STUDY ON ABBE'S PRINCIPLE IN PARALLEL KINEMATICS
For a long time, conventional machine tools or coordinate measuring machines have employed the XYZ mechanism which is consisting of three mutually orthogonal slide mechanisms. It appears, however, the machine accuracy are already at their limit. One cause of the limitation is the violation of the Abbe's principle which is the basis of precision mechanism. In other words, end-effectors of the machines, namely the tool and the probe haven't been located in extensional lines of all scale units or guide ways. In short, there are some offsets between the scale unit axes and the measuring point or the machining point in the XYZ mechanism.
On the other hand, in the parallel kinematic, the tool and the probe can be located in the extension lines of the scale unit axes. Therefore, such the arrangement should decrease the influence on the mechanism motion error. In fact, through studying on coordinate measuring machine using parallel kinematics, the author could have found analytically and experimentally that the measurement error is minimized when the measuring point is located in all scale directions. In this study, the effect of the joint motion errors on the mechanism motion error of Stewart platform mechanism has been analyzed by using a singular value decomposition. Moreover, the relation between the effect and various link layout has been discussed.
In parallel kinematics, rotational error of the spherical joint, in short runout has a strong effect on the motion error of mechanism. This paper investigates the relationship between the link configurations and influences of the joint runout on the motion error in order to inprove the accuracy of the six degree-of-freedom parallel mechanism. The main results obtained by singular value decomposition are as follows: (1) The joint runout in the direction of the actuated link strongly affects the translational motion error of the mechanism. (2) The joint runouts perpendicular to the link direction are negligible. (3) The smallest working space is obtained in the optimum link configuration. (3) In that configuration, the magnifying ratio of the motion error decreases to 0.7. (4) The tool point need not be in the acutuated link directions. (5) The tool extension is optimized when the distance between the extensional line of the link and tool point is minimized in each link configuration.
Fig. The 6-DOF PKM can control 6-DOF motions. In other words, the PKM controls full angular motions. Therefore, the arrangement of sensor system is not restricted by the Abbe's principle.
Takaaki OIWA and Masato TAMAKI:
A Study on Abbe's Principle of Six Degree-of-Freedom Parallel Mechanism ( Effect of Joint Runout on Motion Error of Mechanism), Transactions of the Japan Society of Mechanical Engineers, Vol. C69, No. 678 (2003) pp. 472-477 (in Japanese).H5>
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