Effect of Robot Configuration Parameters, Masses and Friction on Painlevé Paradox for a Sliding Two-Link (P-R) Robot

Authors: Hassan M. Alkomy, Hesham A. Elkaranshawy, Ahmed S. Ashour, Khaled T. Mohamed

Abstract:

For a rigid body sliding on a rough surface, a range of uncertainty or non-uniqueness of solution could be found, which is termed: Painlevé paradox. Painlevé paradox is the reason of a wide range of bouncing motion, observed during sliding of robotic manipulators on rough surfaces. In this research work, the existence of the paradox zone during the sliding motion of a two-link (P-R) robotic manipulator with a unilateral constraint is investigated. Parametric study is performed to investigate the effect of friction, link-length ratio, total height and link-mass ratio on the paradox zone.

Keywords: Dynamical system, friction, multibody system, Painlevé paradox, robotic systems, sliding robots, unilateral constraint.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1338452

References:

[1] Benjamin Hall and Champneys, Alan (2009), "Why does Chalk Squeak?", Master thesis, University of Bristol.
[2] Painlevé, P. (1895), ''Sur le Lois du Frottement de Glissement'', Comptes Rendus Academie Science Paris, Vol. 121, 112-115.
[3] An, L. (1990), “The Painleve Paradox and the Law of Motion of Mechanical Systems with Coulomb Friction”, PMM U. S. S. R., Vol. 54, (4), 430-438.
[4] Liu, C., Zhao, Z. and Chen, C. (2007), “The Bouncing Motion Appearing in the Robotic System with Unilateral Constraint”, Nonlinear Dyn., Vol. 49, 217-232.
[5] Nordmarka, A., Dankowiczb, H. and Champneys, A. (2009), ''Discontinuity Induced Bifurcations in Systems with Impacts and Friction'', International Journal of Non-Linear Mechanics, Vol. 44, 1011- 1023.
[6] Genot, F. and Brogliato, B. (1999), ''New Results on Painlevé Paradox'', Eur. J.Mech. A/Solids Vol. 18, 653-677.
[7] Mason, M.T. and Wang, Y. (1988), ''On the Inconsistency of Rigid- Body Frictional Planar Dynamics'', Proceedings 1988 IEEE Int’l. Conf. Robotics and Automation, Philadelphia, 524-528.
[8] Pay, M. and Glocker C. (2005), ''Oblique Frictional Impact of a Bar: Analysis and Comparison of Different Impact Law'', Nonlinear Dyn. Vol 41, 361-383.
[9] Shen, Y. and Stronge, W., A. (2011), "Painleve Paradox during Oblique Impact with Friction'', European Journal of Mechanics A/Solids, Vol. 30, 457-467.
[10] Leonesio, M. and Bianchi, G. (2009), ''Self-Locking Analysis in Closed Kinematic Chains'', Mechanism and Machine Theory, Vol. 44, 2038– 2052
[11] Zhao, Z., Liu, C., Ma, W. and Chen, B. (2008), ''Experimental Investigation of the Painlevé Paradox in a Robotic System'', J. Appl. Mech., Vol. 75(4), 1-25.
[12] Elkaranshawy, H. and Ghazy, M. (2012), ''Effect of the Link-Length Ratio on Painlevé Paradox for a Sliding Two-Link Robot'', 15th International Conference on Applied Mechanics and Mechanical Engineering, Cairo, Egypt, RC 76-87.
[13] Ghazy, M. and Elkaranshawy, H. (2012), "A Method to Escape Painlevé Paradox in a Two-Link Robotic Manipulator." Proceedings of the International Conference on Engineering and Technology (ICET2012), New Cairo City, Egypt, 214-218.
[14] Elkaranshawy, H. (2011), “Using Self-Motion in Redundant Manipulators to Cope with Painleve Paradox,” Proceedings of the IASTED International Conference on Robotics'', Pittsburgh, USA, 361- 367.