Stiffness analysis of a 3-DOF parallel mechanism for engineering special machining

Abstract

There are considerably rigorous requirements for accuracy and stability of the mechanism to accomplish large-scale and complex surface machining tasks in the aerospace field. In order to improve the stiffness performance of the parallel mechanism, this paper proposes a novel three degrees of freedom (DOF) redundantly actuated 2RPU-2SPR (where R, P, U and S stand for revolute, prismatic, universal and spherical joints, respectively) parallel mechanism. Firstly, the kinematics position inverse solution is derived and a dimensionless generalized Jacobian matrix is established through the driving Jacobian matrix and constraint Jacobian matrix. Secondly, the stiffness model of the parallel mechanism is deduced and the accuracy of the stiffness model is verified through finite-element analysis. Using eigenscrew decomposition to illustrate the physical interpretation of the stiffness matrix, the stiffness matrix is equivalent to six simple screw springs. Finally, the simulation experiment results demonstrate that redundantly actuated parallel mechanism has better stiffness performance compared to the traditional 2RPU-SPR parallel mechanism.