JPH03208554A - Designation of polishing range in polishing device - Google Patents

Abstract

PURPOSE:To designate a polishing range with a high accuracy in less teaching points, by finding the point located on a curved face closest to the teaching point for designating polishing range as the point located on a plane and making the diagram regulated based on the teaching point for designating the polishing range as the polishing range. CONSTITUTION:In the case of designating the polishing range located on the curved face that the curved line of the plane above is stretched in the specific direction, a stretched direction is teached in advance, plural points P1, P2 - Pn+2 located on the curved face on the plane vertical to the stretched direction are teached and the space between adjacent teaching points located on the plane is obtained as the curved line segments S1, S - Sn - 1 expressed by using parameters s1, s2 - sn. Moreover, each teaching points are obtained as the point on the plane determined based on the parameter and coordinate in the stretching direction to teach the curved face. Further, the point on the curved face closest to the teaching point for designating the polishing range is found as the point on the plane and the diagram regulated based on the teaching point for designating all of the polishing range is taken as the polishing range.

Description

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

Prior Art and Problems to be Solved by the Invention When polishing a mold using an industrial robot, it is necessary to accurately specify the polishing range because a good finish is required. In order to accurately specify the polishing range, it is necessary to accurately obtain the teaching point on the polishing surface.

Conventionally, when specifying a polishing range on an arbitrary three-dimensional curved surface, the coordinate values of the corresponding point are determined by touching the desired position of the polishing surface using a touch probe as shown in Figure 6. I'm trying to get it. but,
The teaching point obtained by the touch probe is the point indicated by P in the figure, and the contact position with the polished surface is the point indicated by P'' in the figure, and since the direction of the contact point is unknown, there is no way It is not possible to accurately teach the brushing range.

In addition, when a curved surface obtained by stretching a curved line on a plane in a predetermined direction is used as a polishing surface, the above-mentioned curve is obtained as an equation using a parametric variable, and the teaching point on the curved surface is determined based on the parametric variable and the coordinates in the stretching direction. The coordinates and normal direction on the polishing surface can be obtained by projecting it onto a plane, interpolating between the projected teaching points on the plane, and applying it to the corresponding equation. However, since the point taught using the touch probe is not a point on a curved surface, there is no guarantee that it will be projected as an accurate parametric variable when projected onto a plane determined based on the parametric variable and the coordinates in the stretching direction. Therefore, it is generally projected as a parameter with a considerable error, and the final brushing range will include a considerable area error. As a result, it becomes impossible to accurately specify the polishing range, which in turn makes it impossible to achieve a good finish.

Purpose of the invention> This invention was made in view of the above problems,
To provide a novel polishing range specifying method capable of significantly improving polishing range specification accuracy when specifying a polishing range on a polishing surface having a shape of a flat curve stretched in a predetermined direction.

<Means for Solving the Three Problems> In order to achieve the above object, the method of specifying the polishing range in the polishing device of the present invention is a method of specifying the polishing range on a curved surface obtained by stretching a curved line on a plane in a predetermined direction. In addition to teaching the elongated direction, multiple points on the curved surface are taught on a plane perpendicular to the elongated direction, and a parameter is set between adjacent teaching points on the middle surface. and obtain the curve segment represented using
The curved surface is taught by obtaining each teaching point as a point on a plane determined based on the parametric variables and the coordinates in the stretching direction, and the point for specifying the polishing area is taught, and the point on the curved surface closest to each teaching point is taught. This is a method in which the points on the plane are determined, and all the figures defined based on the teaching points for specifying the polishing area are set as the polishing area. and,
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., and finishing the surface of models.

However, find the value of the above function at the point where the derivative of the function of the square of the distance between the teaching point and a point on the curve is 0 and at both end points of the curve segment, and teach the parametric variable that minimizes the value of the function. It is preferable to use a method in which a parameter corresponds to a point.

In these cases, the polishing surface may be a curved surface obtained by stretching a curve on a plane in a direction perpendicular to the plane, or a curve on a plane in the direction of rotation about a straight line on the plane. It may be a curved surface stretched to
In these cases, the curve may be a cubic spline curve, a quadratic curve, or a quartic or higher order curve.

<Operation> With the above brushing range specification method, when specifying the brushing range on a curved surface obtained by stretching a curved line on a plane in a predetermined direction, the stretched direction is taught in advance, and the stretched A plurality of points on a curved surface are taught on a plane perpendicular to the direction in which the curve is spread, and the distance between adjacent teaching points on the plane is obtained as a curve segment expressed using a parametric variable, and each teaching point is A curved surface is taught by obtaining it as a point on a plane determined based on variables and coordinates in the stretching direction. Then, it is sufficient to teach a point on the curved surface for specifying the brushing range using a touch probe or the like, and instead of the taught point itself, the point on the curved surface closest to the taught point is determined as the point on the plane. All the figures defined based on the teaching points for specifying the polishing range can be set as the polishing range. Therefore, when performing polishing work afterwards, the three-dimensional coordinates can be obtained from the plane coordinates of the point belonging to the polishing range on the above-mentioned plane based on the equation of the curved segment to which the point belongs, so the polishing tool By controlling the position based on the obtained three-dimensional coordinates, etc., it is possible to achieve good mold polishing work.

Then, find the value of the above function at the point where the derivative of the function of the square of the distance between the teaching point and a point on the curve becomes O and at both end points of the curve segment, and teach the parameter that minimizes the value of the function. If the parameter is a parameter corresponding to a point, the function of the square of the distance can be easily obtained, and the derivative of this function can also be easily obtained, so the parameter can be changed sequentially. By doing so, the value of the derivative is found, and by linear interpolation or the like between the points where the sign of the derivative is reversed, the number of mediates at the point where the derivative becomes 0 can be found as a more accurate approximate value. Since the parametric variable corresponding to the minimum value of the function value at this point and the function values at both end points of the curve segment is set as the teaching point, the teaching point for specifying the brushing range is the corresponding parametric variable. It can be obtained as a value.

In these cases, if the curved surface to be taught as a polishing surface is a curved surface obtained by stretching a curve 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 direction of stretching. It is sufficient to map onto a plane determined by the coordinates, 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. The curve may be a cubic spline curve, a quadratic curve, or a quartic or higher curve.

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 brushing surface teaching method of the present invention, in which teaching for teaching the stretching direction is performed on an orthogonal coordinate system in step (3),
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 ■. Find the equation of each cubic spline curve of the curve expressed as a set of parametric cubic spline curves, and in step (2) map the polished surface onto the surface determined by the parametric variables of the above equation and the coordinates in the stretching direction. do. Then, in step ■, the point to specify the brushing range is taught using a touch probe, and in step ■, the parameter corresponding to the point on the curved surface closest to the teaching point is determined, and in step ■, the specification of the brushing range is completed. It is determined whether or not the process has been completed, and if it has not been completed, the process from step (2) onwards is repeated again.

Conversely, if it is determined in step ■ that the specification of the polishing range has been completed, the polishing range of the mapped polishing surface is interpolated in step ■, and the interpolation result and the equation of the corresponding curve are calculated in step [phase]. The coordinate values and normal direction on the orthogonal coordinate system are calculated based on . However, step [phase] 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 Pi obtained in step ■ is n, and This corresponds to the case where the number of curve segments St between points is n-1. Note that the value of the parameter at each teaching point Pi is s
It is set as i.

In step (■), initialization is made to i-0, and s
I−ΣPjPj+1 (however, i # 2 ~ n −1)
Set to .

Then, in step @, a curve segment Sl having the teaching points Pl and P2 as end points 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 P1 is 0, Equation 3 y=Ay s + By s2 + Cy s + Dyx - A
x s +Bx s2+Cx S+D! 3 by calculating all coefficients of the curve segment Sl
seek. That is, for each coordinate, the teaching point P l. P
2. Since three conditional expressions are obtained by passing through P3, and one conditional expression is obtained by the curvature at the teaching point P1 being 0, the coefficients of the above equation can be uniquely determined.

Thereafter, i is set to 1 in step (2), and i is incremented by 1 in step (2).

Then, in step ■, the teaching points Pi, Pil1
Find a curve segment S1 whose end point is .

Specifically, the curve segment Si is at the teaching point Pi. P1+
1 as well as the teaching point Pj+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 S i-1, the equation y=Ay s + By
s2+Cy s+Dy3 X-AX S +Bx s2+Cx S+D! 8 by calculating all the coefficients of the curve segment}Sj
seek.

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 there is no next curve segment, the coefficients of the equation cannot be uniquely determined even if step
The equation for n-2 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 is to be adopted as is, the teaching point P n-1 is set so that the error is as small as possible. Just set it.

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

In the same figure (A), P l, P2. - P n,
P n+1. P n+2 is the teaching point, and the coordinate values (xi.yi, zi) in the orthogonal coordinate system (however, i-1 to n+2
) is taught. The parameter S corresponding to each teaching point P1 is represented by 51, and the teaching point Pi. The curve segment S defined by Pi+1 is represented by St.

In addition, P 1, P 2, ... Pn are teaching points for teaching curves on the instep perpendicular to the stretching direction (
(Refer to FIG. 3B), Pn+L and Pn+2 are teaching points for teaching the stretching direction.

Here, the parameter S is si−ΣPjPj+1 (however,
sl-0), the above curved surface is s-z
It is represented as a rectangle on the surface (see same & (C)). That is, points on the curved surface can be easily calculated by compensating the parameter S and the two coordinate values.

In addition, since the parametric cubic spline curve is uniquely determined as described above, the curve segment S1 is 3 y=fyi(s)-Ayis +Byis2+Cy1
s+Dy1 xmfxl(s)=Axls+Bx1s2+Cxi
As shown in (D) and (E) of the same figure, once the value of the parameter is 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.

``ii Figure 4 is a flowchart showing in detail the operation of step ■ in the flowchart of Figure 1. In step ■, i is initialized to 0, and in step @, both ends of the curve segment S1 (parameters are respectively s i.s i
l1) and teaching point p<xp. The function of the square of the distance from yp> fi (s) = (Ax1s” 10Bx+s +
Cxis +Dx4-xp ) 2+ (Ayis3.
2. 2 +By+s +Cyis+Dyi-yp)2(D4i
1 wo + n respectively fi (si), fi (sil1)
Calculated as Then, in step (2), the curve segment S1 is divided into minute sections, and the parametric variable sij-si+n△S at each dividing point (where n is sij<
s (a natural number within the range of i+1), the derivative f-i (sjj) -2 of the above function fj (s)
(AXIS +Bxis2+Cxis +Dxi-
Xp ) (3A, 3 xis” +2Bxjs 1Cxi) +2 (Ayj
s” +Byi. 9 s +Cyis +Dyi Yp) (3Ayi
s2+2B2 yjs+cyi), and in step (2) it is determined whether there is an interval in which the sign of the derivative fi(sij) changes. If it is determined in step ■ that there is an interval in which the sign of the derivative changes, step ■
In step 2, calculate the point sri where the value of the derivative becomes O by linearly approximating the interval in which the sign of the derivative changes, and in step 2, calculate the function value fi (srD) at this point sri,
In step ■, the above function values fj (s1), fl
(sil1), the minimum value of fi(sr1) is extracted as f■1. Conversely, if it is determined in step [Yes] that there is no section in which the sign changes, the above function values fi (si), f1 are determined in step ■.
The minimum value of (s1+1) is extracted as lsi. Then, after the process in step ■ or the process in step @ is performed, in step ■, the value of i is increased by 1, and in step [phase], it is determined whether or not i is equal to n, and if they are equal. For example, perform the process in step @ again. Conversely, if i is determined to be equal to n in step [phase], fmi (however, i
-1 to n-1) is extracted, and the parameter corresponding to the minimum value is set as the parameter corresponding to the teaching point on the curved surface.

Therefore, by performing the above series of processes every time a point is taught by the touch probe to specify the polishing range, the parameter corresponding to the point closest to the taught point on the polishing surface is obtained, and the obtained parameter is The polishing range can be projected as a polygon on 82 planes based on all the parameters determined.

In addition, as a method of teaching the polished surface, the length between each teaching point is calculated based on each cubic spline curve obtained based on the flowchart in Fig. 2, and the parametric variable corresponding to each teaching point is calculated. It is possible to adopt a method of re-determining the equation of each cubic spline curve of a curve expressed as a set of parametric cubic spline curves based on the obtained parametric variables, and approximating a group of curve segments. Accuracy can be further improved.

When actually polishing molds, etc.,
A polishing trajectory is generated within a polygon that specifies the polishing range on the s-z plane based on a preset polishing pattern, and based on this polishing trajectory, coordinate values (x
．． y, z) and normal direction (f X (s),
f y (s), 0)'X(0,0.1) 1
(However, 1 is transposed) and by orienting the polishing tool in the normal direction, the polishing tool can always be applied perpendicularly to the polishing surface, improving the polishing work efficiency. , a good finish can be achieved.

Embodiment 2> Fig. 5 is a diagram schematically explaining the teaching operation when the rotating body has a polished curved surface. First, the rotation axis is taught, and then 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, and furthermore, the polishing range can be specified easily and with high precision.

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, θ
) may be mapped onto the S-θ plane.

Note that the present invention is not limited to the above-mentioned embodiments, and for example, instead of a curved surface obtained by extending a cubic spline curve in a predetermined direction, a curved surface obtained by extending a quadratic curve or a curve of quartic or higher order in a predetermined direction may be used. Of course, this can be applied to the specification of the brushing range described above.

Effects of the Invention> As described above, the present invention obtains curves between adjacent teaching points as curve segments expressed using parametric variables, thereby defining the polished surface using parametric variables and coordinates in the stretching direction. If a rectangle is obtained as a rectangle on the surface and a point for specifying the polishing area is taught, a parametric variable corresponding to the closest point on the polishing surface is obtained and a polygon on the surface is obtained. This has the unique effect of being able to specify the polishing range with high precision with a small number of teaching points.

The second invention is based on the distance 2 at the end point of the curve segment.
The minimum value is obtained from the values of the above function at the point where the value of the multiplication function and the value of the derivative of this function are O, and the parameter corresponding to the minimum value is obtained, so the nearest value on the polished surface is obtained. The parameter variable corresponding to the point can be obtained in lIfl lli, and the polishing range can be specified with high accuracy with a small number of teaching points, which is a particularly advantageous effect.

[Brief explanation of drawings]

Fig. 41 is a flowchart showing an embodiment of the method for teaching the brushing surface 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 shows the operation of teaching the brushing surface. FIG. 4 is a flowchart that explains in detail another example of the process of step ① in the flowchart of FIG. 1, and FIG. FIG. 6 is a diagram showing a teaching state using a touch probe. (PI) (P2) - (Pn)
(Pn+1) (Pn+2)...Teaching point,

Claims (1)

[Claims] 1. A method for specifying a polishing range on a curved surface obtained by stretching a curved line on a plane in a predetermined direction. Teach multiple points on a curved surface on a perpendicular plane, obtain curve segments between adjacent teaching points on the plane expressed using parametric variables, and convert each teaching point into parametric variables and coordinates in the stretching direction. The curved surface is taught by obtaining the point on the plane determined based on the teaching point, and the point on the curved surface closest to the teaching point for specifying the polishing area is determined as the point on the plane, and all points for specifying the polishing area are obtained. A method for specifying a polishing area in a polishing device, characterized in that the polishing area is a figure defined based on teaching points. 2. Find the value of the above function at the point where the derivative of the function of the square of the distance between the teaching point and a point on the curve becomes 0 and at both end points of the curve segment, and teach the parameter that minimizes the value of the function. Claim 1 above, where the parameter is a parameter corresponding to a point.
How to specify the polishing area in the polishing device described in Section 1.