Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-05T08:57:39.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator

Published online by Cambridge University Press:  01 May 2008

Iman Ebrahimi ,
Juan A. Carretero  and
Roger Boudreau
Iman Ebrahimi
Affiliation:
Department of Mechanical Engineering, University of New Brunswick, Fredericton, Canada
Juan A. Carretero*
Affiliation:
Department of Mechanical Engineering, University of New Brunswick, Fredericton, Canada
Roger Boudreau
Affiliation:
Département de génie mécanique, Université de Moncton, Moncton, Canada
*
*Corresponding author: E-mail address: Juan.Carretero@unb.ca
Get access Rights & Permissions [Opens in a new window]

Summary

In this work, the 3-RPRR, a new kinematically redundant planar parallel manipulator with six-degrees-of-freedom, is presented. First, the manipulator is introduced and its inverse displacement problem discussed. Then, all types of singularities of the 3-RPRR manipulator are analysed and demonstrated. Thereafter, the dexterous workspace is geometrically obtained and compared with the non-redundant 3-PRR planar parallel manipulator. Finally, based on a geometrical measure of proximity to singular configurations and the condition number of the manipulators' Jacobian matrices, actuation schemes for the manipulators are obtained. Different actuation schemes for a given path are obtained and the quality of their actuation schemes are compared. It is shown that the proposed manipulator is capable of following a path while avoiding the singularities.

Keywords

Kinematic redundancyPlanar parallel manipulatorsInverse displacementSingularity analysisWorkspace analysisPath planning3-RPRR
Type
Article
Information
Robotica , Volume 26 , Issue 3 , May 2008 , pp. 405 - 413
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.Merlet, J.-P., Parallel Robots, 2nd ed. (Springer, Heidelberg 2006).Google Scholar
2.Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a planar three-degrees-of-freedom parallel manipulator,” J. Mech. Transm. Autom. Des. 110 (1), 35–41 (1988).Google Scholar
3.Carretero, J. A., Podhorodeski, R. P., Nahon, M. A. and Gosselin, C. M., “Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator,” J. Mech. Des. 122 (1), 17–24 (Mar. 2000).Google Scholar
4.Tsai, K. Y. and Zhou, S. R., “The optimum design of 6-DOF isotropic parallel manipulators,” J. Robot. Syst. 22 (6), 333–340 (2005).CrossRefGoogle Scholar
5.Hao, F. and Merlet, J.-P., “Multi-criteria optimal design of parallel manipulators based on interval analysis,” Mech. Mach. Theory 40 (2), 157–171 (2005).CrossRefGoogle Scholar
6.Kong, X. and Gosselin, C. M., “Type synthesis of three degree-of-freedom spherical parallel manipulators,” Int. J. Robot. Res. 23 (3), 237–245 (2004).Google Scholar
7.Arsenault, M. and Boudreau, R., “Synthesis of planar parallel mechanisms while considering workspace, dexterity, stiffness and singularity avoidance,” J. Mech. Des. 128 (1), 69–78 (2006).Google Scholar
8.Maciejewski, A. A. and Klein, C. A., “Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments,” Int. J. Robot. Res. 4 (3), 109–117 (1985).Google Scholar
9.Nakamura, Y., Hanafusa, H. and Yoshikawa, T., “Task-priority based redundancy control of robot manipulators,” Int. J. Robot. Res. 6 (2), 3–15 (1987).Google Scholar
10.Lee, S. and Kim, S., “Kinematic Analysis of Generalized Parallel Manipulator Systems,” Proceedings of the IEEE Conference on Decision and Control (1993) Vol. 2, pp. 1097–1102.Google Scholar
11.Zanganeh, K. E. and Angeles, J., “Instantaneous Kinematics and Design of a Novel Redundant Parallel Manipulator,” Proceedings of the IEEE Conference on Robotics and Automation, San Diego, USA (May 1994) pp. 3043–3048.Google Scholar
12.Merlet, J.-P., “Redundant parallel manipulators,” Lab. Robot. Autom. 8 (1), 17–24 (1996).Google Scholar
13.Wang, J. and Gosselin, C. M., “Kinematic analysis and design of kinematically redundant parallel mechanisms,” J. Mech. Des. 126 (1), 109–118 (2004).Google Scholar
14.Garg, V., Nokleby, S. B. and Carretero, J. A., “Determining the Force and Moment Workspaces of Redundantly-Actuated Spatial Parallel Manipulators,” Proceedings of the 2007 ASME Design Engineering Technical Conference, Las Vegas, Nevada, USA (September 2007).CrossRefGoogle Scholar
15.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).Google Scholar
16.Hassan, M. and Notash, L., “Design modification of parallel manipulators for optimum fault tolerance to joint jam,” Mech. Mach. Theory 40 (5), 559–577 (2005).Google Scholar
17.Gosselin, C. M., Lemieux, S. and Merlet, J.-P., “A new Architecture of Planar Three-Degree-of-Freedom Parallel Manipulator,” Proceedings of the 1996 IEEE International Conference on Robotics and Automation (Cat. No. 96CH35857), Minneapolis, USA (1996) Vol. 4, pp. 3738–3743.Google Scholar
18.Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).Google Scholar
19.Merlet, J.-P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33 (1), 7–20 (1998).Google Scholar
20.Zanganeh, K. E. and Angeles, J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robot. Res. 16 (2), 185–197 (1997).CrossRefGoogle Scholar
21.Nakamura, Y., Advanced Robotics: Redundancy and Optimization. (Addison-Weslay Publishing Co., Reading, Massachusetts, USA, 1991).Google Scholar
22.Salisbury, J. K. and Craig, J. J., “Articulated hands: Force control and kinematic issues,” Int. J. Robot. Res. 1 (1), 4–17 (1982).CrossRefGoogle Scholar
23.Ebrahimi, I., Carretero, J. A. and Boudreau, R., “Path Planning for the 3-PRRR Redundant Planar Parallel Manipulator,” In: Merlet, J.-P., ed., Proceedings of the 2007 IFToMM World Congress, Besançon, France, (Jun. 2007).Google Scholar
24.Tsai, L.-W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (Wiley-Interscience, New York, USA, 1999).Google Scholar