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Mathematical Problems in Engineering
Volume 2016, Article ID 5091405, 12 pages
Research Article

Kinematics Comparative Study of Two Overconstrained Parallel Manipulators

1Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of Technology, Tianjin, China
2Faculty of Science and Technology, University of Macau, Taipa, Macau

Received 27 June 2016; Revised 12 August 2016; Accepted 21 September 2016

Academic Editor: Alberto Borboni

Copyright © 2016 Qiang Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A comparison study of kinematics characteristics of two overconstrained 2-RPU&SPR parallel manipulators (PMs) is introduced in this paper. The two 2-RPU&SPR PMs have the same kinematics properties in terms of one translational degree of freedom (DOF) and two rotational DOFs kinematics outputs. But there are some differences between the two PMs as far as joints distribution is concerned, leading to the differences in respect of workspace and dexterity of the two PMs. Firstly, based on screw theory, the structural characteristics and DOFs of the two PMs are analyzed. Secondly, the inverse and forward displacements problems for the two PMs are formulated by analytic formulae. Some numerical examples are simulated by software. Thirdly, based on algorithm for the direct displacement solution, the workspace characteristics of the two PMs are analyzed and compared. Then, the Jacobian matrices of the mechanisms are formulated. Based on the Jacobian matrices, the dexterities of the two PMs are established and compared. Finally, according to the comparisons of the properties between the two PMs, some useful conclusions are provided.