Modelling and Control of Inverse Dynamics for a 5-DOF Parallel Kinematic Polishing Machine

Abstract

Currently, about 60% of the finishing works for freeform parts are done manually, in this paper a parallel kinematic polishing machine (PKPM) with five degrees of freedom (DOFs) and with structural configurations of the type T3R2 (three translations and two rotations) is presented. The PKPM is a variation of the existing METROM Pentapod. The PKPM has a large yaw angle space and, with the aid of an NC rotation table, it can access any given point of the freeform part. A kinematic analysis is developed, an inverse dynamic model based on Kane's equation and the affine projection method is set up in detail, and a real-time and highly efficient inverse dynamic algorithm is developed; the simulation results show that the presented PKPM could achieve an acceleration which is twice that of gravity. A mixed ℋ 2 / ℋ ∞ control method is presented and investigated in order to track the error control of the inverse dynamic model; the simulation results from different conditions show that the mixed ℋ 2 / ℋ ∞ control method could achieve an optimal and robust control performance. This work shows that the presented PKPM has a higher dynamic performance than conventional machine tools.