Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T23:28:30.274Z Has data issue: false hasContentIssue false
  • English
  • Français

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: podhoro@me.uvic.ca
Get access Rights & Permissions [Opens in a new window]

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

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

1.Zheng, Y. F. and Luh, J. Y. S., “Optimal Load Distribution for Two Industrial Robots Handling a Single Object,” Proceedings of the 1988 IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA (Apr. 24–29, 1988) pp. 344–349.Google Scholar
2.Kumar, V. and Waldron, K. J., “Force Distribution in Closed Kinematic Chains,” Proceedings of the 1988 IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA (Apr. 24–29, 1988) pp. 114–119.CrossRefGoogle Scholar
3.Tao, J. M. and Luh, J. Y. S., “Coordination of Two Redundant Manipulators,” Proceedings of the 1989 IEEE International Conference on Robotics and Automation, Scottsdale, AZ, USA (May 14–19, 1989) pp. 425–430.CrossRefGoogle Scholar
4.Nahon, M. A. and Angeles, J., “Real-time force optimization in parallel kinematic chains under inequality constraints,” IEEE Trans. Robot. Autom. 8 (4), 439–450 (1992).Google Scholar
5.Kwon, W. and Lee, B. H., “A new optimal force distribution scheme of multiple cooperating robots using dual method,” J. Intell. Robot. Syst. 21 (4), 301–326 (1998).CrossRefGoogle Scholar
6.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
7.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
8.Garg, V., Carretero, J. A. and Nokleby, S. B., “Determining the Force and Moment Workspace Volumes of Redundantly-Actuated Spatial Parallel Manipulators,” Proeedings of the 2007 ASME Design Engineering Technical Conference ASME, Las Vegas, NV, USA (Sep. 4–7, 2007).Google Scholar
9.Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 3–9 (1985).Google Scholar
10.Yoshikawa, T., Foundations of Robotics: Analysis and Control (The MIT Press, Cambridge, MA, USA, 1990).Google Scholar
11.Chiacchio, P., Chiaverini, S., Sciavicco, L. and Siciliano, B., “Global task space manipulability ellipsoids for multiple-arm systems,” IEEE Trans. Robot. Autom. 7 (5), 678–685 (1991).Google Scholar
12.Lee, S. and Kim, S., “A Self-Reconfigurable Dual-Arm System,” Proceedings of the1991 IEEE International Conference on Robotics and Automation, vol. 1, Sacramento, CA, USA, (Apr. 9–11, 1991) pp. 164–169.Google Scholar
13.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, vol. 4, Minneeapolis, MN (Apr. 22–28, 1996) pp. 3520–3525.Google Scholar
14.Chiacchio, P., Bouffard-Vercelli, Y. and Pierrot, F., “Force polytope and force ellipsoid for redundant manipulators,” J. Robot. Syst. 14 (8), 613–620 (1997).Google Scholar
15.Yoshikawa, T., “Dynamic manipulability of robot manipulators,” J. Robot. Syst. 2 (1), 113–124 (1985).Google Scholar
16.Chiacchio, P., “A new dynamic manipulability ellipsoid for redundant manipulators,” Robotica, 18 (4), 381–387 (2000).CrossRefGoogle Scholar
17.Duffy, J., “The fallacy of modern hybrid control theory that is based on ‘orthogonal complements’ of twist and wrench spaces,” J. Robot. Syst. 7 (2), 139–144 (1990).Google Scholar
18.Doty, K. L., Melchiorri, C., Schwartz, E. M. and Bonivento, C., “Robot manipulability,” IEEE Trans. Robot. Autom. 11 (3), 462–468 (1995).Google Scholar
19.Melchiorri, C., “Comments on “Global task space manipulability ellipsoids for multiple-arm systems” and further considerations,” IEEE Trans. Robot. Autom. 9 (2), 232–235 (1993).CrossRefGoogle Scholar
20.Bicchi, A., Melchiorri, C. and Balluchi, D., “On the mobility and manipulability of general multiple limb robotic systems,” IEEE Trans. Robot. Autom. 11 (2), 215–228 (1995).CrossRefGoogle Scholar
21.Bicchi, A., Prattichizzo, D. and Melchiorri, C., “Force and Dynamic Manipulability for Cooperating Robot Systems,” Proceedings of 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, Grenoble, France (Sep. 7–11, 1997) pp. 1479–1484.Google Scholar
22.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
23.Lee, J., “A Study on the Manipulability Measures for Robot Manipulators,” Proceedings of 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, Grenoble, France (Sep. 7–11, 1997) pp. 1458–1465.Google Scholar
24.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, vol. 3, San Francisco, CA, USA (Apr. 24–28, 2000) pp. 2569–2574.Google Scholar
25.Finotello, R., Grasso, T., Rossi, G. and Terribile, A., “Computation of Kinetostatic Performances of Robot Manipulators with Polytopes,” Proceedings of the 1998 IEEE International Conference on Robotics and Automation, vol. 4, Leuven, Belgium (May 16–20, 1998) pp. 3241–3246.Google Scholar
26.Gallina, P., Rosati, G. and Rossi, A., “3-d.o.f. wire driven planar haptic interface,” J. Intell. Robot. Syst. 32 (1), 23–36 (2001).CrossRefGoogle Scholar
27.Lee, J. and Shim, H., “On the Dynamic Manipulability of Cooperating Multiple Arm Robot Systems,” Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 2, Sendai, Japan (Sep. 28–Oct. 2, 2004) pp. 3520–3525.Google Scholar
28.Krut, S., Company, O. and Pierrot, F., “Velocity performance indices for parallel mechanisms with actuation redundancy,” Robotica 22 (2), 129–139 (2004).CrossRefGoogle Scholar
29.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, vol. 4, Sendai, Japan (Sep. 28–Oct. 2, 2004) pp. 3936–3941.Google Scholar
30.Rockafellar, R. T., Convex Analysis, 1st ed. 1970 (Princeton University Press, Princeton, NJ, USA, 1997).CrossRefGoogle Scholar
31.Visvanathan, V. and Milor, L. S., “An Efficient Algorithm to Determine the Image of a Parallelepiped Under a Linear Transformation,” Proceedings of the Second Annual Symposium on Computational Geometry, Yorktown Heights, NY, USA, (1986) pp. 207–215.CrossRefGoogle Scholar
32.Chand, D. R. and Kapur, S. S., “An algorithm for convex polytopes,” J. Assoc. Compu. Mach. 17 (1), 78–86 (1970).CrossRefGoogle Scholar
33.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).Google Scholar
34.Hunt, K. H., Kinematic Geometry of Mechanisms (Oxford University Press, Toronto, ON, Canada, 1978).Google Scholar
35.Ball, R. S., A Treatise of the Theory of Screws (Cambridge University Press, New York, NY, USA, 1900).Google Scholar
36.Zlatanov, D., Fenton, R. G. and Benhabib, B., “Analysis of the Instantaneous Kinematics and Singular Configurations of Hybrid-Chain Manipulators,” Proceedings of the ASME 23rd Biennial Mechanisms Conference, vol. 72, Minneapolis, MN, USA (Sep. 11–14, 1994) pp. 467–476.Google Scholar
37.Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
38.Fisher, R., Podhorodeski, R. P. and Nokleby, S. B., “A Reconfigurable Planar Parallel Manipulator,” J. Robot. Syst. 21 (12), 665–675 (2004).CrossRefGoogle Scholar