Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T02:29:13.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Singularities of a planar 3-RPR parallel manipulator with joint clearance

Published online by Cambridge University Press:  02 April 2018

Marise Gallant  and
Clément Gosselin
Marise Gallant*
Affiliation:
Université de Moncton, Moncton, NB, Canada
Clément Gosselin
Affiliation:
Université Laval, Québec, Canada. E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

If the joint clearances of the joints of a manipulator are considered, an unconstrained motion of the end-effector can be computed. This is true for all poses of the manipulator, even with all actuators locked.

This paper presents how this unconstrained motion can be determined for a planar 3-RPR manipulator. The singularities are then studied. It is shown that when clearances are considered, the singularity curves normally found in the workspace of such a manipulator become singular zones. These zones can be significant and greatly reduce the usable workspace of a manipulator. Since a prescribed configuration that would not, in theory, corresponds to a singular pose can become singular due to the unconstrained motion, the results of this paper are relevant to manipulator design and trajectory planning.

Keywords

Joint clearanceSingularitiesParallel manipulator
Type
Articles
Information
Robotica , Volume 36 , Issue 7 , July 2018 , pp. 1098 - 1109
Copyright
Copyright © Cambridge University Press 2018 

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. Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robotic. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
2. Zlatanov, D., Fenton, R. G. and Benhabib, B., “A unifying framework for classification and interpretation of mechanism singularities,” J. Mech. Des. 117, 566–572 (1995).Google Scholar
3. Zlatanov, D., Fenton, R. G. and Benhabib, B., “Identification and classification of the singular configurations of mechanisms,” Mech. Mach. Theory 33 (6), 743–760 (1998).CrossRefGoogle Scholar
4. Sefrioui, J. and Gosselin, C. M., “On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators,” Mech. Mach. Theory 30 (4), 533–551 (1995).Google Scholar
5. Bonev, I. A., Zlatanov, D. and Gosselin, C. M., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” J. Mech. Des. 125, 573–581 (2003).CrossRefGoogle Scholar
6. Sefrioui, J. and Gosselin, C. M., “Singularity analysis and representation of planar parallel manipulators,” Robot. Auton. Syst. 10, 209–224 (1992).CrossRefGoogle Scholar
7. Mayer St-Onge, B. and Gosselin, C. M., “Singularity Analysis and Representation of Spatial Six-Degree-of-Freedom Parallel Manipulators,” Proceedings of the 5th International Symposium on Advances in Robot Kinematics (ARK) (Lenarcic, J. and Parenti-Castelli, V., eds.) (Portoroz-Bernardin, Slovénie, 1996) pp. 389–398.Google Scholar
8. Bhattacharya, S., Hatwal, H. and Ghosh, A., “Comparison of an exact and an approximate method of singularity avoidance in platform type parallel manipulators,” Mech. Mach. Theory 33 (7), 965–974 (1998).CrossRefGoogle Scholar
9. Dasgupta, B. and Mruthyunjaya, T. S., “Singularity-free path planning for the Stewart platform manipulator,” Mech. Mach. Theory 33 (6), 711–725 (1998).CrossRefGoogle Scholar
10. Liu, S., Qiu, Z.-C., and Zhang, X.-M., “Singularity and path-planning with the working mode conversion of a 3-DOF 3-RRR planar parallel manipulator,” Mech. Mach. Theory 107, 166–182 (2017).Google Scholar
11. Ebrahimi, I., Carretero, J. and Boudreau, R., “A family of kinematically redundant planar parallel manipulators,” ASME J. Mech. Design 130 (6), 062306.1–062306.8 (2008).CrossRefGoogle Scholar
12. Matone, R. and Roth, B., “In-Parallel Manipulators: A Framework on How to Model Actuation Schemes and a Study of their Effects on Singular Postures,” Proceedings of ASME DETC'98, (Atlanta, Georgia) (Sep. 1998) pp. 1–11.CrossRefGoogle Scholar
13. Carricato, M. and Parenti-Castelli, V., “Kinematics of a family of translational parallel mechanisms with three 4-DOF legs and rotary actuators,” J. Robot. Syst. 20 (7), 373–389 (2003).CrossRefGoogle Scholar
14. O'Brien, J. F. and Wen, J. T., “Kinematic Control of Parallel Robots in the Presence of Unstable Singularities,” Proceedings of the 2001 IEEE International Conference on Robotics & Automation, (Seoul, Korea) (May 21–26 2001).Google Scholar
15. Gallant, M. and Boudreau, R., “The synthesis of planar parallel manipulators with prismatic joints for an optimal, singularity-free workspace,” J. Robot. Syst. 19 (1), 13–24 (2002).Google Scholar
16. 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
17. Parenti-Castelli, V. and Venanzi, S., “Clearance influence analysis on mechanisms,” Mech. Mach. Theory 40, 1316–1329 (2005).Google Scholar
18. Innocenti, C., “Kinematic clearance sensitivity analysis of spatial structures with revolute joints,” Trans. ASME 124, 52–57 (2002).Google Scholar
19. Voglewede, P. and Ebert-Uphoff, I., “Application of workspace generation techniques to determine the unconstrained motion of parallel manipulators,” J. Mech. Des. 126 (2), 283–290 (2004).Google Scholar
20. Chebbi, A.-H., Affi, Z. and Romdhane, L., “Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot,” Mech. Mach. Theory 44, 1768–1783 (2009).Google Scholar
21. Zhang, X., Zhang, X. and Chen, Z., “Dynamic analysis of a 3-RRR parallel mechanism with multiple clearance joints,” Mech. Mach. Theory 78, 105–115 (2014).Google Scholar
22. Ting, K.-L., Hsu, K.-L., Yu, Z. and Wang, J., “Clearance-induced output position uncertainty of planar linkages with revolute and prismatic joints,” Mech. Mach. Theory 111, 66–75 (2017).Google Scholar
23. Ting, K.-L., Zhu, J. and Watkins, D., “The effects of joint clearance on position and orientation deviation of linkages and manipulators,” Mech. Mach. Theory 35, 391–401 (2000).Google Scholar
24. Tsai, M.-J. and Lai, T.-H., “Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality,” Mech. Mach. Theory 39, 1189–1206 (2004).Google Scholar
25. Tsai, M.-J. and Lai, T.-H., “Accuracy analysis of a multi-loop linkage with joint clearances,” Mech. Mach. Theory 43, 1141–1157 (2008).Google Scholar
26. Garrett, R. E. and Hall, A. S., “Effect of tolerance and clearance in linkage design,” Trans. ASME, J. Eng. Ind. 91, 198–202 (1969).Google Scholar
27. Sharfi, O. M. A. and Smith, M. R., “A simple method for the allocation of appropriate tolerances and clearances in linkage mechanisms,” Mech. Mach. Theory 18 (2), 123–129 (1983).Google Scholar
28. Gosselin, C., “Determination of the workspace of 6-DOF parallel manipulators,” J. Mech. Des. 112, 331–336 (1990).Google Scholar
29. Briot, S. and Bonev, I. A., “Accuracy analysis of 3-DOF planar parallel robots,” Mech. Mach. Theory 43 (4), 445–458 (2008).CrossRefGoogle Scholar
30. Yu, A., Bonev, I. A. and Zsombor-Murray, P., “Geometric approach to the accuracy analysis of a class of 3-DOF planar parallel robots,” Mech. Mach. Theory 43 (3), 364–375 (2008).Google Scholar