Dynamic Performance Evaluation of a Redundantly Actuated and Over-constrained Parallel Manipulator

This paper presents a redundantly actuated and over-constrained 2RPU-2SPR parallel manipulator with two rotational and one translational coupling degrees of freedom. The kinematics analysis is firstly carried out and the mapping relationship of the velocity, acceleration and the independent parameters between the actuator joint and the moving platform are deduced by using the vector dot product and cross product operation. By employing d′Alembert′s principle and the principle of virtual work, the dynamics equilibrium equation is derived, and the simplified dynamics mathematical model of the parallel manipulator is further derived. Simultaneously, the generalized inertia matrix which can characterize the acceleration performance between joint space and operation space is further separated, and the performance indices including the dynamics dexterity, inertia coupling characteristics, energy transmission efficiency and driving force/torque balance are introduced. The analysis results show that the proposed redundantly actuated and over-constrained 2RPU-2SPR parallel manipulator in comparison with the existing non-redundant one has better dynamic comprehensive performance, which can be demonstrated practically by the successful application of the parallel kinematic machine head module of the hybrid machine tool.