Kinematic Reliability Solution of 3-UPS-PU Parallel Mechanism Based on Monte Carlo Simulation

Guohua Cui1, Muyuan Sun2, Liang Yan2, Hongjuan Hou*, 1, Haiqiang Zhang2
1 Equipment Manufacturing College, Hebei University of Engineering, Handan, Hebei, 056038, P.R. China
2 Mechanical and Electrical Engineering Institute, Hebei University of Engineering, Handan, Hebei, 056038, P.R. China

© 2015 Cui et al

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


In order to research kinematic reliability of 3-UPS-PU parallel mechanism, the structure and kinematics analysis were performed. Inverse kinematics equation can be derived by homogeneous coordinate transformation formula. Position and orientation output error forward kinematics model was obtained by the differential transformation on the basis of inverse kinematic solution of the position. The curves of the position and orientation output errors can be plotted with a large batch production by adopting Monte-Carlo simulation method. Then kinematic reliability of the mechanism can be solved through the probability statistics method and theoretical solution method respectively. Finally, these two methods were compared with each other. The results illustrate that the results of the two methods are basically consistent, and the mechanism can be work reliably and stably under general operations, which provides some valuable references for the related future research.

Keywords: Error analysis , kinematic reliability, kinematics, Monte-Carlo simulation, parallel mechanism.