JPH03208553A - Teaching method for polishing face in polishing device - Google Patents

Abstract

PURPOSE:To remarkably reduce the number of teaching points and to simplify a teaching work by obtaining the curved line between adjacent teaching points as a parametric tertiary spline curved line. CONSTITUTION:In the case of teaching the curved face stretching the curved line located on a plane in the specific direction as a polishing face, the stretched direction is teached and also plural points P1, P2 - Pn, Pn+1, Pn+2 located on the curved line on the plane vertical to the stretched direction are teached. Then, the plural teaching points P1, P2 - Pn, Pn+1, Pn+2 located on the plane are obtained as the parameters s1, s2 - sn of a parametric tertiary spline curved line. Consequently, the teaching work can be simplified and also the processing time can be shortened.

Description

[Detailed Description of the Invention] Industrial Application Field> The present invention relates to a method for teaching a polishing surface in a polishing device, and more specifically, to a method for teaching a curved surface obtained by stretching a curved line on a plane in a predetermined direction as a polishing surface. .

Prior Art and Problems to be Solved by the Invention When polishing a mold using an industrial robot, it is necessary to always polish the polished surface from the vertical direction because a good finish is required. However, in order to reliably perform brushing from the vertical direction, the surface to be brushed must be taught in advance.

Conventionally, when teaching an arbitrary three-dimensional curved surface as a polishing surface, the only methods were to teach the entire range of the curved surface in detail or to memorize the pattern of the curved surface by tracing. Also, when teaching a curved surface obtained by stretching a curved line in a plane in a predetermined direction as a polished surface, the entire range of the curved surface can be taught in detail in the same way as when teaching an arbitrary three-dimensional curved surface, or the curved surface can be polished using the tracing method. The only way was to memorize the pattern.

In the case of the latter curved surface, if the equation of the curve on the plane can be obtained and the stretching direction can be determined, the number of teaching points can be significantly reduced. However, since it may be practically impossible to obtain the equation of a curve on a plane, it is not possible to obtain the equation of the curve based on a small number of teaching points. That is, the curve shown in Fig. 7 (A
), if the y coordinate value is uniquely determined based on the Since the equation only needs to satisfy the conditions that it passes through two adjacent teaching points and that each teaching point has a tangent vector equal to the tangent vector of the adjacent curve, the coefficients of the above equation can be uniquely determined. be able to. However, as shown in FIG. 7(B), the curve is
If the coordinate value is not uniquely determined, simply y
Simply obtaining the coefficients of the equation expressed by -f(x) cannot be used as teaching data for brushing work, and the equation y-fy expressed using parametric variables
(s) and the coefficients of x-fx (s) must be obtained. Specifically, a parametric cubic spline curve y−Ay s +By s2+Cy s+Dy
, 3 x-Ax s +BX s2+Cx s+Dx3 Therefore, it is not possible to uniquely determine all the coefficients only under the above conditions.

Therefore, when teaching a curved surface obtained by stretching a curved line in a plane in a predetermined direction as a polishing surface, the only way is to teach the entire range of the curved surface in detail.

Purpose of the invention> This invention was made in view of the above problems,
It is an object of the present invention to provide a novel polishing surface teaching method that can greatly reduce the number of teaching points when teaching a curved surface having a shape in which a curved line on a plane is stretched in a predetermined direction.

<Means for solving alli> In order to achieve the above-mentioned object, the polishing surface teaching method in the polishing device of the present invention teaches a curved surface obtained by stretching a curved line on a plane in a predetermined direction. In addition to teaching the stretched direction, multiple points on the curve are taught on a plane perpendicular to the stretched direction, and the multiple teaching points on the plane are used as parameters of a parametric cubic spline curve. This is the way to obtain it. In this invention, the term "polishing device" is used as a concept that includes devices for finishing the surface of metal molds, plastic molds, etc., surface finishing of models, and the like.

However, the distance between adjacent teaching points is one curve segment, and the coordinate value of the end point of this curve segment and the tangent vector at the end point are equal to the tangent vector at one end point of the adjacent curve segment, and the corresponding curve segment is A method of obtaining the corresponding curve segment as a parametric cubic spline curve based on the condition that it passes through the other end point of the adjacent curve segment, and obtaining the above teaching point as a parameter of the obtained parametric cubic spline curve. It is preferable that Also, based on the cubic spline curve group obtained by this teaching method, the length between the end points of the teaching points is determined as the length on the curve, and the parametric variable at each teaching point is determined based on the determined length. Preferably, the coefficients of each curve segment are determined again based on the determined parameter.

In these cases, the curved surface to be taught as a polishing surface may be a curved surface obtained by stretching a curved line on a plane in a direction perpendicular to that plane, or a curved surface on a plane drawn by stretching a straight line on that plane. It may be a curved surface stretched in the direction of rotation about the axis.

With the above-described method for teaching a polished surface, when teaching a curved surface obtained by stretching a curved line on a plane in a predetermined direction, it not only teaches the stretched direction but also Since multiple points on the curve are taught on a perpendicular plane and the multiple teaching points on the plane are obtained as parameters of a parametric cubic spline curve, the curved surface can be taught based on a small number of teaching points. The teaching work can be simplified and the processing time can be shortened. In this case, the area between adjacent teaching points is one curve segment, and the coordinate values of the end points of this curve segment and the tangent vector at the end points are equal to the tangent vector at one end point of the adjacent curve segment, and the corresponding curve A method of obtaining a corresponding curve segment as a parametric cubic spline curve based on the condition that the segment passes through the other end point of an adjacent curve segment, and obtaining a teaching point as a parameter of the obtained parametric cubic spline curve. If so, it is assumed that a smoothly continuous curve segment passes not only through both adjacent teaching points but also through the next teaching point, so it is necessary to uniquely determine the coefficients of a parametric cubic spline curve. Since sufficient conditions can be obtained and curves can be approximated with high precision, curved surfaces can also be approximated with high precision. Also, based on the cubic spline curve group obtained by this teaching method, the length between the end points of the teaching points is determined as the length on the curve, and the parameter at each teaching point is determined based on the determined length. If the method is to calculate the coefficients of each curve segment again based on the determined parametric variables, the length between the teaching points can be approximated as the length on the approximated curve rather than as a straight line distance. So,
Approximation accuracy can be further improved.

In these cases, if the curved surface to be taught as a polishing surface is a curved surface obtained by stretching a proof line on a plane in a direction perpendicular to the plane, the teaching point expressed in the orthogonal coordinate system is used as a parameter and the stretching direction. It is sufficient to map onto a plane determined by the coordinates of , and the same effect as above can be achieved. In addition, if the curved surface to be taught as a polishing surface is a curved surface that is a curved line on a plane stretched in the direction of rotation around a straight line on that plane, the teaching point expressed in the cylindrical coordinate system is stretched as a parameter. The same effect as above can be achieved by mapping onto a plane determined by the rotation angle as the coordinate of the direction.

Example Hereinafter, embodiments will be described in detail with reference to the accompanying drawings showing examples.

FIG. 1 is a flowchart showing an embodiment of the method for teaching a polished surface of the present invention. In step (2), teaching for teaching the stretching direction is performed on an orthogonal coordinate system; The teaching of multiple points on a flat plane is performed on an orthogonal coordinate system. and,
In step ■, a parametric variable is calculated based on the length between adjacent teaching points based on the coordinates of the teaching point obtained in step ■, and in step ■, a parametric variable is calculated based on the parametric variable obtained in step ■. The equation of each cubic spline curve of the curve expressed as a set of cubic spline curves is determined, and in step (2), the polished surface is mapped onto a surface determined by the parametric variables of the above equation and the coordinates in the stretching direction. In step (2), the mapped polished surface is interpolated, and in step (2), the coordinate values and normal direction on the orthogonal coordinate system are calculated based on the interpolation result and the equation of the corresponding curve. However, step (2) may be executed when polishing work is performed.

FIG. 2 is a flowchart illustrating in detail an example of the process of step ■■. As shown in FIG. 3 (B), the number of teaching points P1 obtained in step ■ is n, and This corresponds to the case where the number of curve segments Si between points is n-1. Note that the value of the parameter at each teaching point P1 is s
It is set as i.

In step (2), initialization is made to 51 -0, and si -ΣPjPj+1 (however, i-2 to n-1) is set.

Then, in step @, the teaching point PI. A curve segment S1 having P2 as an end point is determined. Specifically, the curve segment Sl is at the teaching point P1. Assuming that it passes through not only P2 but also teaching point P3, and assuming that the curvature at teaching point Pl is 0, the equation y-Ay s" + By s2 + Cy
s1DyX-AX s” +BX s2+Cx s+
curve segment by calculating all coefficients of Dx}
Find Sl. That is, for each coordinate, the teaching point PL.
P2. Since three conditional expressions are obtained by passing through P3, and one conditional expression is obtained by the curvature at the teaching point PI being O, the coefficients of the above equation can be uniquely determined.

Thereafter, i is set to 1 in step [phase], and i is increased by 1 in step [yes].

Then, in step ■, the teaching point Pi, P 141
Find a curve segment S1 whose end point is .

Specifically, the curve segment S1 is the teaching point P1, P1+
The equation y-Ay s3+By is assumed to pass not only through 1 but also through the teaching point P i+2, and on the condition that the tangent vector at the teaching point P1 is equal to the tangent vector at the teaching point PI of the preceding curve segment S1-1.
s2+Cy s+Dyx-Ax s3+Bx s2+C
The curve segment Si is determined by calculating all the coefficients of x s + Dx.

Thereafter, in step [phase], it is determined whether or not i is equal to n-2, and if it is not equal, the process of step 2 is repeated. Conversely, if it is determined in step [phase] that i is equal to n-2, in step @, the curve segment S n obtained immediately before in step ■
-2 is directly adopted as the equation for the last curve segment S n-1. That is, for the last curve segment S n-1, since the next curve segment does not exist, the coefficients of the equation cannot be uniquely determined even if step (2) is applied as is. The equation is adopted as is. However, since it is known in advance that for the last curve segment S n-1, the equation of the previous curve segment S n-2 will be adopted as is, the teaching point P n is set so that the error is as small as possible. It is sufficient to set -1.

FIG. 3 is a diagram schematically explaining the operation of teaching the polished surface, and shows a case where the curved surface shown in FIG. 3(A) is taught.

In the same figure (A), P1. P2. -P n. P n
+1. Pn◆2 is the teaching point, and the coordinate value (xi.yi.zi) in the orthogonal coordinate system (however, i am l~n+2)
is taught. The parameter S corresponding to each teaching point Pi is represented by sj, and the teaching point Pi. The curve segment S defined by Pi+1 is represented by St.

Also, P1. P2. ...Pn is a teaching point for teaching a curve on a plane perpendicular to the stretching direction (see (B) in the same figure), and Pn''l and Pn+2 are teaching points for teaching the stretching direction. It is.

Here, the parameter S is S1-ΣPjPj+1 (however,
s l = 0), the above curved surface is represented as a rectangle on the sz plane (see figure (C)).
. That is, points on the curved surface can be easily calculated by compensating the parameter S and the two coordinate values.

Furthermore, since the parametric cubic spline curve is uniquely determined as described above, the curve segment Si is y-fyi(s)-Ay1s +Byis2+Cyi
s+. 3 Dyi x-fxi(s) -Ax1s +Bxis2+Cx
is ten. 3 Dxi, and as shown in (D) and (E) in the figure, once the values of the parametric variables are determined, the X coordinate value and the y coordinate value are uniquely determined.

Therefore, by making the parametric variable S correspond to the length of the locus of the parametric cubic spline curve and selecting the corresponding curve segment in correspondence with the length of the locus, teaching over the entire range of the curved surface can be achieved. can.

Embodiment 2 FIG. 4 is a flowchart showing another embodiment of the brushing surface teaching method of the present invention, in which teaching of the stretching direction is performed on an orthogonal coordinate system in step
In step (2), a plurality of points are taught on a plane perpendicular to the stretching direction on an orthogonal coordinate system. Then, in step ■, a parametric variable is determined based on the length between adjacent teaching points based on the coordinates of the teaching point obtained in step ■, and in step ■, a parametric variable is determined based on the parametric variable obtained in step ■. The equation of each cubic spline curve of the curve expressed as a set of parametric cubic spline curves is determined using the method, and in step (2), the length between each teaching point is determined based on each cubic spline curve determined in step (2). Calculate and find the mediating variable corresponding to each teaching point,
In step ■, the equation of each cubic spline curve of the curve expressed as a set of parametric cubic spline curves is determined based on the parametric variables obtained in step ■, and in step ■, the parametric variables and extension of the above equation are calculated. The polished surface is mapped onto the surface determined by the coordinates of the direction, and in step (2), the mapped polished surface is interpolated,
In step (2), coordinate values and normal direction on the orthogonal coordinate system are calculated based on the interpolation result and the equation of the corresponding curve. However, step (2) may be executed when polishing work is performed.

FIG. 5 is a flowchart illustrating in detail an example of the process of step ■■. As shown in FIG. 3(B), the number of teaching points Pi obtained in step ■ is n, and This corresponds to the case where the number of curve segments S1 between points is n-1. Note that the value of the parameter at each teaching point Pi is s
It is set as Ni.

In step ■, sN1=o is initialized, and sN1−f (f −xi (s) ) 2+(f
-yi(s)) Set to 2ds.

Thereafter, from step @ to step @, the coefficients of the cubic spline curve are calculated in the same manner as in the flowchart of FIG. 2.

However, step @ can be changed in the same way as in the flowchart of FIG.

Therefore, in this example, first, the length between adjacent teaching points is determined by linear approximation, a group of curve segments is determined using the parametric variables obtained based on this length, and then the determined curve The length between adjacent teaching points is determined again by curve approximation based on the segment group, and the curve segment group is determined again using the parametric variables obtained based on this length, which further improves the approximation accuracy. be able to.

When actually polishing a mold, one polishing trajectory is created in the s-z plane based on a preset polishing pattern, and the coordinates in the orthogonal coordinate system are determined based on this polishing trajectory. value (x, y.2) and normal direction (f-
x (s), f-)' (s)0) X (0.
By calculating 0.1) (where is transposed) and orienting the polishing tool in the normal direction, the polishing tool can always be applied perpendicular to the polishing surface, improving the polishing work efficiency. At the same time, it is possible to achieve a good finish.

Embodiment 3 Fig. 6 is a diagram schematically explaining the teaching operation when the rotating body has a polished curved surface.First, the rotation axis is taught, and the curve on the plane including the rotation axis is taught. It is only necessary to teach in the same manner as in the above embodiment, and teaching of curved surfaces can be easily accomplished.

However, in the case of this embodiment, it is only necessary to adopt a cylindrical coordinate system instead of the orthogonal coordinate system, and the cylindrical coordinate system (x, y,
The teaching point expressed by θ) may be mapped onto the S-θ plane.

Effects of the Invention> As described above, the present invention obtains the curve between adjacent teaching points as a parametric cubic spline curve, so the number of points to be taught can be significantly reduced, simplifying the teaching work. It has the unique advantage of being able to reduce the amount of data required and shorten the processing time.

In the second invention, the curve between adjacent teaching points is defined as both teaching points,
Furthermore, since it can be uniquely determined based on the conditions that the teaching point passes through the adjacent teaching point and the tangent vector at one teaching point is equal to the tangent vector of the adjacent curve, the number of points to be taught can be significantly reduced. This has the unique effect of simplifying the teaching work and shortening the processing time as less data is required.

The third invention has the unique effect that the approximation accuracy can be improved because the parametric variables are obtained again based on the curve obtained by linear approximation of the parametric variables, and the curve is obtained based on this parametric variable. play.

[Brief explanation of drawings]

FIG. 1 is a flowchart showing an embodiment of the brushing surface teaching method of the present invention, FIG. 2 is a flowchart explaining in detail an example of the process of step ■■ in the flowchart of FIG. 1, and FIG. 3 is a brushing surface teaching operation FIG. 4 is a flowchart showing another embodiment of the teaching method for brushing surfaces of the present invention, and FIG. 5 is a diagram illustrating '! A flowchart that explains in detail an example of the process of step ■■ in the flowchart of Figure J4, Figure 6 is a diagram that schematically explains the teaching operation when the rotating body is a polished curved surface, and Figure 7 shows the coefficients of the equation. A diagram showing curves that can be determined and curves that cannot be determined. (PI) (P2)-(Pn)
(Pn+1) (Pn+2)...Teaching point,

Claims (1)

[Claims] 1. A method of teaching a curved surface obtained by stretching a curved line on a plane in a predetermined direction as a polishing surface, the method teaching the stretched direction and also A method for teaching a polishing surface in a polishing device, characterized in that a plurality of points on a curve are taught on a perpendicular plane, and the plurality of teaching points on the plane are obtained as parameters of a parametric cubic spline curve. 2. The area between adjacent teaching points is one curve segment, and the coordinate value of the end point of this curve segment and the tangent vector at the end point are equal to the tangent vector at one end point of the adjacent curve segment, and the corresponding curve segment is Based on the condition that the curve segment passes through the other end point of the adjacent curve segment, the corresponding curve segment is determined as a parametric cubic spline curve, and the above-mentioned teaching point is obtained as a parameter of the determined parametric cubic spline curve. A method for teaching a polishing surface in a polishing device according to claim 1. 3. Based on the cubic spline curve group obtained by the method set forth in claim 2, the length between the end points of the teaching points is determined as the length on the curve, and each teaching point is determined based on the determined length. A method for teaching a polishing surface in a polishing device, in which a parametric variable is determined, and a coefficient of each curve segment is determined again based on the determined parameter.