Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T09:20:14.142Z Has data issue: false hasContentIssue false
  • English
  • Français

Determination of the maximal singularity-free zone of 4-RRR redundant parallel manipulators and its application on investigating length ratios of links

Published online by Cambridge University Press:  08 December 2014

Yuzhe Liu ,
Jun Wu ,
Liping Wang  and
Jinsong Wang
Yuzhe Liu
Affiliation:
State Key Laboratory of Tribology and Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, P. R. China Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing 100084, P. R. China
Jun Wu*
Affiliation:
State Key Laboratory of Tribology and Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, P. R. China Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing 100084, P. R. China
Liping Wang
Affiliation:
State Key Laboratory of Tribology and Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, P. R. China Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing 100084, P. R. China
Jinsong Wang
Affiliation:
State Key Laboratory of Tribology and Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, P. R. China Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing 100084, P. R. China
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents a new numerical approach using a Genetic algorithm (GA) to search for the singularity-free cylindrical space of a 4-RRR planar redundant parallel manipulator and investigates the effects of the joint position (namely the length ratios of two links) of each leg on the singularity-free cylindrical space. A previous method investigated the maximal singularity-free zone in a 3-dimensional (3-D) space within a given workspace. The method in this paper is improved by optimizing the maximal singularity-free zone in a 2-dimensional (2-D) plane while considering the whole workspace. This improvement can be helpful for reducing the searching time and for finding a larger singularity-free zone. Furthermore, the effect of the joint position of each leg on the maximal singularity-free zone is studied in this paper, which reveals a larger singularity-free zone than before. This result shows that changing the joint positions of one or two legs may be more practical than changing the joint positions of more legs. The approach in this paper can be used to analyze the maximal singularity-free zone of any other three-degree-of-freedom (3-DOF) planar parallel mechanisms and will be useful for the optimal design of redundant parallel manipulators.

Keywords

Parallel manipulatorMaximal singularity-free zoneGenetic algorithmSize optimization
Type
Articles
Information
Robotica , Volume 34 , Issue 9 , September 2016 , pp. 2039 - 2055
Copyright
Copyright © Cambridge University Press 2014 

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. Zubizarreta, A., Marcos, M., Cabanes, I., Pinto, C. and Portillo, E., “Redundant sensor based control of the 3RRR parallel robot,” Mech. Mach. Theory 54, 1–17 (2012).Google Scholar
2. Kucuk, S., “A dexterity comparison for 3-DOF planar parallel manipulators with two kinematic chains using genetic algorithms,” Mechatronics 19 (6), 868–877 (2009).Google Scholar
3. Staicu, S., “Power requirement comparison in the 3-RPR planar parallel robot dynamics,” Mech. Mach. Theory 44 (5), 1045–1057 (2009).Google Scholar
4. Dachang, Z., Yanping, F., Jinbao, C. and Guifang, X., “Kinematic Analysis of 3-DoF Perpendicular Parallel Manipulator with Flexure Hinge,” Proceedings of the 3rd International Conference on IEEE Knowledge Discovery and Data Mining, 2010. WKDD'10, Phuket, Thailand (Jan. 2010) pp. 363–366.Google Scholar
5. Dash, A. K., Chen, I. M., Yeo, S. H. and Yang, G., “Singularity-Free Path Planning of Parallel Manipulators using Clustering Algorithm and Line Geometry,” Proceedings of the IEEE International Conference on Robotics and Automation, ICRA'03, Taipei, Taiwan (Sep. 2003) 1, pp. 761–766.Google Scholar
6. Parsa, S. S., Daniali, H. M. and Ghaderi, R., “Optimization of parallel manipulator trajectory for obstacle and singularity avoidances based on neural network,” Int. J. Adv. Manuf. Tech. 51 (5–8), 811–816 (2010).Google Scholar
7. Wu, J., Wang, J., Wang, L. and Li, T., “Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy,” Mech. Mach. Theory 44 (4), 835–849 (2009).CrossRefGoogle Scholar
8. Gosselin, C. M. and Angeles, J., “The optimal kinematic design of a planar three-degree-of-freedom parallel manipulator,” J. Mech. Des. 110 (1), 35–41 (1988).Google Scholar
9. Muller, A., “On the terminology and geometric aspects of redundant parallel manipulators,” Robotica 31 (1), 137–147 (2013).Google Scholar
10. Buttolo, P. and Hannaford, B., “Advantages of Actuation Redundancy for the Design of Haptic Displays,” Proceedings ASME, Fourth Annual Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, San Francisco (Nov. 1995) pp. 623–630.Google Scholar
11. Wu, J., Wang, J., Wang, L. and You, Z., “Performance comparison of three planar 3-DOF parallel manipulators with 4-RRR, 3-RRR and 2-RRR structures,” Mechatronics 20 (4), 510–517 (2010).CrossRefGoogle Scholar
12. Wu, J., Chen, X., Wang, L. and Liu, X., “Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor,” Nonlinear Dyn. 78 (1), 241–250 (2014).CrossRefGoogle Scholar
13. Wu, J., Li, T., Wang, J. and Wang, L., “Performance analysis and comparison of planar 3-DOF parallel manipulators with one and two additional branches,” J. Intell. Robot. Syst. 72 (1), 73–82 (2013).Google Scholar
14. Merlet, J. P., “Redundant parallel manipulators,” Lab. Rob. Autom. 8 (1), 17–24 (1996).3.0.CO;2-#>CrossRefGoogle Scholar
15. 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
16. 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
17. Gallardo-Alvarado, J., Alici, G. and Pérez-González, L., “A new family of constrained redundant parallel manipulators,” Multibody Syst. Dyn. 23 (1), 57–75 (2010).CrossRefGoogle Scholar
18. Liao, H., Li, T. and Tang, X., “Singularity Analysis of Redundant Parallel Manipulators,” Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Hague, Netherlands (Oct. 2004) 5, pp. 4214–4220.Google Scholar
19. Xu, B., Li, T., Liu, X. and Wu, J., “Workspace analysis of the 4RRR planar parallel manipulator with actuation redundancy,” Tsinghua Sci. Technol. 15 (5), 509–516 (2010).Google Scholar
20. Wu, J., Li, T., Wang, J. and Wang, L., “Stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates,” Robot. Auton. Syst. 61 (8), 868–875 (2013).Google Scholar
21. Merlet, J. P., “Determination of the Presence of Singularities in 6D Workspace of a Gough Parallel Manipulator,” In: Advances in Robot Kinematics: Analysis and Control (Springer Netherlands, 1998) pp. 39–48.Google Scholar
22. 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).Google Scholar
23. Li, H., Gosselin, C. M. and Richard, M. J., “Determination of maximal singularity-free zones in the workspace of planar three-degree-of-freedom parallel mechanisms,” Mech. Mach. Theory 41 (10), 1157–1167 (2006).CrossRefGoogle Scholar
24. Li, H., Gosselin, C. M. and Richard, M. J., “Determination of the maximal singularity-free zones in the six-dimensional workspace of the general Gough–Stewart platform,” Mech. Mach. Theory 42 (4), 497–511 (2007).CrossRefGoogle Scholar
25. Masouleh, M. T. and Gosselin, C., “Determination of singularity-free zones in the workspace of planar 3-PRR parallel mechanisms,” J. Mech. Des. 129 (6), 649–652 (2007).Google Scholar
26. Jiang, Q. and Gosselin, C. M., “The maximal singularity-free workspace of the Gough–Stewart platform for a given orientation,” J. Mech. Des. 130 (11), 112304 (2008).Google Scholar
27. Jiang, Q. and Gosselin, C. M., “Determination of the maximal singularity-free orientation workspace for the Gough–Stewart platform,” Mech. Mach. Theory 44 (6), 1281–1293 (2009).Google Scholar
28. Jiang, Q. and Gosselin, C. M., “Geometric synthesis of planar 3-RPR parallel mechanisms for singularity-free workspace,” Trans. Can. Soc. Mech. Eng. 33 (4), 667–678 (2009).Google Scholar
29. Abbasnejad, G., Daniali, H. M. and Kazemi, S. M., “A new approach to determine the maximal singularity-free zone of 3RPR planar parallel manipulator,” Robotica 30 (6), 1005–1012 (2012).CrossRefGoogle Scholar
30. Ahamdi Mousavi, M., Tale Masouleh, M. and Karimi, A., “On the maximal singularity-free ellipse of planar 3-RPR parallel mechanisms via convex optimization,” Robot. Cim-Int. Manuf. 30 (2), 218–227 (2014).Google Scholar
31. Boudreau, R. and Gosselin, C. M., “The synthesis of planar parallel manipulators with a genetic algorithm,” J. Mech. Des. 121 (4), 533–537 (1999).CrossRefGoogle Scholar
32. Boudreau, R. and Gosselin, C. M., “La synthèse d'une plate-forme de Gough–Stewart pour un espace atteignable prescript,” Mech. Mach. Theory 36 (3), 327–342 (2001).CrossRefGoogle Scholar
33. Baron, L., “Workspace-Based Design of Parallel Manipulators of Star Topology with a Genetic Algorithm,” Proceedings of ASME 27th Design Automation Conference, Pittsburgh, Pennsylvania, USA (Sep. 2001).Google Scholar
34. 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