Unified Singularity Modeling and Reconfiguration of 3rTPS Metamorphic Parallel Mechanisms with Parallel Constraint Screws

Abstract

This paper presents a unified singularity modeling and reconfiguration analysis of variable topologies of a class of metamorphic parallel mechanisms with parallel constraint screws. The new parallel mechanisms consist of three reconfigurable rT PS limbs that have two working phases stemming from the reconfigurable Hooke (rT) joint. While one phase has full mobility, the other supplies a constraint force to the platform. Based on these, the platform constraint screw systems show that the new metamorphic parallel mechanisms have four topologies by altering the limb phases with mobility change among 1R2T (one rotation with two translations), 2R2T, and 3R2T and mobility 6. Geometric conditions of the mechanism design are investigated with some special topologies illustrated considering the limb arrangement. Following this and the actuation scheme analysis, a unified Jacobian matrix is formed using screw theory to include the change between geometric constraints and actuation constraints in the topology reconfiguration. Various singular configurations are identified by analyzing screw dependency in the Jacobian matrix. The work in this paper provides basis for singularity-free workspace analysis and optimal design of the class of metamorphic parallel mechanisms with parallel constraint screws which shows simple geometric constraints with potential simple kinematics and dynamics properties.