Motion Branch Transformation of 3(Rc)PU Parallel Mechanism with Reconfigurable Joint and Kinematic Performance Index

Abstract

A novel 3(Rc)PU parallel mechanism based on the reconfigurable circular groove cross joint (Rc joint) is proposed. The motion branch transformation relationship and constraint performance evaluation method for the mechanism are studied. According to constrained screw analysis, the (Rc)PU limb provides a constraint couple to the moving platform in one motion mode and no constraint to the platform in another motion mode. According to the two configurations of the limb, the 3(Rc)PU mechanism has four different motion branches, namely 3T, 1R3T, 2R3T, and 3R3T. Based on the input selection principle, the input selection scheme of the 3(Rc)PU mechanism is determined, and it is concluded that, to achieve stable motion, at least two input drive pairs need to be applied on each limb. A unified kinematic model with four motion branches is established, and the geometric constraint equations of the 3(Rc)PU parallel mechanism are derived. After selecting the input actuated joints, the local minimization transmission index (LMTI) of the reconfigurable mechanism under different motion branches is established to evaluate the motion/force transmission performance of the reconfigurable mechanism under different motion branches. The conclusion shows that the LMTI values satisfy the corresponding constraint conditions, and the 3(Rc)PU parallel mechanism has good motion/force transmission performance.