Dynamic Optimization with a New Performance Index for a 2-DoF Translational Parallel Manipulator

Abstract

The dynamic analysis and optimization problem of a 2-DoF Translational Parallel Manipulator (TPM) is addressed in this paper. Based on the principle of virtual work and the concept of link Jacobian matrix, the explicit expressions of the dynamic model of the 2-DoF TPM in the global task space are derived. Using the dynamic model, a global and comprehensive dynamic performance index (GCDPI) is proposed to evaluate the manipulator capabilities in terms of dynamic manipulability and dexterity in the prescribed task space. The dynamic optimization problem, which aims at providing the largest, the most isotropic and the most uniform dynamic manipulability of the 2-DoF TPM in the task space, is formulated as the minimization of GCDPI subjected to a set of appropriate constraints. Optimization results showed that the dynamic manipulability of the 2-DoF TPM with optimized kinematic and inertial parameters improves greatly in the prescribed task space. The dynamic equations are also incorporated in the hardware in the loop simulation of the 2-DoF TPM and experimental results show the tracking errors of the linear motor can be improved greatly when a nonlinear computed torque feedforward controller is implemented in addition to the cascade position controller.