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Wrench capabilities of planar parallel manipulators. Part II: Redundancy and wrench workspace analysis

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: podhoro@me.uvic.ca
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Summary

This part of the paper investigates the wrench capabilities of redundantly actuated planar parallel manipulators (PPMs). The wrench capabilities of PPMs are determined by mapping a hypercube from the torque space into a polytope in the wrench space. For redundant PPMs, one actuator output capability constrains the wrench space with a smaller polytope that is contained inside the overall polytope. Performance indices are derived from six study cases. These indices are employed to analyze the wrench workspace for constant orientation of the mobile platform of the non-redundant 3-RRR PPM, and actuation redundant 4-RRR and 3-RRR PPMs, where the underline indicates the actuated joints. A comparison of the results shows that both of the redundantly-actuated PPMs give better wrench capabilities than the non-redundant PPM. However, it is shown that scaled for the operational cost (wrench capabilities divided by total actuation output) the non-redundant 3-RRR PPM provides the highest maximum reachable force, the 3-RRR PPM produces the highest isotropic force, and the 4-RRR yields the highest reachable moment.

Keywords

force/moment capabilitiesplanar parallel manipulatorsredundancyforce/moment workspace analysis
Type
Article
Information
Robotica , Volume 26 , Issue 6 , November 2008 , pp. 803 - 815
Copyright
Copyright © Cambridge University Press 2008

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