Skip to main content

Kinematic and dynamic performance investigations of asymmetric (U-shape fixed base) planar parallel manipulators

  • Jayant Kumar Mohanta (a1), Yogesh Singh (a2) and Santhakumar Mohan (a1)

In this paper, a new family of 3-degree-of-freedom planar parallel manipulators (PPMs), namely U-shape fixed base PPMs starting with an active prismatic joint on each leg, is proposed. In order to identify the best manipulators of this family, comparative kinematic and dynamic performance studies are performed. The kinematic performances are quantified through the local performance index, namely the kinematic isotropy. From the kinematic isotropy analysis results, it is observed that PPR-PRP-PRP, PRP-PRP-PRP and PRR-PRP-PRP configurations have better kinematic design aspects compared to other configurations of this family of U-shape fixed base parallel configurations. Further, from the workspace analysis, it is observed that the PPR-PRP-PRP configuration has a higher value of workspace to the total area required ratio compared to other configurations. This paper also presents a comparative dynamic performance analysis of these top-three U-shape fixed base configurations in terms of dynamic driving performance measures, and energy requirements for three different (fixed base size of the manipulators) aspect ratios under two different loading conditions. From the analyses results, it is perceived that the PRP-PRP-PRP configuration is requiring lower energy and dynamic driving performances than others. These analyses are done with the help of multi-body dynamic software, namely MSC ADAMS, and the results are validated through the help of real-time experiments conducted on in-house fabricated prototypes of these three PPMs. In specific, the energy consumption is measured and compared in this study. Experimental results demonstrated that the PRP-PRP-PRP manipulator displays a considerably better performance in terms of minimum energy requirement.

Corresponding author
*Corresponding author. E-mail:
Hide All
1. Briot, S. and Bonev, I. A., “Are parallel robots more accurate than serial robots?,” Trans. Can. Soc. Mech. Eng. 31 (4), 445455 (2007).
2. Merlet, J. P., Parallel Robots, 2nd ed. (Springer, The Netherlands, 2006).
3. Joubair, A., Slamani, M. and Bonev, I. A., “A novel XY-Theta precision table and a geometric procedure for its kinematic calibration,” Robot. Comput. Integr. Manuf. 28 (1), 5765 (2012).
4. Bonev, I. A., “Planar parallel mechanism and method,” US Patent7707907 B2 (2010).
5. Staicu, S., “Inverse dynamics of the 3-PRR planar parallel robot,” Robot. Auton. Syst. 57 (5), 556563 (2009).
6. Choi, K. B., “Kinematic analysis and optimal design of 3-PPR planar parallel manipulator,” KSME Int. J. 17 (4), 528537 (2003).
7. Bai, S. and Caro, S., “Design and Analysis of a 3-PPR Planar Robot with U-shape Base,” Proceedings of the ICAR International Conference on Advanced Robotics, Munich, Germany (2009) pp. 1–6.
8. 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), 510517 (2010).
9. Merlet, J. P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33 (1–2), 720 (1998).
10. Rezaei, A. and Akbarzadeh, A., “Position and stiffness analysis of a new asymmetric 2PRR-PPR parallel CNC machine,” Adv. Robot. 27 (2), 133145 (2013).
11. Gogu, G., Structural Synthesis of Parallel Robots, Part 1: Methodology, 1st ed. (Springer, The Netherlands, 2008).
12. Gogu, G., Structural Synthesis of Parallel Robots, Part 2: Translational Topologies with Two and Three Degrees of Freedom, 1st ed. (Springer, The Netherlands, 2009)
13. Gogu, G., Structural Synthesis of Parallel Robots, Part 3: Topologies with Planar Motion of the Moving Platform, 1st ed. (Springer, The Netherlands, 2010).
14. Gogu, G., Fully-Isotropic T3R1-Type Parallel Manipulators, on Advances in Robot Kinematics (Springer, The Netherlands, 2004) pp. 265272.
15. Yu, A., Bonev, I. A. and Murray, P. Z., “Geometric approach to the accuracy analysis of a class of 3 DOF planar parallel robots,” Mech. Mach. Theory 43, 364375 (2008).
16. Arakelian, V. H. and Smith, M. R., “Design of planar 3 DOF 3-RRR reactionless parallel manipulators,” Mechatronics 18, 601606 (2008).
17. Briot, S. and Bonev, I. A., “Accuracy analysis of 3 DOF planar parallel robots,” Mech. Mach. Theory 43, 445458 (2008).
18. Staicu, S., “Dynamics of a 3-RPR planar parallel robot,” UPB Sci. Bull. Ser. D, 70 (3), 318 (2008).
19. Caro, S., Binaud, N. and Wenger, P., “Sensitivity analysis of 3-RPR planar parallel manipulators,” J. Mech. Des. 131, 121005-1–13 (2009).
20. Binaud, N., Caro, S. and Wenger, P., “Sensitivity comparison of planar parallel manipulators,” Mech. Mach. Theory 45 (11), 14771490 (2010).
21. Wu, J., Wang, J. and You, Z., “A comparison study on the dynamics of planar 3 DOF 4-RRR, 3-RRR and 2-RRR parallel manipulators,” Robot. Comput. Integr. Manuf. 27 (1), 150156 (2011).
22. Wu, G., Bai, S., Kepler, J. A. and Caro, S., “Error modelling and experimental validation of a planar 3-PPR parallel manipulator with joint clearance,” J. Mech. Robot. 4, 041008-1–12 (2012).
23. 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, 7382 (2013)
24. Staicu, S., “Power requirement comparison in the 3-RPR planar parallel robot dynamics,” Mech. Mach. Theory, 44, 10451057 (2009).
25. Binaud, N., Caro, S. and Wenger, P., “Comparison of 3-RPR planar parallel manipulators with regard to their kinetostatic performance and sensitivity to geometric uncertainties,” Meccanica 46, 7588 (2011).
26. Khatib, O., “Inertial properties in robotic manipulation: An object-level framework,” Int. J. Robot. Res., 14, 1936 (1995).
27. Wu, J., Gao, Y., Zhang, B. and Wang, L., “Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment,” Robot. Comput.-Integr. Manuf. 44, 199207 (2017).
28. Liping, W., Huayang, X. and Liwen, G., “Kinematics and inverse dynamics analysis for a novel 3-PUU parallel mechanism,” Robotica 35 (10), 118 (2016).
29. Liang, D., Song, Y., Sun, T. and Dong, G., “Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance,” Nonlinear Dyn. 83 (1), 631658 (2016).
30. Wu, J., Wang, J., Li, T. and Wang, L., “Dynamic analysis of the 2 DOF planar parallel manipulator of a heavy-duty hybrid machine tool,” Int. J. Adv. Manuf. Technol., 34, 413420 (2007).
31. Patel, S. and Sobh, T., “Manipulator performance measures: A comprehensive literature survey,” J. Intell. Robot. Syst. 77 (3), 547570 (2015).
32. Yongjie, Z. and Feng, G., “Dynamic formulation and performance evaluation of the redundant parallel manipulator,” Robot. Comput. Integr. Manuf. 25, 770781 (2009).
33. Keith, L. D., Eric, M. S. and Claudio, B., “Robot manipulability,” IEEE Trans. Robot. Autom. 11 (3), 462468 (1994)
34. Park, F. C. and Brockett, R. W., “Kinematic dexterity of robotic mechanisms,” Int. J. Robot. Res. 13 (2), 115 (1994).
35. Graettinger, T. J. and Krogh, B. H., “The acceleration radius: A global performance measure for robotic manipulators,” IEEE J. Robot. Autom. 4, 6069 (1988).
36. Singh, Y., Performance Investigations on Mechanical Design and Motion Control of Planar Parallel Manipulators, Ph.D. Thesis (Indore, Indian Institute of Technology Indore, 2016).
37. Kucuk, S., “A dexterity comparison for 3 DOF planar parallel manipulators with two kinematic chains using genetic algorithms,” Mechatronics 19 (6), 868877 (2009).
38. Kim, J. O. and Khosla, P. K., “Dexterity Measures for Design and Control of Manipulators,” Proceedings of the IEEE/RSJ International Workshop on Intelligent Robots and Systems, Osaka, Japan (1991) pp. 758–763.
39. Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 39 (1985).
40. Kees, D. and Pai, D. K., “Performance measures for robot manipulators: A unified approach,” Int. J. Robot. Res. 15 (1), 92111 (1996).
41. Kucuk, S. and Bingul, Z., “Comparative study of performance indices for fundamental robot manipulators,” Robot. Auton. Syst. 54 (7), 567573 (2006).
42. Singh, Y. and Mohan, S., “Kinematic Performance Analysis of a New 2PRP-PRR Planar Parallel Robotic Manipulator,” Proceedings of the 4th Joint International Conference on Multibody System Dynamics, Montréal, Québec, Canada (2016).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 26 *
Loading metrics...

Abstract views

Total abstract views: 102 *
Loading metrics...

* Views captured on Cambridge Core between 6th April 2018 - 19th April 2018. This data will be updated every 24 hours.