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Singularity analysis of a 3-RPS parallel manipulator using geometric algebra

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Abstract

Singular configurations must be avoided in path planning and control of a parallel manipulator. However, most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms. Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator. Twist and wrench in screw theory are represented in geometric algebra. Linear dependency of twists and wrenches are described by outer product in geometric algebra. Reciprocity between twists and constraint wrenches are reflected by duality. To compute the positions of the three spherical joints of the 3-RPS parallel manipulator, Tilt-and-Torsion angles are used to describe the orientation of the moving platform. The outer product of twists and constraint wrenches is used as an index for closeness to singularity(ICS) of the 3-RPS parallel manipulator. An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed, which is helpful to design, trajectory planning and control of this kind of parallel manipulator.

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Correspondence to Qinchuan Li.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 51135008), and Zhejiang Provincial Natural Science Foundation of China (Grant No. LZ14E050005)

LI Qinchuan, born in 1975, is currently a professor at Zhejiang Sci-Tech University, China. He received his PhD degree on mechanism design and theory from Yanshan University, China, in 2003. His research interests include mechanism theory of parallel manipulators and application.

XIANG Ji’nan, born in 1990, is currently a master candidate at Mechatronic Institute, Zhejiang Sci-Tech University, China.

CHAI Xinxue, born in 1988, is currently a PhD candidate at Mechatronic Institute, Zhejiang Sci-Tech University, China.

WU Chuanyu, born in 1976, is currently a professor at Zhejiang Sci-Tech University, China. He received his PhD degree on mechanism design and theory at Zhejiang University, China, in 2002. His research interests include intelligentized agricultural machinery and robotics.

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Li, Q., Xiang, J., Chai, X. et al. Singularity analysis of a 3-RPS parallel manipulator using geometric algebra. Chin. J. Mech. Eng. 28, 1204–1212 (2015). https://doi.org/10.3901/CJME.2015.0728.103

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  • DOI: https://doi.org/10.3901/CJME.2015.0728.103

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