JPS6048244A - Cutting path searching method - Google Patents

Abstract

PURPOSE:To find a cutting path, by gicing data specifying a three-dimensional curve and projection curve data projecting the cutting path on a plane surface, while dividing the curve into a lot of minute patches for projection, and using the intersection point with a projection curve of the cutting path. CONSTITUTION:Performance curves 11a, 12a and reference curves 21a, 22a of date specifying a three-dimensional curve 41 and data specifying a projection curve 31a to the specified plane of a cutting path 31 on the curve are all inputted while the three-dimensional curve 41 is divided into each of patches 51, 51... consisting of a lot of minute quadrangles, finding each of intersection points between four sides ia, ib, ja and jb of the quadrangular patch 51 projected on specified XY planes and the projection curve 31a, and each of them is converted into each of points P1i and P1i on the three-dimensional curve 41 whereby the coordinate value is stored in memory, and a passage being made up of connecting the group of points obtained together in consecutive order is set down to the cutting path on the three-dimensional curve 41.

Description

[Detailed Description of the Invention] <Industrial Application Field> The present invention relates to a cutting path search method for finding a cutting path on a three-dimensional curved surface, and in particular, data for specifying a three-dimensional curved surface and a cutting path on the curved surface. The present invention relates to a cutting path searching method that inputs data specifying a projected curve projected onto a predetermined plane and finds a cutting path on a three-dimensional curved surface from these data.

<Prior Art> A curved surface on a design drawing of a three-dimensional mold or the like is generally represented by a plurality of cross-sectional curves, and shape data between one cross-sectional curve and the next does not exist. By the way, in numerical control machining, it is required to process the two cross-sectional curves so as to smoothly connect them, even though the intermediate shape is not provided. In other words, a curved surface between the above two cross-sectional curves is generated from the data of the cross-sectional curve, data regarding the generated curved surface is perforated on an NC tape, and according to commands from the NC tape. This means that it must be processed. For this purpose, a plurality of intermediate cross sections are generated according to a predetermined rule from data specifying several cross-sectional cross-sectional curves of a three-dimensional curved surface body, and a cross-sectional curve (intermediate cross-sectional curve) of the curved surface body by the intermediate cross sections is calculated. A method of generating a curved surface of a three-dimensional curved body using the plurality of generated intermediate cross-sectional curves has been developed and put into practical use. This method is effective because it can generate a smooth curved surface from cross-sectional data.

<Disadvantages of the prior art> By the way, depending on the processing, grooving of a predetermined shape on a curved surface may be required, and although the conventional method can generate a curved surface, it is difficult to cut a three-dimensional path on such a curved surface. could not be generated.

<Objective of the Invention> The object of the present invention is to determine the cutting path on the curved surface from data specifying a three-dimensional curved surface and projection curve data obtained by projecting the cutting path on the curved surface onto a predetermined plane (for example, the X-Y plane). An object of the present invention is to provide a cutting path searching method that can be used to

<Summary of the Invention> FIG. 1 is a schematic explanatory diagram of the present invention, FIG. 1(A) is a curved perspective view, and FIG. 1(B) is a partially enlarged view of FIG. 1(A). The present invention is a cutting path search method for finding a cutting path 31 on a three-dimensional curved surface 41, and includes data for specifying the three-dimensional curved surface 41 (for example, operating curves 11a, 12a, reference curve 21a,
22a) and data specifying the projection curve 31a of the cutting path 31 on the curved surface with respect to a predetermined plane (XY plane) are input, and the three-dimensional curved surface 41 is shaped into batches 51, 51, . . . Find intersection points P1i, P2i where the projection curve 31a intersects the four sides ia, ib, ja, jb of the batch 51 projected on the XY plane, and place the intersection points P1i, P2i on the three-dimensional curved surface 41, respectively. Convert to point P1'iP2'i and store its coordinate values,
This is a cutting route searching method in which a path formed by sequentially connecting the obtained point group is used as the cutting route 31 on the three-dimensional curved surface 41.

<Embodiment> FIG. 2 is a block diagram of an embodiment of the present invention, FIG. 3 is a flowchart of processing, and FIG. 4 is an explanatory diagram of curved surface generation.

In FIG. 2, 101 is a keyboard for data input;
102 is a processor, 103 is a ROM for storing a control program, 104 is a RAM, 105 is a working memory, 106 is a curved surface storage memory for storing generated three-dimensional curved surface data, and 106 is a memory for storing generated cutting paths on paper tape or magnetic tape. 109 is an address bus, and 110 is a data bus.

The cutting path search process according to the present invention will be explained below.

(a) First, data specifying the three-dimensional curved surface 41 and the projection curve 31a obtained by projecting the cutting passage 31 on the three-dimensional curved surface onto the XY plane are inputted from the keyboard 101, respectively.

These input data are stored in the RAM 104.

Note that the three-dimensional curved surface 41 is, for example, the motion curves 11a, 12a.
Also, since it is specified by the reference curves 21a and 22a,
By inputting these curve data, the three-dimensional curved surface 41
is specified.

(b) When data is input, the processor 102 first executes a curved surface generation process using a known method. FIG. 4 is an explanatory diagram of such a curved surface generation process, and in FIG.
a and 12a are cross-sectional curves when the three-dimensional curved surface body 41 is cut by the given surfaces 11 and 12, respectively, and 21 is the first point P on the motion curves 11a and 12a.
1 and P1'respectively; 22 is a second reference plane including second points P2 and P2' on the operating curves 11a and 12a, respectively; 21a and 22a are first and second reference planes, respectively; Exists on the reference planes 21 and 22, and is a three-dimensional curved body 41
The first and second reference curves 13 specify the outer shape of the first and second reference curves 21a and 22a, respectively.
Including points P1'' and P2'' that are internally divided into n, and dividing point P2
This is an intermediate cross section that also includes an intersection point P3'' between a perpendicular drawn to the first reference plane 21 and the first reference plane 21. Now,
The curved surface 41 is generated by the following steps (1) to (6). That is, (1) Cross-sectional information of the target intermediate cross-section 13 (split ratio m:
n). In other words, the reference curves 21a, 22a are
: Intermediate cross section 1 including division points P1'' and P2'' internally divided into n
Generate 3.

(2) Next, the operating curves 11a and 12a and the intermediate cross section 13
Intersection point P1'' with the first and second reference curves 21a and 22a
, P2'' are converted to be on the same plane (Fig. 4 (B)). By performing the following operations (2-1) to (2-3), the intersection points P1'' and P2 of the operating curves 11a and 12a are '' can be considered as curves on the same plane.

(2-1) Let the intersection points P1, P1' and the intersection point P1'' between the reference curve 21a and the given cross sections 11 and 12 be the same point.

(2-2) Considering the intersection lines HL, HL', HL'' between the reference plane 21, the given planes '11, 12, and the intermediate section 13, the respective intersection lines HL, HL', HL'' are at the intersections P1, P1 ',P
Divided into two by 1″.

Overlap these bisected line segments.

(2-3) Pass through the intersections P1, P1'P1'' of the reference curve 21a, the given sections 11, 12, and the intermediate section 13, and the reference curve 2
Straight lines VL, VL', VL'' perpendicular to 1a are drawn on each given section 11.
, 12, and the intermediate cross section 13, each intersection line V
L, VL', and VL'' are divided into two by intersections P1, P1', and P1''. The reference curve 21 of this bisected line segment
Line segments in the same direction relative to a are superimposed.

(3) Using the operating curves 11a' and 12a' (see FIG. 4(B)) on a predetermined plane obtained in step (2) above, an intermediate cross-sectional curve 13b is generated on the plane.

This intermediate cross-sectional curve 13b is generated by the following procedure.

(3-1) Points Q1 and Q2 that divide the line lengths of the operating curves 11a' and 12a' into a:b, respectively, are determined by the following method.

(3-1a) Calculate the length of each element (line segments or circular arcs that make up the motion curve are called elements) of the motion curves 11a', 12a' and add them together to form the motion curves 11a', 12a.
Find the length D of '.

(3-1b) Find a/(a+b)・D=D'.

(3-1c) Extract an element that includes a position of length D' from one end that is the base point of division. This element extraction is performed by finding k when the length of the first element is D1, the length of the next element is D2, and so on D3, . . . , Di, . . . .

(3-1d) For the kth element, find a point on the kth element that is closer to the starting point. These points move the operating curves 11a' and 12a' from one end point P1 and P1' to a
: This is the point of division into b. Furthermore, in (3-1c) k
= 1.

(3-2) Step (1 step) straight line connecting dividing points Q1 and Q2
) is calculated at a division point Ri at a division ratio of m:n (FIG. 4(C)).

In addition, the coordinate values of dividing points Q1 and Q2 are respectively (x1, y1
)+(x2, y2), the coordinate value R1(
X, Y) are calculated by.

(3-3) Set the value of division ratio a:b in step (3-1) to 0.
R1 point while changing sequentially from to 1 (1 = 1.2...)
An intermediate section curve 13b is generated by the point sequence (see Fig. 4 (
C)). Incidentally, by carefully changing the division ratio a:b, a smoother intermediate cross-sectional curve 13b can be obtained.

(4) Using the intermediate cross-sectional curve 13b on the predetermined plane obtained in step (3) above and the intersection points P1'' and P2'', an intermediate cross-sectional curve 13a' is generated on the plane. Note that this intermediate cross-sectional curve 13a' is generated by the following procedure.

(4-1) Starting point P1″ and ending point Pe of intermediate cross-sectional curve 13b
The ratio k/l of the length k of the line segment connecting the above and the length l of the line segment connecting the intersections P1'' and P2'', and the angle PeP1''P2''
The rotation angle θ taken from the line segment P1″Pe to P1″P2″ with the clockwise rotation being positive is calculated (FIG. 4(D)).

(4-2) Determine the dividing point Sl that divides the intermediate cross-sectional curve 13b into a:b using the same method as steps (3-1a) to (3-1d).

(4-3) External division point Sl that externally divides line segment P1Sl by k:l
' is rotated by θ and calculates the point Sl'' (see Figure 4 (
D)).

Note that the dividing point Sl that divides the intermediate cross-sectional curve 13b into a:b
The coordinates of P1″ are (xi, yi), and the coordinates of P1″ are x0, y0)
．． If the coordinates of Sl'' are (X, Y), then the coordinate values of Sl'' will be smaller.

(4-4) - Since the value of the division ratio a/b in step (4-2) is changed sequentially from 0 to 1, the Sl'' point (i=1, 2,
3...) to generate the intermediate cross-sectional curve 13a' (
Figure 4(D)). Incidentally, by carefully changing the division ratio a/b, a smoother intermediate cross-sectional curve 13a' can be obtained.
can be obtained.

(5) - If the intermediate cross-section curve 13a' on the predetermined plane obtained in step (4) is converted onto the intermediate cross-section 13 (Fig. 4 (E)) in the defined space, the reference curves 21a and 22a can be m
: Intermediate cross section 1 including dividing points P1'' and P2'' divided into n
3 is generated.

(6)・Set steps (2) to (5) above in step (1)
), the three-dimensional curved surface 41 is generated by sequentially converting the division ratio m/n from O to 1. Incidentally, as shown in FIG. 5, the intermediate section curve including the j-th division point on the reference curve 21a is expressed as 13a(j),
When expressing the curve formed by connecting the first division points of a(j) (j=1, 2,...n) as 14(i), the curve 13a
(j), 13a (j+1) 14(i), 14(i+1)
The quadrilateral surrounded by is called a batch P(i,j). Then, the four vertices Q1, Q2, Q of batch P(i,j)
3 and Q4 are each created by the above curved surface generation process and stored in the curved surface storage memory 106.

When the curved surface generation process is completed through the above step (b), the processor 102 starts the cutting route search process.

(c) First, let 0→i and 0→j.

(d) The coordinate values of the four vertices Q1 to Q4 of batch P(i, j) are stored in the working memory 10 from the curved surface memory memory 106.
5, and then it is determined whether the quadrilateral formed by projecting the batch P(i, j) onto the XY plane includes the starting point Q5 of the projection curve 31a (does it intersect with the projection curve)?

(e) In step (d), if there is no crossover, i≦(
M-1) (5) Determine whether or not. Note that M is the maximum number of divisions of the intermediate cross-sectional curve.

(v) If the equation (5) is satisfied by the determination in step (e), the process moves to step (2) as i+1→j and performs processing to search for a batch that intersects the projection curve 31a.

(g) If the equation (5) is not satisfied as determined in step (e), 0→1, j+1→j, and the process jumps to step (d) to search for a batch that intersects the projection curve 31a.

On the other hand, in the determination process of step (d), batch P(i
, j) intersects the projection curve 31a, the following processing is performed.

(4) Projection curve 31a and four sides ia, ib, ja, jb (first
(see figure (B)), the intersection point P1iP2 with two predetermined sides
The coordinate values of i (x1i, y1i) and (x2i, y2i) are calculated and stored in working memory 105. By regarding the four sides ia, ib, ja, and jb as straight lines, the coordinate values of the intersection points P1i and P2i can be calculated from the coordinate values of the four vertices Q1 to Q4 of batch P(i, j) and the projection curve data. Calculated. Also, the coordinate values (xi, yi, zi) of the four vertices Q1-Q4 of batch P(i, j) (i=1,
2, 3, and 4) are read out from the curved surface storage memory 106 to the working memory 105.

(li) If the coordinate values of the intersection points P1i and P2i are equal, then the points P1i' and P on the three-dimensional curved surface 41 corresponding to the intersection points
The Z-axis coordinate values z1i and z2i of 2i' are determined by the following equation.

Now, assume that the projection curve 31a intersects sides ia and ib (see Fig. 1(B)), and let the end points of side ia be Q1'Q2', the end points of side ib be Q3' and Q4', and point Q1', Q2′,
The point on the three-dimensional surface corresponding to Q3' and Q4' is Q
1, Q2, Q3, Q4 The coordinate values of each point Q1 to Q4 are (x1, y1, z1), (x2, y2, z2), (x3
, y3, z3), , (x4, y4, z4), then z
1i and z2i are calculated from each. Note that instead of formulas (6) and (7), the two-axis coordinate values of points P1i' and P2i' may be determined.

(nu) After that, (x1i, y1i, z1i), (x2
i, y2i, z2i) as points P1i' and P2i' on the cutting path 31 on the three-dimensional curved surface 41, respectively.
Store in M104.

(l) Next, find the next batch where the projection curves 31a intersect. As is clear from FIG. 6, the next batch where the projection curve 31a intersects is the four batches P(i-1, j), P(i, j-1), P(i, j-1) surrounding the patch P(i, j). P(i+
1, j), P(i, j+1). However, considering the case where the projection curve 31a passes through the vertices Q1' to Q4' of the batch P(i, j), which of the eight batches surrounding the batch P(i, j) is the next batch that the projection curve 31a intersects? However, in the embodiment, the description will be made assuming that the vertices do not pass through the vertices Q1' to Q4'.

Therefore, batches P(i-1,j), P(i,j-1),
Projection curve 3 among P(i+1,j) and P(i,j+1)
Find a batch that intersects with 1a, and create a new batch of P(i
, j), the process jumps to step (h) and performs a cutting route search process. Incidentally, when the intersection point that intersects each patch is found in the direction of the arrow in FIG.
Batch P that intersects (i, j+1) but has already been used
(i, j-1) is discarded.

(2) If there is no batch in which the projection curves intersect in the process of step (1), it is assumed that the cutting path has been generated and the process ends. Thereafter, if the cutting path data stored in the RAM 104 is output to an external storage medium via the output device 107, the NC data creation process is completed.

In addition, although the case where the projection curve data which projected the cutting path on a three-dimensional curved surface on the XY plane was inputted above was described, the present invention is not limited to such a case.
It may be configured to input projection curve data projected onto a YZ plane, a Z-X plane, or the like. Further, although the tool center axis vector has been omitted for convenience of explanation, it goes without saying that the tool center axis vector can be calculated by the proportional allocation method of equations (6) to (7). Furthermore, when searching for a batch that includes the starting point of a projection curve, when the direction of the starting point of the projection curve is downward to the right, upward to the right, downward to the left, or upward to the left, the batches P(0, 0), P(M, O), P(0, N), P(M
, N) in the direction of the arrow in FIG. 6.

Further, if the starting point of the projection curve does not exist on the four sides of the batch, the starting point coordinate value on the curved surface is obtained from the starting point data of the projection curve and the vertex coordinate value of the batch including the starting point.

<Effects of the Invention> As described above, according to the present invention, data specifying a three-dimensional curved surface and data specifying a projection curve of a cutting path on the curved surface with respect to a predetermined plane are input, and the three-dimensional curved surface is shaped into a large number of micro quadrilaterals. Intersection points P1i, P2 where the projection curve intersects the four sides of the batch divided into batches and projected onto the plane.
i, the intersection points P1i and P2i are converted and stored as points on the three-dimensional curved surface into P1i' and P2i', respectively, and a path formed by sequentially connecting the obtained points is created on the three-dimensional curved surface. Since it is a cutting path, it is effective because it can provide NC data such as grooving along a curve on a three-dimensional curved surface.

[Brief explanation of drawings]

FIG. 1 is a schematic explanatory diagram of the present invention, FIG. 2 is a block diagram of an embodiment of the present invention, FIG. 3 is a flowchart of the processing of the present invention, FIG. 4 is an explanatory diagram of the curved surface generation method, and FIGS. 5 and 6 The figure is an explanatory diagram of the present invention. 101...keyboard, 102...processor, 103...R
OM, 104... RAM, 105... Working memory, 106... Three-dimensional curved surface storage memory, 107... NC data output device. Patent applicant FANUC Co., Ltd. Representative Patent Attorney Chiki Mito JF; Kuni CA) Figure 1 (B)

Claims (3)

[Claims] (1) In a cutting path search method for determining a cutting path on a three-dimensional curved surface, inputting data specifying the three-dimensional curved surface and data specifying a projection curve obtained by projecting the cutting path on the curved surface onto a predetermined plane, Divide the three-dimensional curved surface into batches consisting of a large number of micro quadrilaterals, find intersection points where the four sides of the batch projected onto the plane intersect with the projection curve, and place the intersection points on each of the three-dimensional curved surfaces. A cutting path searching method characterized by converting the points into points and storing their coordinate values, and defining a path formed by sequentially connecting a group of similarly obtained points as a cutting path on a three-dimensional curved surface. (2) The coordinate values of points Q1 and Q2 on the three-dimensional curved surface corresponding to the end point Q1'Q2' of the side that intersects the projection curve among the four sides of the batch projected on the plane, and the coordinate value of the intersection point. The method for searching a cutting path according to claim 1, wherein the third axis coordinate value of a point on the three-dimensional curved surface corresponding to the intersection point is determined by proportional allocation using . (3) A patent characterized in that batches on the three-dimensional curved surface are created in a matrix form, and the next batch that intersects with the projection curve is selected from a group of batches surrounding the batch that intersects with the projection curve. Claims paragraph (1) or (2)
Cutting path search method described in section.