Geometric Error Analysis of a 2UPR-RPU Over-Constrained Parallel Manipulator

Abstract

For a 2UPR-RPU over-constrained parallel manipulator, some geometric errors result in internal forces and deformations, which limit the improvement of the pose accuracy of the moving platform and shorten the service life of the manipulator. Analysis of these geometric errors is important for restricting them. In this study, an evaluation model is established to analyse the influence of geometric errors on the limbs’ comprehensive deformations for this manipulator. Firstly, the nominal inverse and actual forward kinematics are analysed according to the vector theory and the local product of the exponential formula. Secondly, the evaluation model of the limbs’ comprehensive deformations is established based on kinematics. Thirdly, 41 geometric errors causing internal forces and deformations are identified and the results are verified through simulations based on the evaluation model. Next, two global sensitivity indices are proposed and a sensitivity analysis is conducted using the Monte Carlo method throughout the reachable workspace of the manipulator. The results of the sensitivity analysis indicate that 10 geometric errors have no effects on the average angular comprehensive deformation and that the identified geometric errors have greater effects on the average linear comprehensive deformation. Therefore, the distribution of the global sensitivity index of the average linear comprehensive deformation is more meaningful for accuracy synthesis. Finally, simulations are performed to verify the results of sensitivity analysis.