A Study on Abbe's Principle of Six Degree-of-Freedom Parallel Mechanism. Effect of Joint Runout on Motion Error of Mechanism.

Abstract

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 paper, the effects of the joint errors on the motion error of Hexapod mechanism has been analyzed by using a singular value decomposition. The obtained main results are as follows : (1) The joint runout in the direction of the actuated prismatic joint strongly affects the translational motion error of the mechanism ; (2) the joint runouts perpendicular to the direction are negligible ; (3) the optimum link configuration which minimizes the working space and the effects of the runouts is found ; (4) the machining point need not be in the prismatic joint directions ; (5) the tool extension is optimized when the distance between the extensional line of the prismatic joints and machining point is minimized in each link configuration.