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A comparative study of elastic motions in trajectory tracking of flexible RPR planar manipulators moving with high speed

Published online by Cambridge University Press:  20 May 2016

Amirhossein Eshaghiyeh Firoozabadi ,
Saeed Ebrahimi  and
Josep M. Font-Llagunes
Amirhossein Eshaghiyeh Firoozabadi
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran. Email: [email protected]
Saeed Ebrahimi*
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran. Email: [email protected]
Josep M. Font-Llagunes
Affiliation:
Department of Mechanical Engineering and Biomedical Engineering Research Centre, Universitat Politècnica de Catalunya, Barcelona, Catalunya, Spain. Email: [email protected]
*
*Corresponding author. Email: [email protected]
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Summary

The study of inertial forces effects at high speeds in flexible parallel manipulators, which generate undesired deviations, is a challenging task due to the coupled and complicated equations of motion. A dynamic model of the Revolute Prismatic Revolute (RPR) planar manipulators (specifically 3-RPR, 2-RPR and 1-RPR) with flexible intermediate links is developed based on the assumed mode method. The flexible intermediate links are modeled as Euler-Bernoulli beams with fixed-free boundary conditions. Using the Lagrange multipliers, a generalized set of differential algebraic equations (DAEs) of motion is developed. In the simulations, the rigid body motion of the end-effector is constrained by some moving constraint equations while the vibrations of the flexible intermediate links cause deviations from the desired trajectory. From this analysis, the dynamic performance of the manipulators when tracking a desired trajectory is evaluated. A comparison of the results indicates that in some cases, adding each extra RPR chain in the n-RPR planar manipulators with flexible intermediate links reduces the stiffness and accuracy due to the inertial forces of the flexible links, which is opposite to what would be expected. The study provides insights to the design, control and suitable selection of the flexible manipulators.

Keywords

Accuracy performanceTrajectory trackingSerial and parallel manipulatorsFlexible manipulatorsAssumed mode method
Type
Articles
Information
Robotica , Volume 35 , Issue 7 , July 2017 , pp. 1523 - 1540
Copyright
Copyright © Cambridge University Press 2016 

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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. Pandilov, Z. and Dukovski, V., “Comparison of the characteristics between serial and parallel robots,” Acta Technica 7 (1), 143–160 (2014).Google Scholar
3. Patel, Y. D. 1 and George, P. M., “Parallel manipulators applications-a survey,” Modern Mech. Eng. 2, 57–64 (2012).Google Scholar
4. Wavering, A. J., “Parallel Kinematic Machine Research at NIST: Past, Present and Future,” In: Parallel Kinematic Machines, Advanced Manufacturing Series (Springer, London, 1999) pp. 17–31.Google Scholar
5. Song, J., Mou, J. -I and King, C., “Error Modeling and Compensation for Parallel Kinematic Machines,” In: Parallel Kinematic Machines, Advanced Manufacturing Series (Springer, London, 1999) pp. 171–187.Google Scholar
6. Guan, L., Yun, Y., Wang, J. and Wang, L., “Kinematics of a Tricept-Like Parallel robot,” Proceedings of the 2004 IEEE International Conference on Systems, Man and Cybernetics, Hague, Netherlands (Oct. 2004) pp. 5312–5316.Google Scholar
7. Rauf, A., Kim, S.-G., and Ryu, J., “A New Measurement Device for Complete Parameter Identification of Parallel Manipulators with Partial Pose Measurements,” The 4th Chemnitz Parallel Kinematics Seminar, Chemnitz, Germany (2004) pp. 89–106.Google Scholar
8. Merlet, J.-P., Parallel Robots, 2nd ed. (Springer, London, 2006) pp. 4–7.Google Scholar
9. Le, T. D., Kang, H. J., Suh, Y.S. and Ro, Y. S., “An online self-gain tuning method using neural networks for nonlinear PD computed torque controller of a 2-DOF parallel manipulator,” Neurocomputing 116, 53–61 (2013).Google Scholar
10. Williams, R. L. II and Joshi, A. R., “Planar Parallel 3-RPR Manipulator,” Proceedings of the Sixth Conference on Applied Mechanisms and Robotics, Cincinnati OH (1999) pp. 1–8.Google Scholar
11. Staicu, S. and Chablat, D., “Internal joint forces in dynamics of a 3-PRP planar parallel robot,” Proc. Romanian Acad. Ser. A 13 (3), 235–242 (2012).Google Scholar
12. Staicu, S., “Joint forces in dynamics of the 3-RRR planar parallel robot,” Int. J. Mech. and Robot. 1 (4), 283–300 (2013).Google Scholar
13. Staicu, S., “Power requirement comparison in the 3-RPR planar parallel robot dynamics,” Mech. Mach. Theory 44, 1045–1057 (2009).Google Scholar
14. Briot, S. and Bonev, I. A., “Are parallel robots more accurate than serial robots?,” CSME Trans. 31 (4), 445–456 (2007).Google Scholar
15. Tsai, L.W. and Joshi, S., “Comparison Study of Architectures of Four 3 Degree-of-Freedom Translational Parallel Manipulators,” Proceedings 2001 ICRA. IEEE International Conference on Robotics & Automation, Seoul, Korea (2001) pp. 1283–1288.Google Scholar
16. Wu, J., Wang, J. S. 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, 150–156 (2011).Google Scholar
17. Wu, J., Wang, J. S., Wang, L. P. and You, Z., “Performance comparison of three planar 3-DOF parallel manipulators with 4-RRR, 3-RRR and 2-RRR structures,” Mechatron. 20 (4), 510–517 (2010).Google Scholar
18. Wu, J., Li, T., Wang, J. S. and Wang, L. P., “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
19. Zhang, D., Gao, Z., Su, X., and Li, J., “A comparison study of three degree-of-freedom parallel robotic machine tools with/without actuation redundancy,” Int. J. Comput. Integr. Manuf. 5 (3), 230–247 (2012).Google Scholar
20. Wu, J., Wang, J. S. and Wang, L. P., “A comparison study of two planar 2-DOF parallel mechanisms: one with 2-RRR and the other with 3-RRR structures,” Robotica 28 (10), 937–942 (2010).Google Scholar
21. Zhao, Y. and Gao, F., “Dynamic performance comparison of the 8PSS redundant parallel manipulator and its non-redundant counterpart- the 6PSS parallel manipulator,” Mech. Mach. Theory 44 (9), 991–1008 (2009).Google Scholar
22. 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 (1), 75–88 (2011).Google Scholar
23. El-Khasawneh, B. and Alazzam, A., “Kinematics, Dynamics and Vibration Models for 3RPR Parallel Kinematics Manipulator,” ASME 2013 International Mechanical Engineering Congress and Exposition 14: Vibration, Acoustics and Wave Propagation, San Diego, California, USA (2013) pp. V014T15A005.Google Scholar
24. Staicu, S., “Power requirement comparison in the 3-RPR planar parallel robot dynamics,” Mech. Mach. Theory 44 (5), 1045–1057 (2009).Google Scholar
25. Staicu, S., “Inverse dynamics of the 3-PRR planar parallel robot,” Robot. Auton. Syst. 57 (5), 556–563 (2009).Google Scholar
26. Briot, S. and Bonev, I. A., “Accuracy analysis of 3-DOF planar parallel robots,” Mech. Mach. Theory 43 (4), 445–458 (2008).Google Scholar
27. 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
28. 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
29. 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
30. Viliani, N. S., Zohoor, H. and Kargarnovin, M. H., “Vibration Analysis of a New Type of Compliant Mechanism with Flexible-Link Using Perturbation Theory,” Hindawi Publishing Corporation, Math. Prob. Eng. (2012), Article ID 857064, pp. 1–19, doi: 10.1155/2012/857064.Google Scholar
31. Sudhakar, U. and Srinvas, J., “A stiffness index prediction approach for 3-RPR planar parallel linkage,” Int. J. Eng. Res. Tech. 2 (9), 2747–2751 (2013).Google Scholar
32. Lee, J. D. and Geng, Z., “A Dynamic model of a flexible Stewart platform,” Comput. Struct. 48, 367–374 (1993).Google Scholar
33. Giovagnoni, M., “Dynamics of Flexible Closed-Chain Manipulator,” ASME Design Technical Conference, Scottsdale, Arizona, USA (1992) pp. 483–490.Google Scholar
34. 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 (1995) pp. 627–632.Google Scholar
35. Kang, B. and Mills, J. K., “Dynamic modeling of structurally-flexible planar parallel manipulator,” Robotica 20, 329–339 (2002).Google Scholar
36. 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
37. 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
38. 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
39. 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
40. Zhang, X., Mills, J. K., Cleghorn, W. L., Jin, J. and Zhao, C., “Trajectory tracking and vibration suppression of a 3-PRR parallel manipulator with flexible links,” Multibody Syst. Dyn. 33, 27–60 (2015), doi: 10.1007/s11044-013-9407-2.Google Scholar
41. Zhengsheng, C., Minxiu, K., Ming, L. and Wei, Y., “Dynamic modeling and trajectory tracking of parallel manipulator with flexible link,” Int. J. Adv. Robot. Syst. 10, 27–60 (2013).Google Scholar
42. Firoozabadi, A. E., Ebrahimi, S. and Amirian, G., “Dynamic characteristics of a 3-RPR planar parallel manipulator with flexible intermediate links,” Robotica 33, 1909–1925 (2015).Google Scholar
43. Rao, S. S., Vibration of Continuous Systems (Wiley, New York, 2007).Google Scholar