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Wrench capabilities of planar parallel manipulators. Part I: Wrench polytopes and performance indices

Published online by Cambridge University Press:  01 November 2008

Flavio Firmani ,
Alp Zibil ,
Scott B. Nokleby  and
Ron P. Podhorodeski
Flavio Firmani
Affiliation:
Robotics and Mechanisms Laboratory, Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, Victoria, B. C, V8W 3P6, Canada
Alp Zibil
Affiliation:
Robotics and Mechanisms Laboratory, Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, Victoria, B. C, V8W 3P6, Canada
Scott B. Nokleby
Affiliation:
Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario, L1H 7K4, Canada
Ron P. Podhorodeski*
Affiliation:
Robotics and Mechanisms Laboratory, Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, Victoria, B. C, V8W 3P6, Canada
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.

Keywords

force/moment capabilitiesplanar parallel manipulatorspolytopeswrench performance indicesscrew theory
Type
Article
Information
Robotica , Volume 26 , Issue 6 , November 2008 , pp. 791 - 802
Copyright
Copyright © Cambridge University Press 2008

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