Unified Kinematics Analysis and Analytic Singularity-Free Workspace of a Metamorphic Parallel Mechanism With Controllable Rotation Center

Abstract

This paper presents a metamorphic parallel mechanism with controllable rotation center in its pure rotation topology. Based on reconfiguration of a reconfigurable Hooke (rT) joint, the rotational center of the mechanism can be altered along the central line perpendicular to the base plane. A unified Dixon resultant based method is proposed to solve the forward kinematics analytically by covering all configurations with variable rotation centers while the rotation motion is expressed using Cayley formula. Then singularity loci are derived and represented in a new coordinate system with the three Rodrigues-Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are also obtained from row vectors of the Jacobian matrix. By using Cayley formula, analytical workspace boundaries are expressed by including the mechanism structure parameters and input actuation limits. Finally, singularity-free workspace of configurations with variable rotation centers is demonstrated in the proposed coordinate system.