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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: [email protected]
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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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References

1.Nokleby, S. B., Fisher, R., Podhorodeski, R. P. and Firmani, F., “Force capabilities of redundantly-actuated parallel manipulators,” Mech. Mach. Theory 40 (5), 578–599 (2005).CrossRefGoogle Scholar
2.Yoshikawa, T., Foundations of Robotics: Analysis and Control (The MIT Press. Cambridge, MA, USA, 1990).Google Scholar
3.Chiacchio, P., Bouffard-Vercelli, Y. and Pierrot, F., “Evaluation of Force Capabilities for Redundant Manipulators,” Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneeapolis, MN (Apr. 22–28, 1996) pp. 3520–3525.Google Scholar
4.Kokkinis, T. and Paden, B., “Kinetostatic Performance Limits of Cooperating Robot Manipulators Using Force-Velocity Polytopes,” Proceedings of the ASME Winter Annual Meeting, San Francisco, CA, USA (1989) pp. 151–155.Google Scholar
5.Chiacchio, P., Bouffard-Vercelli, Y. and Pierrot, F., “Force polytope and force ellipsoid for redundant manipulators,” J. Robot. Syst. 4 (8), 613–620 (1997).3.0.CO;2-P>CrossRefGoogle Scholar
6.Rockafellar, R. T., Convex Analysis, 1st ed. (1970) (Princeton University Press. Princeton, NJ, USA, 1997).CrossRefGoogle Scholar
7.Hwang, Y. S., Lee, J. and Hsia, T. C., “A Recursive Dimension-Growing Method for Computing Robotic Manipulability Polytope,” Proceedings of the 2000 IEEE International Conference on Robotics and Automation, San Francisco, CA, USA (Apr. 24–28, 2000) vol. 3, pp. 2569–2574.Google Scholar
8.Fisher, R., Podhorodeski, R. P. and Nokleby, S. B., “A reconfigurable planar parallel manipulator,” J. Robot. Syst. 21 (12), 665–675 (2004).CrossRefGoogle Scholar
9.Merlet, J. P., “Redundant parallel manipulators,” J. Lab. Robot. Autom. 8, 17–24 (1996).3.0.CO;2-#>CrossRefGoogle Scholar
10.Lee, S. and Kim, S., “Kinematic Analysis of Generalized Parallel Manipulator Systems,” in Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, TX, USA (Dec. 15–17, 1993) vol. 2, pp. 1097–1102,.Google Scholar
11.Ebrahimi, I., Carretero, J. A. and Boudreau, R., “3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses,” Mech. Mach. Theory 42 (8), 1007–1016 (2007).CrossRefGoogle Scholar
12.Wang, J. and Gosselin, C. M., “Kinematic analysis and design of kinematically redundant parallel mechanisms,” Trans. ASME, J. Mech. Des. 126 (1), 109–118 (2004).CrossRefGoogle Scholar
13.Ebrahimi, I., Carretero, J. A. and Boudreau, R., “The 3-RPRR Kinematically Redundant Planar Parallel Manipulator,” The 2007 CCToMM Symposium on Mechanisms, Machines, and Mechatronics, St.-Hubert, QC, Canada (May 31–Jun. 1, 2007).Google Scholar
14.Zibil, A., Firmani, F., Nokleby, S. B. and Podhorodeski, R. P., “An explicit method for determining the force-moment capabilities of redundantly-actuated planar parallel manipulators,” Trans. ASME, J. Mech. Des., 129 (10), 1046–1055 (2007).CrossRefGoogle Scholar
15.Nokleby, S. B., Firmani, F., Zibil, A. and Podhorodeski, R. P., “Force-Moment Capabilities of Redundantly-Actuated Planar-Parallel Architectures,” in Proceedings of the IFToMM 2007 World Congress, Besançon, France, (Jun. 17-21, 2007).Google Scholar
16.Firmani, F. and Podhorodeski, R. P., “Force-unconstrained poses for a redundantly-actuated planar parallel manipulator,” Mech. Mach. Theory 39 (5), 459–476 (2004).CrossRefGoogle Scholar
17.Buttolo, P. and Hannaford, B., “Advantages of Actuation Redundancy for the Design of Haptic Displays,” Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition–Part 2, San Francisco, CA, USA (Nov. 12–17, 1995) pp. 623–630.Google Scholar
18.Gallina, P., Rosati, G. and Rossi, A., “3-d.o.f. wire driven planar haptic interface,” J. Intelli. Robot. Syst. 32 (1), 23–36 (2001).CrossRefGoogle Scholar
19.Krut, S., Company, O. and Pierrot, F., “Force Performance Indexes for Parallel Mechanisms with Actuation Redundancy, Especially for Parallel Wire-Driven Manipulators,” Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan (Sep. 28–Oct. 2, 2004) vol. 4, pp. 3936–3941.Google Scholar
20.Krut, S., Company, O. and Pierrot, F., “Velocity performance indices for parallel mechanisms with actuation redundancy,” Robotica 22 (2), 129–139 (2004).CrossRefGoogle Scholar
21.Nokleby, S. B., Firmani, F., Zibil, A. and Podhorodeski, R. P., “An Analysis of the Force-Moment Capabilities of Branch-Redundant Planar-Parallel Manipulators,” in Proceedings of the 2007 ASME Design Engineering Technical Conference, ASME, Las Vegas, NV, USA, (Sept. 4-7, 2007).CrossRefGoogle Scholar
22.Firmani, F. and Podhorodeski, R. P., “Force-unconstrained poses for parallel manipulators with redundant actuated branches,” Trans. CSME 29 (3), 343–356 (2005).Google Scholar
23.Firmani, F. and Podhorodeski, R. P., “Force-unconstrained poses of the 3-PRR and 4-PRR planar parallel manipulators,” Trans. CSME 29 (4), 617–628 (2005).Google Scholar
24.Firmani, F. and Podhorodeski, R. P., “Singularity Loci of Revolute-Jointed Planar Parallel Manipulators with Redundant Actuated Branches,” in Proceedings of the IFToMM 2007 World Congress, Besançon, France, (Jun. 17-21, 2007)Google Scholar
25.Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator,” Trans. ASME, J. Mech., Trans. Autom. Des. 110, 35–41 (1988).CrossRefGoogle Scholar
26.Merlet, J. P., Gosselin, C. M. and Mouldy, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33 (1), 7–20 (1998).CrossRefGoogle Scholar
27.Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Tran. Robot. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
28.Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators. (USA: John Wiley & Sons. New York, NY, 1999).Google Scholar
29.Hunt, K. H., Kinematic Geometry of Mechanisms (Canada: Oxford University Press. Toronto, ON, 1978).Google Scholar
30.Mohammadi-Daniali, H. R., Zsombor-Murray, P. J. and Angeles, J., “Singularity analysis of planar parallel manipulators,” Mech. Mach. Theory 30 (5), 665–678 (1995).CrossRefGoogle Scholar