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Geometrical method to determine the reciprocal screws and applications to parallel manipulators

Published online by Cambridge University Press:  03 April 2009

Jianguo Zhao ,
Bing Li ,
Xiaojun Yang  and
Hongjian Yu
Jianguo Zhao
Affiliation:
Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
Bing Li*
Affiliation:
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, P.R. China State Key Laboratory of Robotics and System (HIT), Harbin 150001, P.R. China
Xiaojun Yang
Affiliation:
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, P.R. China
Hongjian Yu
Affiliation:
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, P.R. China
*
*Corresponding author. E-mail: [email protected]
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Summary

Screw theory has demonstrated its wide applications in robot kinematics and statics. We aim to propose an intuitive geometrical approach to obtain the reciprocal screws for a given screw system. Compared with the traditional Plücker coordinate method, the new approach is free from algebraic manipulation and can be used to obtain the reciprocal screws just by inspecting the structure of manipulator. The approach is based on three observations that describe the geometrical relation for zero pitch screw and infinite pitch screw. Based on the observations, the reciprocal screw systems of several common kinematic elements are analyzed, including usual kinematic pairs and chains. We also demonstrate usefulness of the geometrical approach by a variety of applications in mobility analysis, Jacobian formulation, and singularity analysis for parallel manipulator. This new approach can facilitate the parallel manipulator design process and provide sufficient insights for existing manipulators.

Keywords

Screw theoryGeometrical methodReciprocal screwLine vectorCouple vector
Type
Article
Information
Robotica , Volume 27 , Issue 6 , October 2009 , pp. 929 - 940
Copyright
Copyright © Cambridge University Press 2009

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