall with a folding line having the development view of FIG. It is a perspective view of the state made into.
As shown in FIGS. 61 and 61B, a development view that forms an isosceles trapezoid in which folding lines are arranged along a spiral can also form a foldable conical wall.
FIG. 62 is a development view of a folding conical wall with a folding line in which the spiral in the circumferential direction of FIG. 51A is raised by one step at the right end.
When the developed view of FIG. 62 is a conical wall, the right and left edges are connected so that the right end points A, B, C,... And the left end points D, E, F, D overlap. To do.
As described above, when the equiangular helix or the inverted equiangular helix is combined, the folding condition at the node is automatically established, but the circumferential folding condition is the sum of the folding angles at each point in the circumferential direction. Should be set to 2π using FIG. 45 or the previous geometrical considerations.
Further, the nodes on these development views can be determined from the intersection of the concentric circles and the radii of the radii p, p \ t2 \ t, p \ t3 \ t ... by obtaining the previous p value.
5). Produced folding cone shell and its characteristics
Using a polypropylene sheet having a thickness of 0.2 mm, observe the folding state of the conical shell of FIG. 51B produced by the development shown in FIG. 51A and the conical shell of FIG. 56B produced by the development shown by FIG. 56A. did. As a result, it was found that good folding was possible as predicted by the origami model.
6). Consideration
Assuming that N = 6 mainly, the creation of a conical structure capable of axial folding was geometrically studied using an origami model, and it was shown that this is possible. Here, since these conical shells are formed by folding lines, it becomes a pseudo conical shape, and it is difficult to extend it to a conical shape obtained by joining fan-shaped development views.
These structures can be manufactured by connecting thin metal plates processed into triangles and trapezoidal elements with joints, etc., and low-elasticity thin polymer materials can be processed into household goods by molding. Seems to get.
The folding mechanism shown here is considered to be a basic model of a large structure such as a foldable dome roof or a tent structure. There are many problems that need to be overcome in realizing these, but it seems that if another idea is added to the proposed folding model, new forms of processing and products will be born.
7). Summary
For the purpose of creating a conical shell structure that can be folded in the axial direction, which has not been reported so far, several types of developments have been newly proposed, and the folding conditions have been verified geometrically. It was shown to be represented by a combination of equiangular spirals. As a result of examining folding characteristics using origami and thin polymer plates, it was confirmed that folding was possible as expected in all of the proposed models.
(4) Disc-shaped folding structure with folding lines
By forming a folding line using the Archimedes spiral and the Bernoulli spiral (conformal spiral), it is possible to create a disk-like folding structure with folding lines that can be folded in the radial direction or the circumferential direction.
1. Basic relationship
FIG. 63 is an explanatory diagram of the simplest folding method for origami.
In FIG. 63, one contact point (black dot) is composed of four folding lines. If the mountain fold is (1), (2), (3), and the valley fold is (4), the angle α formed by the extension lines (5) and (2) of (1) and the fold lines (3) and (4 ) Can be folded when the angle between them is equal.
This folding condition is also interpreted as follows. A line segment that bisects the angle formed by the mountain fold lines (2) and (3) is defined as (A), and a line segment perpendicular thereto is defined as (B). The angle formed by the valley fold line (4) and the extension line (5) of (1) is divided into two equal parts (by angle β) by (A). At this time, the angle formed by (1) and (A) is also β. Considering (B) as a mirror surface, (2) and (3) can be regarded as incident light, and (4) can be regarded as reflected light.
That is, when the intersection of two orthogonal lines considered as mirror surfaces is a node, and two zig / zag folding lines are incident and reflected at equal angles at this point, the folding condition is satisfied at this point. Is satisfied. This is named the “mirror rule” of the 4-fold line method.
2. Folding method in radius / circumferential direction
64 is an explanatory view of a development view of a folding structure with a folding line, FIG. 64A is an enlarged view of a main part for explaining folding conditions, and FIG. 64B is an overall view.
As shown in FIG. 64A, a method of folding in the center direction by combining the zig / zag fold line (1) and the circumferential direction (2) in the center direction will be considered.
Radius R with N isosceles triangular elements (ΔOAB, ΔOBC...) With apex angle 2Θ.₀(2ΘN = 2π, base angle = π / 2−Θ). .. Are drawn from the main radiations OA, OB, OC... Constituting the .DELTA.OAB, .DELTA.OBC. A straight line is drawn from the outer points A, B, C... To form the angle φ with the main radiation, the intersections with the secondary radiation are F, G, H..., And the radius from the center point O is R¹And
Also, concentric circles (radius R²) The points I, J, K... Above are taken on the original radiation OA, OB, OC. With such a procedure, a zig / zag folding line is drawn in the radial direction. Circumferential folding lines, FG, GH..., IJ, JK rotate around the center at an angle 2Θ due to symmetry.
If the intersection of the extended line of the line segment OG and the outer circumference circle is a point E, ΔOBE becomes an isosceles triangle with an apex angle 2θ, and ∠OBE = (π / 2) −θ.
Since ∠OBC = (π / 2) −Θ, the following equation (35) is obtained.
∠CBE = Θ-θ (35)
When ∠OBG = φ is used as p≡∠BGE and the external angle relationship of ΔOBG is considered, the following equation (36) is obtained.
p = φ + 2θ (36)
∠GBC = (π / 2) -Θ-φ≡α
And using the previous equation (36), the following equation (37) is obtained.
p = (π / 2) − (α + Θ) + 2θ (37)
Next, consider the folding condition at point G.
When the angle formed by the extension line of the line segment GH and the line segment GB is ζ, the folding condition at the point G is
ζ = ∠FGJ
Given in.
ζ = π−∠ EGH−p = π− (π / 2 + Θ) −p = α−2θ
Therefore, the folding condition at the point G is expressed by the following equation (38) as β∠∠FGJ.
β = α-2θ (38)
Defining ∠JGO∠p,
q + β = (π / 2) −Θ
The following formula (39) is obtained.
q = (π / 2−Θ) − (α−2θ)
= Π / 2− (α + Θ) + 2θ (39)
From Equations (37) and (39), p = q (this relationship is point G, corresponding to the establishment of a mirror surface rule with the radiation OE as a mirror surface).
Next, when ΔOJG is set as ∠BJG∠r, r = q + 2θ is obtained. The folding condition at the point J is given by r = s where the line segment OB is considered as a mirror surface (∠OJP∠s). Since ∠OJK = π / 2−Θ = ∠OJP + ∠PJK, when ∠PJK = γ, γ is given by the following equation (40).
γ = (π / 2−Θ) −s
= (Π / 2-Θ)-(q + 2θ)
= Π / 2-Θ-2θ- {π / 2- (α + Θ) + 2θ} = α-4θ (40)
When the “swing angle” of the zig / zag fold line in the radial direction is 2θ, the fold line BGJP in the radial direction is set to α at the point B on the outer side, and β = α−2θ, γ = α A value obtained by subtracting the angle by 2θ, such as −4θ.
The relationship between the incident angle and reflection angle when the two main and secondary radiations (OB and OG) are considered to be mirror surfaces.
p = q = π / 2− (α + Θ) + 2θ = φ + 2θ,
r = s = π / 2− (α + Θ) + 4θ = φ + 4θ (41)
The angle is increased by 2θ.
Radius OB = R of disc₀, R length of line segment OG, OJ, OP₁, R₂, R₃As
When the sine theorem is used for ΔOBG, ΔOGJ..., The following equation (42) is obtained.
R₁/ R₀= Sinφ / sin (φ + 2θ),
R₂/ R₀= Sinφ / sin (φ + 4θ),
R₃/ R₀= Sinφ / sin (φ + 6θ) (42)
After obtaining main and sub radiation groups from the center, give φ and radius R₁/ R₀, R₂/ R₀If concentric circles are drawn and these intersection points are nodes, an expanded view satisfying the folding condition is obtained at all nodes.
FIG. 65 is an enlarged view of a development view of the folding structure with a folding line shown in FIG. 64B.
FIG. 66 is a perspective view of the folding structure with a folding line having the developed view of FIG. 65 in a half-folded state and a small amount of folding.
FIG. 67 is a perspective view of the folding structure with a folding line having the developed view of FIG. 65 in a half-folded state and a large amount of folding.
FIG. 68 is a perspective view of a state in which the disk-like folding structure with a folding line having the developed view of FIG. 65 is completely folded.
65 to 68 has a circular hole Sa formed in the center in the development view shown in FIG. The circular hole Sa has an inner diameter that becomes smaller as it is folded from FIGS. 66, 67, and 68 sequentially from the expanded state of FIG.
In FIG. 65, the disk-like folded structure S with fold lines is formed with a large number of mountain fold lines M whose upper surface is convex and a large number of valley fold lines V which are concave when in the half-folded state.
At the node that is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. The number of mountain fold lines M intersecting at each node = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1). That is, the fold line pattern of the foldable circular colored sheet is a 1-node 4-fold line. The folding line is formed along a plurality of equiangular spirals so as to satisfy the folding condition of the circular sheet.
65 to 68, the fold-lined disk-like folding structure S has a beautiful shape according to the amount of folding when it is composed of a colored sheet or the like that can be folded. The color that appears is also changing. A large sized disc-shaped folding structure S with a fold line can be used as an interior decoration, and a small one can be used as a body decoration such as a brooch.
FIG. 69 is an explanatory view of a development view of a disk-like folding structure with a folding line when the swing angle of the zig / zag folding line in the radial direction is increased toward the center, and FIG. 69A is for explaining folding conditions. FIG. 69B is an enlarged view of the main part of FIG.
If the zig / zag fold line is drawn with the same swing angle, the distance between the fold lines becomes abruptly smaller toward the center, so that the swing angle is gradually increased (FIG. 69A).
When the folding lines BG and GJ are drawn at the initial swing angle 2θ, r = p + 2θ when p = q. Next, assuming that s = r from point J and the swing angle is, for example, 4θ, the angle t in FIG. 69 is s + 4θ. A line segment PQ is drawn at an angle t = u based on the specular law at the point P, and the point Q is determined. When the fold lines are sequentially obtained according to the specular rule, the angular relationship when the swing angles are 2θ, 4θ, and 6θ is given by the following equation (43).
p = q = π / 2− (α + Θ) + 2θ = φ + 2θ,
r = s = φ + 4θ, t = u = φ + 8θ (43)
Given in. Line segment OG = R₁, Line segment OJ = R₂... can be formulated in the same procedure as that for obtaining the equation (42).
FIG. 70 is a development view of a disk-like folding structure with a folding line when the swing angle of the zig / zag folding line in the radial direction is increased toward the center and the folding line in the circumferential direction is also zig / zag. FIG. 70A is an explanatory view, FIG. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.
In FIG. 70A, radius R₀And R₀ ^*(R₀> R₀ ^*) Are alternately drawn, and sub-radiations OF, OG,. Here, F, G, and H are the intersection points of the line segment drawn from the points A, B, and C so as to form an angle φ with the main radiation and the auxiliary radiation. As described above, when the drawing is performed according to the mirror surface rule, the folding condition is satisfied at all the nodes.
64B is divided into N = 36 (2Θ = 100), and FIGS. 69B and 70B are divided into N = 18. The folding line method was followed up to the 8th step from the outer periphery. In the central part, mountain folds and valley fold lines facing the center were alternately provided to avoid a blank area in the central part.
3. Folding combining Archimedes spiral winding and radial folding
FIG. 71 is an explanatory diagram of a conventionally known winding method in which the intersection of spiral fold lines is on the Archimedean spiral.
In FIG. 64A, let us consider eliminating the folding line zig / zag in the radial direction.
In FIG. 71, the blank area at the center is indicated by a regular N-gon. A perpendicular line is drawn from the apex B of the regular N-gon to the side AB, and the intersection of the perpendicular line and the folding line AF ((1)) is defined as C. A line segment CD is drawn so as to be symmetric with respect to the fold line (1) (∠ACD = 2π / N).
In this way, when N fold lines are drawn from the vertices of a regular N-gon so as to be symmetric each time they intersect with the fold line, an equidistant spiral pattern is obtained. It is easy to see that the intersection of the radial fold line and this spiral fold line is on the Archimedean spiral with the center as the origin.
This is the basic form of the folding (winding) method proposed by Guest et al.
72 is a diagram showing a new fold line considered by the present inventor. FIG. 72A is a fold line in which the fold line (1) in the radial direction has one bending point in FIG. 71 and the spiral is reversed at this bending point. 72B is a diagram in which the outside of the bending point in FIG. 72A is replaced by a method of folding in the radial direction.
When a large number of bending points are introduced into the folding line in the radial direction as shown in FIG. 72A, a new folding (winding) structure in which the Archimedean spiral is combined with the developed view of FIG. 64B is created.
In the case of FIGS. 72A and 72B, if N is set to a large value (N> 20), the interval between the folding lines becomes fine, so that the folding angle becomes extremely small at the time of winding, and this is practically replaced by elastic deformation. It becomes possible. Only the main fold line is sufficient for winding a polymer material film or fabric having a low elastic modulus, and the introduction of the Archimedean spiral is practical.
4). Folding method by conformal spiral style
The folding method by the conformal spiral mode means a folding method having a linear folding line formed along the conformal spiral.
Here, a method of folding a circular film using an equiangular spiral will be described.
4.1 Basic relational expression
FIG. 73 is an explanatory diagram of a fold line when a fold line for folding a circular film, a partial circular film (fan-shaped film) or the like in the radial direction and the circumferential direction is formed along an equiangular spiral.
As shown in FIG. 73, the circular film is divided at equal angles by radial radiation from N centers, and this is replaced by N isosceles triangular elements (ΔOAM, ΔOMN...) Having an apex angle 2Θ (2Θ · N = 2π). Each point is defined as shown in the figure. From the point A on the outer side, a straight line forming the radiation and each φ is drawn, and an intersection point with the radiation (OM) rotated by 2Θ at the central angle is determined as a point B.
A point A is set as the starting point, a straight line that forms φ with the radiation OA is drawn, and an intersection point with the radiation OM rotated by 2Θ is defined as B. Next, a straight line that forms an angle χ with the radiation OM is drawn to determine an intersection C with the radiation ON rotated by 2Θ. Next, the points D, E... Are determined by alternately taking the angles φ, χ in the same procedure. Let this zigzag line be (1). Here, the angle between the line segment AB and the base of the isosceles triangle is defined as β. That is, β∠90 ° −Θ−φ. In addition, an angle formed by the line segment BC and the MN (that is, an angle formed by the line segment BB ′ drawn in parallel to the MN from the line B and the line segment BC) is represented by γ. γ = (90 ° −Θ) −χ is defined. The value of γ is positive when C is on the same side as the center O with respect to the line segment BB ′, and negative when C is on the opposite side of the center O. When γ = 0, the line segments BC and MN are parallel.
The radius of the circular plate is R₀Assuming that the sine theorem is used for ΔOAB, the radius length of point B (OB) ∠R₁Is given by the following equation (44).
R₁/ R₀= {Sinφ / sin (φ + 2Θ)} ∠p (44)
Further, the radius length (OC) of the point C is set to R₂And using the sine theorem for ΔOBC, R₂/ R₁Is represented by the following equation (45).
R₂/ R₁= Sinχ / sin (χ + 2Θ) ∠q (45)
That is, R₂/ R₀If the equations (44) and (45) are used, the following equation (46) is obtained.
p · q = R₂/ R₀
= Sinφ · sinχ / {sin (φ + 2Θ) · sin (χ + 2Θ)} (46)
That is, the radius R of the circular film at points D, E, F.₀Radius p made dimensionless by²q, p²q², P³q²It is given as a value obtained by alternately multiplying p and q.
Now, assuming that the line (2) connecting the points A, C, E, G,... That gives the lower limit of the zigzag line (1), the dimensionless radius of each of these points is 1, pq, (pq), respectively.², (Pq)³,..., Each of these points is given by the intersection of an equiangular helix and the radiation drawn every 4Θ. (3) connecting the points B, D, F, H,... Giving the upper limit of the zigzag line is also given by the intersection of the equiangular spiral and the radiation.
FIG. 74 is a basic explanatory view of a fold line when forming a fold line that folds in a circumferential direction while winding a circular film or a partial circular film (fan-shaped film) around the central axis along an equiangular spiral.
Next, as shown in FIG. 74, points P and Q that have advanced clockwise from the start point A of the folding line (1) by an odd multiple of 2Θ (described later) are determined. Similarly, zigzag fold lines (4) and (5) are drawn.
At this time, fold lines (1) and (5) are alternately defined as mountain fold lines, and fold line (4) is alternately defined as valley fold lines.
Name the points on the fold line (1) as I, J, K, the points on the fold line (4) as R, S, T, and the points on the fold line (5) as Q, U, V as shown in the figure. The points Q, R, I and U, S, J on the radiation shifted counterclockwise by 2Θ are connected by a straight line, and these are connected to another fold line group (6), (7), (8 ).
As shown in FIG. 74, when points P, Q,... Are taken every time five isosceles triangular elements are passed, the number of zigzags n (1 zigzag and n = 1) is zigzag when n = 2. Since it repeats twice, it proceeds five counterclockwise triangles counterclockwise (for example, if zigzag is repeated twice along the fold line (4) from point P in FIG. 74, it reaches point R, and from point Q (It intersects with the fold line (6) that comes out. If the isosceles triangle through which the fold line (6) passes is included, it means that the five isosceles triangles are advanced counterclockwise.)
The dimensionless radius of the points Q, R, I ... is 1, (pq)², (Pq)⁴Thus, ΔOQR and ΔORI in the figure are similar.
That is, the new folding line groups (6) to (8) are also equiangular spirals toward the center O. If the QR of the fold line (6) and the angle between the PE of the fold line (9) and the radiation are ψ, α in the figure is α = (90 ° −Θ) −ψ. Let α be the angle formed with the outer side (the base of the isosceles triangular element).
The zigzag fold line (4) is repeated n times to reach the point R in the figure (n = 2 in FIG. 74). At this time, the radius of the point R is (p · q)ⁿGiven in.
On the other hand, since the angle formed by the spiral (6) from the point Q on the outer side with radiation is ψ, the value of the dimensionless radius that gives the point R is expressed by sinψ / sin (ψ + 2Θ). If this value is equal to the expression (46), the following expression (47) is obtained.
pⁿqⁿ
= [Sin φsinχ / {sin (φ + 2Θ) sin (χ + 2Θ)}]ⁿ
= Sinψ / sin (ψ + 2Θ) (47)
The above equation (47) is the angular relationship to be satisfied by the spirals (1), (4), (5) heading toward the center while rotating clockwise and the spirals (6)-(8) crossing them counterclockwise. Is given.
4.2 Folding conditions
As described above, consider the case where the equiangular helix is bent every 2Θ. The point S of FIG. 74 consisting of the valley fold line 3 and the mountain fold line 1 and the point U consisting of the mountain fold line 1 are taken as representative points, and the folding conditions at these points are considered.
FIG. 75 is an enlarged view of a main part of FIG.
FIG. 75 shows an enlarged view of FIG. 74 near the points S and U. At point S, since ∠OSJ = ψ, ∠SJR = ψ + 2Θ. Since ∠ORS = φ, considering ΔJSR, ∠JSR = π− (ψ + 2Θ) −φ. If the extension line of the line segment RS is SS ′, ∠S′SJ = π−∠JSR = ψ + 2Θ + φ.
When ∠USQ = ψ + 2Θ is used, ∠TSU = π−χ−∠USQ = π−χ−ψ-2Θ. When ∠S′SJ = ∠TSU is set according to the folding condition, the following formula (48) is obtained as the folding condition at the point R.
2ψ + φ + χ = π-4Θ (48)
As is clear from FIG. 75, since the angular relationship is the same as that of the point S, the equation (48) is the folding condition. That is, when the equation (48) is satisfied, the folding condition is satisfied at all the nodes.
FIG. 76 is an explanatory diagram of folding conditions when forming a folding line along the equiangular spiral while folding a circular film or a partial circular film (fan-shaped film) around the central axis.
76, as shown in FIG. 76, when the χ value is larger than π / 2−Θ, that is, the folding line is turned upward at points B, D... Conditions are given.
4.3 Continuity of the spiral group in the circumferential direction
In the above, the folding condition is obtained, but these spiral groups are equally distributed around the central axis, and a condition for maintaining the continuity of the spiral is derived. Consider a case in which m zig / zag spirals (fold line (1)) start from the outer peripheral point after passing through n isosceles triangular elements.
At this time, these start points rotate around the center by (2n + 1) · (2Θ) (n: integer). That is, the relationship between the number N of isosceles triangle elements and these values is given by (2n + 1) m = N. In the case of a circular film, it is necessary to equally divide the central angle 2π by (2n + 1) m.
That is, the division angle (vertical angle of isosceles triangular element; 2Θ) for satisfying continuity is given by the following equation (49).
2Θ = 2π / {(2n + 1) · m} (49)
Only by dividing the circular membrane in this way a condition is achieved in which the continuity of the m helical groups is satisfied in the entire region of the membrane.
When φ = π−2ψ−χ−4Θ obtained from the equation (48) is used in the equation (47), the following equation (50) is obtained.
(Pq)ⁿ
= [Sin (2ψ + χ + 4Θ) · sinχ / {sin (2ψ + χ + 2Θ) sin (χ + 2Θ)}]ⁿ
= Sinψ / sin (ψ + 2Θ) (50)
When 2Θ and χ value divided so as to satisfy Expression (49) are given, ψ satisfying Expression (50) can be calculated by numerical calculation. Further, the φ value is also obtained by the equation (48), and a development view by a spiral folding line that satisfies the folding condition is drawn at all the nodes.
4.4 When bending the sub-fold line at an arbitrary rotation angle (when φ = χ)
Above, a circular film was equally divided by N isosceles triangular elements having an apex angle of 2Θ, and a development view formed by folding a folding line every time passing through these elements was obtained. In the case of FIG. 76, in the special case where the m spirals are always folded upward at the same angle (φ = χ), another folding development view can be configured.
FIG. 77 is an explanatory diagram of folding conditions when the main folding line is folded at an equal angle with respect to the radiation.
Points A, B, C and A ', B' on the outer circumference of the circle are determined as shown in FIG. A fold line (1) rising to the right is drawn from point A, and a fold line (2) rising to the left is drawn from point B. (1) is the central angle 2θ₁(The angle of the string AA '), (2) is the central angle 2θ₂It progresses by the angle of the string A′B and intersects at the point D. The folding line (1) is the radiation from the center and the angle ψ (the angle α formed with the outer side AI), and the folding line (2) is the radiation. And an angle φ (angle β formed with the outer side BI).
The folding conditions at point D are considered below.
∠ADA '= φ + 2θ₁, ∠BDA '= ψ + 2θ₂
It becomes. If the extension point of BD is I,
∠ADI = π − {(φ + ψ) +2 (θ₁+ Θ₂)}
It becomes.
Since ∠FDO = φ and ∠GDO = ψ,
∠FDG = φ + ψ
It becomes.
When fold lines (2), (1), (3) are mountain folds, GD ((4)) is a valley fold line, and the folding condition at point D is that す る と ADI and ∠FDG are placed equally, 51).
φ + ψ = π / 2−Θ or (α + β) = π / 2 (51)
OD to R₁Then, when the sine theorem is used for ΔOAD, the following equation (52) is obtained.
R₁/ R₀= Sinψ / sin (ψ + 2θ₁) (52)
On the other hand, the following equation (53) is obtained for ΔOBD.
R₁/ R₀= Sinφ / sin (φ + 2θ₂) (53)
Since both of these values give the radius of the point D, when the same ψ = π / 2−φ−Θ is used, the following equation (54) is obtained.
sin (β-θ₁) / Sin (β + θ₁)
= Sin (π / 2−θ₂-Β) / sin (π / 2 + θ₂-Β) (54)
θ₁, Θ₂Is given, φ satisfying the equation (53) is determined by numerical calculation. Ψ is obtained from equation (51), and when these values are used, a development view satisfying the folding condition at all nodes is obtained.
4.5 Application to the production of conical shells
In FIG. 74, it is assumed that the zigzag spiral (fold line (1)) consists of m pieces, and the angle formed by the starting point on the outer side is (2n + 1) · (2Θ). In the case of a disc, (2n + 1) · m · (2Θ) = 2π, but if this (2n + 1) · m · (2Θ) value is smaller than 2π, the cone will be expanded, and in this case it will be folded as well. Is possible.
5). Folding product example
FIG. 78 to FIG. 80 show development views obtained by the theory described above and folding examples thereof.
FIG. 78 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 20 degrees.
FIG. 79 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 79 is an example of a folded development view when γ = 0 °, and shows an example in which the angle of the folding line with respect to radiation is different from FIG. 78.
FIG. 80 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 10, the number of isosceles triangle elements N = (2n + 1) m = 42, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
78 to 80 are 2Θ = 20 °, 20 °, and 180 ° / 21, respectively, and these values and γ values determined by χ (γ = χ−90 ° + Θ) are respectively γ = π / 9, 0 and 0 were given, and the ψ value satisfying the equation (50) was obtained by numerical calculation. Substituting this ψ value into equation (48) determines φ.
From α + ψ = 90 ° −Θ and β + φ = 90 ° −Θ, the values of α and β in FIGS. 78 to 80 can be obtained. For example, in FIG. 78, α = 69.763..., Β = 20.474.
In the example of FIGS. 78 to 80, a circular film having a main fold line composed of two spirals is folded into a new plane. In the state of the side surface after folding in FIGS. 78 and 79, when the γ value increases, the side portion is folded in a shape protruding upward. This is advantageous during the operation of folding / unfolding the structure. When FIG. 79 and FIG. 80 are compared, the larger the number of divisions, the smaller the folding.
FIG. 81 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, It is a figure which shows the example of the expanded view of a disk-shaped folding structure with a folding line in the case of (gamma) = 0 degree.
FIG. 82 is a perspective view of the folding structure with a folding line having the developed view of FIG. 81 in a half-folded state and a small amount of folding.
FIG. 83 is a perspective view of the folding structure with a folding line having the developed view of FIG. 81 in a half-folded state and a large amount of folding.
FIG. 84 is a perspective view of a state in which the disk-like folding structure with a folding line having the developed view of FIG. 81 is completely folded.
81 to 84 fold the disk-like folded structure S with folding lines, and fold the circular sheet (folded disk-like folded structure with folding lines) as shown in FIG. 81 along the folding lines M and V. In the half-folded state where the folding amount is small, the state is as shown in FIG. 82, and when the folding amount is increased, the state shown in FIG. 83 is obtained. FIG. 84 is almost in a folded state, and when it is completely folded, it is folded on a plane.
81 to 84 has a folding line-shaped disk-like folding structure S having different folding lines M and V from those in FIGS. 65 to 68. When configured, a shape change and a color change different from those of FIGS. 65 to 68 are obtained.
Like the disc-shaped folding structure S with fold lines, the fold-lined disc-shaped folding structure S can be used as an interior decoration, and the small size can be used as a body such as a brooch. It can be used as a decoration.
FIG. 85 to FIG. 87 show development views in the case of three spirals, four spirals, and one spiral.
FIG. 85 shows an example in which four zigzag spirals (m = 4) are folded around the center, and n = 7, the number of equilateral triangle elements N = (2n + 1) m = 60, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
FIG. 86 shows an example in which three zigzag spirals (m = 3) are folded around the center, and n = 8, the number of equilateral triangle elements N = (2n + 1) m = 51, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
FIG. 87 shows an example of folding around a center with one zigzag spiral (m = 1) as the fold line, where n = 10, the number of equilateral triangle elements N = (2n + 1) m = 21, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
When the main fold line in FIG. 85 has four spirals, it is folded so as to wind around a quadrilateral shape, and when the main fold line in FIG. 86 has three spirals, it is folded into a triangle shape. In the case of one spiral in FIG. 87, it is folded so as to be wound around the central axis.
When γ = 0 ° and α and β values are obtained in the same manner as described above, the following results are obtained.
In FIG. 85, γ = 0 °, α = 75.432..., Β = 29.132.
86, γ = 0 °, α = 76.233..., Β = 27.533.
In FIG. 87, γ = 0 °, α = 76.714..., Β = 26.572.
FIG. 88 shows an example in which four zigzag spirals (m = 4) are folded around the center, and n = 7, the number of equilateral triangle elements N = (2n + 1) m = 60, It is a figure which shows the example of the expanded view of a disk-shaped folding structure with a folding line in the case of (gamma) = 0 degree.
FIG. 89 is a perspective view of the folding structure with a folding line having the developed view of FIG. 88 in a half-folded state and a small amount of folding.
FIG. 90 is a perspective view of the folding structure with a folding line having the developed view of FIG. 88 in a half-folded state and a large amount of folding.
FIG. 91 is a perspective view of a state in which the folding structure with a folding line having the developed view of FIG. 88 is completely folded.
88 to 91, a circular hole Sa is formed in the center in the development view shown in FIG. 88. The circular hole Sa has a smaller inner diameter as it is sequentially folded from the developed state of FIG. 88 with FIGS. 89, 90, and 91.
88 to 91, the fold line-equipped disk-like folding structure S folds the circular sheet (folded line-equipped disk-like fold structure) as shown in FIG. 88 along the fold lines M and V. When the folding amount is small, the folding state is as shown in FIG. 89. When the folding amount is increased, the state shown in FIG. 90 is obtained. When fully folded, the state shown in FIG. 91 is obtained.
88 to 91 is a foldable colored sheet S because the shapes of the fold lines M and V are different from those of FIGS. 65 to 68 and 81 to 84 described above. When configured by the above, a shape change and a color change different from those in FIGS. 65 to 68 and FIGS. 81 to 84 are obtained.
FIG. 92 is a development view when the number of spirals as the main fold line is large (m = 12).
In FIG. 92, m = 12, n = 1, and the disk is divided into 36 equal parts. When γ = 25 ° is given and α and β are obtained in the same manner as described above, the result is as follows.
α = 55.270 ... °, β = 44.46 ... °.
In this folding, if the number of divisions of the central angle is doubled, the folding efficiency is halved, but the number of folding lines increases, which is unsuitable for engineering. This is rather interesting from a modeling point of view.
FIG. 93 is a developed view composed of two types of equiangular spirals based on FIG. Number of divisions N = 12, θ₁= Π / 180, θ₂= 29π / 180, and φ is approximately π / 18. When the developed view of FIG. 93 is folded, it is wound up well around the center symmetrically in the vertical direction. The thing of FIG. 93 suggests that these folding lines are replaced by elastic deformation at the time of winding since the sub folding lines are fine.
Based on the developed view of FIG. 93, a circular stainless steel thin plate (thickness t = 0.05 mm, radius R = 140 mm) is cut into 12 pieces by a main fold line, and these are joined by a transparent craft film. Was made. This can be wound up in the same manner as in FIG. 93, and can be accommodated only by the main fold line without introducing a fine sub-fold line.
FIG. 94 is a development view of a disk-like folding structure with fold lines in which mountain fold lines and valley fold lines are alternately provided.
In FIG. 94, the disk-like folded structure S with a folding line has a mountain fold line M along an equiangular spiral toward the center from a point where the outer periphery is equally divided into N (N is a positive integer, N ≧ 4). A valley fold line V is formed along an equiangular helix formed from a point obtained by further dividing the equally divided outer periphery into two.
The folding structure S with a folding line shown in FIG. 94 can be folded and unfolded by a simple folding line, and can be expanded by elastic deformation, so that it can be self-deployed. Since the fold line group becomes fine at the center, it is necessary to engineering with the folding method such as the Guest, etc., except for a soft and thin cloth or rubber.
FIG. 95 is a development of a disk-like folding structure with folding lines in which mountain fold lines and valley fold lines are alternately provided and the circumferential lengths of the valley fold lines and the left and right mountain fold lines are different on the left and right sides. FIG.
In FIG. 95, the disk-like folded structure S with a folding line has a mountain fold line M along an equiangular spiral toward the center from a point where the outer periphery is equally divided by N (N is a positive integer, N ≧ 4). A valley fold line V is formed along the equiangular spiral from the point formed and further divided into two by the appropriate division ratio. The equiangular spiral of FIG. 95 is wound counterclockwise from the center toward the outer periphery, and the angle between the valley fold line V and the mountain fold line M adjacent to the right is β, and the mountain fold line M adjacent to the left is If the angle formed by α is α, then α> β.
In this case, when folding is performed along the folding line of the disk-shaped folding structure S with folding lines, the outer peripheral portion is folded while being displaced downward in the axial direction.
FIG. 96 is a view in which a fan-shaped portion between adjacent mountain fold lines in FIG. 95 is removed.
When the outer edges at both ends in the circumferential direction in FIG. 96 are connected to overlap each other, a conical wall is formed. This conical wall can also be folded along the mountain fold line M and the valley fold line V. This conical wall is also folded while the outer peripheral portion is shifted downward in the axial direction.
(5) Application of folding structures with folding lines
Based on the results of the folding method for flat plates and cylinders, we will explain the results of basic research aiming at their practical application. Here, the following points are mainly described.
(A) Folding method modeling and processing method for creating a high-rigidity and high-strength core material by bending a flat plate in a zigzag manner and making it three-dimensional.
(B) A cylindrical deployment structure model of a simple mechanism devised on the basis of the folding characteristic of the cylinder in the axial direction.
The former considers not only the creation of high-strength members for aerospace, but also the realization of reuse of waste paper, etc., and the latter is considered to be used for consumer use such as shooters.
1. Folding and non-folding conditions
97 is an explanatory view of the folding condition of the sheet-like member, FIG. 97A is a development view before folding, and FIG. 97B is a diagram showing a state folded at the folding line of FIG. 97A.
Consider the circular thin flat paper shown in FIG. 97A, where the center is O, the line segments OA, OC, OD are fold-folded, and OB is valley-folded. The angles formed by these line segments are set as α to δ as shown in FIG. 97A.
Now, when OB is valley-folded, the coordinate axes are determined as shown in FIG. 97B, and the line segment OA is on the X-axis, the coordinates of the points B, C, and D are (−cos β, sin β, O), (x, y, z), (−cos α, sin α, O).
The angle between the line segments OB and OC is γ, the angle between the line segments OD and OC is δ, and α + β + γ + δ = 2π, x²+ Y²+ Z²When = 1 is used, the z coordinate of the point C is given by the following equation (55).
(1-z²) Sin (α-β)
= Cos²γ + cos²δ-2 cos γ cos δ cos (α-β) (55)
Since the coordinates of the point C are determined by the equation (55), the angle formed by the plane OBC and the bottom surface (xy plane) is obtained. If z = 0 in the equation (55), the folding condition is satisfied.
When z = 0 and δ is eliminated from the right side and compared with the left side, the following equation (56) is obtained.
cos²(Α + β + γ) + cos²γ = cos²α + cos²β,
cos (α + β + γ) · cosγ = cosαcosβ (56)
The relationship satisfying these two expressions (55) and (56) is given by the following expressions (57) and (58).
α + γ = π (57)
β + γ = π (58)
Since Expression (58) is a condition for folding a circular plane in half, Expression (57) is adopted here as the folding condition.
A structure made in a state satisfying the folding condition is low in stability, and a structure not satisfying the folding condition generally tends to have high stability as a structure. Therefore, in this report, the condition that is not folded is mainly used for (a), and the folding condition is used for (b).
2. Core material modeling
2.1 Origami model
About the creation of the core material using the origami model, the concept has already been proposed by Miura. A typical example is a duouble corrugated core (DCC) based on a plate folding method (miura ori).
FIG. 98 is an explanatory diagram of a DCC (duouble corrugated core) and is a diagram in which the DCC is developed.
FIG. 99 is a diagram showing the vertical fold line group of FIG. 98 as zig / zag.
These nodes are composed of four folding lines, and the folding conditions are satisfied at all the nodes. Therefore, when subjected to surface pressure, these cores are structures that are spread out to the original plane and are unstable.
In order to avoid this, it is essential that the upper and lower surfaces of the core are firmly bonded to the surface material. However, since the bonding portion is not a surface, the bonding technique is considered to dominate the success or failure of this structure.
FIG. 100 is an explanatory diagram of a newly devised core model with joints, FIG. 100A is a development view, FIG. 100B is a plan view of the development view of FIG. 100A in a half-folded state, and FIG. It is an external view of what folded the figure and made it three-dimensional.
FIG. 101 is an explanatory view of another model of the core having a joint portion newly devised, FIG. 101A is a development view, FIG. 101B is a plan view of the development view of FIG. 101A in a half-folded state, and FIG. FIG.
It can be seen that the A part is the upper surface and the B part is the lower surface, and has a large joint. Here, the node is composed of 4 or 5 folding lines.
FIGS. 102A and 102B are explanatory diagrams of a model that does not satisfy another folding condition of the core with the joint devised by the present inventor. FIG. 102A is a development view, and FIG. 102B is an enlarged view of a main part of FIG.
103 is an explanatory view of a core created by folding the developed view of FIG. 102A, FIG. 103A is a perspective view of the folded core, and FIG. 103B is a perspective view of a sheet bonded to the lower surface of the core of FIG. 103A. .
The fold line shown in FIG. 102A does not satisfy the folding condition, and is considered so that the fold line has a grid shape when the flat plate is three-dimensionalized. In FIG. 102B, the diagonal fold lines DB, EC, A′E ′, B′F ′ and the like are 45 ° with respect to the vertical fold lines AC, DF, A′C ′, D′ F ′.
When the valley fold line D-B is folded, the A-E portion comes into contact, and ΔABD and ΔEDB are joined. The joint parts similar to the joint parts S1 and S2 are all indicated by S1 and S2.
Further, when the valley fold line A′-E ′ is folded, the B′-D ′ member comes into contact, and ΔD′A′E ′ and ΔB′A′E ′ are joined. The joint parts similar to the joint parts S3 and S4 are all indicated by S3 and S4.
When the joint portions S1 and S2 are bonded together and the joint portions S3 and S4 are bonded together, a structurally stable core material (FIG. 103A) constituted by a grid-like fold line is created. The one shown in FIG. 103B in which a sheet is bonded to the lower surface of the core can withstand a large compressive force.
FIG. 104 is an explanatory view of a model that does not satisfy another folding condition of the core with the joint devised by the present inventor, FIG. 104A is a development view, and FIG. 104B is an enlarged view of a main part of FIG. 104A.
The fold line shown in FIG. 104A does not satisfy the folding condition, and is considered so that the fold line has a grid shape when the flat plate is three-dimensionalized. In FIG. 104B, CD, BE, etc. are 60 ° with respect to the vertical folding lines AD, CB. When the valley fold line CD is folded, the AB portion comes into contact, and ΔACE and ΔBCE are joined. Bonding the joints creates a structurally stable core material (FIG. 104A) composed of grid-like fold lines.
3.2 Honeycomb core model
The honeycomb core is a typical lightweight structure.
FIG. 105 is an explanatory diagram of a method for manufacturing a honeycomb core from a single plate, FIG. 105A is a development view, and FIG. 105B is a diagram of a honeycomb core manufactured from a plate having the development view of FIG. 105A.
In FIG. 105A, a dotted line is a valley fold line, and a mountain fold line indicated by a broken line has a cut line (cut portion) C. When the joints A-B on both sides of the valley fold line in FIG. 105A are bonded to every other valley fold line and spread on both sides, a mesh-like honeycomb core shown in FIG. 105B can be manufactured. In addition, when this manufacturing method is used, it has the characteristic which becomes a cylindrical honeycomb core.
4). Production of core material
4.1 Core material manufacturing method
Two metal molds in which a 0.2 to 0.3 mm phosphorous copper plate or steel plate is cut at the folding line shown in FIGS. If a thin paper to be processed or an aluminum alloy plate (up to 0.08 mm) is inserted between them and bent, a product as shown in FIGS. 101B to 102B can be manufactured instantaneously. .
By bonding only the joining regions S1 and S2 of FIG. 102B, without bonding S3 and S4, and by bonding a thin film on one side (or the reverse bonding) in a cylindrical shape It is possible to produce a lightweight and highly rigid pipe.
FIG. 106 is a diagram showing a fold line forming apparatus for producing the core material shown in FIG. 103A.
In FIG. 106, a kraft film F is adhered to both surfaces of a large number of square parts (metal thin plates) P1 and parallelogram parts P2 separated by folding lines, thereby forming a folding line forming mold K. The fold line forming mold K has a pair of foldable flexible molds K1 and K2 that are configured to be symmetrical with respect to the central axis L. When each of the flexible molds (folding molds) K1 and K2 is manufactured and a crease is once attached as a mountain fold line and a valley fold line, the mountain fold and valley fold can be easily performed from the next time. Accordingly, when the flexible mold K1 is folded along the opening / closing axis L in a state where a paper or a resin sheet is placed on the surface of the flexible mold K2 on one side of the opening / closing axis L, the paper or the resin sheet is paired with flexible. It is sandwiched between molds K1 and K2. When flexible molds K1 and K2 are simultaneously folded along a fold line in this state (in a state where flexible molds K1 and K2 are overlapped), a fold line is formed on paper or a resin sheet.
4.2 Core material produced
A paper core and an aluminum core were manufactured using the folding mold described above in the model shown in FIG. The paper core is shown in FIG. 103A.
107 is an explanatory view of the manufactured aluminum core, FIG. 107A is a perspective view, FIG. 107B is a development view, and has the same shape as the paper development view shown in FIG. 103A.
The compression strength of these products is approximately 0.4 to 0.8 Mpa (specific gravity; 80 to 120 Kg / m) for paper products.³), About 1 to 1.5 MPa (about 100 kg / m) for aluminum products³(A grid size of 10 to 11 mm, a sample size of 50 × 50 mm).
5). Folding / unfolding model
In the above-mentioned column “(2) Cylindrical Folded Structure with Fold Line”, a plurality of examples of the method of folding the cylinder in the axial direction have been described. FIG. 108 to FIG. 109 show development views of these representative ones and examples of new structures using them.
FIG. 108 is an explanatory view of an application example of a structure with a cylindrical folding line, and FIG. 108A is a development view.
If a cylindrical body is manufactured after cutting the valley fold line (dotted line) in FIG. 108 and joining A and B, a structure composed of hexagonal members is obtained. When the hexagonal member portion is replaced with a narrow plate, a truss structure that can expand and contract in the axial direction can be manufactured.
FIG. 109 is an explanatory view of an application example of a spiral cylindrical fold line structure, FIG. 109A is a development view, and FIG. 109B is a view showing an inflatable structure that can be expanded and contracted based on FIG. 109A.
In view of the above-mentioned research results, the present invention has the following description (1) as a problem.
(1) A novel fold line for a structure with a fold line, in which a wall-like structure is divided into polygonal flat plate walls by a large number of fold lines, and the fold lines at the boundary portions of the divided flat plate walls can be folded. And providing a foldable new fold lined structure using the new fold line, a novel fold method, and a new fold line forming mold and fold line forming method.
Disclosure of the invention
Next, the present invention that solves the above problems will be described. In order to facilitate correspondence with the elements of the embodiments described later, the elements of the present invention are those in which the reference numerals of the elements of the embodiments are enclosed in parentheses. Appendices.
The reason why the present invention is described in correspondence with the reference numerals of the embodiments described later is to facilitate the understanding of the present invention, and not to limit the scope of the present invention to the embodiments.
(First invention)
In order to solve the above-mentioned problem, the structure with a fold line of the first invention is characterized by comprising the following structural requirements (A01) to (A05):
(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other A fold line-equipped structure provided with a fold line (M, V) that is foldable along the straight part connecting portion, wherein the fold line (M, V) is a fold line The structure with a fold line having a plurality of mountain fold lines (M) in which the one surface side is mountain-folded when viewed from one surface side of the attached structure and one or more valley fold lines in which valley folds are formed;
(A02) A plurality of nodes that are intersections of the mountain fold line (M) and the valley fold line are arranged at a predetermined interval, and the number of mountain fold lines (M) that intersect at one node and the number of valley fold lines The plurality of fold lines (M, V) formed so that the difference is 2;
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and second The one-node four-fold line formed by the first valley fold line (V1) disposed between the mountain fold lines (M2) and disposed on the opposite side of the third mountain fold line (M3). A plurality of folding lines (M1 to M3, V1),
(A04) The nodal point is the origin O, the X-axis is taken in the direction of the extension line of the third mountain fold line (M3), and one of the first mountain fold line (M1) and the second mountain fold line (M2) When the angle between one mountain fold line and the X axis is α and the angle between the other mountain fold line and the first valley fold line (V1) is γ, the angle is formed so that α = γ. The plurality of folding lines (M1 to M3, V1),
(A05) The fold lined structure having the quadrilateral parts (P; P1, P2; P1 to P5) other than the parallelogram.
(Operation of the first invention)
In the structure with a folding line of the first invention having the above-described configuration, the node is set as the origin O, the X-axis is taken in the extension line direction of the third mountain folding line (M3), and the first mountain folding line (M1 ) Or the second mountain fold line (M2), the angle between one mountain fold line and the X axis is α, and the angle between the other mountain fold line and the first valley fold line (V1) is γ. In this case, a plurality of polygonal parts (P; P1, P2; P1 to P5) can be folded by the plurality of folding lines (M, V) formed to satisfy α = γ. For this reason, the structure with a fold line can be changed from a folded state having a small outer shape to an extended state having a large outer shape.
Moreover, since the said structure with a fold line has parts (P; P1, P2; P1-P5) of the shape (a quadrangle other than a parallelogram) different from the conventional shape, a folding state with a small external shape and In a stretched state with a large outer shape, a structure with a folding line having a shape different from the conventional one can be manufactured.
(Embodiment 1 of the first invention)
The structure with a fold line according to the first embodiment of the first invention is characterized in that in the first invention, the following structural requirement (A06) is provided.
(A06) The structure with a fold line in which the part and the part connection portion provided with the fold line are configured by separate members.
(Operation of the first embodiment of the first invention)
In the structure with fold line according to Embodiment 1 of the first invention having the above-described configuration, the part and the part connecting portion provided with the fold line are configured by separate members. It can be constituted by a rigid thin plate such as a metal plate, and the part connecting portion can be constituted by a hinge member. Therefore, a robust structure with a fold line can be provided.
(Embodiment 2 of the first invention)
The structure with a fold line according to the second embodiment of the first invention is characterized in that in the first invention, the following structural requirement (A07) is provided.
(A07) The structure with a fold line constituted by an integrally molded product with a fold line.
(Operation of the second embodiment of the first invention)
Since the structure with a fold line according to the second embodiment of the first invention having the above-described structure is configured by an integrally molded product with a fold line, the structure with a fold line can be easily manufactured by integral molding. it can. The fold line can be formed at the same time as forming, but if the structure with fold line is a sheet-like member, it is also possible to form a fold line on the integrally formed sheet-like member. It is.
(Second invention)
The structure with a folding line of the second invention is characterized by comprising the following structural requirements (A01) to (A04), (A08),
(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(A02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2. The plurality of fold lines (M, V) formed in
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and second The one-node four-fold line formed by the first valley fold line (V1) disposed between the mountain fold lines (M2) and disposed on the opposite side of the third mountain fold line (M3). A plurality of folding lines (M1 to M3, V1),
(A04) The nodal point is the origin O, the X-axis is taken in the direction of the extension line of the third mountain fold line (M3), and one of the first mountain fold line (M1) and the second mountain fold line (M2) When the angle between one mountain fold line and the X axis is α and the angle between the other mountain fold line and the first valley fold line (V1) is γ, the angle is formed so that α = γ. The plurality of folding lines (M1 to M3, V1),
(A08) The structure with fold lines having the quadrilateral and triangular parts (P; P1, P2).
(Operation of the second invention)
Since the structure with a folding line of the second invention having the above configuration has quadrilateral and triangular parts (P; P1, P2; P1 to P5), in a folded state in which the outer shape is small and an extended state in which the outer shape is large. A structure with a folding line having a shape different from the conventional one can be produced.
(Third invention)
The structure with a fold line according to the third aspect of the invention is characterized by comprising the following constituent elements (A01) to (A05), (A09):
(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(A02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2. The plurality of fold lines (M1 to M3, V1) formed in
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and second The one-node four-fold line formed by the first valley fold line (V1) disposed between the mountain fold lines (M2) and disposed on the opposite side of the third mountain fold line (M3). Multiple folding lines,
(A04) The nodal point is the origin O, the X-axis is taken in the direction of the extension line of the third mountain fold line (M3), and one of the first mountain fold line (M1) and the second mountain fold line (M2) When the angle between one mountain fold line and the X axis is α and the angle between the other mountain fold line and the first valley fold line (V1) is γ, the angle is formed so that α = γ. The plurality of folding lines (M1 to M3, V1),
(A05) The fold lined structure having the quadrilateral parts (P; P1, P2; P1 to P5) other than the parallelogram.
(A09) In a state where the fold line is extended, it becomes a flat plate shape, and in a state where the fold line is bent along the mountain fold line and the valley fold line, the outer shape is reduced and the surface has irregularities on the surface. The structure with a fold line that can be folded and extended in a flat plate shape so that the outer shape is further reduced in a state of being completely folded along a valley fold line.
(Operation of the third invention)
Since the structure with a folding line of the third invention having the above-described structure has quadrilateral parts (P; P1, P2; P1 to P5) other than the parallelogram, the folded state is small and the outline is extended greatly. In this state, a flat plate-like fold lined structure having a different shape from the conventional flat plate-like fold line structure can be manufactured.
(Fourth invention)
The structure with a folding line of the fourth invention is characterized by comprising the following constituent elements (A01) to (A04), (A010), (A011),
(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(A02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2. The plurality of fold lines (M1 to M3, V1) formed in
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and second The one-node four-fold line formed by the first valley fold line (V1) disposed between the mountain fold lines (M2) and disposed on the opposite side of the third mountain fold line (M3). A plurality of folding lines (M1 to M3, V1),
(A04) The nodal point is the origin O, the X-axis is taken in the direction of the extension line of the third mountain fold line (M3), and one of the first mountain fold line (M1) and the second mountain fold line (M2) When the angle between one mountain fold line and the X axis is α and the angle between the other mountain fold line and the first valley fold line (V1) is γ, the angle is formed so that α = γ. The plurality of folding lines (M1 to M3, V1),
(A010) A cylindrical wall or a conical wall that has a cylindrical wall or a conical wall in a state where the fold line is extended, and has an unevenness whose outer shape is reduced in a state where the fold line is bent in accordance with a mountain fold line and a valley fold line The structure with a fold line that forms a cylindrical wall or a cone wall having a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along the mountain fold line and the valley fold line,
(A011) The structure with a fold line having a plurality of fold lines (M1 to M3, V1) continuous in a plane perpendicular to the axis of the cylindrical wall or the cone wall.
(Operation of the fourth invention)
Since the structure with a fold line of the fourth invention having the above-described structure has a plurality of fold lines (M1 to M3, V1) continuous in a plane perpendicular to the axis of the cylindrical wall or the cone wall, the outer shape is small. A cylindrical or conical fold lined structure having a different shape from the conventional fold line structure can be manufactured in the folded state and the extended state of the outer shape.
(Fifth invention)
The structure with a folding line of the fifth invention is characterized by comprising the following constituent elements (A01) to (A04), (A012), (A013),
(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(A02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2. The plurality of fold lines (M1 to M3, V1) formed in
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and second The one-node four-fold line formed by the first valley fold line (V1) disposed between the mountain fold lines (M2) and disposed on the opposite side of the third mountain fold line (M3). A plurality of folding lines (M1 to M3, V1),
(A04) The nodal point is the origin O, the X-axis is taken in the direction of the extension of the third mountain fold line (M3), and one of the first mountain fold line (M1) and the second mountain fold line (M2) When the angle between one mountain fold line and the X-axis is α and the angle between the other mountain fold line and the first valley fold line (V1) is γ, α is formed to be γ. The plurality of folding lines (M1 to M3, V1),
(A012) A cylindrical wall or a conical wall that has a cylindrical wall or a conical wall in the state in which the fold line is extended, and has an unevenness whose outer shape is reduced in a state in which the fold line is bent in accordance with the mountain fold line and the valley fold line The structure with a fold line that forms a cylindrical wall or a cone wall having a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along the mountain fold line and the valley fold line,
(A013) The structure with a folding line in which the parts (P; P1, P2; P1 to P5) have a polygonal shape of a quadrangle or more.
(Operation of the fifth invention)
Since the structure with a fold line of the fifth invention having the above-described configuration has polygonal parts (P; P1, P2; P1 to P5) of quadrilateral or more, the folded state has a small outer shape and the extended state has a large outer shape. A cylindrical or conical fold-lined structure having a different shape from that of the conventional fold-lined structure can be manufactured.
(Sixth invention)
The structure with a fold line according to the sixth aspect of the invention is characterized by comprising the following constituent elements (B01) to (B04):
(B01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other; A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(B02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2. The plurality of fold lines (M1 to M4, V1, V2) formed in
(B03) a first mountain fold line (M1), a second mountain fold line (M2), a third mountain fold line (M3) and a fourth mountain fold line (M4) extending radially from one node; A first valley formed between the mountain fold line (M1) and the second mountain fold line (M2) and disposed on the opposite side of the third mountain fold line (M3) and the fourth mountain fold line (M4) A fold line (V1) is disposed between the third mountain fold line (M3) and the fourth mountain fold line (M4), and the first mountain fold line (M1) and the second mountain fold line (M2). Has a second valley fold line disposed on the opposite side, the first mountain fold line (M1) and the fourth mountain fold line (M4) are adjacent, and the second mountain fold line (M2) and the third The plurality of fold lines (M1 to M4, V1, V2) having a one-node 6 fold line arranged adjacently to a mountain fold line (M3),
(B04) The node is the origin O, the X-axis is taken in the direction of the extended line of the first valley fold line (V1), and the first mountain fold line (M1) and the second mountain fold line (M2) are the first The angles formed with the first valley fold line (V1) are α and β, respectively, and the angles between the third mountain fold line (M3) and the fourth mountain fold line (M4) with the second valley fold line are γ and δ, respectively. And a plurality of fold lines (M1 to M4, V1, V2) formed such that β−α = δ−γ + θ, where θ is an angle between the X axis and the second valley fold line.
(Operation of the sixth invention)
In the structure with a fold line of the sixth invention having the above-described configuration, the node is the origin O, the X-axis is taken in the direction of the extension of the first valley fold line (V1), and the first mountain fold line (M1 ) And the second mountain fold line (M2) are α and β, respectively, and the third mountain fold line (M3) and the fourth mountain fold line (M4) are The plurality of angles formed to satisfy β−α = δ−γ + θ, where γ and δ are angles formed with the second valley fold line, and θ is an angle formed between the X axis and the second valley fold line. Fold lines (M1 to M4, V1, V2), parts having different shapes (P; P1, P2; P1 to P5) can be used, and each part (P; P1, P2; P1 P5) can be folded. For this reason, the structure with a fold line can be changed from a folded state having a small outer shape to an extended state having a large outer shape.
Moreover, in the folded state and the extended state, it is possible to provide a structure with a folding line having a shape different from the conventional one.
(Embodiment 1 of the sixth invention)
The structure with a fold line according to Embodiment 1 of the sixth invention is characterized in that, in the sixth invention, the following structural requirement (B05) is provided.
(B05) When the fold line is extended, it becomes a flat plate shape, and when folded along the mountain fold line (M) and the valley fold line, the outer shape is reduced and the surface has an uneven surface, The structure with a fold line that can be folded and extended in a flat plate shape so that the outer shape is further reduced in a state of being completely folded along the fold line (M) and the valley fold line.
(Operation of the first embodiment of the sixth invention)
The structure with a fold line according to the first embodiment of the sixth invention having the above configuration provides a plate-like structure with a fold line having a shape different from the conventional one in a folded state where the outer shape is small and an extended state where the outer shape is large. be able to.
(Embodiment 2 of the sixth invention)
The structure with a fold line according to Embodiment 2 of the sixth invention is characterized in that, in the sixth invention, the following structural requirement (B06) is provided:
(B06) A cylindrical wall having a concavity and convexity that forms a cylindrical wall or a conical wall in the state in which the fold line is extended, and has an outer shape reduced in a state in which it is bent in accordance with the mountain fold line (M) and valley fold line of the fold line Alternatively, a conical wall is formed, and when folded completely along the mountain fold line (M) and the valley fold line, it is folded so as to form a thick cylindrical wall or a conical wall having irregularities whose outer shape is further reduced. The expandable structure with fold lines.
(Operation of the second embodiment of the sixth invention)
In the structure with a fold line according to the second embodiment of the sixth invention having the above-described configuration, the structure with a cylindrical or conical fold line having a different shape from the conventional one in the folded state with a small outer shape and the extended state with a large outer shape. Can be provided.
(Seventh invention)
The structure with a fold line of the seventh invention is characterized by comprising the following structural requirements (C01) to (C04):
(C01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other; A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines (M1 to M4, V1, V2) formed in
(C03) A cylindrical wall is formed in a state where the fold line is extended, and a cylindrical wall having irregularities whose outer shape is reduced is formed in a state where the fold line is folded according to a mountain fold line and a valley fold line of the fold line, The structure with a fold line that forms a cylindrical wall having a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along a fold line and a valley fold line,
(C04) The structure with a fold line having a fold line that forms a closed polygon that is continuous along a plane perpendicular to the axis of the cylindrical wall.
(Operation of the seventh invention)
Since the structure with a fold line of the seventh invention having the above configuration has a plurality of fold lines (M1 to M4, V1, V2) continuous in a plane perpendicular to the axis of the cylindrical wall, the fold line has a small outer shape. A cylindrical fold line structure having a different shape from the conventional fold line structure can be manufactured in a state where the state and the outer shape are greatly extended.
(Eighth invention)
The structure with a folding line of the eighth invention is characterized by comprising the following structural requirements (C01) to (C03), (C05):
(C01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other; A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines (M, V) formed in
(C03) A cylindrical wall is formed in a state where the fold line is extended, and a cylindrical wall having irregularities whose outer shape is reduced is formed in a state where the fold line is folded according to a mountain fold line and a valley fold line of the fold line, The structure with a fold line that forms a cylindrical wall having a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along a fold line and a valley fold line,
(C05) The structure with fold lines, wherein the parts (P; P1, P2; P1 to P5) have a quadrangular or more polygonal shape.
(Operation of the eighth invention)
In the structure with a folding line of the eighth invention having the above configuration, the parts (P; P1, P2; P1 to P5) have a polygonal shape of a quadrangle or more, so that the outer shape is small and the outer shape is folded. In a large stretched state, it is possible to manufacture a cylindrical fold lined structure having a different shape from the cylindrical fold lined structure having the conventional triangular parts (P; P1, P2; P1 to P5). .
(9th invention)
The structure with a fold line according to the ninth invention is characterized by comprising the following structural requirements (C01) to (C03), (C06), (C07),
(C01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the parts (P; P1, P2; P1 to P5) to each other; A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines (M, V) formed in
(C03) A cylindrical wall is formed in a state where the fold line is extended, and a cylindrical wall having irregularities whose outer shape is reduced is formed in a state where the fold line is folded according to a mountain fold line and a valley fold line of the fold line, The structure with a fold line that forms a cylindrical wall having a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along a fold line and a valley fold line,
(C06) The fold lines are all formed along a spiral, and the parts (P; P1, P2; P1 to P5) are only obtuse triangles formed by dividing a parallelogram into two by diagonal lines. Wire structure,
(C07) A structure with a fold line having the above-described configuration having the obtuse triangular part (P; P1, P2; P1 to P5) in which one of the base angles is 35 ° or more.
(Operation of the ninth invention)
In the structure with a folding line of the ninth invention having the above configuration, the folding lines are all formed along a spiral, and the parts (P; P1, P2; P1 to P5) are divided into two parallelograms by diagonal lines. In the conventional structure with a fold line that is only an obtuse angle triangle formed as described above, the obtuse angle triangle part (P; P1, P2; P1 to P5) in which one of the base angles is 35 ° or more is used. Produces a cylindrical fold lined structure with a different shape from the conventional cylindrical fold lined structure having obtuse triangular parts (P; P1, P2; P1 to P5) with a base angle of about 30 ° can do.
(10th invention)
The structure with a folding line of the tenth invention is characterized by comprising the following constituent elements (D01) to (D03),
(D01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and linear part connecting portions that connect the outer sides of the respective parts (P; P1, P2; P1 to P5) to each other; A fold lined structure provided with a foldable linear fold line that can be folded along the linear part connecting portion, wherein the fold line is viewed from one side of the fold lined structure. The structure with a fold line having a plurality of mountain fold lines (M) whose one side is a mountain fold and one or more valley fold lines (V) which are valley folds,
(D02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at a predetermined interval, so that the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is 2. The plurality of fold lines (M, V) formed in
(D03) A conical wall is formed in the state where the fold line is extended, and a conical wall having irregularities whose outer shape is reduced is formed in a state where the fold line is folded according to the mountain fold line and the valley fold line of the fold line. The said structure with a fold line which forms the cone wall with the thickness which has the unevenness | corrugation into which the external shape reduced further in the state folded completely along the fold line and the valley fold line.
(Operation of the tenth invention)
The structure with a fold line of the tenth invention having the above configuration forms a conical wall when the fold line is extended, and has an outer shape when folded according to the mountain fold line and the valley fold line of the fold line. A conical wall having a reduced unevenness is formed, and in a state where the cone wall is completely folded along the mountain fold line and the valley fold line, a thick cone wall having an unevenness whose outer shape is further reduced is formed.
That is, the tenth aspect of the invention can provide a foldable conical structure with a folding line, which is not conventionally known.
(Embodiment 1 of the tenth invention)
The structure with a folding line according to the first embodiment of the tenth aspect of the invention is characterized in that, in the tenth aspect of the invention, the following structural requirements (D04) and (D05) are provided.
(D04) of the first mountain fold line (M1), the second mountain fold line (M2) and the third mountain fold line (M3), and the first mountain fold line (M1) and the second mountain fold line (M2) The plurality of fold lines (M1 to M1) having a one-node four-fold line formed by a first valley fold line (V1) disposed between and a first valley fold line (V1) disposed on the opposite side to the third mountain fold line (M3) M3, V1),
(D05) The nodal point is the origin O, the X-axis is taken in the direction of the extension of the third mountain fold line (M3), and one of the first mountain fold line (M1) and the second mountain fold line (M2) When the angle between one mountain fold line and the X axis is α and the angle between the other mountain fold line and the first valley fold line (V1) is γ, the angle is formed so that α = γ. The plurality of folding lines (M1 to M3, V1).
(Operation of Embodiment 1 of Tenth Invention)
The structure with a fold line according to the first embodiment of the tenth invention having the above configuration provides a conical structure with a fold line that is not conventionally known in a folded state with a small outer shape and an extended state with a large outer shape. be able to.
(Embodiment 10 of the tenth invention)
The structure with a fold line according to Embodiment 2 of the tenth aspect of the invention is characterized in that, in the tenth aspect of the invention, the following structural requirements (D06) and (D07) are provided.
(D06) the first mountain fold line (M1), the second mountain fold line (M2), the third mountain fold line (M3) and the fourth mountain fold line (M4), and the first mountain fold line (M1) and A first valley fold line (V1) formed between the second mountain fold line (M2) and disposed on the opposite side of the third mountain fold line (M3) and the fourth mountain fold line (M4); Arranged between the third mountain fold line (M3) and the fourth mountain fold line (M4) and disposed opposite to the first mountain fold line (M1) and the second mountain fold line (M2) A second valley fold line (V2), the first mountain fold line (M1) and the fourth mountain fold line (M4) are adjacent to each other, and the second mountain fold line (M2) and the third mountain fold line ( A plurality of fold lines (M1 to M4, V1, V2) having one node 6 fold lines arranged adjacent to each other;
(D07) The nodal point is the origin O, the X-axis is taken in the direction of the extended line of the first valley fold line (V1), and the first mountain fold line (M1) and the second mountain fold line (M2) are the first The angles formed with the first valley fold line (V1) are α and β, respectively, and the third mountain fold line (M3) and the fourth mountain fold line (M4) are formed with the second valley fold line (V2). The plurality of fold lines (M1 to M1) formed such that β−α = δ−γ + θ, where γ and δ are defined, and the angle between the X axis and the second valley fold line (V2) is θ. M4, V1, V2).
(Operation of the second embodiment of the tenth invention)
The structure with a fold line according to the second embodiment of the tenth invention having the above configuration provides a conical structure with a fold line that is not conventionally known in a folded state with a small outer shape and an extended state with a large outer shape. be able to.
(Third embodiment of the tenth invention)
The structure with a folding line according to Embodiment 3 of the tenth aspect of the invention is characterized in that, in the tenth aspect of the invention, the following structural requirements (D08) and (D09) are provided.
(D08) the first mountain fold line (M1), the second mountain fold line (M2), the third mountain fold line (M3) and the fourth mountain fold line (M4), and the first mountain fold line (M1) and A first valley fold line (V1) formed between the second mountain fold line (M2) and a second valley fold line (M2) disposed between the second mountain fold line (M2) and the third mountain fold line (M3). And the fourth mountain fold line (M4) is between the first mountain fold line (M1) and the third mountain fold line (M3), and the second mountain fold line (V4). The plurality of fold lines (M1 to M4, V1, V2) having one-node 6 fold lines arranged on the side opposite to (M2),
(D09) The node is the origin O, the X-axis is taken in the direction of the extension of the fourth mountain fold line (M4), and the first mountain fold line (M1) and the second mountain fold line (M2) are the first The angles formed with the first valley fold line (V1) are θ1 and θ2, respectively, and the angles between the second mountain fold line (M2) and the third mountain fold line (M3) with the second valley fold line (V2), respectively. θ3 and θ4, and the angle between the X axis and the first fold line (M1) is α^*And the angle between the X-axis and the third fold line (M3) is β^*If α^*= Θ2 + θ4, β^*The plurality of folding lines (M1 to M4, V1, and V2) formed so as to be = θ1 + θ3.
(Operation of Third Embodiment of Tenth Invention)
In the structure with a fold line according to the third embodiment of the tenth invention, it is possible to provide a conical structure with a fold line that is not conventionally known in a folded state having a small outer shape and an extended state having a large outer shape.
(11th invention)
The structure with a folding line of the eleventh invention is characterized by comprising the following constituent elements (E01) to (E04):
(E01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and a linear part connecting part that connects the outer sides of each part to each other. A fold lined structure provided with linear fold lines (M, V) that can be folded along the fold line (M, V) when viewed from one side of the fold line structure. The structure with fold lines (A; B; C; having a plurality of mountain fold lines (M) whose sides are mountain folds and one or more valley fold lines (V) which are valley folds,
(E02) A plurality of nodes that are intersections of the mountain fold line (M) and the valley fold line are arranged at a predetermined interval, and the number of mountain fold lines (M) and the number of valley fold lines that intersect at one node The plurality of fold lines (M, V) formed so that the difference is 2;
(E03) The structure with a fold line constituted by a sheet-like member in which a fold line along a spiral is formed
(E04) In the state where the fold line is extended, it is a circular sheet shape, and in the state where the fold line is bent according to the mountain fold line (M) and the valley fold line, it is a disk shape having unevenness whose outer shape is reduced. The structure with a fold line, which has a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along the mountain fold line (M) and the valley fold line.
(Operation of the eleventh invention)
The structure with a fold line of the present invention having the above-described configuration is a mountain fold line (a plurality of nodes that are intersections of the mountain fold line (M) and the valley fold line are arranged at a predetermined interval and intersect at one node ( Since the plurality of fold lines (M, V) are formed so that the difference between the number of M) and the number of valley fold lines is 2, in the folded state where the outer shape is small and the extended state where the outer shape is large, It is possible to provide a foldable structure in the form of a foldable circular sheet that is not known.
The folding line forming mold of the present invention can be provided with the following structural requirements (F01) and (F02).
(F01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A pair of fold line forming members provided, wherein the fold line is a plurality of mountain fold lines (M) in which the one surface side is mountain-folded when viewed from one surface side of the fold linear molding and one or more valleys in which valley folds are formed The number of mountain fold lines (M) having a fold line, and a plurality of nodes that are intersections of the mountain fold line (M) and the valley fold line are arranged at a predetermined interval and intersect at one node and the valley fold line A pair of fold line forming members having the plurality of fold lines (M, V) formed so that a difference from the number of
(F02) A folded linearly formed connecting member that supports or connects the pair of folding line forming members so as to be movable between an overlapped state and an open state.
In the folding line forming mold of the present invention having the above-described configuration, a sheet-like member is formed by simultaneously folding a pair of folding line-forming members in a state where the sheet-like member is sandwiched between the pair of folding line-forming members. The mountain fold line (M) and the valley fold line necessary for the above can be formed.
The folding line forming method of the present invention can include the following constituent elements (G01) and (G02).
(G01) A linear fold line that includes a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines (M) in which the one surface side is mountain-folded when viewed from one surface side of the structure with fold lines, and one or more fold lines are valley-folded. The number of mountain fold lines (M) having a valley fold line, and a plurality of nodes that are intersections of the mountain fold line (M) and the valley fold line are arranged at a predetermined interval and intersect at one node, and valley folds. A sheet-like member in which a foldable integrated sheet-like member is sandwiched between a pair of fold-line forming members having the plurality of fold lines (M, V) formed so that the difference from the number of lines is two Member clamping process,
(G02) A fold line forming step of forming a fold line on the sheet-like member by simultaneously folding the pair of fold-line forming members sandwiching the sheet-like member along the mountain fold line (M) and the valley fold line.
(Operation of the thirteenth invention)
In the fold line forming method of the thirteenth aspect of the present invention having the above-described configuration, a sheet having an integral structure that can be folded between a pair of fold line forming members having the plurality of fold lines (M, V) in the sheet-like member clamping step. Sandwich the shaped member.
Next, in the fold line forming step, the pair of fold line forming members sandwiching the sheet-like member are simultaneously folded along the mountain fold line (M) and the valley fold line to form a fold line on the sheet-like member. To do.
[Brief description of the drawings]
FIG. 1 is a fold line explanatory view showing a typical example of a fold line that is a folded straight line of origami or a folded structure and a node that is an intersection of a plurality of fold lines.
FIG. 2 is an explanatory view of a so-called “Miura oil” folding structure devised by Miura for the development of space structures.
FIG. 3 is a diagram in which the horizontal folding lines shown in FIG.
FIG. 4 is a diagram illustrating an example of a foldable folding line of a part of a disk (fan-shaped portion) formed by six fan-shaped elements having an apex angle 2Θ.
FIG. 5 is a diagram in which the horizontal fold line group shown in FIG. 2 is set at an arbitrary inclination. The fold lines (7) to (9) are equal to the fold lines (1) to (6) at all nodes. It is the figure drawn in the angle and symmetry.
FIG. 6 is a diagram showing an example of folding lines taking into account the periodicity of the folding method of FIG.
FIG. 7 is a diagram showing an example of the folding method considered by the present inventor, showing plane folding by the 1-node 4-fold line method and the 1-node 6-fold line method.
FIG. 8 is a diagram showing folding conditions of one node where six folding lines among the nodes shown in FIG. 7 intersect and six surrounding folding lines (one node six folding lines).
FIG. 9 is a diagram for explaining the conditions under which both ends of the band plate are joined to form a cylinder when the band plate is folded along the fold line, and FIG. 9A shows the angle between the band plate, the fold line, and the fold line. FIG. 9B is a diagram showing a change in the orientation of the reference axis when folded along the fold line shown in FIG. 9A.
FIG. 10 is an explanatory diagram of an example in which the formula (5) is satisfied and the folding direction is folded into a regular quadrangle by a folding line in the same direction (either mountain fold or valley fold), and FIG. 10A is in an unfolded state. FIG. 10B is a diagram showing a state during folding, and FIG. 10C is a diagram showing a folded state. FIG. 10B is a diagram showing folding lines (1), (2), (3), and (4).
FIG. 11 is an explanatory diagram of an example in which the expression (5) is satisfied and the folding direction is folded into a regular hexagon by a fold line in the same direction (either mountain fold or valley fold), and FIG. 11A is in an unfolded state. Fig. 11B is a diagram showing the folding line (1), (2), (3), (4), (5), (6) of the band plate, Fig. 11B is a diagram showing a state during folding, and Fig. 11C is a folded state. FIG.
FIG. 12 is an explanatory view of an example in which the above formula (5) is satisfied and the folding direction is folded in a regular octagon by a folding line having the same folding direction, and FIG. 12A is a folding line (1), (2 ),..., (8), FIG. 12B is a diagram showing a state during folding, and FIG. 12C is a diagram showing a folded state.
FIG. 13 is an explanatory diagram of an example in which the expression (5) is satisfied and the folding direction is alternately reversed (reversed in the mountain folding direction and the valley folding direction) and folded into a regular hexagon. FIG. 13A is developed. FIGS. 13B to 13F are diagrams showing a state in the middle of folding, and FIG. 13G is a diagram showing a folded state.
FIG. 14 is a typical developed view in the case where the belt-like plate shown in FIG. 9A is bent in the same direction by π · (N−2) / N in the same direction to form a regular N-gon and N = 6. FIG.
15 is composed of trapezoidal elements with unequal sides by disassembling twice the angle (π / 3) of the mountain fold line and the horizontal fold line in FIG. 14 to α = 2π / 9 and β = π / 9. FIG.
16 introduces six sets of folding lines obtained by decomposing the mountain fold line in the Y-axis direction of FIG. 14 into a mountain fold line I of α = π / 3 and a valley fold line II of β = π / 6. FIG. 16A is a developed view, FIG. 16B is a diagram showing a half-folded state of a folded cylinder produced when both ends of the developed view of FIG. 16A are joined, and FIG. 16C is a diagram of FIG. 16B. It is the perspective view seen from a different direction of the same thing.
FIG. 17 is a diagram in which the points A and B in FIG. 14 are matched, and the mountain fold portion is eliminated from the horizontal fold line, and the diamond pattern ((1) ˜ It is an expanded view of (3)).
FIG. 18 is a development view of a deformed diamond pattern composed of unequal triangular elements.
FIG. 19 is an explanatory view of a pseudo-cylindrical body having a developed view that is symmetrical with respect to a horizontal folding line and that can be folded. FIG. 19A is a developed view, and FIG. 19B is an end view of the developed view of FIG. FIG. 19C is a diagram showing a half-folded state of the folding cylinder manufactured when the two are joined, and FIG. 19C is a diagram showing the same thing as FIG. 19B seen from a different direction.
FIG. 20 is a diagram showing an example of a development view of a fold composed only of fold lines similar to the point B in FIG.
FIG. 21 is a developed view of a foldable cylindrical wall having a plurality of polygonal parts (flat plate walls) formed by folding lines.
FIG. 22 shows a cylindrical structure when the connecting portion of the divided flat plate made of the triangular divided flat plate studied by Guest et al. Is spiral, and the spiral (1) rises one step each time they make a round. Is shown in a developed view by the present inventor.
FIG. 23 corresponds to the whole of FIG. 17 inclined by ψ = π / 6, and has three diamond patterns in an oblique direction.
FIG. 24 is an explanatory view of a pseudo-cylindrical body having a development view equivalent to FIG. 23, FIG. 24A is a development view, and FIG. 24B is a fold produced when both ends of the development views of FIG. 23 and FIG. It is a figure which shows the cylinder half-folded state.
FIG. 25 is an explanatory view of a pseudo cylinder k having a developed view in which FIG. 14 is inclined by π / 6. FIG. 25A is a developed view, and FIG. 25B is manufactured when both ends of the developed view of FIG. It is a figure which shows the half-folded state of a folding cylinder.
26 is an explanatory view of a pseudo-cylindrical body having a developed view in which FIG. 15 is inclined by π / 6. FIG. 26A is a developed view, and FIG. 26B is manufactured when both ends of the developed view of FIG. 26A are joined. It is a figure which shows the half-folded state of a folding cylinder.
FIG. 27 is a developed view in which FIG. 16 is inclined by π / 6.
FIG. 28 is the spiral type of FIG. 19 and is obtained by cutting along a straight line connecting points A and D in FIG. The angle (˜0.193π) shown in FIG. 28 indicates the angle formed by the cutting line and the horizontal line. In this case, since the shape of the triangular element is given, the angle of the valley fold line is limited. Become.
29 is an explanatory view of a spiral folding cylinder having a fold line generalized from FIG. 24. FIG. 29A is a developed view, and FIG. 29B is manufactured when both ends of the developed view of FIG. 29A are joined. It is a figure which shows the half-folded state of a folding cylinder.
FIG. 30 is a development view when the six-stage development view of FIG. 29 is changed into three stages and the value of β is changed for each stage.
FIG. 31 is a development view of a repetitive spiral type obtained by reversing the spiral mountain fold line and valley fold line of FIG. 29 for each stage. This development is also obtained by matching points A and B in FIG.
FIG. 32 is a diagram showing a portion cut by two parallel straight lines AB ′ and C′D in the developed view of the cylindrical body shown in FIG. 21 so that A and B ′ and D and C ′ overlap. It is an expanded view of what becomes a foldable cylindrical body by connecting the left and right end edges of FIG.
FIG. 33 is a developed view of a collapsible cylinder having a rectangular element (part) having an arbitrary shape.
FIG. 34 is an explanatory view of a method for maintaining continuity when both ends of the developed view are joined.
FIG. 35 is a diagram showing an angular relationship between folding lines that satisfy folding conditions when a valley folding line is inserted symmetrically in the case of a 1-node 6 folding line, and the folding conditions in the case of FIGS. It is explanatory drawing.
FIG. 36 is a diagram showing an angular relationship between folding lines that satisfy the folding condition when valley folding lines (V1) and (V2) are alternately inserted between mountain folding lines (M1), (M2), and (M3). FIG. 56B is an explanatory diagram of folding conditions in the case of FIGS. 56B and 57 described later.
FIG. 37 shows the case of a 1-node 4-fold line. The folding conditional expression is obtained in the same procedure as above.
FIG. 38 is an enlarged view of the main part of the development view when the development view in the cone whose main fold line is parallel to the outer side of the development view is composed of N isosceles triangles having the apex angle 2Θ.
39 is an explanatory view of a pseudo-cone wall having a development view of a pseudo-cone wall with a folding line obtained using the value obtained by the equation (14), FIG. 39A is a development view, and FIG. 39B is a development view of FIG. 39A. It is a perspective view of the half-folded state of the conical wall with a fold line which has.
FIG. 40 is an enlarged view of a main part of a developed view of a conical wall with a folding line when it is divided into unequal triangular elements by folding lines.
FIG. 41 is a development view of a conical wall with fold lines when it is divided into unequal triangular elements by fold lines, where N = 3, 2Θ = π / 9, α = π / 9, and δ = π / 6. Fig.^*= About 0.0688π).
FIG. 42 is a developed view of a conical wall with fold lines when it is divided into inequilateral triangular elements by a fold line having an angle α in the upper right direction and an angle δ in the upper left direction at the point F in FIG. , Δ values are the same as those in FIG.
FIG. 43 is an enlarged view of a main part of a developed view of a conical wall with a folding line when divided by a trapezoidal element instead of the division by the isosceles triangular element of FIG.
44 shows a conical wall with a folding line that is divided into an isosceles trapezoid by a folding line and folded into a regular N pyramid, N = 6, φ in FIG.^*FIG. 44A is a development view, and FIG. 44B is a half-fold view of the cone wall with a folding line having the development view of FIG. 44A. It is a perspective view of the state made into.
FIG. 45 is a developed view of a conical wall with folding lines composed of N isosceles triangular elements (vertical angle 2Θ), and only one of them is written as a curved belt-like portion.
FIG. 46 is a developed view of a conical wall with a fold line having a simple, spiral developed view of three isosceles triangular elements.
FIG. 47 is a top view when the developed view of FIG. 46 is folded.
48 is an explanatory diagram of a practical model obtained by modifying the model described with reference to FIGS. 45 and 46, FIG. 48A is an explanatory diagram of a deformation method, and FIG. 48B is an enlarged view of a main part of FIG. 48A.
FIG. 49 is a view showing a state in which the figure ABGHFE formed by the fold line of FIG. 48A is sequentially folded at the fold lines AF and BF, and FIG. FIG. 49B is a diagram showing a state after further mountain-folding at B′F (original line segment BF) in the state of FIG. 49A.
FIG. 50 is a diagram showing a portion corresponding to the first-stage strip shown in FIG. 48A and a portion corresponding to the second-stage strip.
51 shows a conical wall with a folding line having the folding lines shown in FIGS. 48 to 50, where N = 6 and γ + ψ.^*= Π / 3, ψ^*FIG. 51A is a developed view, and FIG. 51B is a developed view of FIG. 51. FIG. 51A is a developed view of a pseudo-conical wall having a developed view (2Θ = π / 18) when γ = π / 6 and γ = π / 6 It is a perspective view of the state which folded the conical wall with a fold line in half.
FIG. 52 shows a conical wall with fold lines having the fold lines shown in FIGS. 48 to 50, where N = 6 and γ + ψ.^*= Π / 3, ψ^*FIG. 6 is a development view (2Θ = π / 6) when = π / 4 and γ = π / 12.
FIG. 53 is a development diagram of FIG.^*It is an expanded view when the value of is increased.
FIG. 54 is a development view in which the same cone wall as the folding cone wall having the development view of FIG. 53 is formed.
FIG. 55 is a diagram in the case where the second-stage valley fold line in FIG. 50 is taken in the opposite direction to that of the first stage at an angle γ.
56 is an explanatory view of a pseudo cone having a development view in which FIG. 51 is repetitively spiraled, FIG. 56A is a development view, and FIG. 56B is a half-fold view of a cone wall with a folding line having the development view of FIG. FIG.
FIG. 57 is a development view (N = 6) of the repetitive spiral type obtained as 2Θ = π / 6, ψ ¥ t * ¥ t = π / 6, γ = π / 6.
58 is an explanatory view of a developed view of a foldable conical wall having a fold line along an equiangular spiral, FIG. 58A is an overall explanatory view, and FIG. 58B is an enlarged view of a main part of FIG. 58A.
FIG. 59 is an explanatory view of a developed view of a conical wall with a folding line when the spiral of FIG. 58 is reversed.
FIG. 60 is an explanatory diagram of how to draw the developed view of FIG. 44A.
FIG. 61 is an explanatory view of a pseudo cone having a development view in which the above FIG. 44 is an equiangular spiral shape, FIG. 61A is a development view, and FIG. 61B is a half-folded view of the cone wall with a folding line having the development view of FIG. It is a perspective view of the state made into.
FIG. 62 is a development view of a folding conical wall with a folding line in which the spiral in the circumferential direction of FIG. 51A is raised by one step at the right end.
FIG. 63 is an explanatory diagram of the simplest folding method for origami.
64 is an explanatory view of a development view of a folding structure with a folding line, FIG. 64A is an enlarged view of a main part for explaining folding conditions, and FIG. 64B is an overall view.
FIG. 65 is an enlarged view of a development view of the folding structure with a folding line shown in FIG. 64B.
FIG. 66 is a perspective view of the folding structure with a folding line having the developed view of FIG. 65 in a half-folded state and a small amount of folding.
FIG. 67 is a perspective view of the folding structure with a folding line having the developed view of FIG. 65 in a half-folded state and a large amount of folding.
FIG. 68 is a perspective view of a state in which the disk-like folding structure with a folding line having the developed view of FIG. 65 is completely folded.
FIG. 69 is an explanatory view of a developed view of a disk-like folding structure with a folding line when the swing angle of the Zig / Zag folding line in the radial direction is increased toward the center, and FIG. 69A is for explaining folding conditions. FIG. 69B is an enlarged view of the main part of FIG.
FIG. 70 is a development view of a disk-shaped folding structure with a folding line when the swing angle of the Zig / Zag folding line in the radial direction is increased toward the center and the folding line in the circumferential direction is also Zig / Zag. FIG. 70A is an explanatory view, FIG. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.
FIG. 71 is an explanatory diagram of a conventionally known winding method in which the intersection of spiral fold lines is on the Archimedean spiral.
72 is a diagram showing a new fold line considered by the present inventor. FIG. 72A is a fold line in which the fold line (1) in the radial direction has one bending point in FIG. 71 and the spiral is reversed at this bending point. 72B is a diagram in which the outside of the bending point in FIG. 72A is replaced by a method of folding in the radial direction.
FIG. 73 is an explanatory diagram of a fold line when a fold line for folding a circular film, a partial circular film (fan-shaped film) or the like in the radial direction and the circumferential direction is formed along an equiangular spiral.
FIG. 74 is an explanatory diagram of a fold line when forming a fold line that folds in a circumferential direction while winding a circular film or a partial circular film (fan-shaped film) around the central axis along an equiangular spiral.
FIG. 75 is an enlarged view of a main part of FIG.
FIG. 76 is an explanatory diagram of folding conditions when forming a folding line along the equiangular spiral while folding a circular film or a partial circular film (fan-shaped film) around the central axis.
FIG. 77 is an explanatory diagram of folding conditions when the main folding line is folded at an equal angle with respect to the radiation.
FIG. 78 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 20 degrees.
FIG. 79 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 79 is an example of a folded development view when γ = 0 °, and shows an example in which the angle of the folding line with respect to radiation is different from FIG. 78.
FIG. 80 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 10, the number of isosceles triangle elements N = (2N + 1) m = 42, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
FIG. 81 shows an example in which two zigzag spirals (m = 2) are folded around the center, and n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, It is a figure which shows the example of the expanded view of a disk-shaped folding structure with a folding line in the case of (gamma) = 0 degree.
FIG. 82 is a perspective view of the folding line disk-like folding structure having the developed view of FIG. 81 in a half-folded state and a small amount of folding.
FIG. 83 is a perspective view of the folding structure with a folding line having the developed view of FIG. 81 in a half-folded state and a large amount of folding.
FIG. 84 is a perspective view of a state in which the disk-like folding structure with a folding line having the developed view of FIG. 81 is completely folded.
FIG. 85 shows an example in which four zigzag spirals (m = 4) are folded around the center, and n = 7, the number of equilateral triangle elements N = (2n + 1) m = 60, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
FIG. 86 shows an example in which three zigzag spirals (m = 3) are folded around the center, and n = 8, the number of equilateral triangle elements N = (2n + 1) m = 51, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
FIG. 87 shows an example of folding around a center with one zigzag spiral (m = 1) as the fold line, where n = 10, the number of equilateral triangle elements N = (2n + 1) m = 21, It is a figure which shows the example of a folding expanded view in the case of (gamma) = 0 degree.
FIG. 88 shows an example in which four zigzag spirals (m = 4) are folded around the center, and n = 7, the number of equilateral triangle elements N = (2n + 1) m = 61, It is a figure which shows the example of the expanded view of a disk-shaped folding structure with a folding line in the case of (gamma) = 0 degree.
FIG. 89 is a perspective view of the folding structure with a folding line having the developed view of FIG. 88 in a half-folded state and a small amount of folding.
FIG. 90 is a perspective view of the folding structure with a folding line having the developed view of FIG. 88 in a half-folded state and a large amount of folding.
FIG. 91 is a perspective view of a state in which the folding structure with a folding line having the developed view of FIG. 88 is completely folded.
FIG. 92 is a development view when the number of spirals as the main fold line is large (m = 12).
FIG. 93 is a developed view composed of two types of equiangular spirals based on FIG. Number of divisions N = 12, θ₁= Π / 180, θ₂= 29π / 180, and φ is approximately π / 18. When the developed view of FIG. 93 is folded, it is wound up well around the center symmetrically in the vertical direction. The thing of FIG. 93 suggests that these folding lines are replaced by elastic deformation at the time of winding since the sub folding lines are fine.
FIG. 94 is a development view of a disk-like folding structure with folding lines in which mountain fold lines and valley fold lines are alternately provided.
FIG. 95 is a development of a disk-like folding structure with folding lines in which mountain fold lines and valley fold lines are alternately provided and the circumferential lengths of the valley fold lines and the left and right mountain fold lines are different on the left and right sides. FIG.
FIG. 96 is a view in which a fan-shaped portion between adjacent mountain fold lines in FIG. 95 is removed.
97 is an explanatory view of the folding condition of the sheet-like member, FIG. 97A is a development view before folding, and FIG. 97B is a diagram showing a state folded at the folding line of FIG. 97A.
FIG. 98 is an explanatory diagram of a DCC (double correlated core), FIG. 98A is a development view of the DCC, and FIG. 98B is an external view of the half-folded state.
FIG. 99 is an explanatory diagram showing the vertical fold line group in FIG. 98 as zig / zag.
FIG. 100 is an explanatory diagram of a newly devised core model with joints, FIG. 100A is a development view, FIG. 100B is a plan view of the development view of FIG. 100A in a half-folded state, and FIG. It is an external view of what folded the figure and made it three-dimensional.
FIG. 101 is an explanatory view of another model of the core having a joint portion newly devised, FIG. 101A is a development view, FIG. 101B is a plan view of the development view of FIG. 101A in a half-folded state, and FIG. FIG.
FIGS. 102A and 102B are explanatory diagrams of a model that does not satisfy another folding condition of the core with the joint devised by the present inventor. FIG. 102A is a development view, and FIG. 102B is an enlarged view of a main part of FIG.
103 is an explanatory view of a core created by folding the developed view of FIG. 102A, FIG. 103A is a perspective view of the folded core, and FIG. 103B is a perspective view of a sheet bonded to the lower surface of the core of FIG. 103A. .
FIG. 104 is an explanatory view of a model that does not satisfy another folding condition of the core with the joint devised by the present inventor, FIG. 104A is a development view, and FIG. 104B is an enlarged view of a main part of FIG. 104A.
FIG. 105 is an explanatory diagram of a method for manufacturing a honeycomb core from a single plate, FIG. 105A is a development view, and FIG. 105B is a diagram of a honeycomb core manufactured from a plate having the development view of FIG. 105A.
FIG. 106 is a view showing a folding mold for producing the core material shown in FIG. 103A.
107 is an explanatory view of the manufactured aluminum core, FIG. 107A is a perspective view, FIG. 107B is a development view, and has the same shape as the paper development view shown in FIG. 103A.
FIG. 108 is an explanatory view of an application example of a structure with a cylindrical folding line, and FIG. 108A is a development view.
FIG. 109 is an explanatory view of an application example of a spiral cylindrical folding lined structure, FIG. 109A is a developed view, and FIG. 109B is a view showing an inflatable structure that can be expanded and contracted based on FIG. 109A. .
FIG. 110 is a plan view of a folding line forming mold according to the first embodiment of the present invention.
FIG. 111 is a perspective view of a paper or resin sheet on which a fold line is formed.
FIG. 112 is an explanatory diagram of a folding line forming mold according to Embodiment 2 of the present invention, and is a perspective view of one flexible mold of a pair of flexible molds for sandwiching both surfaces of a sheet-like member forming a folding line. FIG.
FIG. 113 is a plan view of a folding line forming mold according to Embodiment 3 of the present invention.
FIG. 114 is an explanatory diagram of the usage state of the fold line forming mold shown in FIG. 113, FIG. 114A is a view showing a state where the fold line forming mold is folded in two, and FIG. 114B is a half fold shown in FIG. It is a figure which shows the state which folded the type | mold for fold line formation.
115 is an explanatory view of a sheet-like member in which a fold line is formed using the fold line forming mold shown in FIGS. 113 and 114, FIG. 115A is a plan view of the sheet-like member in a half-folded state, and FIG. It is a top view of the state folded completely.
FIG. 116 is an explanatory view of the folded sheet-like member shown in FIG. 115B, FIG. 116A is a perspective view, and FIG. 116B is a planar sheet-like member on one surface (lower surface) of the folded sheet-like member shown in FIG. It is a perspective view of what adhere | attached.
FIG. 117 is a side view of a plastic bottle as a structure with a folding line according to the fourth embodiment of the present invention.
118 is a sectional side view of the plastic bottle of Example 4. FIG.
FIG. 119 is an explanatory view of the plastic bottle of FIG. 117 compressed in the axial direction (half-folded state), FIG. 119A is a view showing the half-folded state, and FIG. 119B is a cover in the opening portion in the almost completely folded state. FIG.
FIG. 120 is an explanatory view of the manufacturing method of the plastic bottle A, and shows a state in which a mold (mold having a fold line forming surface) is opened.
FIG. 121 is an explanatory diagram of the method for manufacturing the PET bottle A, and shows a state in which the mold is closed and a tubular or bag-shaped blank (parison) is extended in the mold.
FIG. 122 is a view showing a state in which compressed air is blown into the raw pipe of FIG. 121 to be expanded.
FIG. 123 is an explanatory view of a plastic bottle as Example 5 of the structure with a fold line of the present invention, and shows a structure with a fold line (pet bottle) formed along a spiral.
FIG. 124 is an explanatory view of a plastic bottle as Example 6 of the structure with a folding line of the present invention, and shows a structure with a folding line (pet bottle) having a cylindrical wall formed along a spiral.
FIG. 125 is a side view of a coffee can as a structure with a folding line according to a seventh embodiment of the present invention.
126 is a side sectional view of the coffee can of Example 7. FIG.
FIG. 127 is an explanatory view of the coffee can of FIG. 126 compressed in the axial direction (half-folded state), FIG. 127A is a side view of the half-folded state, and FIG. 127B is a side view of the almost completely folded state. .
128 is an explanatory view of the method for manufacturing the coffee can A, and is an explanatory view of an inner mold (mold having a fold line forming surface) disposed on the inner surface of the cylindrical member. FIG. FIG. 128B is a plan sectional view in which a pair of inner second molds are inserted between the pair of inner first molds in FIG. 128A. 128C is a cross-sectional plan view of the inner first and second molds shown in FIG. 128B with the cam rod inserted in the center thereof. FIG. 128D is a rotation of the cam rod shown in FIG. 128C to move the inner second mold outward. It is a figure which shows the state which pushed the inner side 1st and 2nd metal mold | die outward by pushing out.
FIG. 129 is an explanatory view of the manufacturing method of the coffee can A, and FIG. 129A is a state before the outer mold K2 is clamped with the inner mold (mold having a folding line forming surface) set on the inner surface of the cylindrical member. FIG. 129B is a diagram showing a state where the mold is clamped from the state of FIG. 129A.
FIG. 130 is an explanatory view of a coffee can as an eighth embodiment of the structure with a fold line of the present invention, and shows a structure with a fold line (coffee can) having a cylindrical wall formed along a spiral.
FIG. 131 is an explanatory diagram of another embodiment of the method for manufacturing the coffee can A.
132 is an explanatory view of a small container as a structure with a folding line according to the ninth embodiment of the present invention, FIG. 132A is a perspective view of a lid of the small container, and FIG. 132B is a perspective view of the small container in an extended state.
133 is an explanatory view of the small container of Example 9, FIG. 133A is a perspective view of the small container in a folded state, FIG. 133B is a sectional view taken along line 133B-133B of FIG. 133A, and FIG. 133C is a small figure of FIG. It is sectional drawing of the state which covered the container.
FIG. 134 is an explanatory view of the manufacturing method of the small container B, and shows a state in which a mold (mold having a fold line forming surface) is closed.
FIG. 135 is an explanatory diagram of a paper pack as a fold lined structure according to the tenth embodiment of the present invention, and is a perspective view of a use state in which the paper pack is extended.
136 is a view showing a state in the middle of folding the paper pack of FIG.
FIG. 137 is a view showing a state where the paper pack of FIG. 136 is further folded.
FIG. 138 is a developed view of the paper pack shown in FIGS. 135 to 137.
FIG. 139 is an explanatory diagram of a paper pack as a fold lined structure according to an eleventh embodiment of the present invention, and is a perspective view of a use state in which the paper pack is extended.
FIG. 140 is a diagram showing a state in the middle of folding the paper pack of FIG. 139.
FIG. 141 is a view showing a state in which the paper pack of FIG. 140 is further folded.
FIG. 142 is a development view of the paper pack shown in FIGS. 139 to 141.
FIG. 143 is an explanatory diagram of a paper pack as a fold lined structure according to a twelfth embodiment of the present invention, and is a perspective view showing a use state in which the paper pack is extended.
FIG. 144 is a diagram showing a state in the middle of folding the paper pack of FIG. 143.
FIG. 145 is a view showing a state where the paper pack of FIG. 144 is further folded.
FIG. 146 is a development view of the paper pack shown in FIGS. 143 to 145.
FIG. 147 is an explanatory diagram of a paper pack as a fold lined structure according to the thirteenth embodiment of the present invention, and is a perspective view showing a use state in which the paper pack is extended.
148 is a diagram showing a state in the middle of folding the paper pack of FIG. 147. FIG.
FIG. 149 is a view showing a state where the paper pack of FIG. 148 is further folded.
FIG. 150 is a developed view of the paper pack shown in FIGS. 147 to 149.
FIG. 151 is an explanatory diagram of a pump as a structure with a folding line according to the fourteenth embodiment of the present invention.
FIGS. 152A and 152B are explanatory views of a trash box as a structure with folding lines according to the fifteenth embodiment of the present invention. FIG. 152A is a side view and FIG. 152B is a side sectional view.
FIG. 153 is an explanatory diagram of a pencil stand as a structure with folding lines according to the sixteenth embodiment of the present invention. FIG. 153A is a side view and FIG. 153B is a side sectional view.
FIG. 154 is an explanatory view of a gusset (box internal partition member) as a structure with a folding line of Embodiment 17 of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 155 is a perspective view of the guess of FIG.
FIG. 156 is a developed view of the guess of FIG.
FIG. 157 is an explanatory view of a gusset (box internal partition member) as a fold lined structure of the eighteenth embodiment of the present invention, and is a perspective view of the gusset taken out from the paper box.
FIG. 158 is a developed view of the guess of FIG.
FIG. 159 is an explanatory view of a gusset (box internal partition member) as a fold lined structure of the nineteenth embodiment of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 160 is a perspective view of the guess of FIG.
FIG. 161 is a developed view of the guess of FIG.
FIG. 162 is an explanatory view of a gusset (box internal partition member) as a fold lined structure according to a twentieth embodiment of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 163 is a perspective view of the guess of FIG.
FIG. 164 is a developed view of the guess of FIG. 163.
FIG. 165 is an explanatory diagram of a gusset (box internal partition member) as a fold lined structure according to the twenty-first embodiment of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 166 is a perspective view of the guess of FIG.
FIG. 167 is a developed view of the guess of FIG.
FIG. 168 is an explanatory view of the folding passage cover, FIG. 168A is a perspective view in a half-folded state, and FIG. 168B is a perspective view in a completely folded state.
FIG. 169 is a development view of a folding passage cover as a structure with a folding line according to the twenty-second embodiment of the present invention.
170A and 170B are explanatory views of a folding path cover as a structure with a folding line according to the twenty-third embodiment of the present invention. FIG. 170A is a perspective view in a half-folded state, and FIG. 170B is a perspective view in a completely folded state.
FIG. 171 is a developed view of the folding passage cover of FIG.
FIG. 172 is an explanatory diagram of a lamp shade as a structure with folding lines according to a twenty-fourth embodiment of the present invention. FIG. 172A is a development view of a sheet-like member that is a material for manufacturing the lamp shade, and FIG. FIG. 5 is a perspective view of a lamp shade that is formed by joining the left and right sides of a shaped member to produce a pseudocone in a half-folded state.
FIG. 173 is an explanatory view of a Christmas card as a fold lined structure of Example 25 of the present invention. FIG. 173A is a plan view of the folded Christmas card, and FIG. 173B is a plan view of the opened FIG. 173A. FIG. 173C is a view as seen from diagonally above the arrow 173C in FIG. 173B.
FIG. 174 is an explanatory view of a cap as a fold lined structure of Embodiment 26 of the present invention, FIG. 174A is a perspective view of the cap, FIG. 174B is a sectional view taken along the line 174B-174B of FIG. It is the figure seen from the arrow 174C of 174B.
FIG. 175 is an explanatory view of the cap of Example 26, FIG. 175A is a plan view of the cap folded, and FIG. 175B is a view as seen from the arrow 175B of FIG. 175A.
FIG. 176 is an explanatory view of a hat as a structure with folding lines according to a twenty-seventh embodiment of the present invention, FIG. 176A is a perspective view of the hat, FIG. 176B is a sectional view taken along the line 176B-174B of FIG. 176A, and FIG. It is the figure seen from arrow 176C of 176B.
FIG. 177 is an explanatory diagram of the cap of Example 27, FIG. 177A is a plan view of the cap folded, and FIG. 177B is a view seen from the arrow 177B of FIG. 177A.
FIG. 178 is a perspective view of a winding type cap as a structure with a folding line of the embodiment 28 of the present invention.
FIG. 179 is a perspective view of the winding type cap of FIG. 178 in the middle of folding.
FIG. 180 is a perspective view of a wind-up type cap that is further folded from the state of FIG. 179.
181 is an explanatory view of the method for manufacturing the winding type cap shown in FIGS. 178 to 180. FIG. 181A is a development view of FIG. 178 heel A, FIG. 181B is a development view of the temporal region B, and FIG. FIG. 3 is a development view of the crown C.
FIG. 182 is an explanatory view of another manufacturing method of the winding type cap shown in FIGS. 178 to 181.
FIG. 183 is a perspective view of a winding tent as a structure with a folding line according to the twenty-ninth embodiment of the present invention.
FIG. 184 is a perspective view of the winding type tent of FIG. 183 in the middle of folding.
FIG. 185 is a perspective view of the tent in a further folded state from the state of FIG.
FIG. 186 is an explanatory view of a method for manufacturing the winding tent shown in FIGS. 183 to 185. FIG. 186A is a drawing showing a dome shape having a parabolic curved surface in an expanded state, divided in the circumferential direction. FIG. 186B is a diagram showing a conical wall formed when the end portion AB of the part shown in FIG. 186A is connected to the CD.
FIG. 187 is an explanatory view of the method for manufacturing the winding tent shown in FIGS. 183 to 185. FIG. 187 shows the winding tent that has a radius r1 in the extended state and the coordinates of the center position of the dome shape. Is set to r = 0, j = 1, 2,..., 10 and is divided into 10 by a circle whose radius is a coordinate rj (rj = r1 × (11−j) / 10) at a position equally divided into 10 in the radial direction. It is a figure which shows the shape of the part (conical wall) (j) formed in this.
FIG. 188 is a diagram showing the part number (j), the shape and length Lj of the bus bar, and the inclination θj of FIG. 187.
FIG. 189 shows divided parts (J: J = 1, 2,...) When the developed views of the parts (1), (2),..., (10) shown in FIGS. , 10) is an explanatory diagram of the shape, FIG. 189A shows that each part (j) is composed of 16 divided parts (J), and FIG. 189B shows the divided parts (J) connected in the radial direction. FIG.
FIG. 190 is a perspective view of a take-up tent as a structure with a folding line according to a thirty-third embodiment of the present invention.
FIG. 191 is a perspective view of the winding-type tent of FIG. 190 in the middle of folding.
FIG. 192 is a perspective view of the tent in a further folded state from the state of FIG.
BEST MODE FOR CARRYING OUT THE INVENTION
Next, specific examples (examples) of the embodiments of the present invention will be described with reference to the drawings, but the present invention is not limited to the following examples.
(Example 1)
FIG. 110 is a plan view of a folding line forming mold according to the first embodiment of the present invention.
110, the fold line forming mold 1 has a pair of flexible molds 2 and 2 as a pair of foldable fold line forming members arranged symmetrically with respect to the opening / closing axis L. The flexible mold 2 includes a plurality of rhombus parts P and a craft film 3 bonded to both surfaces of each part P in a state where the outer sides of the plurality of parts P are adjacent to each other. The adjacent outer sides of the parts P are connected by the craft film 3, and a linear fold line that can be folded by the craft film 3 of the connecting portion (part connecting portion) is formed.
Nodes that are the intersections of the plurality of folding lines are arranged at a predetermined interval, and a total of four folding lines intersect at one node. The fold line includes a mountain fold line where the one surface side is a mountain fold and a valley fold line which is a valley fold when viewed from one surface side of the flexible mold (fold line forming member) 2, and a mountain which intersects at one node. The difference between the number of folding lines and the number of valley folding lines is two. In the first embodiment, the number of fold lines intersecting at one node is 4, and at each node, three mountain fold lines and one valley fold line intersect, or three mountain fold lines. And one valley fold line intersect.
The fold line and the valley fold line of the flexible molds 2, 2 in a state of being folded along the open / close axis L are overlapped.
Flexible molds made by bonding craft films to both sides of each part (each part, ie, each thin metal plate) P can be easily performed from the next time by attaching creases once to the mountain fold line and the valley fold line. Mountain folds and valley folds are possible. Accordingly, when a folding mold is folded along the opening / closing axis L with a paper or resin sheet or the like placed on the surface of the flexible mold on one side of the opening / closing axis L, the paper or resin sheet is a pair of flexible molds. Sandwiched between. When the flexible mold is folded along the fold line in this state, a fold line is formed on the sheet-like member S such as paper or a resin sheet.
FIG. 111 is a perspective view of a paper or resin sheet on which a fold line is formed.
As can be seen from FIG. 111, by using the folding line forming mold 1 shown in FIG. 110, a folding line can be easily formed on the sheet-like member S such as paper or a resin sheet.
(Example 2)
FIG. 112 is an explanatory diagram of a folding line forming mold according to Embodiment 2 of the present invention, and is a perspective view of one flexible mold of a pair of flexible molds for sandwiching both surfaces of a sheet-like member forming a folding line. FIG.
In FIG. 112, the flexible mold 2 forming the folding line forming mold 1 of the second embodiment of the present invention is formed by a plurality of rhombus parts P, and each part P is formed on the side edge of each part. The hinges Pa are rotatably connected.
The hinge Pa of each part P is arranged on the same surface side of each part, and the sheet-like member is sandwiched by the surface opposite to the surface on which the hinge Pa is provided.
Other configurations are the same as those in the first embodiment.
(Example 3)
FIG. 113 is a plan view of a folding line forming mold according to Embodiment 3 of the present invention.
FIG. 114 is an explanatory diagram of the usage state of the fold line forming mold shown in FIG. 113, FIG. 114A is a view showing a state where the fold line forming mold is folded in two, and FIG. 114B is a half fold shown in FIG. It is a figure which shows the state which folded the type | mold for fold line formation.
In FIG. 113, the fold line forming die 1 has a pair of flexible molds 2 and 2 as a pair of foldable fold line forming members arranged symmetrically with respect to the opening / closing axis L. The flexible mold 2 is a craft film in which a plurality of square parts P1, a parallelogram part P2, and a plurality of parts P1, P2 are adhered to both sides of the parts P1, P2 with their outer sides adjacent to each other. 3.
The smaller one of the inner angles of the parallelogram is 60 °.
When the folding line forming mold 1 is folded along the opening / closing axis L in a state where a sheet-like member such as paper or a resin sheet is placed on the surface of the flexible mold 2 on one side of the opening / closing axis L, the paper or the resin sheet, etc. Is sandwiched between a pair of flexible molds 2 and 2. In this state, when the flexible molds 2 and 2 overlapped with each other are folded in the state shown in FIG. 114A by the fold line, and further folded in the state shown in FIG. 114B, the sheet-like member S such as paper or resin sheet is easily folded. Can be formed.
115 is an explanatory view of a sheet-like member in which a fold line is formed using the fold line forming mold shown in FIGS. 113 and 114, FIG. 115A is a plan view of the sheet-like member in a half-folded state, and FIG. It is a top view of the state folded completely.
FIG. 116 is an explanatory view of the folded sheet-like member shown in FIG. 115B, FIG. 116A is a perspective view, and FIG. 116B is a planar sheet-like member on one surface (lower surface) of the folded sheet-like member shown in FIG. It is a perspective view of what adhere | attached.
The regions S1 and S2 and S3 and S4 of the sheet-like member S in the half-folded state shown in FIG. 115A are joined in the fully-folded state shown in FIG. 115B or FIG. Therefore, a strong core member can be formed by applying an adhesive to one of the joints S1 and S2 and one of S3 and S4 when folded. 116A can be produced by adhering the sheet S ′ (see FIG. 116) to one surface (lower surface) or both surfaces of the folded sheet member S shown in FIG. 116A with an adhesive.
The fold line forming mold described in the first and third embodiments uses a pair of fold line forming members (flexible molds) for sandwiching the sheet member, but the fold line forming mold is one sheet. It is possible to form a fold line on a sheet-like member using a fold line forming member (flexible mold). In that case, a small suction port is formed in each part of the fold line forming member, the one side of the fold line forming member is set to a negative pressure, and the sheet member is adsorbed to the other side of the fold line forming member ( A folding line can be formed on the sheet member by folding the flexible mold.
In addition, a configuration in which a pair of fold line forming members are supported by separate support members, and the other fold line forming member is mechanically moved to a close contact position with respect to one fold line forming member or separated. It is possible to adopt.
(Example 4)
FIG. 117 is a side view of a plastic bottle as a structure with a folding line according to the fourth embodiment of the present invention.
118 is a sectional side view of the plastic bottle of Example 4. FIG.
FIG. 119 is an explanatory view of the plastic bottle of FIG. 117 compressed in the axial direction (half-folded state), FIG. 119A is a view showing the half-folded state, and FIG. 119B is a cover in the opening portion in the almost completely folded state. FIG.
117 and 118, the plastic bottle A has a bottom wall A0, a cylindrical wall A1, a conical wall A2, and an opening A3. As shown in FIGS. 117 and 118, the cylindrical wall A1 has a large number of mountain fold lines M (see the solid line in FIG. 117) whose outer surface is convex and a large number of valley fold lines V (see 1 in FIG. 117) which are concave. (See dotted line).
117 and 118, in the plastic bottle A of the fourth embodiment, the part P that is a part formed (enclosed) by the folding lines M and V is formed in a shape (square). At the node that is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. The number of mountain fold lines M intersecting at the nodes = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1).
When the cylindrical wall A1 of the plastic bottle A of Example 4 is compressed in the axial direction, it is folded along the folding lines M and V, and is folded into the state of FIG. 119B through the state of FIG. 119A. The folded plastic bottle tends to return to its original shape (elongated shape) due to elasticity, but when folded into the state shown in FIG. 119B, a lid (cap) C is placed on the opening A3 to put the plastic bottle A inside. When air is prevented from flowing in, the plastic bottle A is held in a folded state (the state shown in FIG. 122B). In this folded state, the space required to accommodate the cylindrical wall A1 can be reduced to 1/3 or less of the state shown in FIGS.
Therefore, the space required for storage until the cylindrical wall A1 of the used plastic bottle A is recycled can be reduced.
FIG. 120 is an explanatory view of the manufacturing method of the plastic bottle A, and shows a state in which a mold (mold having a fold line forming surface) is opened.
FIG. 121 is an explanatory diagram of the method for manufacturing the PET bottle A, and shows a state in which the mold is closed and a tubular or bag-shaped blank (parison) is extended in the mold.
FIG. 122 is a view showing a state in which compressed air is blown into the raw pipe of FIG. 121 to be expanded.
In FIG. 120, a mold K includes a circular bottom mold K1, an intermediate mold K2a, K2a obtained by dividing a cylinder into two, and an upper first mold that clamps the upper ends of the intermediate molds K2a, K2a. K3a and an upper second mold K3b supported on the upper surface thereof. As shown in FIG. 120, the raw tube C is arranged in a state of covering the tip portion of the air supply pipe B, and the mold is clamped as shown in FIG. Next, as shown in FIG. 122, when air is blown out from the air supply pipe B, a plastic bottle A is manufactured. The shape of the mold cavity is transferred to the outer wall of the plastic bottle A by cooling the plastic bottle A of FIG. Therefore, a mountain fold line M or a valley fold line V can be formed on the outer wall of the plastic bottle A by forming a concave portion or a convex portion on the inner surface of the mold.
(Example 5)
FIG. 123 is an explanatory view of a plastic bottle as Example 5 of the structure with a fold line of the present invention, and shows a structure with a fold line (pet bottle) formed along a spiral.
In the description of the fifth embodiment, components corresponding to those of the fourth embodiment are denoted by the same reference numerals, and detailed description thereof is omitted.
The fifth embodiment is different from the fourth embodiment in the following points, but is configured in the same manner as the fourth embodiment in other points.
In FIG. 123, the plastic bottle A of the fifth embodiment is different from the fourth embodiment in the shape of a part P that is a part formed (enclosed) by the folding lines M and V. That is, the shape of the part P of the fifth embodiment is a trapezoid as in the fourth embodiment, but the height of the trapezoid is lower than that of the fourth embodiment. The folding lines M and V of the fifth embodiment have folding lines formed along a spiral.
As in the fifth embodiment, the cylindrical wall (structure with a cylindrical fold line) A1 having a fold line along the spiral is folded when compressed in the axial direction while twisting, and the outer shape becomes small, while twisting. When pulled in the axial direction, the outer shape expands and expands.
(Example 6)
FIG. 124 is an explanatory view of a plastic bottle as Example 6 of the structure with a folding line of the present invention, and shows a structure with a folding line (pet bottle) having a cylindrical wall formed along a spiral.
In the description of the sixth embodiment, components corresponding to those of the fifth embodiment are denoted by the same reference numerals, and detailed description thereof is omitted.
The sixth embodiment is different from the fifth embodiment in the following points, but is configured in the same manner as the fifth embodiment in other points.
In FIG. 124, the plastic bottle A of the sixth embodiment is different from the fourth embodiment in the shape of the part P that is a part formed (enclosed) by the folding lines M and V. That is, the shape of the part P of the sixth embodiment is a trapezoid as in the fifth embodiment, but the height of the trapezoid is higher than that of the fourth embodiment. Further, the folding lines M and V of the sixth embodiment have folding lines formed along the spiral as in the fifth embodiment, but the inclination of the spiral is larger than that of the first embodiment. The inclination angle is about 45 °.
The cylindrical wall (structure with a cylindrical fold line) A1 having a fold line along a spiral with a large inclination angle as in the sixth embodiment is folded when compressed in the axial direction while twisting, and the outer shape becomes smaller. Is the same as that of the fifth embodiment, but requires a slightly larger force than the fifth embodiment when folding. And once folded, since the cylindrical wall A1 of a plastic bottle deforms plastically, the cylindrical wall A1 does not automatically return to its original shape due to elasticity. For this reason, when the plastic bottle is used, if it is compressed and folded in the axial direction while twisting, the folded state can be maintained without covering the opening A3.
(Example 7)
FIG. 125 is a side view of a coffee can as a structure with a folding line according to a seventh embodiment of the present invention.
126 is a side sectional view of the coffee can of Example 7. FIG.
FIG. 127 is an explanatory view of the coffee can of FIG. 126 compressed in the axial direction (half-folded state), FIG. 127A is a side view of the half-folded state, and FIG. 127B is a side view of the almost completely folded state. .
125 and 126, the coffee can A has a bottom wall portion A0, a cylindrical wall A1 and an upper wall portion A2 made of aluminum or steel, and the cylindrical portion of the plastic bottle shown in FIGS. It has the same shape. 125 and 126, the cylindrical wall A1 has a large number of mountain fold lines M (see the solid line in FIG. 125) whose outer surface is convex and a large number of valley fold lines V (see 1 in FIG. 125) that are concave. (See dotted line).
In the coffee can A of the seventh embodiment, a part P that is a part formed (enclosed) by the folding lines M and V is formed in a trapezoidal shape (rectangular shape). At the node that is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. The number of mountain fold lines M intersecting at the nodes = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1).
When the cylindrical wall A1 of the coffee can A of Example 7 is compressed in the axial direction, it is folded along the folding lines M and V, and is plastically deformed into the folded state of FIG. 127B through the state of FIG. 127A.
If a thin can such as a coffee can has a pattern as shown in FIG. 33 on the outer periphery of the central portion in the axial direction, if the coffee can is twisted at the time of disposal, the fold line extends from the pattern as a base point. Folded.
Therefore, the space required for storage until the cylindrical shape A1 of the used coffee can A is recycled can be reduced.
128 is an explanatory view of the method for manufacturing the coffee can A, and is an explanatory view of an inner mold (mold having a fold line forming surface) disposed on the inner surface of the cylindrical member. FIG. FIG. 128B is a plan sectional view in which a pair of inner second molds are inserted between the pair of inner first molds in FIG. 128A. 128C is a cross-sectional plan view of the inner first and second molds shown in FIG. 128B with the cam rod inserted in the center thereof. FIG. 128D is a rotation of the cam rod shown in FIG. 128C to move the inner second mold outward. It is a figure which shows the state which pushed the inner side 1st and 2nd metal mold | die outward by pushing out.
FIG. 129 is an explanatory view of the manufacturing method of the coffee can A, and FIG. 129A is a state before the outer mold K2 is clamped with the inner mold (mold having a folding line forming surface) set on the inner surface of the cylindrical member. FIG. 129B is a diagram showing a state where the mold is clamped from the state of FIG. 129A.
The inner mold K1 shown in FIGS. 128 and 129 includes a pair of inner first molds K1a and K1a disposed to face each other, and a pair of inner second molds K1b and K1b disposed therebetween. And a cam rod K1c inserted between the inner first and second molds K1a, K1a, K1b, K1b. On the outer surface of the inner first and second molds K1a, K1a, K1b, K1b, uneven surfaces forming the mountain fold line M and the valley fold line V of the coffee can A shown in FIGS. 125 and 126 (FIG. (Not shown) is formed. The outer mold K2 has four outer divided molds K2a configured by dividing the cylindrical mold into four equal parts, and the inner surface of each outer divided mold K2a has the above-described FIGS. 125 and 126. The uneven surface (not shown) which forms the mountain fold line M and the valley fold line V of the coffee can A shown in FIG.
As shown in FIG. 128C, when the inner mold K1 is set inside an aluminum cylindrical member that is a material for manufacturing the coffee can A, and the cam rod K1c is rotated by 90 ° in this state, the inner first and second molds K1a, K1a, K1b, and K1b are pushed outward to the state shown in FIG. 128D.
In this state, the outer mold K2 of FIG. 129A is clamped to the state of FIG. 129B, whereby the coffee can A having the folding lines M and V shown in FIGS. 125 and 126 can be manufactured.
The inner first and second molds K1a, K1a, K1b, and K1b of the inner mold K1 have air vent holes (not shown) for discharging the air in the recesses formed on the outer surfaces thereof. The coffee can A can be easily formed by forming between the concave portion on the outer side surface and the inner side surface.
(Example 8)
FIG. 130 is an explanatory view of a coffee can as an eighth embodiment of the structure with a fold line of the present invention, and shows a structure with a fold line (coffee can) having a cylindrical wall formed along a spiral.
In the description of the eighth embodiment, components corresponding to those of the seventh embodiment are denoted by the same reference numerals, and detailed description thereof is omitted.
Example 8 is different from Example 7 in the following points, but is configured in the same manner as Example 7 in other points.
In FIG. 130, in the coffee can A of the eighth embodiment, a part P, which is a part formed (enclosed) by fold lines M and V, is formed along a spiral having an inclination angle of 45 °.
As in the eighth embodiment, the cylindrical wall (structure with a cylindrical fold line) A1 having a fold line along a spiral having an inclination angle of 20 ° to 30 ° or more is folded when compressed in the axial direction while twisting. Since the outer shape becomes small and the cylindrical wall A1 of the coffee can A is plastically deformed once folded, the cylindrical wall A1 does not automatically return to its original shape. For this reason, when the coffee can A is used, it can be kept in a small folded state by being compressed and folded in the axial direction while twisting.
FIG. 131 is an explanatory diagram of another embodiment of the method for manufacturing the coffee can A.
In FIG. 131, the inner mold K1 set inside the cylindrical wall A1 having the bottom wall A0 is fixed to the upper end of the liquid container V, and the cylindrical wall A1 is accommodated in the liquid container V. Fill with liquid. A tube T is connected to the upper end of the liquid container V, and the liquid is also filled inside the tube T.
In this state, when an impact pressure is applied to the liquid in the tube T by the piston P, a fold line corresponding to the unevenness on the surface of the inner mold K1 is formed on the cylindrical wall A1.
Example 9
132 is an explanatory view of a small container as a structure with a folding line according to the ninth embodiment of the present invention, FIG. 132A is a perspective view of a lid of the small container, and FIG. 132B is a perspective view of the small container in an extended state.
133 is an explanatory view of the small container of Example 9, FIG. 133A is a perspective view of the small container in a folded state, FIG. 133B is a sectional view taken along line 133B-133B of FIG. 133A, and FIG. 133C is a small figure of FIG. It is sectional drawing of the state which covered the container.
132 and 133, the small container B (see FIG. 132B) has a circular bottom plate 6, an upper end plate 7, and a foldable pseudo cylindrical wall 8. The outer shape of the upper end plate 7 is circular, and a hexagonal opening 7a is formed at the center.
As shown in FIG. 132B, the pseudo-cylindrical wall 8 is formed with a large number of mountain fold lines M whose outer surface is convex and a large number of valley fold lines V which are concave.
132B and 133, the pseudo-cylindrical wall 8 of the small container B of the ninth embodiment has a plurality of parts P1 and P2 that are parts formed (enclosed) by the folding lines M and V. The part P1 has a triangular shape and one side thereof is foldably connected to the bottom plate 6, and the part P2 has a triangular shape and one side thereof is foldably connected to the upper end plate 7. Mountain fold lines M, M,... Are formed at a connection portion between the bottom plate 6 and one side of each of the six parts P1, and the mountain fold lines M, M,. Connected to the endless.
Mountain fold lines M, M,... Are formed at a connection portion between the upper end plate 7 and one side of each of the six parts P2, and the mountain fold lines M, M,. Is connected endlessly.
The mountain fold lines M, M,... Connected endlessly form a closed and continuous polygon along a plane perpendicular to the axis of the pseudo cylindrical wall 8.
When the pseudo cylindrical wall 8 of the small container B of the ninth embodiment is compressed in the axial direction while twisting, the pseudo cylindrical wall 8 is folded along the fold lines M and V to be in the state shown in FIGS. 133A and 133B.
A lid 9 (see FIGS. 132A and 133C) for opening and closing the hexagonal opening 7a at the upper end of the small container B includes a circular upper surface plate 9a, a short cylindrical wall 9b provided on the outer periphery of the upper surface plate 9a, and a cylinder. A pair of projecting portions 9c, 9c extending downward from the lower end of the wall 9b, a lower end locking portion 9d projecting inwardly provided at the lower end of the projecting portions 9c, 9c, and a cylindrical wall 9b above the projecting portions 9c, 9c And an upper locking portion 9e that protrudes small on the inner surface.
When the small container B is not used, when the cylindrical wall 9b of the lid 9 is fitted to the upper end plate 7 of the small container B with the small container B folded, as shown in FIG. 9 d locks the lower surface of the bottom plate 6, and the locking portions 9 e and 9 e lock the lower surface of the upper end plate 7. In this state, the volume of the small container B and the lid 9 is small, so that the storage space is small.
When the small container B is used, when the cylindrical wall 9b of the lid 9 is fitted to the upper end plate 7 of the small container B with the small container B extended (see FIG. 132B), the locking portions 9e and 9e are The upper end plate 7 is locked to the lower surface. In this state, the lid 9 is held at the upper end of the small container B in a state where the opening 7a of the extended small container B is closed. Therefore, it is possible to protect the internal container that blocks the object stored in the small container B from the outside air.
FIG. 134 is an explanatory view of the manufacturing method of the small container B, and shows a state in which a mold (mold having a fold line forming surface) is closed.
In FIG. 134, the mold 11 is divided into upper molds 11a and 11b and a lower mold 11c. The upper molds 11a and 11b are molds divided along dividing lines L1 and L2 formed along the mountain fold lines M and M arranged at positions facing each other in FIG. 132B.
After the resin is injected into the cavity 12 formed in the mold 11 and cured to form the small container B, the upper molds 11a and 11b are opened. Thereafter, when the small container B formed on the lower mold 11c is pulled upward while being twisted, the formed small container B can be easily taken out from the lower mold 11C.
(Example 10)
FIG. 135 is an explanatory diagram of a paper pack as a fold lined structure according to the tenth embodiment of the present invention, and is a perspective view of a use state in which the paper pack is extended.
136 is a view showing a state in the middle of folding the paper pack of FIG.
FIG. 137 is a view showing a state where the paper pack of FIG. 136 is further folded.
FIG. 138 is a developed view of the paper pack shown in FIGS. 135 to 137.
FIG. 138 is a developed view of a paper pack that is folded in two stages by a folding line that satisfies the folding condition, and a one-dot chain line in the vertical direction is a mountain folding line in the state of FIG. The left and right side edges of FIG. 138 are bonded to form a cylindrical shape, and then folded along horizontal and vertical mountain fold lines M and valley fold lines V, so that the paper pack of FIG. ) Can be configured.
135 can be folded from the state of FIG. 136 to the state of FIG. 137 by folding along the oblique mountain fold line M and valley fold line V.
(Example 11)
FIG. 139 is an explanatory diagram of a paper pack as a fold lined structure according to an eleventh embodiment of the present invention, and is a perspective view of a use state in which the paper pack is extended.
FIG. 140 is a diagram showing a state in the middle of folding the paper pack of FIG. 139.
FIG. 141 is a view showing a state in which the paper pack of FIG. 140 is further folded.
FIG. 142 is a development view of the paper pack shown in FIGS. 139 to 141.
FIG. 142 is a development view of a paper pack that is folded in four stages by folding lines that satisfy the folding condition, and is different from the development view of FIG. 138 that is folded in two stages. 142 is a mountain fold line in the state of FIG. 139. 142 is bonded to the left and right side edges to form a cylindrical shape, and then folded along horizontal and vertical mountain fold lines M and valley fold lines V, so that the paper pack of FIG. ) Can be configured. Other configurations and operations are the same as those in the tenth embodiment.
(Example 12)
FIG. 143 is an explanatory diagram of a paper pack as a fold lined structure according to a twelfth embodiment of the present invention, and is a perspective view showing a use state in which the paper pack is extended.
FIG. 144 is a diagram showing a state in the middle of folding the paper pack of FIG. 143.
FIG. 145 is a view showing a state where the paper pack of FIG. 144 is further folded.
FIG. 146 is a development view of the paper pack shown in FIGS. 143 to 145.
FIG. 146 is a developed view of a paper pack that is folded in four stages by folding lines that satisfy the folding condition, and vertical mountain folding lines M are formed so as to be alternately inclined. After the left and right side edges of FIG. 146 are bonded to form a cylindrical shape, the paper pack of FIG. 143 (paper pack in use) is configured by folding along the mountain fold line M and the valley fold line V. be able to. Other configurations and operations are the same as those of the eleventh embodiment.
(Example 13)
FIG. 147 is an explanatory diagram of a paper pack as a fold lined structure according to the thirteenth embodiment of the present invention, and is a perspective view showing a use state in which the paper pack is extended.
148 is a diagram showing a state in the middle of folding the paper pack of FIG. 147. FIG.
FIG. 149 is a view showing a state where the paper pack of FIG. 148 is further folded.
FIG. 150 is a developed view of the paper pack shown in FIGS. 147 to 149.
FIG. 150 is a developed view of a paper pack that is folded in four stages by folding lines that satisfy the folding condition, and vertical mountain folding lines M are formed to be inclined in the same direction. The paper pack of FIG. 147 (paper pack in use) is formed by bonding the left and right side edges of FIG. 150 to form a cylindrical shape and then folding along the mountain fold line M and valley fold line V. be able to. As can be seen from FIG. 147, since the paper pack is twisted in a certain direction from the upper end to the lower end, the paper pack can be easily expanded or folded by changing the direction in which the paper pack is twisted. Other configurations and operations are the same as those of the twelfth embodiment.
(Example 14)
FIG. 151 is an explanatory diagram of a pump as a structure with a folding line according to the fourteenth embodiment of the present invention.
In FIG. 151, the pump chamber A is configured similarly to the plastic bottle A of the fifth embodiment, and the opening at the upper end is opened and closed by a cap C. The upper end of the fluid tube T is connected to the lower end of the pump chamber A. The fluid tube T has a suction tube T1 and a discharge tube T2. The suction tube T1 is provided with a suction valve V1, and the discharge tube T2 is provided with a discharge valve V2. When the pump chamber A is contracted with the cap C closed, V1 is closed and V2 is opened, and the fluid in the pump chamber A is discharged from the discharge tube T2. When the pump chamber A is expanded, V1 is opened and V2 is closed, and fluid flows into the pump chamber A from the suction tube T1.
The pump of the fourth embodiment can be used for kerosene refueling, bicycle inflation, and the like.
(Example 15)
FIGS. 152A and 152B are explanatory views of a trash box as a structure with folding lines according to the fifteenth embodiment of the present invention. FIG. 152A is a side view and FIG. 152B is a side sectional view.
In FIG. 152, the trash box A is formed of a cylinder with a folding line made of the paper or resin, and has a bottom wall portion A0, a cylindrical wall A1, and an upper wall portion A2. An opening A2a for introducing garbage is formed in the upper wall portion A2. A cylindrical wall A1 of the trash box A is formed of a plurality of trapezoidal parts P that are inclined obliquely and formed by a mountain fold line M and a valley fold line V. Since the part P is formed along an inclined spiral of about 45 °, the extended trash box A can maintain the state (shape).
(Example 16)
FIG. 153 is an explanatory diagram of a pencil stand as a structure with folding lines according to the sixteenth embodiment of the present invention. FIG. 153A is a side view and FIG. 153B is a side sectional view.
In FIG. 153, the writing brush A is formed of a cylindrical body with a folding line made of the paper or resin, and has a bottom wall portion A0, a cylindrical wall A1, and an upper wall portion A2. An opening A2a for inserting a writing instrument such as a pencil is formed in the upper wall portion A2. The cylindrical wall A1 of the writing brush A is formed of a plurality of trapezoidal parts P inclined at an angle formed by a mountain fold line M and a valley fold line V. Since the part P is formed along an inclined spiral of about 45 °, the brush holder A in an extended state can maintain its shape.
(Example 17)
FIG. 154 is an explanatory view of a gusset (box internal partition member) as a structure with a folding line of Embodiment 17 of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 155 is a perspective view of the guess of FIG.
FIG. 156 is a developed view of the guess of FIG.
In FIG. 154, Guess G is accommodated in the paper box C. The guess G is manufactured by folding along the mountain fold line M and the valley fold line V of the development shown in FIG. In the guess G of the seventeenth embodiment, two rows of rising walls G1 are formed, and the rising walls G1 are formed as partition walls. The storage object support surface G2 formed between the rising walls G1 is a surface that supports storage objects such as wharves and cookies, and is inclined in this embodiment 17.
Since the guess G is made of one sheet of paper, the time required for the work of setting can be shortened compared to the case where the guess composed of a plurality of sheets of paper is set in the paper box C. .
(Example 18)
FIG. 157 is an explanatory view of a gusset (box internal partition member) as a fold lined structure of the eighteenth embodiment of the present invention, and is a perspective view of the gusset taken out from the paper box.
FIG. 158 is a developed view of the guess of FIG.
In the guess G of FIGS. 157 and 158, rising walls G1 are also formed on both sides of the guess G of the seventeenth embodiment. Since the rising walls G1 on both sides of the gusset G are supported by the side walls of the paper box C when accommodated in the paper box C (not shown), the position of the gusset G in the paper box C is stabilized, and The rigidity of the accommodation support surface G2 is reinforced.
(Example 19)
FIG. 159 is an explanatory view of a gusset (box internal partition member) as a fold lined structure of the nineteenth embodiment of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 160 is a perspective view of the guess of FIG.
FIG. 161 is a developed view of the guess of FIG.
In FIG. 159, Guess G is accommodated in the paper box C. The storage object support surface G2 formed between the rising walls G1 of the guess G is a surface that supports storage objects such as a bun or a cookie, and the nineteenth embodiment is horizontal (parallel to the bottom surface of the paper box C). Is formed. The nineteenth embodiment is provided with a rising wall G3 extending in a direction perpendicular to the rising wall G1. The storage object support surface G2 is formed so as to be surrounded by the rising walls G1 and G2.
Since the guess G of the nineteenth embodiment is made of a single sheet of paper, the time required for the setting work can be reduced as compared with the case where a guess composed of a plurality of sheets of paper is set in the paper box C. It can be shortened.
(Example 20)
FIG. 162 is an explanatory view of a gusset (box internal partition member) as a fold lined structure according to a twentieth embodiment of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 163 is a perspective view of the guess of FIG.
FIG. 164 is a developed view of the guess of FIG. 163.
In FIG. 163, Guess G is accommodated in the paper box C. The rising walls G1 and G3 of the guess G are formed so as to extend in directions perpendicular to each other, and a storage object support surface G2 is formed between the rising walls G1 and G3. The storage object support surface G2 is a surface that supports storage objects such as wharves and cookies, and this Example 20 is formed horizontally (parallel to the bottom surface of the paper box C).
Since the guess G of the twentieth embodiment is also made of a single sheet of paper, the time required for the setting work can be reduced as compared with the case where a guess composed of a plurality of sheets of paper is set in the paper box C. It can be shortened.
(Example 21)
FIG. 165 is an explanatory diagram of a gusset (box internal partition member) as a fold lined structure according to the twenty-first embodiment of the present invention, and is a perspective view showing a state in which the gusset is housed in a paper box.
FIG. 166 is a perspective view of the guess of FIG.
FIG. 167 is a developed view of the guess of FIG.
In FIG. 165, Guess G is accommodated in the paper box C. The rising walls G1 and G3 of the guess G are formed so as to extend in directions perpendicular to each other, and a storage object support surface G2 is formed between the rising walls G1 and G3. The storage object support surface G2 is a surface that supports storage objects such as wharves and cookies, and this Example 21 is formed horizontally (parallel to the bottom surface of the paper box C).
The guess G of Example 21 is formed by bending a square sheet along a mountain fold line M and a valley fold line V formed in a diagonal direction. Since the twenty-first embodiment is also made of a single sheet of paper, the time required for the setting operation can be shortened compared to the case where a guess made up of a plurality of sheets of paper is set in the paper box C. it can.
(Example 22)
FIG. 168 is an explanatory view of the folding passage cover, FIG. 168A is a perspective view in a half-folded state, and FIG. 168B is a perspective view in a completely folded state.
FIG. 169 is a development view of a foldable passage cover as a fold lined structure according to the twenty-second embodiment of the present invention.
The foldable passage cover 16 shown in FIG. 168 is a member that is arranged and used so as to cover the upper side and both sides of the passage through which a person passes. It is a passage through which a person passes, such as a passage between the tip of an airport terminal bridge and an aircraft entrance, and is preferably used in a place where the distance between structures at both ends of the passage is not fixed.
The foldable passage cover 16 is a member obtained by forming a fold line on an elastic flexible sheet-like member and can be folded at a fold line portion. In the half-folded state, the foldable passage cover 16 has the shape of FIG. 168 and is disposed so as to cover the upper and left and right sides of the passage along the passage, and both end portions in the passage direction are fixed to the structure.
In the developed view of the foldable passage cover 16 shown in FIG. 169, the foldable passage cover 16 includes a large number of mountain fold lines M having convex outer sides and a number of valley folds having concave when used in a half-folded state. A line V is formed.
At the node that is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. The number of mountain fold lines M intersecting at each node = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1). That is, the fold line pattern of the foldable passage cover 16 according to the twenty-second embodiment is a 1-node 4-fold line.
In FIG. 169, the foldable passage cover 16 of the twenty-second embodiment has a plurality of parts P1, P2, and P3 that are parts formed (enclosed) by the fold lines M and V. Part P1 is a triangle, part P2 is an isosceles trapezoid, and part P3 is a trapezoid.
The folding passage cover 16 is folded into a state where the outer shape is reduced as shown in FIG.
(Example 23)
170A and 170B are explanatory views of a folding path cover as a structure with a folding line according to the twenty-third embodiment of the present invention. FIG. 170A is a perspective view in a half-folded state, and FIG. 170B is a perspective view in a completely folded state.
FIG. 171 is a developed view of the folding passage cover of FIG.
In the description of the twenty-third embodiment, components corresponding to those of the twenty-second embodiment are denoted by the same reference numerals, and detailed description thereof is omitted.
The twenty-third embodiment is different from the twenty-second embodiment in the following points, but is configured in the same manner as the twenty-second embodiment in other points.
170, a folding passage cover 16 shown in FIG. 170 is a passage through which people pass, such as a passage portion of a connection portion between vehicles of a railway vehicle, a passage between an end of an airport terminal bridge and an aircraft entrance. And it is used suitably in the place where the space | interval of the structure of the both ends of the channel | path is not fixed.
The foldable passage cover 16 shown in FIG. 171 has an outer shape excluding the fan-shaped center portion in the developed view. The foldable passage cover 16 is formed with a number of mountain fold lines M that are convex on the outer surface and a number of valley fold lines V that are concave when used in a half-folded state. is there. In addition, the folding conditions are satisfied at each node.
In FIG. 171, the foldable passage cover 16 of the twenty-third embodiment has a plurality of parts P1, P2, P3, and P4 that are parts formed (enclosed) by the fold lines M and V. The part P1 is a triangle, and the parts P2 to P4 are all quadrilaterals.
The folding-type passage cover 16 according to the twenty-third embodiment is folded into a state where the outer shape is reduced as shown in FIG. 170B when stored or transported, as in the twenty-second embodiment.
(Example 24)
FIG. 172 is an explanatory diagram of a lamp shade as a structure with folding lines according to a twenty-fourth embodiment of the present invention. FIG. 172A is a development view of a sheet-like member that is a material for manufacturing the lamp shade, and FIG. FIG. 5 is a perspective view of a lamp shade that is formed by joining the left and right sides of a shaped member to produce a pseudocone in a half-folded state.
The lamp shade 17 showing the half-folded state shown in FIG. 172B is a member used as a lamp umbrella in an extended state, and is made of a sheet-like resin.
In the developed view of the lamp shade 17 shown in FIG. 172A, the transparent resin sheet for manufacturing the lamp shade 17 of FIG. 172B has a shape excluding the center portion of the sector shape. An adhesive margin 17a for bonding is provided on one of both sides of the resin sheet that are joined to each other. A fold line is formed on the unfolded resin sheet by the same member as the fold line forming mold shown in Example 1 or Example 3, and then the adhesive margin 17a has elasticity when cured. An adhesive is applied to adhere to the other of the both sides. At this time, a foldable pseudo-conical wall can be manufactured by the transparent resin sheet.
The foldable pseudo-cylindrical wall of the transparent resin sheet is formed with a large number of mountain fold lines M that are convex on the outer surface and a large number of valley fold lines V that are concave when in the half-folded state.
At the node that is the intersection of the mountain fold line M and the valley fold line V, a total of six fold lines of the four mountain fold lines M and the two valley fold lines V intersect. The number of mountain fold lines M intersecting at each node = 4, the number of valley fold lines V = 2, and the difference is 2 (= 4-2). That is, the fold line pattern of the foldable pseudo-conical wall of the twenty-fourth embodiment is a 1-node 6 fold line.
In FIG. 172, the foldable pseudo-conical wall of the embodiment 24 has a plurality of parts P1a, P1b, P2a, P2b,... Which are parts formed (enclosed) by the fold lines M and V. . The shapes of the parts P1a, P2a,... Are similar triangles with different sizes, and the shapes of the parts P2a, P2b,.
The lamp shade 17 is configured by pasting transparent cellophane paper or normal colored paper with a favorite color such as red, blue, yellow, etc. on each of the parts P1a, P1b, P2a,. The lamp shade 17 is folded into a small outer shape when stored or transported, and is extended into a pseudo cone having a large outer shape when used.
(Example 25)
FIG. 173 is an explanatory view of a Christmas card as a fold lined structure of Example 25 of the present invention. FIG. 173A is a plan view of the folded Christmas card, and FIG. 173B is a plan view of the opened FIG. 173A. FIG. 173C is a view as seen from diagonally above the arrow 173C in FIG. 173B.
In FIG. 173, the Christmas card C has a tree bonding portion C1 to which the Christmas tree T is bonded and a tree pressing portion C2 for pressing the Christmas tree. The Christmas tree T is formed by a conical wall with a folding line made of a colored sheet that satisfies the folding conditions. As shown in FIG. 173A, when the Christmas card C is folded, the Christmas tree T is held in a folded state.
When the Christmas card C is opened as shown in FIG. 173, the Christmas tree T expands due to elasticity, and has a three-dimensional shape shown in FIG. 173C when viewed obliquely from above. Therefore, it is possible to make the person who received the Christmas card C feel unusual and fun.
(Example 26)
FIG. 174 is an explanatory view of a cap as a fold lined structure of Embodiment 26 of the present invention, FIG. 174A is a perspective view of the cap, FIG. 174B is a sectional view taken along the line 174B-174B of FIG. It is the figure seen from the arrow 174C of 174B.
FIG. 175 is an explanatory view of the cap of Example 26, FIG. 175A is a plan view of the cap folded, and FIG. 175B is a view as seen from the arrow 175B of FIG. 175A.
In FIGS. 174 and 175, the cap C (see FIG. 174) has a donut-shaped collar 13 and a crown 14 foldably provided on the upper surface of the central portion of the collar 13. The crown 14 has a hexagonal upper surface portion 14a and a side surface portion (pseudo-conical wall) 14b formed by twisting a hexagonal pyramid.
As shown in FIG. 174B, the side surface portion (pseudo-conical wall) 14b is formed with a large number of mountain fold lines M that are convex on the outer surface and a large number of valley fold lines V that are concave.
At the node that is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. The number of mountain fold lines M intersecting at each node = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1). That is, the fold line pattern of the side surface portion (pseudo-conical wall) 14b of Example 26 is a 1-node 4-fold line.
In FIGS. 174 and 175, the side head portion 14 b of the hat C of the twenty-sixth embodiment has a plurality of parts P <b> 1 and P <b> 2 that are portions formed (enclosed) by the folding lines M and V. The part P1 is a triangle and one side thereof is foldably connected to the collar 13, and the part P2 is a triangle and one side thereof is foldably connected to the upper surface portion 14a. A mountain fold line M, M,... Is formed at a connection portion between the collar 13 and one side of each of the six parts P1, and the mountain fold lines M, M,. Connected to the endless.
Mountain fold lines M, M,... Are formed at a connection portion between the upper surface member 14a and one side of each of the six parts P2, and the mountain fold lines M, M,. Is connected endlessly.
Each of the endlessly connected fold lines M, M,... Is perpendicular to the axis of the side surface (pseudo-conical wall) 14b when the side surface (pseudo-conical wall) 14b is extended and folded. A closed polygon is formed in a flat plane.
When the side head portion 14b of the cap C of Example 26 is compressed in the axial direction while twisting, the side head portion 14b is folded along the fold lines M and V to be in the state of FIGS. 175A and 175B.
The angle formed by the mountain fold line M formed at the connecting portion between the collar 13 and one side of the part P1 and the valley fold line V is set to an angle larger than 45 °. For this reason, even if the side head 14b is small in rigidity, when the side head 14b is extended, it is easy to hold the side head 14b in an extended state due to the rigidity.
When the cap C is not used, as shown in FIG. 175B, if the cap C is in a folded state, the space required for housing the cap C can be reduced.
(Example 27)
FIG. 176 is an explanatory view of a cap as a structure with folding lines according to a twenty-seventh embodiment of the present invention. FIG. 176A is a perspective view of the cap, FIG. 176B is a sectional view taken along the line 176B-176B of FIG. It is the figure seen from arrow 176C of 176B.
FIG. 177 is an explanatory diagram of the cap of Example 27, FIG. 177A is a plan view of the cap folded, and FIG. 177B is a view seen from the arrow 177B of FIG. 177A.
In the description of the twenty-seventh embodiment, components corresponding to those of the twenty-sixth embodiment are denoted by the same reference numerals, and detailed description thereof is omitted.
The twenty-seventh embodiment is different from the twenty-sixth embodiment in the following points, but is configured in the same manner as the twenty-sixth embodiment in other points.
In FIG. 176A, a plurality of isosceles trapezoidal parts P1 to P5 are formed on the temporal region (pseudo-conical wall) 14b by a large number of 1-node 4-fold lines. Each fold line is formed by joining and sewing the ends of the fabric. Mountain folds and valley folds of the fold line are determined by the joining state of the end portions of the fabric. When the end portions protrude outward, a mountain fold line M is formed, and when the end portions protrude inward, a valley fold line is formed. V is formed. The isosceles trapezoidal parts P1 to P5 are sequentially reduced in size from the part P1 arranged at the bottom to the part P5 arranged at the top.
Each of the parts P1 of the isosceles trapezoid is connected so that one bottom side can be folded on the collar 13, and one of the bottom sides of the part P5 is connected so as to be folded on the upper surface part 14a. A mountain fold line M and a valley fold line V are formed so as to be alternately connected to a connecting portion between the collar 13 and one side of each of the six parts P1, and the three peaks connected alternately. The fold line M and the three valley fold lines V are connected endlessly so as to form a hexagon.
Three mountain fold lines M and three valley fold lines V are alternately connected to a connection portion between the upper surface member 14a and one side of each of the six parts P5, and a total of six fold lines are Endlessly connected to form a hexagon.
Similar to the isosceles trapezoidal parts P1 and P2, six parts P2 to P4 are respectively arranged in the circumferential direction, and the bases of the isosceles trapezoids alternately form a mountain fold line and a valley fold line. It is connected endlessly in the circumferential direction.
That is, the three mountain fold lines M and the three valley fold lines V that are alternately and endlessly connected are in the state where the side head (pseudo-conical wall) 14b is extended and folded. A closed polygon is formed in a plane perpendicular to the axis of the temporal portion (pseudo-conical wall) 14b.
When the side head 14b of the cap C of Example 27 is compressed in the axial direction, it is folded along the fold lines M and V to the state shown in FIGS. 177A and 177B.
When the cap C is not used, as shown in FIG. 177, if the cap C is in a folded state, the space required for housing the cap C can be reduced.
(Example 28)
FIG. 178 is a perspective view of a winding type cap as a structure with a folding line of the embodiment 28 of the present invention.
FIG. 179 is a perspective view of the winding type cap of FIG. 178 in the middle of folding.
FIG. 180 is a perspective view of a wind-up type cap that is further folded from the state of FIG. 179.
In FIG. 178, the wind-up type cap H is composed of a heel part A, a temporal part B, and a top part C. As shown in FIGS. 179 and 180, a mountain fold line M and a valley fold line V are provided. Can be rolled up while folding along.
181 is an explanatory view of the method for manufacturing the winding type cap shown in FIGS. 178 to 180. FIG. 181A is a development view of FIG. 178 heel A, FIG. 181B is a development view of the temporal region B, and FIG. FIG. 3 is a development view of the crown C.
As shown in FIG. 181A, an inner radius RAi (“i” means in) is drawn on a sector shape (outer radius RAo: “o” means out) with a central angle Θ1, and the outer circumference is equally divided into N (even numbers). A1, A2, A3,... Are defined, and N equiangular spirals (angle φ = 5 to 10 ° with respect to the radial direction) from these points toward the center in the counterclockwise direction are drawn. If the intersection points are B1, B2, B3,..., The line segments B1B2, B2B3, B3B4,. The fan shape is cut by these line segments, and this is defined as a buttock A. When winding and storing, the spiral is alternately turned into a mountain fold and a valley fold line. In FIG. 181A, Θ1 = 300 ° and N = 12. When both ends of this curved strip-shaped element are joined, a frustoconical shape is formed, and since Θ1 <360 °, a tapered ridge A is obtained.
Similarly, the temporal portion B is manufactured from a curved strip-shaped element cut out from a sector shape. However, as shown in FIG. 181B, an extremely small apex angle Θ2 is used as compared with the central angle Θ1 of the buttock. The outer peripheral part of this curved strip-shaped element is represented by points C1, C2, C3, C4,. Here, these points are on concentric circles, and the radius is RBo. From these points, draw N spirals or inclined straight lines at an angle φ = 5 to 10 ° in the same manner as above, determine points D1, D2, D3, D4,... Determine the inner circumference of the element. When both ends of a curved strip-shaped element are joined together, a frustoconical shell close to a cylinder is obtained because the Θ2 value is small. The arc length B1B2 = B2B3 = B3B4,... And the arc length C1C2 = C2C3 = C3C4,... Part B is joined or stitched.
Next, the top portion C is similarly made of a sector film having an apex angle Θ3 close to 360 ° or a circular film having Θ3 = 360 °. FIG. 181C shows a case where Θ3 = 360 °, and the center angle Θ3 is equally divided into N (= 12) to determine points E1, E2, E3, E4,. The arc length E1E2 = E2E3 = E3E4,... Of the outer periphery of the crown C is taken to be equal to that of the inner periphery of the temporal region B (D1D2 = D2D3 = D3D4 = D4D5,...) Join to the inner periphery. That is, when these three elements are joined, a hat shown in FIG. 178 is obtained. When twelve fold lines are alternately mountain-folded and valley-folded and wound around the central axis, the result is as shown in FIG.
FIG. 182 is an explanatory view of another manufacturing method of the winding type cap shown in FIGS. 178 to 181.
In FIG. 182, twelve sub-elements obtained by dividing three elements into even numbers (the sector elements shown in FIG. 182 in which a, b, and c in FIGS. 181A, 181B, and 181C are stacked) are manufactured. The side A1B1C1D1E1 and the side A1B1C1D1E1 are joined or stitched so that the points A1 and A1, B1 and B1, C1 and C1, D1 and D1, and E1 and E1 coincide with each other. As a result, the take-up and storage type hat shown in FIGS. 178 to 180 is also manufactured.
(Example 29)
FIG. 183 is a perspective view of a winding tent as a structure with a folding line according to the twenty-ninth embodiment of the present invention.
FIG. 184 is a perspective view of the winding type tent of FIG. 183 in the middle of folding.
FIG. 185 is a perspective view of the tent in a further folded state from the state of FIG.
In FIG. 183, the winding type tent H has a mountain fold line M and a valley fold line V formed along an equiangular spiral (Bernoulli spiral). The part can be wound while being folded along the fold lines M and V. The tent H has a dome shape in the extended state, and ring-shaped flexible tubes H1 and H2 extending in the circumferential direction are fixed to the outer peripheral portion and the radial center portion of the outer surface of the tent H, respectively. The tent H is maintained in the extended state of FIG. 183 by inflating it by supplying air to the flexible tubes H1 and H2.
FIG. 186 is an explanatory view of a method for manufacturing the winding tent shown in FIGS. 183 to 185. FIG. 186A is a drawing showing a dome shape having a parabolic curved surface in an expanded state, divided in the circumferential direction. FIG. 186B is a diagram showing a conical wall formed when the end portion AB of the part shown in FIG. 186A is connected to the CD.
FIG. 187 is an explanatory view of the method for manufacturing the winding tent shown in FIGS. 183 to 185. FIG. 187 shows the winding tent that has a radius r1 in the extended state and the coordinates of the center position of the dome shape. Is set to r = 0, j = 1, 2,..., 10 and is divided into 10 by a circle whose radius is a coordinate rj (rj = r1 × (11−j) / 10) at a position equally divided into 10 in the radial direction. It is a figure which shows the shape of the part (conical wall) (j) formed in this.
FIG. 188 is a diagram showing the part number (j), the shape and length Lj of the bus bar, and the inclination θj of FIG. 187.
FIG. 189 shows divided parts (J: J = 1, 2,...) When the developed views of the parts (1), (2),..., (10) shown in FIGS. , 10) is an explanatory diagram of the shape, FIG. 189A shows that each part (j) is composed of 16 divided parts (J), and FIG. 189B shows the divided parts (J) connected in the radial direction. FIG.
As shown in FIG. 186A, consider a curved strip ABCD having a curvature having a width L at the outer peripheral portion on a sector shape (peripheral radius R *) having a central angle Θ. When the left and right ends AB and CD of this strip are joined, a truncated cone shape as shown in FIG. 186B is obtained. If the radius of the bottom surface of this truncated cone is R ′ and the apex angle of the conical shell obtained by extending this truncated cone is 2θ, the outer circumference of the bottom of the truncated cone and the outer circumference of the strip are placed equally.
2πR ′ = R * · Θ (59)
Get. Since sin θ = R ′ / R * from FIG. 186B, Θ is given by the following equation (60).
Θ = 2πsinθ (60)
A thin film-like rotating shell obtained by rotating a curve passing through a gentle origin such as a parabola as shown in FIG. . The upper end radius of the container-like rotary shell obtained by this rotation is r1. This rotating shell is divided into n by a plane perpendicular to the Z-axis, and this rotating shell is approximated by n frustoconical elements using the relationship shown in FIG. The intersecting line between the split surface and the shell forms a circle. Let the radius of this circle be r2, r3,. Further, n truncated cone elements are sequentially named (1), (2), (3),..., And when these are opened and expanded, angles corresponding to the Θ values in FIG. Let Θ3 be ...
Since the inner diameter of the element (1) is equal to the outer diameter of the element (2), and the inner diameter of the element (2) is equal to the outer diameter of the element (3), the following equation (61) is established for the i-th element and the j + 1-th element.
2πrjΘj = 2πrj + 1Θj + 1 (61)
Now, assuming that the previous rotating shell is a paraboloid, Z = C (r / r0) ¥ t2 ¥ t, n = 10, and the cutting radius is r2 = 0.9r1, r3 = 0.8r1, r4 Consider the simple case given by = 0.7r1,. The cross-sectional shape after division when C = 0.8, cut along the Z-X plane, and approximates each element in a truncated cone shape as shown above is as shown in FIG. The length Lj (corresponding to L in FIG. 186) of each element when the n truncated cone elements (1), (2), (3),. In addition, since the angle θj (θ in FIG. 186B) formed by these elements with respect to the Z-axis can be obtained, the Θj value of each element can be calculated using Equation (60). The width of element (1) is W1 and the outer peripheral length is 2πr1. The ratio of width to length is set as κ1 as an aspect ratio (κ1 = W1 / 2πr1). When this strip element is drawn on a circle with a radius Ro, the apex angle Θ1 becomes the width W1 = κ1 · Θ1 · Ro = (W1 / 2πr1) · Θ1 · Ro = W1 {Θ1 / (2πr1)} Ro. That is, the dimensionless width W1 / Ro when expressed on the radius Ro circle is given by W1Θ1 / (2πr1). Other elements are generally given by the following equation (62), with αj∠Wj / (2πrj).
Lj / Ro = αjΘj (62)
When the outer peripheral radius of the sector element j is (Rj) o and the inner peripheral radius is (Rj) i,
Lj = (Rj) o- (Rj) i (63)
(Rj) iΘj = (Rj + 1) oΘj + 1. That is, in FIG. 189A, (R1) iΘ1 = (R2) oΘ2. Using this relationship and equations (59) to (63), Θj, Lj, Wj, and (Rj) i, (Rj) o values can be calculated in the order of elements (1), (2),. A developed view of each element (j) obtained using these values is shown in FIG. 189A.
The numerical values in FIG. 188 are as follows.

Next, the developed view of each element in FIG. 189A is divided into 2N equal parts (N: integer). At this time, a dividing line is drawn on the development view at an angle that forms an angle θ with the radial direction so as to form a spiral fold line. FIG. 189A shows each development view divided into 16 equal parts. The divided small elements are stacked in the radial direction to create a new sector element. Stacked sector elements are shown in FIG. 189B, which represents a curved shaped sector element. When 16 curved fan-shaped elements are joined and the joining lines are alternately made into ridges and valley fold lines, a parabolic shell having a spiral fold line (see FIG. 183) is obtained. FIGS. 184 and 185 show windings around the central axis passing through the apex of the parabolic shell of FIG. 183.
(Example 30)
FIG. 190 is a perspective view of a take-up tent as a structure with a folding line according to a thirty-third embodiment of the present invention.
FIG. 191 is a perspective view of the winding-type tent of FIG. 190 in the middle of folding.
FIG. 192 is a perspective view of the tent in a further folded state from the state of FIG.
In FIG. 190, a winding tent H has a mountain fold line M and a valley fold line V formed along an equiangular spiral (Bernoulli spiral), and a fan-shaped tent H The part can be wound while being folded along the fold lines M and V. The tent H has a dome shape in the extended state, and ring-shaped flexible tubes H1 and H2 extending in the circumferential direction are fixed to the outer peripheral portion and the radial center portion of the outer surface of the tent H, respectively. The tent H is held in the extended state of FIG. 190 by supplying air to the flexible tubes H1 and H2 and inflating.
In Example 30, when the film thickness constituting the shell is large, the winding may be tight in the central portion. To avoid this, when dividing FIG. Is appropriately divided into equal parts.
That is, after dividing into eight equal parts, this was further divided into two parts with a central angle ratio of 0.475: 0.525, and eight sets of curved fan-shaped elements (16 elements) were joined alternately. The curved surface is shown in FIG. Here, when the left side of the element having a small central angle is valley-folded and the right side is mountain-folded, the element is wound while being shifted downward around the central axis. This is shown in FIGS. 191 and 192. This winding method has an advantage of relaxing the above-described degree of buckling.
These models can be used to form the parabolic surface of a parabolic antenna, in addition to a large tent that can be wound / deployed.
Industrial applicability
As mentioned above, although the Example of this invention was explained in full detail, this invention is not limited to the said Example, A various change is performed within the range of the summary of this invention described in the claim. It is possible. Modified embodiments of the present invention are illustrated below.
(1) In the first and second embodiments, the fold line forming mold has a pair of foldable fold line forming members (flexible metal), and the sheet-like member is sandwiched between the pair of fold line forming members. In this configuration, the pair of fold line forming members are folded at the same time to form a fold line on the sheet-like member. However, the foldable fold line forming members (flexible molds) are not a pair but may be only one sheet. . When the number of fold line forming members is one, the sheet-like member may be folded on the one surface side. As a method of adsorbing the sheet-like member, for example, it is possible to adsorb the sheet-like member on one surface side by opening a vent hole in the part of the fold line forming member and lowering the other surface side Become.
It is also possible to form a fold line by folding the fold line forming member with the sheet-like member sandwiched between a fold line forming member using magnetized material parts and a flexible magnetic rubber sheet. It becomes.
(2) As can be understood from the research results of the inventor and the description of each example, the present invention enables the use of fold lines and parts of various shapes by the use of a new foldable fold line. It is possible to obtain a foldable structure with a simple fold line. Therefore, the present invention can constitute a space structure that can be expanded and contracted in various shapes.

Claims (19)

A structure with a fold line characterized by comprising the following structural requirements (H01) to (H03);
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H03) The plurality of polygonal parts include triangular and trapezoidal parts, and the triangular parts have parts in which all of the fold lines forming the parts are connection lines with other parts; and The structure with a fold line which is flat when the fold line is extended. A structure with a fold line, characterized by comprising the following structural requirements (H01), (H02), (H04),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H04) The structure with fold lines, wherein the plurality of polygonal parts include unequal-sided quadrangle parts that do not include parallel sides and are flat when the fold line is extended. A structure with a fold line characterized by comprising the following structural requirements (H01), (H02), and (H05):
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H05) The plurality of polygonal parts include only parts other than right triangles, and a linear connection fold line is formed in which the plurality of fold lines are connected along a straight line, and the linear connection fold is formed. The said structure with a fold line which has the parts arrange | positioned at the both sides of a line with the line | wire not symmetrical with respect to the said linear connection folding line. A structure with a folding line, characterized by comprising the following structural requirements (H01), (H02), (H06):
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H06) The structure with a fold line that has the plurality of fold lines formed along a spiral and is flat when the fold lines are extended. A structure with a fold line characterized by comprising the following structural requirements (H01), (H02), (H07) to (H011),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H07) The first mountain fold line, the second mountain fold line, and the third mountain fold line that extend radially from one node, and the third mountain fold line and the third mountain fold line are arranged between the first mountain fold line and the third mountain fold line. The plurality of fold lines having a one-node four-fold line formed by the first valley fold line disposed on the side opposite to the mountain fold line;
(H08) The node is the origin, the X axis is taken in the direction of extension of the third mountain fold line, and one of the first mountain fold line or the second mountain fold line is the X axis. A plurality of fold lines having a fold line satisfying the fold condition where α = γ, where α is a corner and γ is an angle between the other mountain fold line and the first valley fold line;
(H09) Radiation in which a plurality of the nodes extend radially from a center point, and the plurality of fold lines arranged along an arc centered on the center point,
(H010) The angles formed by the first mountain fold line and the second mountain fold line that intersect at a node on the radiation with respect to the radiation passing through a plurality of the nodes are the same value, and the radiation The plurality of fold lines satisfying the mirror surface rule that the angles formed by the third fold line and the first valley fold line with respect to a straight line orthogonal to
(H011) The center point is O, one of the two radiations extending radially from the center point O and forming a center angle θ ′ is the first radiation OB, and the other radiation is the second radiation OE. In this case, the first node B arranged on the first radiation OB and the second node arranged on the second radiation OE and shorter than the first node B to the center point O A plurality of fold lines formed so as to satisfy the relationship of p = φ + θ ′ when 折 り OBG = φ and ∠BGE = p. line. A structure with a fold line characterized by comprising the following structural requirements (H01), (H02), (H012) to (H014),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H012) In the state where the fold line is extended, a cylindrical wall is formed, and in a state where the fold line is bent according to the mountain fold line and the valley fold line, a cylindrical wall having irregularities whose outer shape is reduced is formed. The structure with a fold line that forms a cylindrical wall having a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along a fold line and a valley fold line,
(H013) The plurality of fold lines having fold lines that are sequentially connected in a plane perpendicular to the axis of the cylindrical wall to form a loop;
(H014) Each of the above parts having only polygonal parts other than trapezoid, isosceles triangle and right triangle. A structure with a fold line characterized by comprising the following structural requirements (H01), (H02), (H012), (H015), (H016),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H012) In the state where the fold line is extended, a cylindrical wall is formed, and in a state where the fold line is bent according to the mountain fold line and the valley fold line, a cylindrical wall having irregularities whose outer shape is reduced is formed. The structure with a fold line that forms a cylindrical wall having a thickness having an unevenness whose outer shape is further reduced in a state of being completely folded along a fold line and a valley fold line,
(H015) the plurality of fold lines not having fold lines that are sequentially connected in a plane perpendicular to the axis of the cylindrical wall to form a loop;
(H016) Each of the parts having a polygonal part other than an isosceles triangle. The structure with a folding line according to claim 7, comprising the following constituent elements (H017) and (H018):
(H017) Each of the parts having an isosceles trapezoidal part,
(H018) In the cylindrical wall having a developed view in which the bottom and top sides of adjacent isosceles trapezoidal parts are alternately connected along a straight line, and the fold line of the cylindrical wall is extended, The cylinder wall forms a spiral with respect to the central axis of the cylinder wall. A structure with a folding line, characterized by comprising the following structural requirements (H01), (H02), (H07), (H08), (H019),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H07) The first mountain fold line, the second mountain fold line, and the third mountain fold line that extend radially from one node, and the third mountain fold line and the third mountain fold line are arranged between the first mountain fold line and the third mountain fold line. The plurality of fold lines having a one-node four-fold line formed by the first valley fold line disposed on the side opposite to the mountain fold line;
(H08) The node is the origin, the X axis is taken in the direction of extension of the third mountain fold line, and one of the first mountain fold line or the second mountain fold line is the X axis. A plurality of fold lines having a fold line satisfying the fold condition where α = γ, where α is a corner and γ is an angle between the other mountain fold line and the first valley fold line;
(H019) A conical wall is formed in the state where the fold line is extended, and a conical wall having irregularities whose outer shape is reduced is formed in a state where the fold line is bent according to the mountain fold line and the valley fold line of the fold line. The said structure with a fold line which forms the cone wall with the thickness which has the unevenness | corrugation into which the external shape reduced further in the state folded completely along the fold line and the valley fold line. A structure with a folding line, comprising the following constituent elements (H01), (H02), (H019) to (H021),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in close contact with each other,
(H019) A conical wall is formed in the state where the fold line is extended, and a conical wall having irregularities whose outer shape is reduced is formed in a state where the fold line is bent according to the mountain fold line and the valley fold line of the fold line. The fold lined structure for forming a thick cone wall having an unevenness whose outer shape is further reduced in a state of being completely folded along a fold line and a valley fold line;
(H020) Between the first mountain fold line, the second mountain fold line, the third mountain fold line and the fourth mountain fold line extending radially from one node, and between the first mountain fold line and the second mountain fold line A first valley fold line formed and disposed on the opposite side of the third mountain fold line and the fourth mountain fold line; and disposed between the third mountain fold line and the fourth mountain fold line and the first fold line. And a second valley fold line disposed on the opposite side of the first mountain fold line and the second mountain fold line, the first mountain fold line and the fourth mountain fold line are adjacent to each other, and the second mountain fold line and The plurality of fold lines having a one-node 6 fold line adjacent to a third mountain fold line;
(H021) The node is the origin, the X-axis is in the extension war direction of the first valley fold line, and the angle between the first mountain fold line and the second mountain fold line with the first valley fold line is α And β, the angles formed by the third fold line and the fourth fold line with the second valley fold line are γ and δ, respectively, and the angle formed between the X axis and the second valley fold line is θ. The plurality of fold lines having fold lines satisfying a fold condition of β−α = δ−γ + θ. A structure with a fold line characterized by comprising the following structural requirements (H01), (H02), (H020 ′), (H021 ′), (H022),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines intersecting at one node and the number of valley fold lines is 2 The plurality of fold lines having a fold line that satisfies a fold condition that is a condition in which each part including a plurality of fold lines that intersect at the one node can be folded in a close contact state,
(H020 ′) Between the first mountain fold line, the second mountain fold line, the third mountain fold line, and the fourth mountain fold line extending radially from one node, and between the first mountain fold line and the second mountain fold line And a second valley fold line disposed between the second mountain fold line and the third mountain fold line, wherein the fourth mountain fold line is the first mountain fold line. The plurality of fold lines having a one-node 6 fold line disposed between the fold line and the third mountain fold line and opposite to the second mountain fold line;
(H021 ′) The angle between the first node fold line and the first valley fold line is θ1 with the node as the origin, the X axis in the extending direction of the fourth fold line, and the first valley fold line. And θ2, angles formed by the second mountain fold line and the third mountain fold line with the second valley fold line are θ3 and θ4, respectively, and an angle formed between the X axis and the first mountain fold line is α *. A plurality of fold lines having fold lines satisfying a fold condition of α * = θ2 + θ4, β * = θ1 + 03, where β * is an angle formed between the X axis and the third fold line;
(H022) A cylindrical wall or a cone wall that forms a cylindrical wall or a cone wall in the state where the fold line is extended, and has a concavity and convexity whose outer shape is reduced in a state folded according to the mountain fold line and the valley fold line of the fold line The structure with a fold line which forms a cylindrical wall or a cone wall having a thickness having a concavity and convexity whose outer shape is further reduced in a state of being completely folded along the mountain fold line and the valley fold line. The structure with a fold line according to claim 6, comprising the following constituent elements (H023):
(H023) The structure with a fold line in which the cylindrical wall or the cone wall is formed of any one of paper, cloth, resin, and metal. A structure with a fold line characterized by comprising the following constituent elements (H01), (H024) to (H026),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H024) Folding is a condition in which a plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and each part including a plurality of fold lines that intersect at one node can be folded in close contact. The plurality of fold lines having fold lines not satisfying the conditions;
(H025) In a state where the fold line is extended, it is a sheet shape, and in a state where the fold line is folded along the mountain fold line and the valley fold line, a plurality of rising walls rising toward one surface side of the structure with a fold line; The folded structure with a fold line formed by the container support surface divided by the rising wall and supporting the lower surface of the object to be stored,
(H026) The plurality of polygons having a wall forming part that forms the rising wall and a support surface forming part that forms the container support surface, wherein the support surface forming parts are arranged on the same plane. Parts. A structure with a fold line, characterized by comprising the following structural requirements (H01), (H024), (H025), (H026 ′),
(H01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(H024) Folding is a condition in which a plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and each part including a plurality of fold lines that intersect at one node can be folded in close contact. The plurality of fold lines having fold lines not satisfying the conditions;
(H025) In a state where the fold line is extended, it is a sheet shape, and in a state where the fold line is folded along the mountain fold line and the valley fold line, a plurality of rising walls rising toward one surface side of the structure with a fold line; The folded structure with a fold line formed by the container support surface divided by the rising wall and supporting the lower surface of the object to be stored,
(H026 ′) The plurality of polygons having a wall forming part that forms the rising wall and a support surface forming part that forms the accommodation support surface, and no cut portion is provided between the wall forming parts. Parts. A structure with a fold line, characterized by comprising the following structural requirements (H029) to (H031);
(H029) A structure with a fold line having a plurality of polygonal parts and a part connection part for connecting the outer sides of each part to each other and provided with a fold line that can be folded along the part connection part. The fold line has a fold line structure having a mountain fold line and a valley fold line that are valley-folded when viewed from one surface side of the structure with fold line,
(H030) The structure with fold lines in which the mountain fold lines and valley fold lines formed along a spiral extending from one point of convergence are alternately arranged adjacent to each other;
(H031) When the fold line is extended, the fold line is flat, and when folded according to the mountain fold line and the valley fold line of the fold line, the fold line is folded while being wound around the convergent point. The structure with a fold line. A structure with a fold line, characterized by comprising the following structural requirements (H029), (H030), (H032),
(H029) A structure with a fold line having a plurality of polygonal parts and a part connection part for connecting the outer sides of each part to each other and provided with a fold line that can be folded along the part connection part. The fold line has a fold line structure having a mountain fold line and a valley fold line that are valley-folded when viewed from one surface side of the structure with fold line,
(H030) The structure with fold lines in which the mountain fold lines and valley fold lines formed along a spiral extending from one point of convergence are alternately arranged adjacent to each other;
(H032) In the state where the fold line is extended, it is a conical wall shape or a dome shape, and in the state where the fold line is folded according to the mountain fold line and the valley fold line, the fold line is wound around the converging point. The structure with a fold line that is folded in a folded state. A structure with a fold line characterized by comprising the following structural requirements (E01) to (E04);
(E01) A linear fold line that includes a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A structure with fold lines provided, wherein the fold line is a plurality of mountain fold lines in which the one surface side is mountain-folded when viewed from one side of the structure with fold lines, and one or more valley fold lines in which valley folds are formed. A structure with a fold line,
(E02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval so that the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2. The plurality of fold lines formed in
(E03) The structure with a fold line constituted by a sheet-like member formed with a fold line along a spiral;
(E04) In the state where the fold line is extended, it is a circular sheet shape, and in a state where the fold line is bent according to the mountain fold line and the valley fold line, the fold line is a disk shape having unevenness whose outer shape is reduced. The said structure with a fold line used as the shape with the thickness which has the unevenness | corrugation which further reduced the external shape in the state folded completely along the fold line and the valley fold line. A fold line forming mold comprising the following structural requirements (F01) and (F02):
(F01) A linear fold line that includes a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part is provided. A pair of fold line forming members, wherein the fold line includes a plurality of mountain fold lines and one or more valley fold lines that form valley fold lines when viewed from one surface side of the fold linear molding. A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2 A pair of fold line forming members having the plurality of fold lines formed on
(F02) A folded linearly formed connecting member that supports or connects the pair of folding line forming members so as to be movable between an overlapped state and an open state. A folding line forming method comprising the following constituent requirements (G01) and (G02):
(G01) A linear fold line that includes a plurality of polygonal parts and a linear part connecting part that connects the outer sides of each part to each other and is foldable along the linear part connecting part. A fold line-attached structure provided, wherein the fold line is a plurality of mountain fold lines and one or more valley fold lines where the one surface side is a mountain fold when viewed from one side of the fold line structure. A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at a predetermined interval, and the difference between the number of mountain fold lines and the number of valley fold lines that intersect at one node is 2 A sheet-like member sandwiching step of sandwiching a foldable integral sheet-like member between a pair of flat plate-like fold line forming members having the plurality of fold lines formed to be
(G02) A fold line forming step of forming the fold line on the sheet-like member by simultaneously folding the pair of fold-line forming members sandwiching the sheet-like member along the mountain fold line and the valley fold line.

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