Orientation Capability, Error Analysis, and Dimensional Optimization of Two Articulated Tool Heads With Parallel Kinematics

Because of the increasing demand in industry for A/B-axis tool heads, particularly in thin wall machining applications for structural aluminium aerospace components, the three-degree-of-freedom articulated tool head with parallel kinematics has become very popular. This paper addresses the dimensional optimization of two types of tool head with $3-P̱VPHS$ and $3-P̱VRS$ parallel kinematics (P, R, and S standing for prismatic, revolute, and spherical joint, respectively; the subscripts V and H indicating that the direction of the P joint is vertical or horizontal, and the joint symbol with underline means the joint is active) by considering their orientation capability and positioning accuracy. We first investigate the tilt angle of the spherical joint, the orientation capability, and the error of one point from the mobile platform caused by input errors. Optimization of the $3-P̱VPHS$ tool head is easy. For the $3-P̱VRS$ tool head, a design space is developed to illustrate how the orientation capability and error index are related to the link lengths. An optimization process is accordingly presented. Using the optimization method introduced here, it is not difficult to find all the possible optimal solutions.