Dynamic Modeling and Analysis of a 3 PRS Parallel Mechanism Using Constrained Robotic Approach

In this paper, a novel model is developed to analyze a 3-PRS parallel mechanism. The 3-PRS mechanism consists of a moving platform which is manipulated by three actuated fingers. Since the fingertips are constrained by the moving platform, three holonomic constraint equations are derived and the associated constraint forces are studied based on the theory of differential geometry. The developed model could be utilized to separate the dynamics of the fingers and that of the moving platform such that the coupling behaviors of the fingers can be investigated. It is found that the reaction forces applied at the fingertips of the parallel manipulator include not only the driving forces to the moving platform but also the constraint forces. Besides, the constraint forces are determined to be internal forces which would not generate a net force or torque to drive the moving platform. Simulations are performed to study the dynamic behavior of the reaction forces and it is found that the constraint forces have significant effect on the actuated fingers.