Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T08:12:13.120Z Has data issue: false hasContentIssue false
  • English
  • Français

Singular curves in the joint space and cusp points of 3-RPR parallel manipulators

Published online by Cambridge University Press:  01 November 2007

Mazen Zein ,
Philippe Wenger  and
Damien Chablat
Mazen Zein*
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes UMR CNRS 6597, 44312 Nantes Cedex 03, France.
Philippe Wenger
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes UMR CNRS 6597, 44312 Nantes Cedex 03, France.
Damien Chablat
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes UMR CNRS 6597, 44312 Nantes Cedex 03, France.
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper investigates the singular curves in the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it exposes a method to compute joint space singular curves of 3-RPR planar parallel manipulators. Second, it presents an algorithm for detecting and computing all cusp points in the joint space of these same manipulators.

Type
Article
Information
Robotica , Volume 25 , Issue 6 , November 2007 , pp. 717 - 724
Copyright
Copyright © Cambridge University Press 2007

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 (Kluwer Academics, Norwell, MA, 2000).CrossRefGoogle Scholar
2.Gosselin, C. and Angeles, J., “Singularity analysis of closed loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
3.Gosselin, C., Sefrioui, J. and Richard, M. J., “Solution polynomiale au problème de la cinématique directe des manipulateurs parallèles plans à 3 degrés de liberté,” Mech. Mach. Theory 27 (2), 107–119 (1992).CrossRefGoogle Scholar
4.Sefrioui, J. and Gosselin, C., “On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators,” Mech. Mach. Theory 30 (4), 535–551 (1995).CrossRefGoogle Scholar
5.Wenger, P. and Chablat, D., “Definition Sets for the Direct Kinematics of Parallel Manipulators,” Proceedings of the 8th Conference on Advanced Robotics (1997) pp. 859–864.Google Scholar
6.Bonev, I., Zlatanov, D. and Gosselin, C., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” ASME J. Mech. Des. 125 (3), 573–581 (2003).CrossRefGoogle Scholar
7.Hunt, K. H. and Primrose, E. J. F., “Assembly configurations of some In-parallel-actuated manipulators,” Mech. Mach. Theory 28 (1), 31–42 (1993).CrossRefGoogle Scholar
8.Innocenti, C. and Parenti-Castelli, V., “Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators,” ASME Mech. Des. 120 (2), 293–298 (1998).CrossRefGoogle Scholar
9.McAree, P. R. and Daniel, R. W., “An explanation of never-special assembly changing motions for 3-3 parallel manipulators,” Int. J. Robot. Res. 18 (6), 556–574 (1999).CrossRefGoogle Scholar
10.Kong, X. and Gosselin, C. M., “Forward displacement analysis of third-class analytic 3-RPR planar parallel manipulators,” Mech. Mach. Theory 36 (9), 1009–1018 (2001).CrossRefGoogle Scholar
11.Burdick, J. W., “A Classification of 3R regional manipulator Singularities and Geometries,” Proceedings of the IEEE International Conference on Robotics and Automation, Sacramento, California (1991) pp. 2670–2675.Google Scholar
12.Wenger, Ph., “A New General Formalism for the Kinematic Analysis for all Non-Redundant Manipulators,” Proceeding International Conference on Robotics and Automation, Nice, France (1992) pp. 442–447.Google Scholar
13.El Omri, J. and Wenger, P., “How to Recognize Simply a Non-Singular Posture Changing 3-DOF Manipulator,” Proceedings of the 7th International Conference on Advanced Robotics (1995) pp. 215–222.Google Scholar
14.Ottaviano, E., Husty, M. and Ceccarelli, M., “A Cartesian Representation for the Boundary Workspace of 3R Manipulators,” Proceedings on Advances on Robots Kinematics (2004) pp. 247–254.Google Scholar
15.Wenger, Ph. and Chablat, D., “Workspace and assembly modes in fully-parallel manipulators: A descriptive study,” Adv. Robot Kinematics Computat. Geom., 117–126 (1998).Google Scholar
16.Zein, M., Wenger, Ph. and Chablat, D., “Singular Curves and Cusp Points in the Joint Space of 3-RPR Parallel Manipulators,” Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, Florida (May 2006) pp. 776–782.Google Scholar
17.Hunt, K. H., Geometry of Mechanisms (Clarendon Press, Oxford, 1978.Google Scholar
18.Buchberger, B., Collins, G. E. and Loos, R.. Computer Algebra: Symbolic and Algebraic Computation (Springer-Verlag, Wien, 1982) pp. 115–138.CrossRefGoogle Scholar
19.Baili, M., Wenger, P. and Chablat, D., “A Classification of 3R Orthogonal Manipulators by the Topology of Their Workspace,” Proceedings of the IEEE International Conference on Robotics and Automation, Louisiana (2004) pp. 1933–1938.Google Scholar