Unified kinematics and optimal design of a 3rRPS metamorphic parallel mechanism with a reconfigurable revolute joint

Abstract

This paper introduces a new metamorphic parallel mechanism based on a reconfigurable revolute (rR) joint and the mechanism consists of three rRPS (rR joint-prismatic joint-spherical joint) limbs. Reconfiguration principle of the rR joint and the rRPS limb is explained, based on which the 3rRPS metamorphic parallel mechanism can be reconfigurable between two working motion types, pure rotation (3R) motion and one translation and two rotation (1T2R) motion. Using the limb geometric constraint model, analytical forward kinematics is solved in a unified way for both motion types. Reciprocal screw based Jacobian is obtained for singularity analysis which is then used for singularity-free workspace analysis. Based on those, maximum singularity-free workspace and kinematics performance based criteria are applied in optimizing basic mechanism parameters considering input and passive joint limitations. A unified objective function with variable design priorities represented by function weights of the two topologies is proposed and examples are illustrated. The introduced new parallel mechanism covers the two very useful motion types, 3R and 1T2R, while the model in the paper provides basis of modeling and optimal design for further applications.