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Pick and place trajectory planning of planar 3-RRR parallel manipulator in the presence of joint clearance

Published online by Cambridge University Press:  03 March 2015

M. Farajtabar ,
H. M. Daniali  and
S. M. Varedi
M. Farajtabar
Affiliation:
Department of Mechanical Engineering, Babol University of Technology, P.O. Box 484, Babol, Iran.
H. M. Daniali*
Affiliation:
Department of Mechanical Engineering, Babol University of Technology, P.O. Box 484, Babol, Iran.
S. M. Varedi
Affiliation:
Department of Mechanical Engineering, Babol University of Technology, P.O. Box 484, Babol, Iran.
*
*Corresponding author. E-mail: mohammadi@nit.ac.ir
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Summary

In this paper, the pick and place trajectory planning of a planar 3-RRR parallel manipulator is studied in the presence of joint clearance, which is one of the main sources of error in the positioning accuracy. Joint clearance can be modeled as a massless virtual link, with its direction determined from dynamic analysis. A 3–4–5 interpolating polynomial is used to plan the trajectories for the manipulator in the vertical and horizontal planes, in the presence of clearances. We compare the trajectories with those in the ideal cases, i.e., without clearances at the joints, and demonstrate that one can easily compensate for the errors in the trajectories by appropriate changes of the inputs. A similar method works for the compensation of the errors due to clearances at the joints, in trajectory planning of any parallel manipulator with any running speeds and payloads.

Keywords

Parallel manipulatorTrajectory planningClearanceInverse kinematicsDirect kinematics
Type
Articles
Information
Robotica , Volume 35 , Issue 2 , February 2017 , pp. 241 - 253
Copyright
Copyright © Cambridge University Press 2015 

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References

1. Erkaya, S. and Uzmay, I., “Determining link parameters using genetic algorithm in mechanisms with joint clearance,” Mech. Mach. Theory 44 (1), 222–234 (2009).CrossRefGoogle Scholar
2. Erkaya, S. and Uzmay, I., “Investigation on effect of joint clearance on dynamics of four-bar mechanism,” Nonlinear Dyn. 58 (1–2), 179–198 (2009).Google Scholar
3. Altuzarra, O., Aginaga, J., Hernández, A. and Zabalza, I., “Workspace analysis of positioning discontinuities due to clearances in parallel manipulators,” Mech. Mach. Theory 46 (5), 577–592 (2011).Google Scholar
4. 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 (3), 391–401 (2000).CrossRefGoogle Scholar
5. Tsai, M. J. and Lai, T.H., “Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality,” Mech. Mach. Theory 39 (11), 1189–1206 (2004).Google Scholar
6. Shi, Z., Yang, X., Yang, W. and Cheng, Q., “Robust synthesis of path generating linkages,” Mech. Mach. Theory 40 (1), 45–54 (2005).CrossRefGoogle Scholar
7. Wu, W. D. and Rao, S. S., “Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis,” Reliab. Eng. Syst. Saf. 92 (1), 54–64 (2007).CrossRefGoogle Scholar
8. Wu, W. D. and Rao, S. S., “Interval approach for the modeling of tolerances and clearances in mechanism analysis,” J. Mech. Des. Trans. ASME 126 (4), 581–592 (2004).CrossRefGoogle Scholar
9. Huang, T., Chetwynd, D. G., Mei, J. P. and Zhao, X. M., “Tolerance design of a 2-DOF overconstrained translational parallel robot,” IEEE Trans. Robot. 22 (1), 167–172 (2006).CrossRefGoogle Scholar
10. Shim, H. S., Seo, T. W. and Lee, J. W., “Optimal torque distribution method for a redundantly actuated 3-RRR parallel robot using a geometrical approach,” Robotica 31 (4), 549–554 (2013).Google Scholar
11. Jawale, H. P. and Thorat, H. T., “Investigation of positional error in two degree of freedom mechanism with joint clearance,” ASME J. Mech. Robot. 4 (1), 011002 (2012).Google Scholar
12. Subudhi, B. and Morris, A. S., “Dynamic modeling, simulation and control of a manipulator with flexible links and joints,” Robot. Auton. Syst. 41 (4), 257–270 (2002).Google Scholar
13. 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
14. Lankarani, H. M. and Nikravesh, P. E., “A contact force model with hysteresis damping for impact analysis of multibody systems,” J. Mech. Des. 112, 369–376 (1990).Google Scholar
15. Flores, P., Machado, M., Seabra, E. and Sliva, M. T., “A parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems,” ASME J. Comput. Nonlinear Dyn. 6 (1), 011019/1–9 (2011).Google Scholar
16. Flores, P., “A parametric study on the dynamic response of planar multibody systems with multiple clearance joints,” Nonlinear Dyn. 61 (4), 633–653 (2010).CrossRefGoogle Scholar
17. Flores, P., Koshy, C. S., Lankarani, H. M., Ambrósio, J. and Claro, J. C. P., “Numerical and experimental investigation on multibody systems with revolute clearance joints,” Nonlinear Dyn. 65 (4), 383–398 (2011).Google Scholar
18. Xu, L. X., Yang, Y. H., Li, Y. G., Li, C. N. and Wang, S. Y., “Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance,” Mech. Mach. Theory, 56, 69–88 (2012).Google Scholar
19. Flores, P., Ambrosio, I., Claro, J. C. P. and Lankarani, H. M., “Dynamic behaviour of planar rigid multi-body systems including revolute joints with clearance,” Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics 221 (2), (2007) pp. 161–174.Google Scholar
20. Bai, Z. F., Zhao, Y. and Wang, X. G., “A nonlinear contact force model for revolute joint with clearance,” J. Mech. 29 (4), 653–660 (2013).Google Scholar
21. Xu, L. X. and Li, Y. G., “Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator,” Robot. Comput.-Integr. Manuf. 30 (1), 62–73 (2014).Google Scholar
22. Xu, L. X. and Li, Y. G., “An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems,” Nonlinear Dyn. 70 (3), 2145–2161 (2012).Google Scholar
23. Angeles, J., Rojas, A., Lopez, A. and Cajum, C. S., “Trajectory planning in robotics continuous-path application,” IEEE J. Robot. Autom. RA 4, 380–385 (1988).CrossRefGoogle Scholar
24. Ambike, S. and Schmiedeler, J. P., “A methodology for implementingthe curative theory approach to path tracking with planar robots,” Mech. Mach. Theory 43 (10), 1225–1235 (2008).Google Scholar
25. 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. Technol. 51 (5–8), 811–816 (2010).Google Scholar
26. Kosinska, A., Galicki, M. and Kedzior, K., “Design of parameters of parallel manipulators for a specified workspace,” Robotica 21 (5), 575–579 (2003).CrossRefGoogle Scholar
27. Bu, W., Liu, Z., Tan, J. and Gao, S., “Detachment avoidance of joint elements of a robotic manipulator with clearances based on trajectory planning,” Mech. Mach. Theory 45 (6), 925–940 (2010).Google Scholar
28. Alba, O. G., Pamanes, J. A. and Wenger, P., “Trajectory Planning of a Redundant Parallel Manipulator Changing of Working Mode,” In 12th IFToMM World Congress, (2007) pp. 18–21.Google Scholar
29. Zhe, L. and Shixian, B., “Amendments to a criterion of contact loss between pairing elements in planar linkages with clearances,” Mech. Mach. Theory 26 (7), 669–676 (1991).Google Scholar
30. Zhe, L., Li, L. and Shixian, B., “A new method of predicting the occurrence of contact loss between pairing elements in planar linkages with clearances,” Mech. Mach. Theory 27 (3), 295–301 (1992).Google Scholar
31. Gosselin, C., Kinematics Analysis, Optimization and Programming of Parallel Robotic Manipulators, Ph.D. Thesis (Montreal, Quebec, Canada: McGill University, 1989).Google Scholar
32. Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 4th ed. (Springer, New York, 2014).Google Scholar