Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T04:03:37.890Z Has data issue: false hasContentIssue false
  • English
  • Français

Wrench Capabilities of a Kinematically Redundant Planar Parallel Manipulator

Published online by Cambridge University Press:  26 January 2021

Roger Boudreau Open the ORCID record for Roger Boudreau [Opens in a new window] ,
Scott Nokleby  and
Marise Gallant
Roger Boudreau*
Affiliation:
Université de Moncton, E-mail: [email protected]
Scott Nokleby
Affiliation:
Ontario Tech University, E-mail: [email protected]
Marise Gallant
Affiliation:
Université de Moncton, E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents a methodology to obtain the wrench capabilities of a kinematically redundant planar parallel manipulator using a wrench polytope approach. A methodology proposed by others for non-redundant and actuation-redundant manipulators is adapted to a kinematically redundant manipulator. Four wrench capabilities are examined: a pure force analysis, the maximum force for a prescribed moment, the maximum reachable force, and the maximum moment with a prescribed force. The proposed methodology, which finds the exact explicit solution for three of the four wrench capabilities, does not use optimization and is very efficient.

Keywords

Parallel manipulatorsRedundant manipulatorsPolytopesForce/moment capabilitiesWrench performance indices
Type
Article
Information
Robotica , Volume 39 , Issue 9 , September 2021 , pp. 1601 - 1616
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Nokleby, S., Fisher, R., Podhorodeski, R. and Firmani, F., “Force capabilities of redundantly-actuated parallel manipulators,” Mech. Mach. Theory 40(5), 578–599 (2005).CrossRefGoogle Scholar
Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Automat. 6(3), 281–290 (1990).CrossRefGoogle Scholar
Zanganeh, K. and Angeles, J., “Instantaneous Kinematics and Design of a Novel Redundant Parallel Manipulator,” In: Proceedings of IEEE Conference on Robotics and Automation (1994) pp. 3043–3048.Google Scholar
Wang, J. and Gosselin, C., “Kinematic analysis and design of kinematically redundant parallel mechanisms,” ASME J. Mech. Des. 126(1), 109–118 (2004).CrossRefGoogle Scholar
Mohamed, M. G. and Gosselin, C. M., “Design and analysis of kinematically redundant parallel manipulators with configurable platforms,” IEEE Trans. Robot. 21(3), 277–287 (2005).CrossRefGoogle Scholar
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 (2009).CrossRefGoogle Scholar
Cha, S.-H., Lasky, T. A. and Velinsky, S. A., “ Determination of the kinematically redundant active prismatic joint variable ranges of a planar parallel mechanism for singularity-free trajectories,” Mech. Mach. Theory 44(5), 1032–1044 (2009).CrossRefGoogle Scholar
Boudreau, R. and Nokleby, S., “Force optimization of kinematically-redundant planar parallel manipulators following a desired trajectory,” Mech. Mach. Theory 56(10), 138–155 (2012).CrossRefGoogle Scholar
Ruiz, A. G., Santos, J. C., Croes, J., Desmet, W. and da Silva, M. M., “On redundancy resolution and energy consumption of kinematically redundant planar parallel manipulators,” Robotica 36(6), 809–821 (2018).CrossRefGoogle Scholar
Gosselin, C., Laliberté, T. and Veillette, A., “Singularity-free kinematically redundant planar parallel mechanisms with unlimited rotational capability,” IEEE Trans. Robot. 31(2), 457–467 (2016).CrossRefGoogle Scholar
Schreiber, L.-T. and Gosselin, C., “Kinematically redundant planar parallel mechanisms: Kinematics, workspace and trajectory planning,” Mech. Mach. Theory 119, 91–105 (2018).CrossRefGoogle Scholar
Merlet, J.-P., “Redundant parallel manipulators,” J. Lab. Robot. Automat. 8(1), 17–24 (1996).3.0.CO;2-#>CrossRefGoogle Scholar
Kock, S. and Schumacher, W., “Parallel x-y Manipulator with Actuation Redundancy for High-Speed and Active-Stiffness Applications,” In: Proceedings of IEEE Conference on Robotics and Automation (1998) pp. 2295–2300.Google Scholar
Firmani, F. and Podhorodeski, R., “Force-unconstrained poses for a redundantly actuated planar parallel manipulator,” Mech. Mach. Theory 39(5), 459–476 (2004).CrossRefGoogle Scholar
Gosselin, C. and Schreiber, L.-T., “Redundancy in parallel mechanisms: A review,” ASME Appl. Mech. Rev. 70(1), 15 pages (2018).CrossRefGoogle Scholar
Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 42(2), 3–9 (1985).CrossRefGoogle Scholar
Kokkinis, T. and Paden, B., “Kinetostatic Performance Limits of Cooperating Robot Manipulators,” In: Proceedings of the ASME Winter Annual Meeting (1989) pp. 151–155.Google Scholar
Firmani, F., Zibil, A., Nokleby, S. and Podhorodeski, R., “Wrench capabilities of planar parallel manipulators - Part I: Wrench polytopes and performance indices,” Robotica 26(6), 791–802 (2008).CrossRefGoogle Scholar
Mejia, L., Simas, H. and Martins, D., “Force capability in general 3 DoF planar mechanisms,” Mech. Mach. Theory 26, 120–134 (2015).CrossRefGoogle Scholar
Zibil, A., Firmani, F., Nokleby, S. and Podhorodeski, R., “An explicit method for determining the force moment capabilities of redundantly actuated planar parallel manipulators,” ASME J. Mech. Des. 129(10), 1046–1055 (2007).CrossRefGoogle Scholar
Mejia, L., Simas, H. and Martins, D., “Wrench capability in redundant planar parallel manipulators with net degree of constraint equal to four, five or six,” Mech. Mach. Theory 105, 58–79 (2016).CrossRefGoogle Scholar
Firmani, F., Zibil, A., Nokleby, S. and Podhorodeski, R., “Wrench capabilities of planar parallel manipulators - Part II: Redundancy and wrench workspace analysis,” Robotica 26(6), 803–815 (2008).CrossRefGoogle Scholar
Weihmann, L., Martins, D. and Coelho, L., “Force capabilities of kinematically redundant planar parallel manipulators,” In: Proceedings of 13th World Congress in Mechanism and Machine Science (2011) 8 pages.Google Scholar
Boudreau, R., Nokleby, S. and Gallant, M., “Investigating the Wrench Capabilities of a Kinematically-Redundant Planar Parallel Manipulator,” In: Proceedings of the 2019 CCToMM Symposium on Mechanisms, Machines and Mechatronics (2019) 12 pages.Google Scholar
Gosselin, C. and Angeles, J., “The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator,” J. Mech. Trans. Automat. Des. 110(1), 35–41 (1988).CrossRefGoogle Scholar
Bonev, I. A., Zlatanov, D. and Gosselin, C., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” J. Mech. Des. 125(3), 573–581 (2003).CrossRefGoogle Scholar
Arsenault, M. and Boudreau, R., “The synthesis of three-degree-of-freedom planar parallel mechanisms with revolute joints (3-RRR) for an optimal singularity-free workspace,” J. Robot. Syst. 21(5), 259–274 (2004).CrossRefGoogle Scholar
Kucuk, S., “Simulation and design tool for performance analysis of planar parallel manipulators,” Simulation. 88(5), 542–556 (2012).CrossRefGoogle Scholar
Firmani, F., Zibil, A., Nokleby, S. and Podhorodeski, R., “Force-moment capabilities of revolute-jointed planar parallel manipulators with additional actuated branches,” Trans. CSME 31(4), 469–482 (2007).Google Scholar