A study of the instantaneous kinematics of the 5-RSP parallel mechanism using screw theory

Abstract

This paper presents a detailed study of the instantaneous kinematics of the 5-RSP parallel mechanism with centralized motion. The study uses screw theory to investigate the mobility and the singular configurations of the mechanism. The constraint-screw set of the platform is obtained from an analysis of the motion-screw sets comprised by each kinematic chain. The analysis shows that the platform has a screw motion, that is, a one degree-of-freedom motion consisting of a rotation and a translation about an invariant axis. The motion-screw sets are also used to obtain the Jacobian matrix of the mechanism which provides closed-form solutions for the inverse and forward instantaneous kinematic problems. This matrix also provides insight into the singular configurations by investigating the constraint-screws and the motion-screws of the platform in these configurations. Finally, two numerical examples and a motion simulation of the mechanism are presented to illustrate the significance of the analytical results. © Springer-Verlag 2012.