A virtual power algorithm for dynamics analysis of a 3-RRcP spherical parallel robot using the screw theory

Abstract

Due to their closed-loop structure and kinematic constraints, dynamic modelling of parallel manipulators presents an inherent complexity. In the present research, an approach to obtain the nonlinear dynamics equations of motion of a 3-RRcP spherical parallel manipulator is presented. The proposed approach is based on the principle of virtual power and the screw theory. To obtain the dynamics equations of motion, we propose an influence matrix which relates the passive joint rates to the actuated joint rates for each branch. The presented method allows a straightforward computation of torques of the actuated joints in terms of the resultant external forces and the desired trajectory. In order to represent correctness and accuracy of the obtained equations of motion, two case studies are considered that their solutions are compared by a commercial dynamics software package (CDSP).