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Principle of Force Analysis of Overconstrained Parallel Mechanisms Considering Link Weight

Published online by Cambridge University Press:  18 February 2019

Yundou Xu
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao, China
Ling Lu
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn School of Mechanical Engineering, Yanshan University, Qinhuangdao, China
Wenlan Liu
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn
Jinwei Guo
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn
Jiantao Yao
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao, China
Yongsheng Zhao*
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao, China
*
*Corresponding author. E-mail: yszhao@ysu.edu.cn

Summary

The fundamental cause for the statically indeterminate problem in the force analysis of overconstrained parallel mechanisms (PMs) is found to be the presence of the linearly dependent overconstrained wrenches. Based on the fundamental cause, a unified expression of the solution for the magnitudes of the constraint wrenches of both the limb stiffness decoupled and limb stiffness coupled overconstrained PMs is derived. When the weight of each link is considered, depending on whether additional component forces are generated along the axes of the overconstrained wrenches, two different situations should be considered. One situation is that no additional component force is generated along the axes of the overconstrained wrenches under the weight of the links in the corresponding limb. In this case, the added constraint wrenches at the limb’s end can be calculated directly, and used as a part of the generalized external wrench. The other situation is that additional component forces are generated. In this case, the elastic deformations in the axes of the overconstrained wrenches generated by those component forces should be considered, and the deformation compatibility equations between the overconstrained wrenches are reformulated.

Type
Articles
Copyright
© Cambridge University Press 2019 

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