Mobility is a basic property of a mechanism. The aim of mobility analysis is to determine the number of degrees-of-freedom (DOF) and the motion pattern of a mechanism. The existing methods for mobility analysis have some drawbacks when being applied to limited-DOF parallel mechanisms (PMs). Particularly, it is difficult to obtain a symbolic or closed-form expression of mobility and its geometric interpretations are not always straightforward. This paper presents a general method for mobility analysis of limited-DOF PMs in the framework of geometric algebra. The motion space and constraint space of each limb are expressed using geometric algebra. Then the mobility of the PM can be calculated based on the orthogonal complement relationship between the motion space and the constraint space. The detailed mobility analyses of a 3-RPS PM and a 3-RPC PM are presented. It is shown that this method can obtain a symbolic expression of mobility with straightforward geometric interpretations and is applicable to limited-DOF PMs with or without redundant constraints. Without solving complicated symbolic linear equations, this method also has computational advantages.
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August 2016
Research-Article
Mobility Analysis of Limited-Degrees-of-Freedom Parallel Mechanisms in the Framework of Geometric Algebra
Qinchuan Li,
Qinchuan Li
Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: qchuan@zstu.edu.cn
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: qchuan@zstu.edu.cn
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Xinxue Chai,
Xinxue Chai
Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: jxcxx88@163.com
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: jxcxx88@163.com
Search for other works by this author on:
Ji'nan Xiang
Ji'nan Xiang
Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: xjinan@163.com
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: xjinan@163.com
Search for other works by this author on:
Qinchuan Li
Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: qchuan@zstu.edu.cn
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: qchuan@zstu.edu.cn
Xinxue Chai
Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: jxcxx88@163.com
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: jxcxx88@163.com
Ji'nan Xiang
Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: xjinan@163.com
Zhejiang Sci-Tech University,
Hangzhou,
Zhejiang Province 310018, China
e-mail: xjinan@163.com
1Corresponding author.
Manuscript received July 28, 2015; final manuscript received November 23, 2015; published online March 7, 2016. Assoc. Editor: Yuefa Fang.
J. Mechanisms Robotics. Aug 2016, 8(4): 041005 (9 pages)
Published Online: March 7, 2016
Article history
Received:
July 28, 2015
Revised:
November 23, 2015
Citation
Li, Q., Chai, X., and Xiang, J. (March 7, 2016). "Mobility Analysis of Limited-Degrees-of-Freedom Parallel Mechanisms in the Framework of Geometric Algebra." ASME. J. Mechanisms Robotics. August 2016; 8(4): 041005. https://doi.org/10.1115/1.4032210
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