Study on Abbe's Principle in 6 DOF Parallel Kinematics

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  • 122 6 自由度パラレルメカニズムにおけるアッベの原理に関する研究

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Conventional machine tools or coordinate measuring machines consisting of XYZ mechanism have difficulty to satisfy the Abbe's principle which is the basis of the precision mechanism. In other words, there are some offsets between the scale unit axes and the machining point or the measuring point. However, the machining point of machines based on the parallel kinematics can be located in the extension lines of the axes. In this study, the effects of the joint errors on the motion error of Hexapod mechanism has been analyzed by using a singular value decomposition. In this paper, it is proved that the point don't have to be located in the lines in the Hexapod. Because six actuating struts are employed, not only positions but also attitudes of the moving platform are able to be measured and actuated. In other word, the Hexapod can control the whole positions and attitudes of the platform. Thus, even if any offset exists between the machining point and the extensional lines, the point can be positioned precisely. Consequently, Hexapod enables to realize accurate machining and measurement regardless of Abbe's principle.

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