Inverse dynamics analysis for a 3-PRS parallel mechanism based on a special decomposition of the reaction forces

In this paper, a novel approach is proposed to analyze the inverse dynamics of a 3-PRS (Prismatic, Revolute, Spherical) parallel mechanism. The dynamic equations of the actuated legs and the moving platform are formulated in the joint and the task space, respectively. The reaction forces applied at the spherical joints are utilized to integrate the complete equations and a special decomposition is proposed for efficient calculation. By employing the Jacobian analysis, the constraint forces in the joint coordinates are recognized to be the internal forces for the moving platform and lead to the special decomposition. The proposed algorithm can provide higher computational efficiency as compared to the conventional approach. Computer simulations on tracking circular motion are performed to analyze the inverse dynamics of the 3-PRS mechanism and it is shown that the proposed decomposition of the reaction forces could be utilized to provide a deeper understanding for the interactions between the legs and moving platform. Since the closed-loop kinematic constraints are inherent for parallel manipulators, the proposed methodology could also be applied to other parallel mechanisms. In real-time control, the proposed algorithm with high computational efficiency might be utilized for dynamic compensation.