Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T03:24:14.949Z Has data issue: false hasContentIssue false
  • English
  • Français

Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators

Published online by Cambridge University Press:  05 October 2016

M. Ganesh ,
Banke Bihari ,
Vijay Singh Rathore ,
Dhiraj Kumar ,
Chandan Kumar ,
Apelagunta Ramya Sree ,
Karanam Naga Sowmya  and
Anjan Kumar Dash
M. Ganesh*
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
Banke Bihari
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
Vijay Singh Rathore
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
Dhiraj Kumar
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
Chandan Kumar
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
Apelagunta Ramya Sree
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
Karanam Naga Sowmya
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
Anjan Kumar Dash
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur, 613401, Tamil Nadu, India
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Optimization is an important step in the design and development of a planar parallel manipulator. For optimization processes, workspace analysis is a crucial and preliminary objective. Generally, the workspace analysis for such manipulators is carried out using a non-dimensional approach. For planar parallel manipulators of two degrees of freedom (2-DOF), a non-dimensional workspace analysis is very advantageous. However, it becomes very difficult in the case of 3-DOF and higher DOF manipulators because of the complex shape of the workspace. In this study, the workspace shape is classified as a function of the geometric parameters, and the closed-form area expressions are derived for a constant orientation workspace of a three revolute–revolute–revolute (3-RRR) planar manipulator. The approach is also shown to be feasible for different orientations of a mobile platform. An optimization procedure for the design of planar 3-RRR manipulators is proposed for a prescribed workspace area. It is observed that the closed-form area expression for all the possible shapes of the workspace provides a larger solution space, which is further optimized considering singularity, mass of the manipulator, and a force transmission index.

Keywords

3-DOF planar parallel manipulatorsGeometrical approachWorkspace shapeClosed-form workspace areaOptimization
Type
Articles
Information
Robotica , Volume 35 , Issue 10 , October 2017 , pp. 2056 - 2075
Copyright
Copyright © Cambridge University Press 2016 

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., Gosselin, C. M. and Mouly, N., Workspaces of Planar Parallel Manipulators (Vienna: Springer, 1997) pp. 37–44.Google Scholar
2. Kumar, V., “Characterization of workspaces of parallel manipulators,” ASME J. Mech. Des. 114, 368–375 (1992).CrossRefGoogle Scholar
3. Chablat, D., Wenger, P. and Angeles, J., “Working Modes and Aspects in Fully-Parallel Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation (1998) pp. 1964–1969.Google Scholar
4. Daniali, M. H. R. and Angeles, J., “Singularity analysis of planar parallel manipulators,” Mech. Mach. Theory 30 (5), 665–678 (1995).CrossRefGoogle Scholar
5. Bonev, I. A. and Gosselin, C. M., “Singularity Loci of Planar Parallel Manipulators with Revolute Joints,” Proceedings of the 2nd Workshop on Computational Kinematics CK2001, Seoul, South Korea (May 20–22, 2001) pp. 291–299.Google Scholar
6. Gao, F., Zhang, X., Zhao, Y. and Wang, H., “A physical model of the solution space and the atlases of the reachable workspaces for 2-DOF parallel plane wrists,” Mech. Mach. Theory 31 (2) pp. 173–184 (1996).Google Scholar
7. Cervantes-Sanchez, J. J., Hernandez-Rodriguez, J. C. and Angeles, J., “On the kinematic design of the 5R planar, symmetric manipulator,” Mech. Mach. Theory 36 (11), 1301–1313 (2001).CrossRefGoogle Scholar
8. Gürsel, A. and Shirinzadeh, B., “Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing,” Robotica 22 (01) 97–10 (2004).Google Scholar
9. Chablat, D., Wenger, Ph., “The Kinematic Analysis of a Symmetrical Three-Degree-of-Freedom Planar Parallel Manipulator,” Proceedings of the CISM-IFToMM Symposium on Robot Design, Dynamics and Control, Montreal (2004).Google Scholar
10. Rizk, R., Munteanu, M., Fauroux, J. and Gogu, G., “A Semi-Analytical Stiffness Model of Parallel Robots from the Isoglide Family Via the Sub-Structuring Principle,” Proceedings of 12th IFToMM World Congress, France (2007).Google Scholar
11. Firmani, F., Zibil, A., Podhorodeski, R. P. and Nokleby, S. B., Wrench Capabilities of Planar Parallel Manipulators and their Effects Under Redundancy (Croatia-EUROPEAN UNION: INTECH Open Access Publisher, 2008).CrossRefGoogle Scholar
12. 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
13. Merlet, J. P., “Direct kinematics and assembly modes of parallel manipulators,” Int. J. Robot. Res. 11 (2), 150–162 (1992).Google Scholar
14. Ottaviano, E. and Ceccarelli, M., “Multi-criteria optimum design of manipulators,” Bull. Polish Acad. Tech. Sci. 53 (1), 9–18 (2005).Google Scholar
15. Tsai, L.-W. and Joshi, S., “Comparison Study of Architectures of Four 3 Degree-of-freedom Translational Parallel Manipulators,” Proceedings of the 2001 IEEE International Conference on, Robotics and Automation ICRA,. vol. 2 (2005) pp. 1283–1288.Google Scholar
16. Stamper, R. E., Tsai, L. W. and Walsh, G. C., “Optimization of a Three DOF Translational Platform for Well-Conditioned Workspace,” Proceedings of the IEEE International Conference on Robotics and Automation (1997) pp. 3250–3255.Google Scholar
17. Gallant, A., Boudreau, R. and Gallant, M., “Geometric determination of the dexterous workspace of n-RRRR and n-RRPR manipulators,” Mech. Mach. Theory 51, 159–171 (2012).Google Scholar
18. Dash, A. K., Chen, I-M., Yeo, S. H. and Yang, G., “Workspace generation and planning singularity-free path for parallel manipulators,” Mech. Mach. Theory 40 (7), 776–805 (2005).Google Scholar
19. Hosseini, M. A., Daniali, H.-R. M. and Taghirad, H. D., “Dexterous workspace optimization of a tricept parallel manipulator,” Adv. Robot. 25 (13–14), 1697–1712 (2011).Google Scholar
20. Liu, X.-J., Wang, J. and Pritschow, G., “Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms,” Mech. Mach. Theory 41 (2), 145–169 (2006).Google Scholar
21. Gao, F., Liu, X.-J. and Chen, X., “The relationships between the shapes of the workspaces and the link lengths of 3-DOF symmetrical planar parallel manipulators,” Mech. Mach. Theory 36 (2), 205–220 (2001).CrossRefGoogle Scholar
22. Chablat, D., Caro, S., Ur-Rehman, R. and Wenger, P., “Comparison of Planar Parallel Manipulator Architectures based on a Multi-objective Design Optimization Approach,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2010) pp. 861–870.Google Scholar
23. Lou, Y., Liu, G. and Li, Z., “Randomized optimal design of parallel manipulators,” IEEE Trans. Autom. Sci. Eng. 5 (2), 223–233 (2008).Google Scholar
24. Bihari, B., Chandan, D. K., Rathore, V. S. and Dash, A. K., “A geometric approach for the workspace analysis of two symmetric planar parallel manipulators,” Robotica, 1–26 (2014).Google Scholar
25. Chang, W.-T., Lin, C.-C. and Lee, J.-J., “Force transmissibility performance of parallel manipulators,” J. Robot. Syst. 20 (11), 659–670 (2003).CrossRefGoogle Scholar
26. Reveles, D. and Wenger, P., “Trajectory planning of kinematically redundant parallel manipulators by using multiple working modes,” Mech. Mach. Theory 98, 216–230 (2016).Google Scholar
27. Alba-Gomez, O., Wenger, P. and Pamanes, A., “Consistent Kinetostatic Indices for Planar 3-DOF Parallel Manipulators, Application to the Optimal Kinematic Inversion,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2005) pp. 765–774.Google Scholar
28. 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).Google Scholar
29. Gao, F., Zhang, X. Q., Zhao, Y.-S. and Wang, H.-R., “A physical model of the solution space and the atlas of the reachable workspace for 2-dof parallel planar manipulators,” Mech. Mach. Theory, 31 (2), 173–184 (1996).Google Scholar
30. Gosselin, C. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” J. Mech. Des. 113 (3), 220–226 (1991).CrossRefGoogle Scholar
31. Yang, G., Chen, I.-M., Chen, W. and Lin, W., “Kinematic design of a six-DOF parallel-kinematics machine with decoupled-motion architecture,” IEEE Trans. Robot. 20 (5), 876–884 (2004).Google Scholar
32. Firmani, F. and Podhorodeski, R. P., “Singularity analysis of planar parallel manipulators based on forward kinematic solutions,” Mech. Mach. Theory 44 (7), 1386–1399 (2009).Google Scholar
33. Dash, A. K., Kinematic Design of Reconfigurable Parallel Manipulators, Ph.D. Thesis (Singapore: Nanyang Technological University, 2002).Google Scholar