JPS63300903A - System for speeding up interference decision making - Google Patents

Abstract

PURPOSE:To accurately decide interference between even very close bodies at a high speed by approximating a sensor and a work as rectangular prismatic sets, and projecting constitution planes of both on respective coordinate systems in three axial directions. CONSTITUTION:Sensors (41-48) as measurement heads and works (51-58) are approximates as rectangular prismatic sets as shown in a figure (d), and an orthogonal coordinate system O-xyz which include three independent sides of a rectangular prism as its axes is assumed for one or both of the sensors and works. The constitution planes of the opposite solid are projected on a two-dimensional plane including those axes as normals as shown in figures (a)-(c), and if there is even one combination of interferring planes whose projections are all put one over another, the interference between rectangular prisms is decided. Then plane confrontation is checked not by a combination of all planes of both rectangular prismatic bodies, but a combination of irreducible planes facing each other, thereby determining whether or not cubic bodies interfere with each other. If both rectangular prismatic bodies are parallel to each other, one rectangular prismatic body is rotated slightly around the three axes to limit the combination of the planes.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to verifying the suitability or inadequacy of a movement path of a measurement head created by off-line teaching in a three-dimensional measuring device, and in particular, to checking for surface-to-surface interference. When doing,
The present invention relates to a method for increasing the speed of interference determination suitable for limiting the number of combinations of surfaces to be subjected to interference determination.

[Conventional technology]

Conventionally, a teaching playback method has been used to teach the movement path of a measurement head in a three-dimensional measurement device. However, when measuring a large number of point sequences or shapes, it is necessary to input many teaching points, which requires a lot of time to teach each point. In order to solve this problem, it is effective to adopt a teaching method in which numerical values are input through offline teaching based on CAD data. but,
The measurement head movement data created by this offline teaching often contains errors such as entering a path that the measurement head cannot pass or a position where it will collide with a workpiece. Therefore, conventionally, when performing measurements using this data, it is necessary to operate the measurement head without setting the workpiece and visually verify the movement path of the measurement head, or to slow down the movement speed and make an emergency stop at a point where a collision is likely. It was necessary to confirm the travel route while preparing for the installation. Regarding interference checking methods for the purpose of pre-checking interference in this type of problem by simulation, for example, Japanese Patent Laid-Open Nos. 61-127007 and 58-
22690, and other methods of this type include Communications of the Association for Computing Machinery, 22-1 (1).
979) Pages 3 to 9 (Communic
ations of the ACM January
979 vol, 22 Na 1).

[Problem that the invention seeks to solve]

Now, in these conventional techniques, the object for interference determination is approximated by a square prism or a cylinder, and interference is determined using the distance between the centers of these.However, in the measuring device of the present invention,
It is necessary to bring the sensor close to the workpiece for measurement.
In the prior art, no consideration was given to the accuracy when determining such minute intervals, and there was a problem in that the rate of false determinations in close work was high. In addition, in other conventional technologies,
Interference is investigated by expressing the surfaces and sides of the object for collision detection mathematically and calculating their intersection points and lines, but if the shape of the object for collision judgment is complex or there are many measurement points. There was a problem in that the interference detection time was prolonged.

The purpose of the present invention is to accurately detect objects that are very close together on the same dirt floor.
Another object of the present invention is to provide an interference determination method that allows interference to be determined at high speed.

[Means for solving problems]

The above purpose is to describe the measurement head and the workpiece as a set of rectangular parallelepipeds, then create a Cartesian coordinate system with the three independent sides of the rectangular parallelepiped as axes for one or both, and have each of these axes as the normal. The constituent surfaces of the other solid are projected onto a two-dimensional plane, and then the overlap between each projected figure is determined to determine whether there is interference between the two solids, and the interference between the constituent surfaces at both positions is determined. When determining interference between solids, it is necessary to check surface-to-surface interference only between opposing surfaces as the minimum combination of surfaces, and if the rectangular parallelepipeds that are the object of interference determination are located parallel to each other. If this happens, rotate one side of the rectangular parallelepiped a little around the three axes to reduce the number of combinations of opposing surfaces, and check for interference between one surface and the resulting combination of opposing surfaces. This is achieved by determining interference between solids.

[Effect]

In this case, the sensor and workpiece are approximated by a set of rectangular parallelepipeds,
By projecting both constituent planes one by one in the three-axis directions for each coordinate system, it was found that the constituent planes do not interfere with each other unless the projected figures in at least one axis overlap. do.

In addition, the surface-to-surface check is not performed on the combination of the entire surface of the sensor-side rectangular parallelepiped and the work-side rectangular parallelepiped, but is performed only on the surfaces facing each other to determine interference between solids. The number of times decreased from 36 times to 18 times in one space.

Computation time can be reduced. In addition, in the case of rectangular parallelepipeds that are parallel to each other, there are five opposing surfaces (including perpendicular surfaces) to the sensor surface, so 30 face-to-face checks are required between the two solids. However, by slightly rotating one solid around the three axes and checking the original parallel position between the opposing surfaces, only 18 checks are required, reducing calculation time. can.

〔Example〕

Hereinafter, one embodiment of the present invention will be described in detail using the drawings.

FIG. 6 is a system configuration diagram showing an embodiment in which the interference check method of the present invention is applied to a three-dimensional workpiece shape measuring machine.

In order to teach measurement points, the data input device 22 is used to input the shape of the workpiece, the moving position and angle of the sensor. This data is used to simulate the movement of the re-sensor and determine interference, using an interference determination table @22, and an interference determination result display device 23 that displays the determination results and informs the operator.
An interference determination system is constituted by a data modification device 24 that modifies data in order to avoid interference when interference occurs.

FIG. 1(d) shows a case where the interference check method of the present invention is applied to a three-dimensional workpiece shape measuring machine.

- It is a perspective view showing the positional relationship between the sensor approximation rectangular parallelepiped 40 and the workpiece approximation rectangular parallelepiped 50 at the measurement position.

Figure 1 (a), (b), and (c) are X-z and y, respectively.
It is a diagram in which the workpiece approximation rectangular parallelepiped and the sensor approximation rectangular parallelepiped at the position of FIG. 1(d) are projected onto the -z, xz plane.

The interference checking method in the present invention is as follows: (1) approximating the workpiece and the sensor with a set of rectangular parallelepipeds, (2) taking out the constituent surfaces of the workpiece approximating rectangular parallelepiped and the constituent surfaces of the sensor approximating rectangular parallelepiped one by one, and converting each surface to −2, Project onto a plane,
■If the projected figures of the two rectangular parallelepiped planes all overlap on the three projection planes, it is determined that there is a possibility of interference between the surfaces, and ■If there is interference between the surfaces, it is determined that there is interference between the rectangular parallelepipeds. It is something.

The present invention is a method for reducing the number of face-to-face interference checks using this interference check method, and an embodiment thereof will be described in detail below.

First, as shown in FIG. 1(d), a sensor and a workpiece are approximated by a set of rectangular parallelepipeds, and one sensor-approximating rectangular parallelepiped and one workpiece-approximating rectangular parallelepiped are extracted.

Thereafter, the sensor approximation rectangular parallelepiped is moved to the sensor drive position. At this time, the near positions of the workpiece and the sensor, and the coordinates of each vertex of the rectangular parallelepiped are determined by the coordinate system 0-x whose origin is the reference point of the rectangular parallelepiped approximating the workpiece (vertex 51 is the reference point in FIG. 1(d)).
Describe it for yz and save it as data.

On the other hand, each constituent surface of the sensor body and the workpiece approximation rectangular parallelepiped is described as a sequence of vertex numbers of each rectangular parallelepiped.

For example, as shown in FIG. 1(d), 41 to 48 are placed at the vertices of the rectangular parallelepiped approximating the sensor, and 51 to 5 are placed at the vertices of the rectangular parallelepiped approximating the workpiece.
8, the constituent faces of the work approximating rectangular parallelepiped and the constituent faces of the sensor approximating rectangular parallelepiped can be described by columns of vertex numbers, as shown in Tables 1 and 2.

Table 1 Table 2 For example, the first surface of the workpiece approximation rectangular parallelepiped is represented by a column of vertex numbers 5152535451 as in the first row of Table 1. This order of vertex numbers is obtained by arranging the vertex numbers in counterclockwise order when looking at the surface of the approximate rectangular parallelepiped from the outside. By defining it in this way, when calculating the normal vector I of the surface later, it can be calculated by taking the cross product of two arbitrary consecutive sides.

In the interference check method of the present invention, a face-to-face interference check is performed between the work surface and the sensor surface. At this time, take out one surface from the work surface and one from the sensor surface, and based on the reference coordinate system 0-xyz on the work side, each surface is
Project onto the −z plane (c), the xy plane (a), and the yz plane (b). If even one of the projected figures does not overlap among the projections onto these three surfaces, it can be determined that there is no interference between the surfaces.

In this method, the six sides of the workpiece are compared to the six sides of the sensor.
We project each object three times and examine the overlap of the shapes, so
It was necessary to check a total of 108 projection planes: maximum right plane x six planes x three projections. However, in order to determine whether rectangular parallelepipeds interfere with each other, it is not necessary to check all combinations of surfaces. If a combination is found in the face-to-face interference check that also interferes with the negative pair, the remaining combinations can be omitted. Therefore, a method is used that starts the interference check from the surface with a higher possibility of interference.

When two rectangular parallelepipeds approach and touch, causing interference,
The surfaces that initially touch each other are those that face each other. Therefore, the surfaces to be checked for surface-to-surface interference are limited to surfaces that face each other. This limitation is subject to the following three conditions.

■Assume that the two rectangular parallelepipeds do not interfere in their initial positions.

■Check for interference at points that are moved along the movement path at certain distance intervals from the initial position. ■The certain distance interval described in the previous section shall be less than half the length of the shortest diagonal of the six rectangular diagonals that make up the two rectangular parallelepipeds.

The facing faces are defined below. First, the surface normal vector of the sensor surface is N5(xs, ys, zs
), → the surface normal vector of the work surface is N w (xw, yw,
zw), the inner product A of these two vectors is
== I Nsl l Nwl cos 0-
It is expressed as (2). When this inner product A satisfies the following relationship, the two surfaces are said to face each other.

As2...(3) In other words, in equation (2), if the relationship is 90''≦θ≦270@...(4), the two surfaces face each other, and -90''<0<90' - In the case of (5), assume that the two surfaces are back to back.

- For example, if the sensor approximation rectangular parallelepiped and the workpiece rectangular parallelepiped are located at the positions shown in FIG. 1(d), and the surface numbers of each rectangular parallelepiped are defined as shown in Tables 1 and 2, Table 3 summarizes the combinations of surfaces to be checked.

Table 3 In Table 3, this is a case where the faces marked with an O face each other and need to be checked. The combinations of faces marked - are those in which one face is back-to-back, and this check can be omitted.

In this way, by checking only the faces that face each other, it is possible to determine whether there is interference between the rectangular parallelepipeds,
With this method, when the rectangular parallelepipeds do not interfere with each other, the number of face-to-face interference checks can be halved from 36 times to 18 times, and the calculation time can be reduced.

Next, an example will be given to explain the interference checking method after the combination of surfaces that requires a one-surface, two-face interference check is known.

In Figure 1(d), the fourth side of the sensor surface (42464743
42) and the fifth surface (5357585453) of the work surface are surfaces to be checked for interference.

The x-y plane projected figure of the sensor surface is the mouth 424 in FIG. 1(a).
64743, the projected figure on the work surface is mouth 53575854
The two shapes overlap on this projection plane, but on the next projection plane xz plane, the mouths 42464743 and -5453
Since they do not overlap, if there is no overlap even on the -projection plane, it is determined that the surfaces do not interfere with each other, and the process proceeds to check the next combination of surfaces.

If there is interference between rectangular parallelepipeds, the judgment is made by finding one face that has interference between faces, so the judgment time will be affected by the order of interference checks for the five faces, but in general, the Since there are many cases where two faces interfere with each other, simulations have confirmed that checking for interference is faster when checking only the faces that face each other.

Next, as another example, when the sensor approximation rectangular parallelepiped and the workpiece approximation rectangular parallelepiped are located at the positions shown in FIG. 2(d) (when the positional relationship between the two rectangular parallelepipeds has only a translation component) The interference check surface reduction method will be explained. Table 4 shows a table of combinations of surfaces to be checked for interference in the positional relationship shown in FIG. 2(d).

Table 4 Including the combination of surfaces marked with Δ for which the inner product is O, the number of combinations of facing surfaces is 06 and Δ24, totaling 30.

The surface that is actually interfering is indicated by an X mark, and since this surface is the surface to be checked, it is possible to accurately determine the interference of the rectangular parallelepiped, but if there is no interference, it is necessary to check 30 times, which takes time. Therefore, as shown in Figure 3(d), one side (
In this case, the rectangular parallelepiped (sensor side) is set at a small angle Δ around the x, y, and z axes of the coordinate system with the center of the rectangular parallelepiped as the origin.
Rotate by θ, Δψ, and Δφ. Then, by calculating the inner product of the surface normal vector of the sensor surface and the surface normal vector of the workpiece surface and selecting the surface to be checked for interference, the combinations shown in Table 5 are obtained, and the 30 pairs in Table 4 are The number of target surfaces can be reduced to 18 pairs.

Table 5 Therefore, for these 18 pairs, interference between rectangular parallelepipeds is checked by projecting each surface using the original vertex coordinates shown in FIG. 2(d) and checking for overlap.

In this way, when checking for interference between rectangular parallelepipeds that are parallel to each other, one side of the rectangular parallelepiped is rotated by a small angle, and the opposing surfaces are projected at their original parallel positions to check for interference between the surfaces. If there is no interference, then 18/3
The calculation time can be reduced to 0, and even if there is interference, the presence of interference can be determined quickly.

Further, as another example, FIG. 4 shows an xy plane projection view and a yz plane projection view when a cylinder is approximated by a rectangular parallelepiped. In the case of Fig. 4(b), each side of the rectangular parallelepiped that approximates a cylinder is parallel or perpendicular to each side of the rectangular parallelepiped that approximates the workpiece, and the two rectangular parallelepipeds are in a positional relationship that has only a translational component. . In this case, the number of surfaces to be checked is 30, as in the case shown in Table 4, and it is necessary to reduce the number of surfaces to be checked by performing slight rotational transformation around the x, y, and z axes.

However, if the workpiece is approximated in advance using a rectangular parallelepiped whose sides are not parallel to the axis of the coordinate system (as shown in FIG. 5, for example), the number of surfaces to be checked can be reduced to 24.

In this way, when approximating an object such as a cylinder with a rectangular parallelepiped, by approximating it in advance with a rectangular parallelepiped whose sides are not parallel to the sides of the other rectangular parallelepiped to be checked for interference,
This has the effect of reducing the number of surfaces to be checked for interference and shortening the calculation time for coordinate transformation and the calculation time for interference check.

Table 6 [Effects of the Invention] According to the present invention, the number of times of interference determination between surfaces required to determine interference between rectangular parallelepipeds is reduced to a maximum of 1/2 when there is no interference, and Even if there is interference,
Interference can be determined based on aspects with a high possibility of interference, and determination results can be derived quickly and accurately regardless of whether there is interference or not.

[Brief explanation of the drawing]

FIG. 1 is a perspective view showing the position of an approximate rectangular parallelepiped in one embodiment of the present invention, FIG. 2 is a perspective view showing the position of an approximate rectangular parallelepiped in another embodiment, and FIG. 3 is an approximate view after slight rotation. FIGS. 4 and 5 are perspective views showing the positions of the rectangular parallelepipeds, projection views showing the positions of approximate rectangular parallelepipeds in other embodiments, and FIG. 6 is a system configuration diagram. 4o... Sensor approximation rectangular parallelepiped, 50... Work approximation rectangular parallelepiped, 41-48... sensor vertex number, 51-58.
...Work vertex number.

Claims (1)

[Claims] 1. In an interference check method in which the presence or absence of interference between two rectangular parallelepipeds existing in a space is determined based on the presence or absence of interference between the surfaces constituting the respective rectangular parallelepipeds, among the combinations of surfaces: , a method for speeding up interference determination, characterized in that the number of combinations of surface-to-surface interference checks is reduced by the value of the inner product of the surface normal vectors of the two surfaces. 2. In claim 1, among surface-to-surface combinations, surface-to-surface interference check is performed for only combinations of surfaces in which the value of the inner product of the outward surface normal vectors of two surfaces is 0 or less. A method for increasing the speed of interference determination, characterized in that the presence or absence of interference between rectangular parallelepipeds is determined based on the results. 3. Claims 1 or 2 are characterized in that, while checking for interference between surfaces, it is determined that there is interference between rectangular parallelepipeds by checking the surface that is first determined to have interference. A method for speeding up interference detection. 4. Claim 1 or 2 is characterized in that it is determined that there is no interference between rectangular parallelepipeds when it is determined that there is no interference in all of the reduced combinations of face-to-face interference checks. A method for speeding up interference detection. 5. A method for speeding up interference determination, characterized in that both of the speeding methods set forth in claim 3 or 4 are used. 6. In claim 1, when the sides constituting two rectangular parallelepipeds are parallel or at right angles, one of the rectangular parallelepipeds is defined as having the sides that are parallel or at right angles, A method for speeding up interference detection characterized by reducing the number of combinations of surface-to-surface interference checks by performing a slight rotation so that the two surfaces have a non-parallel relationship, and then using an inner product of the surface normal vectors of the two surfaces. . 7. In claim 6, a surface-to-surface interference check is performed for only combinations of surfaces in which the inner product of the outward normal vectors of the two surfaces is 0 or less, and based on the results, interference between rectangular parallelepipeds is determined. A method for speeding up interference determination, characterized by determining the presence or absence of. 8. In claim 6 or 7, after limiting the surfaces to be subjected to interference determination by the surface normals of the slightly rotated rectangular parallelepiped, the corresponding surfaces of the original rectangular parallelepiped before being slightly rotated;
A method for increasing the speed of interference determination, which is characterized by performing a surface-to-surface interference check with a corresponding surface of another rectangular parallelepiped. 9. In an interference check method in which the presence or absence of interference between two objects existing in space is determined by approximating the two objects with rectangular parallelepipeds and then determining the presence or absence of interference between the surfaces that make up each rectangular parallelepiped, the two approximate rectangular parallelepipeds A method for speeding up interference determination, characterized by configuring an approximate rectangular parallelepiped such that its sides are less likely to be perpendicular or parallel to each other, thereby reducing the number of surfaces to be subjected to subsequent surface-to-surface interference determination.