Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-09T02:59:33.234Z Has data issue: false hasContentIssue false
  • English
  • Français

A novel spherical parallel manipulator: forward position problem, singularity analysis, and isotropy design

Published online by Cambridge University Press:  08 September 2008

Javad Enferadi  and
Alireza Akbarzadeh Tootoonchi
Javad Enferadi*
Affiliation:
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
Alireza Akbarzadeh Tootoonchi
Affiliation:
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
*
*Corresponding author. E-mail: Javadenferadi@gmail.com
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper, a novel spherical parallel manipulator and its isotropic design is introduced. This manipulator has good accuracy and relatively a larger workspace which is free of singularities. Utilizing spherical configuration the forward position problem is solved by equivalent angle–axis representation and Bezout's method which leads to a polynomial of degree 8. Two examples are given, one for isotropic and one for nonisotrpoic design. The first case results in eight real solutions, therefore, the polynomial being minimal. Using invariant form, we study acceleration analysis, conditions for singularity and find infinite isotropic structures. Accuracy and workspace analysis are also performed and are shown to have good global conditioning index and relatively large workspace. Using isotropic design and singularity requirements, we show the workspace of isotropic design is free of singularity.

Keywords

Spherical parallel manipulatorForward position problemBezout's elimination methodIsotropy designSingularity analysis

Information

Type
Article
Information
Robotica , Volume 27 , Issue 5 , September 2009 , pp. 663 - 676
Copyright
Copyright © Cambridge University Press 2008

References

1. Chablat, D. and Angeles, J., “The computation of all 4R serial spherical wrists with an isotropic architecture,” ASME J. Mech. Des. 125 (2), 275–280 (2003).CrossRefGoogle Scholar
2. Gosselin, C. M. and Angeles, J., “The optimum kinematics design of a spherical three-degree-of-freedom parallel manipulator,” ASME J. Mech. Des. 111 (2), 202–207 (1989).Google Scholar
3. Gosselin, C. M., Sefrioui, J. and Richard, M. J., “On the direct kinematics of spherical three-degree-of-freedom parallel manipulators of general architecture,” ASME J. Mech. Des. 116 (2), 594–598 (1994).CrossRefGoogle Scholar
4. Gosselin, C. M., Perreault, L. and Vaillancourt, C., “Simulation and computer-aided kinematics design of three-degree-of-freedom spherical parallel manipulators,” J. Rob. Syst. 12 (12), 857–869 (1995).CrossRefGoogle Scholar
5. Alizade, R. I., Tagiyiev, N. R. and Duffy, J., “A forward and reverse displacement analysis of an in-parallel spherical manipulator,” Mech. Mach. Theory 29 (1), 125–137 (1994).CrossRefGoogle Scholar
6. Wiitala, J. M. and Stanisic, M. M., “Design of an overconstrained and dexterous spherical wrist,”, ASME J. Mech. Des. 122 (3), 347–353 (2000).CrossRefGoogle Scholar
7. Alici, G. and Shirinzadeh, B., “Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint,” Mech. Mach. Theory 39, 215–235 (2004).CrossRefGoogle Scholar
8. Innocenti, C. and Parenti-Castelli, V., “Echelon form solution of direct kinematics for the general fully-parallel spherical wrist,” Mech. Mach. Theory 28 (4), 553–561 (1993).CrossRefGoogle Scholar
9. Wohlhart, K., “Displacement analysis of the general spherical Stewart platform,” Mech. Mach. Theory 29 (4), 581–589 (1994).CrossRefGoogle Scholar
10. Karouia, M. and Herve, J. M., “A three-dof tripod for generating spherical rotation,” In: Advances in Robot Kinematics (Lenarcic, J. and Stanisic, M. M., eds.), (Kluwer Academic Publishers, Netherlands, 2000) pp. 395–402.CrossRefGoogle Scholar
11. Di Gregorio, R., “A new parallel wrist employing just revolute pairs: The 3-RUU wrist,” Robotica 19 (3), 305–309 (2000).CrossRefGoogle Scholar
12. Di Gregorio, R., “Kinematics of a new spherical parallel manipulator with three equal legs: The 3-URC wrist,” J. Rob. Syst. 18 (5), 213–219 (2001).CrossRefGoogle Scholar
13. Di Gregorio, R., “The 3-RRS wrist: A new, simpleand non-overconstrained spherical parallel manipulator,” ASME J. Mech. Des. 126, 850–855 (2004).CrossRefGoogle Scholar
14. Vertechy, R. and Parenti-Castelli, V., “Real-time direct position analysis of parallel spherical wrists by using extra sensors,” ASME J. Mech. Des. 128, 288–294 (2006).CrossRefGoogle Scholar
15. Karouia, M. and Herve, J. M., “Asymmetrical 3-dof spherical parallel mechanisms,” Eur. J. Mech. 24, 47–57 (2005).CrossRefGoogle Scholar
16. Cervantes-Sanchez, J. J., Hernandez-Rodriguez, J. C. and Gonzalez-Galvan, E. J., “On the 5R spherical, symmetric manipulator: workspace and singularity characterization,” Mech. Mach. Theory 39, 409–429 (2004).CrossRefGoogle Scholar
17. Mohammadi Daniali, H. R., Zsombor-Murray, P. J. and Angeles, J., “The kinematics of 3-dof planar and spherical double-triangular parallel manipulators,” In: Computational Kinematics (Angeles, J., Hommel, G. and Kovacs, P., eds.) (Kluwer Academic Publishers, Dordecht, 1993) pp. 153–164.CrossRefGoogle Scholar
18. Gosselin, C., Kinematic Analysis Optimization and Programming of Parallel Robotic Manipulators, h. D. Thesis (McGill University, Montréal, Canada, 1988).Google Scholar