JP2000003212A - Method for interpolating curve - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for interpolating a curve for generating an approximate straight line for utilizing the allowable range of tolerance to the maximum and for making the number of the approximate straight lines smaller than that in a conventional curve interpolation system. SOLUTION: A curve 20 is calculated from inputted curve data, a tolerance circle 21 with tolerance as a radius is prepared within a plane with the tangential direction of the curve as a normal direction at each point on the curve from the curve 20 and the inputted tolerance and upper and lower tolerance lines 26A and 26B are calculated based on the circle. Then, the start point and the end point of the curve 20 are connected through a straight line and the end point of the straight line is made close to the end point unit it enters the inside of the upper and lower tolerance lines 26A and 26B. The line is extended, and a cross point 24A between the upper and lower tolerance lines 26A and 26B is calculated to make the point the end point of the straight line and to decide an initial approximate straight line 25A as well. The end point is used as the start point of the second straight line and all approximate straight lines are decided by repeating the same way. Afterwards, an interpolation arithmetic operation is executed along the approximate straight line to make it command data.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curve interpolation method capable of performing efficient and efficient curve interpolation in a control device such as a machine tool or a robot.

[0002]

2. Description of the Related Art Conventionally, when a curve is drawn by a numerical controller, the curve is drawn by replacing a large number of straight lines, and the curve is apparently approximated. As shown in the conceptual diagram of FIG. 6, the curve interpolation method is based on a given curve 6 from a start point 63 to an end point 64.
1 is appropriately divided, passing points are taken, a large number of straight lines connecting continuous passing points are provided, connected by broken lines, and a straight line group 62 is formed, and the curve is approximated by the many straight lines. The curve was approximated by interpolation of a simple approximation straight line. In the case of approximation by this method, as shown in FIG. 7, the passing points 74 and 75 on the curve are selected so as to keep the maximum error 72 between the part 71 of the curve and the approximate straight line 73, that is, the tolerance within an allowable range. Was out.

[0003]

However, in the above-mentioned conventional example, the starting point 75 and the ending point 74 of the approximate straight line 73 are different.
Is always on the part 71 of the given curve, so the smaller the tolerance, the larger the number of approximate straight lines,
There is a problem that the cutting surface by the curve interpolation becomes rough beyond the processing capability of the numerical controller. In addition, it cannot be said that the allowable range of the tolerance by the linear approximation is fully utilized. Therefore, an object of the present invention is to generate an approximate straight line that makes maximum use of the tolerance of the tolerance, and to reduce the number of the approximate straight lines as compared with the conventional curve interpolation method.

[0004]

According to a first aspect of the present invention, there is provided a curve interpolation in a numerical controller, wherein input curve data and an interpolation tolerance are calculated.
That is, from the tolerance, a tolerance circle having the center at the point and the radius of the interpolation tolerance is created on a plane whose normal direction is the tangent direction of the curve at each point of the curve data, and the tolerance circle is defined as A vertical trajectory is obtained based on the vertical trajectory, and a linear trajectory that passes through the inside of the vertical tolerance line at each point of the entire curve generated by the curve data is generated, and the linear trajectory is interpolated. According to a second aspect of the present invention, in the curve interpolation in the numerical controller, a plane having a tangent direction of a curve at each point of the curve data as a normal direction from the input curve data and an interpolation allowable error, that is, tolerance. On the top, a tolerance circle having the radius as the interpolation permissible error centering on each point is created, an outer tolerance line is obtained based on the tolerance circle, and the outer tolerance line is determined at each point of the entire curve generated by the curve data. A linear trajectory passing between the tolerance line and the curve is generated, and the linear trajectory is interpolated. According to a third aspect of the present invention, in the curve interpolation method, the curve data is a part obtained by dividing a series of curve data. According to the above configuration, the approximate straight line is generated so as to make maximum use of the tolerance, so that the number of approximate straight lines can be reduced while keeping the tolerance within an allowable range.

[0005]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a curve interpolation method according to the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a configuration of an apparatus suitable for implementing the curve interpolation method of the present invention, and FIG. 2 is a diagram for explaining a procedure for obtaining an approximate straight line of the present invention. FIG. 3 is a flowchart showing a procedure of a process in which the apparatus of FIG. 1 operates. In FIG. 1, reference numeral 11 denotes a curve generation unit that generates an equation of the input curve when curve data is input, and 12 generates a tolerance circle at each point of the curve generated by the curve generation unit 11 when a tolerance is input. A tolerance circle creating unit for finding a tolerance line, 13 is an approximate straight line creating unit that creates an approximate straight line based on the upper and lower tolerance lines created by the tolerance circle creating unit 12, and 14 is a unit that creates position command data based on the input approximate straight line. Is a linear interpolation execution unit to be executed. In such a configuration, when curve data is given, the curve generation unit 11 first generates a curve equation. Upon inputting the value of the tolerance, the tolerance circle creating unit 12 receiving the curve formula creates a tolerance circle at each point at a predetermined interval on the curve. Then, based on the tolerance circle, upper and lower tolerance lines on both sides of the curve which is the envelope of the tolerance circle are obtained. The approximate straight line generator 13 that has input the upper and lower tolerance lines generates an approximate straight line based on the upper and lower tolerance lines. The linear interpolation execution unit 14 obtains a point on the approximate straight line by interpolation calculation, and generates position command data.

Next, a situation in which an approximate straight line is obtained in the approximate straight line generator 12 will be described with reference to FIG. In the figure, when a curve having a start point 22A and an end point 22B is given, a straight line having the start point 22A as a start point and the end point 22B is obtained. The straight line is the vertical tolerance line 26A,
If the straight line is beyond 26B, the end point of the straight line is shifted by a predetermined amount toward 22A. And the vertical tolerance line 26A again,
A check is made to see if it does not exceed 26B, and the same is repeated until it does not exceed 26B. At that time, the end point of the approximate straight line 25A, that is, the division point of the curve is 23A. Next, the straight line is extended and the vertical tolerance line 26A is extended.
Alternatively, a point 24A intersecting with 26B is set as a connection point, and is set as a start point of the next approximate straight line 25B. The end point of the approximate straight line 25B is initially set at 22B, and the division point 23B is obtained through the same procedure as in the case of the approximate straight line 25A. Thereafter, an approximate straight line is obtained in a similar manner.

Next, the processing procedure of the apparatus of FIG. 1 for performing the above operation will be described with reference to the flowchart of FIG.
First, S1: curve data is input to the curve generator 11, and S2: a curve is generated. Next, S3: When the tolerance is input to the tolerance circle creating unit 12 to which the curve is input, S4: The tolerance circle creating unit 12 generates the tolerance circle at each point of the curve. Further, based on the circle, an upper and lower tolerance line which is an envelope of the tolerance circle is obtained. Then, the approximate straight line generator 13 generates an approximate straight line having S5: the start point of the curve as the start point of the approximate straight line, and S6: the end point of the curve as the end point. At this time, S7: It is determined whether or not the created approximate straight line protrudes from the upper and lower tolerance lines. If not, this approximate straight line is determined as an interpolation straight line, and all the interpolation straight lines are determined. . However, if it protrudes, S
8: The end point of the approximate straight line is shifted by a predetermined amount along the curve toward the start point of the curve, and a new approximate straight line is generated. And S
9: It is determined again whether or not the created approximate straight line protrudes from the upper and lower tolerance lines.
And the above processing is repeated. If it does not protrude,
S10: The current approximate line is determined, the end point is extended, and the intersection with one of the upper and lower tolerance lines is set as the start point of the next approximate line. Thereafter, the process returns to S6 and repeats the above processing.

Next, an embodiment of the present invention according to claim 2 will be described with reference to FIGS. The present invention is used when it is desired to make a cylinder which can be formed into a hole and fit into the hole, and is an application of the invention of claim 1. When making such a hole and a cylinder, theoretically the diameter of the hole and the cylinder is made the same, but in fact, it is made by processing the diameter of the hole slightly larger than the cylinder. In this example, a situation in which an approximate straight line is obtained will be described with reference to FIG. Starting point 4 in the figure
Given a curve 40 having 2A and an end point 42B, a tangent to the curve 40 is first determined at a start point 42A. The point 44A where the tangent intersects the outer tolerance line 46A is the approximate straight line 4
The end point of 5A is determined, and the first approximate straight line is determined. The end point is the start point of the next approximate straight line, and is the connection point 44A between the two approximate straight lines. The end point of the new approximate straight line is set to the closest point on the curve, and it is determined whether the new approximate straight line is tangent to the curve 40. If not, the end point of the approximate straight line is moved to the end point of the curve by a predetermined amount, and the same is repeated until the approximate straight line becomes tangent to the curve. If it becomes tangential, extend it to the outer tolerance line 46
The intersection 44B with A is set as the end point of the approximate straight line, the next approximate straight line is determined, and the similar procedure is repeated to obtain an approximate straight line group.

Next, the processing procedure of the apparatus of FIG. 1 for performing the above operation will be described with reference to the flowchart of FIG.
First, S1: curve data is input to the curve generator 11, and S2: curve 40 is generated. Next, S3: When the tolerance is input to the tolerance circle creating unit 12 to which the curve 40 is input, S4: The tolerance circle creating unit 12 inputs the curve 40.
Are generated at each point. Further, based on the circle, an outer tolerance line 46A that is an envelope outside the tolerance circle is obtained. Then, the approximate straight line generator 13 sets S5: the starting point 42A of the curve 40 as the starting point of the approximate straight line, and S6: obtains the tangent of the curve at that point. S7: An intersection 44A between the curve 40 and the outer tolerance line 46A is obtained and set as an end point of the approximate straight line, and an approximate straight line 45A is determined. S8: The end point of the previous approximate line is set as the start point of the next approximate line, and the point on the curve closest to this is set as the end point. S9: If the end point has reached the end point 42B of the curve 40, the determination of all approximate straight lines ends. S10: If the end point 42B of the curve has not been reached, it is determined whether or not the approximate straight line is a tangent to the curve 40. Return. If it is a tangent, S12: extend the approximate straight line and extend the outer tolerance line 46A.
Is determined, an approximate straight line is determined as the end point of the approximate straight line, the process returns to S8, and the above processing is repeated.

As described above, according to the first embodiment of the present invention, when interpolating a given curve, the longest approximate straight line among the approximate straight lines satisfying the tolerance condition can be generated. The number can be reduced. Further, according to the second embodiment, the longest approximate straight line can be generated while obtaining the situation where the diameter of the machined hole does not fall below the diameter of the cylinder, and the number of approximate straight lines can be similarly reduced. You can. In the two embodiments, the case where the approximate straight line is obtained at once for the entire range of the curve has been described. However, when the curve is long, it may be time-consuming to obtain the approximate straight line at first. . Thus, when approximating a continuous long curve,
First, the curve may be divided into several curves, and the above procedure may be taken for each of the divided curves, so that a high-speed linear approximation can be performed while maintaining the tolerance as a whole.

[0011]

As described above, according to the present invention,
When the given curve is interpolated, an approximate straight line is generated so as to make maximum use of the tolerance. Therefore, the number of approximate straight lines can be reduced while keeping the tolerance within an allowable range. And the processing speed can be kept high at the same time.

[Brief description of the drawings]

FIG. 1 is a conceptual block diagram of an apparatus for implementing the method of the present invention.

FIG. 2 is a diagram illustrating a straight line approximation method according to the present invention.

FIG. 3 is a flowchart showing a processing procedure of the apparatus of FIG. 1;

FIG. 4 is a diagram illustrating a second straight line approximation method according to the present invention.

FIG. 5 is a flowchart showing a second processing procedure of the apparatus of FIG. 1;

FIG. 6 is a diagram illustrating a conventional linear approximation method.

FIG. 7 is a diagram showing a definition of tolerance.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 11 Curve generation part 12 Tolerance circle creation part 13 Approximate straight line generation part 14 Linear interpolation execution part 20, 40, 61 Curve 21 Tolerance circle 22A, 42A, 63, 75 Start point 22B, 42B, 64, 74 End point 23A, 23B Division point 24A , 24B, 44A, 44B Connection points 25A, 25B, 45A, 45B, 45C, 73 Approximate straight line 26A Upper tolerance line 26B Lower tolerance line 46A Outer tolerance line 62 Straight line group 43A, 43B Contact point 71 Part of curve 72 Maximum error reduction No. 12526

Claims (3)

[Claims] 1. A curve interpolation method in a numerical controller, comprising: obtaining an approximate straight line in the following step; and interpolating the approximate straight line. (1) Generate a curve from the input curve data. (2) A tolerance circle and a vertical tolerance line are obtained from the input tolerance and the curve. (3) The starting point of the curve is set as the starting point of the approximate curve. (4) Generate an approximate straight line with the end point of the curve as the end point. (5) It is determined whether or not the approximate straight line protrudes from the upper and lower tolerance lines. If not, all approximate straight lines are obtained, and the process is completed. (6) If it does, the end point of the approximate straight line is shifted by a predetermined amount along the curve toward the start point of the curve, and a new approximate straight line is generated. (7) It is determined whether or not the new approximate straight line protrudes from the upper and lower tolerance lines, and if so, the process returns to (6). (8) If it does not protrude, the current interpolation straight line is determined, the end point is extended, the intersection with one of the upper and lower tolerance lines is set as the start point of the next approximate straight line, and the process returns to (4). 2. A curve interpolation method in a numerical control device, comprising: obtaining an approximate straight line in the following step; and interpolating the approximate straight line. (1) Generate a curve from the input curve data. (2) A tolerance circle and an outer tolerance line are obtained from the input tolerance and the curve. (3) The starting point of the curve is set as the starting point of the approximate curve. (4) A tangent to the curve is obtained from the starting point. (5) The intersection of the curve and the outer tolerance line is set as the end point of the approximate line, and the approximate line is determined. (6) The end point of the approximate straight line is set as the start point of the next approximate straight line, and the point on the curve closest to this is set as the end point. (7) If the end point has reached the end point of the curve, all interpolation straight lines are determined, and the process is terminated. (8) If the end point has not been reached, it is determined whether or not the approximate straight line is tangent to the curve. If not, the end point is moved to the end point of the curve by a predetermined amount and the process returns to (7). (9) If it is a tangent line in (8), the straight line is extended to find an intersection with the outer tolerance line, an approximate straight line is determined as the end point of the approximate straight line, and the process returns to (5). 3. A curve interpolation method according to claim 1, wherein said curve data is a part of a series of curve data divided.