Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-29T12:08:22.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic characteristics of a 3-RPR planar parallel manipulator with flexible intermediate links

Published online by Cambridge University Press:  13 May 2014

Amirhossein Eshaghiyeh Firoozabadi ,
Saeed Ebrahimi  and
Ghasem Amirian
Amirhossein Eshaghiyeh Firoozabadi
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran
Saeed Ebrahimi*
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran
Ghasem Amirian
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran
*
*Corresponding author. E-mail: ebrahimi@yazd.ac.ir
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents the dynamic modeling of a 3-RPR planar parallel manipulator with three flexible intermediate links in order to investigate the effects of the intermediate links flexibility on the undesired vibrations of the end-effector. For this purpose, the intermediate links are modeled as Euler--Bernoulli beams with two types of fixed-pinned and fixed-free boundary conditions based on the assumed mode method (AMM). The equations of motion of the 3-RPR manipulator are formulated using the augmented Lagrange multipliers method in the form of differential algebraic equations (DAEs) by incorporating the elastic and rigid coordinates in the set of generalized coordinates. After defining the initial conditions and imposing external forces to the manipulator, the equations are then solved numerically using the Modified Extended Backward-Differentiation Formula Implicit (MEBDFI) approach. Comparison of the simulation results for two different boundary conditions shows clearly the effects of flexibility of the intermediate links on the vibration of the end-effector trajectory. Results of this work can be used for the dynamic modeling of other manipulators or to design a controller for reducing the undesired vibrations.

Keywords

Flexible manipulatorsParallel manipulatorsAssumed mode methodEuler–Bernoulli beam
Type
Articles
Information
Robotica , Volume 33 , Issue 9 , November 2015 , pp. 1909 - 1925
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. Dwivedy, S. K. and Eberhard, P., “Dynamic analysis of flexible manipulators, a literature review,” Mech. Mach. Theory 41, 749–777 (2006).Google Scholar
2. Theodore, R. J. and Ghosal, A., “Comparison of the assumed modes and finite element models for flexible multi-link manipulators,” Int. J. Robot. Res. 14, 91–111 (1995).Google Scholar
3. Lee, J. D. and Geng, Z., “A Dynamic model of a flexible Stewart platform,” Comput. Struct. 48, 367–374 (1993).Google Scholar
4. Giovagnoni, M., “Dynamics of Flexible Closed-Chain Manipulator,” ASME Design Technical Conference, Scottsdale, Arizona, USA (Sep. 13–16, 1992) pp. 483–490.Google Scholar
5. Fattah, A., Angeles, J. and Misra, A. K., “Dynamics of a 3-DOF Spatial Parallel Manipulator with Flexible Links,” Proceedings IEEE International Conference on Robotics and Automation, Nagoya, Japan (May 21–27, 1995) pp. 627–632.Google Scholar
6. Kang, B. and Mills, J. K., “Dynamic modeling of structurally-flexible planar parallel manipulator,” Robotica 20, 329–339 (2002).Google Scholar
7. Wang, X. and Mills, J. K., “Experimental Modal Analysis of Flexible Linkages in a Smart Parallel Platform,” Proceeding of the 7th CANSMART Meeting – International Workshop on Smart Materials and Structures, Montreal, Canada (Oct. 21–22, 2004) pp. 37–46.Google Scholar
8. Piras, G., Cleghorn, W. L., and Mills, J. K., “Dynamic finite-element analysis of a planar high speed, high-precision parallel manipulator with flexible links,” Mech. Mach. Theory 40, 849–862 (2005).Google Scholar
9. Wang, X., and Mills, J. K., “FEM dynamic model for active vibration control of flexible linkages and its application to a planar parallel manipulator,” J. Appl. Acoust. 66, 1151–1161 (2005).Google Scholar
10. Zhou, Z., Xi, J. and Mechefske, C. K., “Modeling of a fully flexible 3PRS manipulator for vibration analsysis,” J. Mech. Des. 128, 403–412 (2006).Google Scholar
11. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Study on the Effect of Elastic Deformations on Rigid Body Motions of a 3-PRR Flexible Parallel Manipulator,” Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, Harbin, China (Aug. 5–8, 2007) pp. 1805–1810.Google Scholar
12. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Dynamic modeling and experimental validation of a 3-PRR parallel manipulator with flexible intermediate links,” J. Intell. Robot. Syst. 50, 323–340 (2007).Google Scholar
13. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Coupling characteristics of rigid body motion and elastic deformation of a 3-PRR parallel manipulator with flexible links,” Multibody Syst. Dyn. 21, 167–192 (2009).Google Scholar
14. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Investigation of axial forces on dynamic properties of a flexible 3-PRR planar parallel manipulator moving with high speed,” Robotica 28, 607–619 (2010).Google Scholar
15. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Multi-Mode vibration control and position error analysis of parallel manipulator with multiple flexible links,” Trans. Can. Soc. Mech. Eng. 34, 197–213 (2010).Google Scholar
16. Kang, B. and Mills, J. K., “Dynamic Modelling and Vibration Control of a Planar Parallel Manipulator with Structurally Flexible Linkages,” In: Parallel Manipulators, New Developments (Ryu, J. H., ed.), (Vienna, Austria, 2008) pp. 405–426.Google Scholar
17. Zhang, J., Li, Y. and Huang, T., “Dynamic modeling and eigenvalue evaluation of a 3-DOF PKM module,” Chinese J. Mech. Eng. 23, 166–173 (2010).Google Scholar
18. Liu, S. Z., Yu, Y. Q. and Zhu, Z. C., “Dynamic modeling and analysis of 3-RRS parallel manipulator with flexible links,” J. Cent. South Univ. Technol. 17, 323–331 (2010).Google Scholar
19. Gosselin, C. and Angeles, J., “The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator,” ASME J. Mech. Trans. Auto. Des. 110, 35–41 (1988).Google Scholar
20. Pennock, G. R. and Kassner, D. J., “Kinematic analysis of a planar eight-bar linkage: application to a platform-type robot,” J. Mech. Des. 114, 87–95 (1992).Google Scholar
21. Williams, R. L. and Joshi, A. R., “Planar Parallel 3-RPR Manipulator,” Proceedings of the Sixth Conference on Applied Mechanisms and Robotics, Cincinnati, USA (Dec. 12–15, 1999) pp. 1–8.Google Scholar
22. Bonev, I., Zlatanov, D. and Gosselin, C., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” J. Mech. Des. 25, 573–581 (2003).Google Scholar
23. Staicu, S., Carp-Ciocardia, D. C. and Codoban, A., “Kinematics modelling of a planar parallel robot with prismatic actuators,” U.P.B. Sci. Bull., Series D 69, 3–14 (2007).Google Scholar
24. Briot, S., Bonev, I., Chablat, D., Wenger, P. and Arakelian, V., “Self-motions of general 3-RPR planar parallel robots,” Int. J. Robot. Res. 27, 855–866 (2008).Google Scholar
25. Rao, S. S., Vibration of Continuous Systems (Wiley, New York, 2007).Google Scholar