JP3663318B2 - Method and apparatus for correcting motion error of parallel mechanism - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a motion error correction method and apparatus for improving motion accuracy in a parallel mechanism in which closed link mechanisms are connected in parallel.
[0002]
[Prior art]
In recent years, in the field of industrial robots and machine tools, research on parallel mechanisms in which closed link mechanisms are connected in parallel has been actively conducted. Compared to the conventional serial mechanisms such as Cartesian coordinate machine tools and arm type robots with a stacked structure, it is not a beam structure but a rigid truss structure, the mass of each axis does not accumulate, the moving speed is high, each Axis positioning error does not accumulate and accuracy can be averaged, and Abbe's principle, which is the basis of precision machinery (measurement points on a three-dimensional coordinate measuring machine as an extension line of a length measurement unit (scale) This is because the measurement error can be reduced by being less susceptible to the influence of the posture change, and it is advantageous in terms of rigidity, accuracy, motion speed, and the like.
[0003]
[Problems to be solved by the invention]
In such a parallel mechanism, the rotational accuracy of the joint (pair) that connects the base and the stage in parallel by the closed link mechanism strongly affects the motion accuracy of the mechanism. That is, in order to increase the movement accuracy of the mechanism, it is necessary to improve the rotation accuracy of each joint. As shown in FIG. 1 , the strut 2 that is an actuator has a built-in length measuring device (scale, etc.) for measuring the length. Therefore, if the joint 3 has no rotation error, the position and posture of the stage 4 are struts. It is uniquely determined by the length. However, in reality, the joint 3 generates a rotation error due to its shape error or deformation due to an external force, which causes a motion error of the stage 4. Therefore, in order to increase the motion accuracy of the stage 4, it is necessary to use the joint 3 with higher accuracy and rigidity, or measure the rotation error of the joint 3 and correct the motion error of the stage 4 using the value. . The former are difficult to cost and technical realization, the latter determine the rotation error of the joint 3, generally, to measure the three directions of rotational error orthogonal per spherical joints 3 as shown in FIG. 10 Three displacement sensors were required, and as a result, a huge number of displacement sensors were required for the entire mechanism. In a general 6-degree-of-freedom parallel mechanism, 12 spherical joints are used in the whole mechanism, and the number of sensors reaches 36 at least.
[0004]
Therefore, in the present invention, the knowledge that the component of the joint rotation error only in the strut direction, which is the actuator, strongly influences the motion error of the mechanism, and the other component, that is, the component in the right direction of the strut has no influence. Solves the problems of the conventional parallel mechanism, and provides a motion error correction method and apparatus for the parallel mechanism that can accurately correct the rotation error of the joint even with a small number of displacement sensors and improve the motion accuracy of the mechanism. The purpose is to do.
[0005]
[Means for Solving the Problems]
Therefore, the present invention corrects the movement error of the link mechanism due to the rotation error of the joint (pair) in the parallel mechanism in which the closed link mechanisms having at least three degrees of freedom are connected in parallel. Is measured, an error in the driving direction of the actuator constituting the link mechanism is measured to correct the movement error of the link mechanism.
According to another aspect of the present invention, there is provided a parallel mechanism for measuring a rotation error of a joint composed of a base and a stage in which closed link mechanisms having at least three degrees of freedom are connected in parallel and correcting a movement error of the link mechanism. Further, a displacement sensor for measuring an error in the driving direction of the actuator is provided to correct a motion error of the link mechanism.
The present invention is characterized in that the actuator is composed of a strut incorporating a length measuring means, and these are means for solving the problems.
[0006]
Embodiment
A parallel mechanism motion error correction method and apparatus according to a first embodiment of the present invention will be described below with reference to FIGS.
1A is an overall perspective view of an apparatus that realizes a motion error correction method for a parallel mechanism according to the present invention, FIG. 1B is an enlarged sectional view of a connecting portion between a strut that is an actuator and a joint, and FIG. FIG. 3 is a relationship diagram between the probe length and the determinant value, and FIG. 4 is a relationship diagram between the probe length and the singular value.
The present invention has obtained the knowledge that the component of the joint rotation error only in the strut direction, which is the actuator, strongly influences the motion error of the mechanism, and the other component, that is, the component in the right angle direction of the strut does not affect, In order to solve the problem of the parallel mechanism, the rotational error of the joint is accurately corrected even with a small number of displacement sensors, and the movement accuracy of the mechanism is improved.
[0007]
In a series of studies from which the present invention was derived, a new three-dimensional coordinate measuring instrument (hereinafter referred to as a parallel CMM) using a parallel mechanism has been proposed. The conventional Cartesian CMM does not satisfy Abbe's principle. That is, the measurement point is not on the extension line of the length measurement unit (scale), and the measurement value is easily affected by the change in the posture of the mechanism, causing a measurement error. In the parallel CMM, the measurement points can be arranged near the extension line of the scale, and the present inventors have experimentally found that the variation in the measured value is the smallest in such an arrangement.
This is similar to Abbe's principle in length measuring instruments, even if the measurement point has a motion error due to backlash or rotation error of the even number (joint), the component in the scale direction becomes a secondary error, This is considered to be because the influence on the measured value is minimized.
In the following, error analysis using micro-kinematics will be described with reference to FIGS. 2 to 4 in order to investigate the effect of joint rotation error on the motion error of the mechanism in the parallel mechanism that has led to the present invention.
[0008]
<Analysis method>
First, as shown in FIG. 2, the rotational error of the rotary joints 3-4, 3-5, 3-6 on the stage 4 on which the probe tip 8 is installed is expressed as a radial component δrs = (δrs _1, δrs _2, δrs ₃ ) ^T ( ^T represents a turning value), circumferential direction component δθs = (δθs _1, δθs _2, δθs ₃ ) ^T , Z direction component δhs = (δhs _1, δhs _2, δhs ₃ ) ^T , scale ( Strut 2) Decomposed into directional components δls = (δls _1, δls _2, δls ₃ ) ^T and components around Z axis δγs = (δγs _1, δγs _2, δγs ₃ ) ^T , and spherical joint 3-1 on the base 1 surface 3-2 and 3-3, the rotational direction component δrB = (δrB _1, δrB _2, δrB ₃ ) ^T , the scale direction component δlB = (δlB _1, δlB _2, δlB ₃ ) ^T and the circumferential direction The component δθB = (δθB _1, δθB _2, δθB ₃ ) ^T. At this time, for example, the relationship between the minute displacement δrs and the minute displacement δ _x = (δ _x , δ _y , δ _z ) ^T of the probe 8 is
δ _x = Jrs δrs (1)
It is represented by Here, Jrs is a 3 × 3 Jacobian matrix, and the forward kinematics of the mechanism (Takaaki Oiwa “3D coordinate measuring machine using parallel mechanism-basic principle and kinematics”, Journal of Precision Engineering, 64.12 (1998) 1791).
[0009]
The Jacobian matrix indicates the relationship between the rotation error of the joint 3 and the movement error of the probe 8. Therefore, by obtaining the singular value of this matrix and the value detJrs of the determinant, it becomes possible to examine the magnitude of the influence of the rotation error of the joint 3 on the measurement accuracy. Similarly, the influence of the rotational error component in the other direction of the joint 3 can also be obtained from the Jacobian matrix Jθs, Jhs, Jls, Jγs, JrB, JlB and JθB. In the calculation, the radius position of the spherical joint 3 on the base 1 is rB = 550, the radius rs = 100 of the stage 4, and the coordinate position of the tip of the probe 8 is an isotropic point (0, 0, 388) where the resolution in the XYZ directions becomes equal. .9 (= 0.707 rB)).
[0010]
<Analysis Result> First, as shown in FIG. 3, the relationship between the rotation error components and the length ls of the probe 8 of the Jacobian matrix was obtained. When the influence of the errors δγs, δθs, δθB other than the rotational errors δrs, δhs, δrB in the translation direction is ls = 70.7 (= 0.707rs), that is, the tip of the probe 8 is positioned on the extension line of the strut 2 It is understood that it will be very small.
This indicates that a measurement error does not occur even if a rotation error in the circumferential direction and around the Z axis occurs in the joint 3. The error in the translation direction is 1 or less in the range of ls = 0 to 100, indicating that the error does not expand beyond the rotation error.
[0011]
Next, FIG. 4 shows the result of obtaining the relationship between the maximum singular value and the minimum singular value of the Jacobian matrix [Jrs, Jhs, Jθs] regarding the rotation error of the rotary joint 3-4 on the stage 4.
The minimum singular value is 1 regardless of the length ls of the probe 8, but the maximum singular value decreases rapidly and becomes the minimum value 1 in the vicinity of ls = 70.7. Similar results were obtained for the Jacobian matrix [JrB, JθB] relating to the error of 1.
The results of calculating the Jacobian matrix values detJl, detJt, detJn and singular values for the scale direction component δl and the two components δt and δn perpendicular to the scale direction component δl of the rotation error of both joints are shown in FIGS. Show. The Jacobian matrix value and singular value for the scale direction component δl are 1 when ls = 70.7, and the determinant value and singular value for the components δt and δn in the direction perpendicular thereto are almost zero. Here, the subscript t represents the tangential direction of the stage circle and the base circle, and the subscript n represents the direction perpendicular to the strut direction and the tangential direction (see FIG. 7).
From the above, it can be inferred that when the probe 8 is on the extension line of the scale, only the error δl in the joint scale direction becomes the motion error of the mechanism, and the influence of the error in the translation direction and the rotation direction perpendicular to the mechanism is eliminated.
[0012]
<Conclusion>
In order to investigate the effect of parallel CMM joint rotation error on measurement values, error analysis by micro kinematics revealed that rotation errors other than the direction of the scale can be ignored when the measurement point is on the extension line of the scale. .
[0013]
Based on the above knowledge, a mechanism device that realizes the motion error correction method for the parallel mechanism of the present invention as shown in FIG. 1 was produced.
FIG. 1A shows a general parallel mechanism with six degrees of freedom. A base 1 and a strut 2 that can be expanded and contracted by an actuator are connected by a spherical joint 3, and each spherical joint 3 has three rotational degrees of freedom around an XYZ axis. Have A stage 4 is connected to the other end of the strut 2 through a similar spherical joint 3.
The parallel mechanism of 6 degrees of freedom configured in this way can move the stage 4 in the direction of 6 degrees of freedom (translation 3 directions, rotation 3 directions) by extending and contracting the six struts 2.
[0014]
The strut 2 includes a length measuring device (such as a scale) for measuring the length. If the joint 3 has no rotation error, the position and posture of the stage 4 are uniquely determined by the length of the strut 2. However, when a rotational error in each of the three-dimensional directions due to the shape error of the joint 3 or deformation due to an external force occurs, in the present invention, as shown in FIG. A spherical surface pivotally supported through a bearing on a holder 5 fixed to the end of the strut 2 in order to measure the error only in the driving direction of the actuator (strut 2) constituting the shaft and correct the movement error of the link mechanism. A displacement sensor 6 that measures only an error in the expansion / contraction direction of the strut 2 between the joint 3 and the strut 2 is embedded in the strut 2 and installed.
[0015]
With this configuration, when the six struts 2 are appropriately expanded and contracted to move the stage 4 in the direction of six degrees of freedom, each of the three-dimensional components caused by deformation due to the shape error of each joint 3 or external force Even if a rotation error occurs in the direction, the effects of the translational direction perpendicular to the strut 2 and the error in the rotation direction can be almost ignored. Therefore, only the error in the expansion / contraction direction of the strut 2 is measured by the displacement sensor 6. The motion error of the link mechanism in the parallel mechanism can be corrected with high accuracy only (by simply adding the rotation error component in the strut direction of the upper and lower joints and the value of the length measuring device built in the strut) In other words, in addition to the length of the strut obtained with the built-in length measuring instrument, the strut becomes longer (or shorter) due to the rotation error of the joint. The number of sensors can be significantly reduced, in addition to simplified and lower cost of the apparatus can be realized, thereby also simplifying the correction control mechanism based on error measurement.
[0016]
FIG. 8 shows a second embodiment of the motion error correction device for the parallel mechanism of the present invention . In this embodiment, the first holder 5A provided with a recess for accommodating the spherical joint 3 without excess or deficiency, The second holder 5B is fastened and fixed to the end portion of the strut 2, and a displacement sensor 6 for measuring only an error in the expansion / contraction direction of the strut 2 is embedded and installed between the strut 2 and the second holder 5B. is there. Thus, the spherical holder 3 is more easily installed on the holder by the first holder 5A and the second holder 5B. In the present embodiment, only the error in the expansion / contraction direction of the strut 2 is detected by the displacement sensor 6. Since the movement error of the link mechanism in the parallel mechanism can be corrected with high accuracy only by measuring, the number of sensors can be greatly reduced, and the same effects as those of the first embodiment can be achieved. Demonstrate.
[0017]
FIG. 9 shows a third embodiment of a motion error correction apparatus for a parallel mechanism according to the present invention, and this embodiment is an example adopted for a three-degree-of-freedom parallel mechanism. In this case, the rotational freedom degree of the rotary joint 7 on the stage 4 side is 1, and the rotational freedom degree of the spherical joint 3 on the base 1 side is 3. In the present embodiment, not only the rotary joint 7 on the stage 4 side but also the spherical joint 3 on the base 1 side, only the error in the expansion / contraction direction of the strut 2 may be measured by the displacement sensor. Therefore, if a total of 24 rotational error measuring displacement sensors should be installed, 15 on the stage 4 side and 9 on the base 1 side, it is only necessary to install a total of 6 displacement sensors, 3 each. Become.
[0018]
Although the embodiment of the present invention has been described above, within the scope of the present invention, the shape of the base and stage as a parallel mechanism, the ratio of their sizes, the shape, type, number and number of struts that are actuators The positional relationship between the base and the stage, the shape and type of the spherical joint, the installation form of the spherical joint on the base and stage and the holder, the type and installation form of the displacement sensor can be selected as appropriate.
[0019]
【The invention's effect】
As described in detail above, the present invention corrects a motion error of the link mechanism due to a rotation error of a joint (an even number) in a parallel mechanism in which closed link mechanisms having at least three degrees of freedom are connected in parallel. When measuring the rotation error of each joint, the error in the driving direction of the actuator that constitutes the link mechanism is measured to correct the movement error of the link mechanism. Even if the resulting three-dimensional rotation error occurs, the effects of the translational direction perpendicular to the strut and the error in the rotation direction can be almost ignored. It is possible to correct the link mechanism motion error in the parallel mechanism with high accuracy just by measuring. Able to significantly reduce the number of servers, in addition to simplified and lower cost of the apparatus can be realized, thereby also simplifying the correction control mechanism based on error measurement.
[0020]
Further, in the parallel mechanism for correcting the movement error of the link mechanism by measuring the rotation error of the joint composed of the base and the stage in which the closed link mechanism having at least three degrees of freedom is connected in parallel, Since the displacement sensor for measuring the error in the driving direction is arranged to correct the movement error of the link mechanism, the degree of freedom is 6 degrees or more from the parallel mechanism of 3 degrees of freedom with relatively few degrees of freedom. For the parallel mechanism with a degree, the measurement of the error in the translational direction and the rotation direction perpendicular to the actuator strut is abolished, and it is only necessary to install a displacement sensor that measures the error in the driving direction of the actuator at the joint. Reduces the number of parts and simplifies the equipment, resulting in lower costs and error Simplified correction control based on the measurement mechanism also useful will be attained.
Further, since the actuator is composed of a strut incorporating a length measuring means, the movement control of the actuator when correcting the motion error of the mechanism based on the rotation error by the joint portion is directly reflected in the length measuring means. Control is further simplified.
Thus, according to the present invention, there is provided a motion error correction method and apparatus for a parallel mechanism that can accurately correct the rotation error of the joint even with a small number of displacement sensors and can improve the motion accuracy of the mechanism.
[Brief description of the drawings]
FIG. 1A is an overall perspective view of an apparatus that realizes a motion error correction method for a parallel mechanism according to the present invention, and FIG. 1B is an enlarged cross-sectional view of a connecting portion between a strut that is an actuator and a joint. is there.
FIG. 2 is a relationship diagram between a rotation error of a joint and a motion error of a probe tip on a stage.
FIG. 3 is a diagram showing the relationship between the length of a probe and the value of a determinant according to an analysis based on the present invention.
FIG. 4 is a diagram showing the relationship between probe length and singular value based on the analysis based on the present invention.
FIG. 5 is a detailed relationship diagram between the length of a probe and the value of a determinant according to the analysis on which the present invention is based.
FIG. 6 is a detailed relationship diagram of probe length and singular value based on analysis based on the present invention.
FIG. 7 is a relationship diagram of joint rotation error based on the analysis that is the basis of the present invention.
FIG. 8 is an enlarged cross-sectional view of a connecting portion between a strut and a joint, showing a second embodiment of the motion error correction apparatus for the parallel mechanism of the present invention.
FIG. 9 is an overall perspective view showing a third embodiment of a motion error correction apparatus for a parallel mechanism according to the present invention.
FIG. 10 is a diagram showing errors in three directions of the joint in the parallel mechanism.
[Explanation of symbols]
1 Base 2 Strut (actuator)
3 Joint 4 Stage 5 Holder 6 Displacement sensor 7 Rotary joint 8 Probe

Claims (3)

In order to correct the movement error of the link mechanism due to the rotation error of the joint (pair) in a parallel mechanism in which closed link mechanisms having at least three degrees of freedom are connected in parallel, when measuring the rotation error of each joint, A motion error correction method for a parallel mechanism, wherein an error in a driving direction of an actuator constituting a link mechanism is measured to correct a motion error of the link mechanism. In a parallel mechanism that corrects a movement error of the link mechanism by measuring a rotation error of a joint composed of a base and a stage in which closed link mechanisms having at least three degrees of freedom are connected in parallel. A parallel mechanism motion error correction apparatus, wherein a displacement sensor for measuring the error of the link mechanism is arranged to correct the motion error of the link mechanism. 3. The motion error correction device for a parallel mechanism according to claim 2, wherein the actuator is composed of a strut incorporating a length measuring means.

Images