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Zhao Zhen, Liu Caishany, Chen Bin. THEORETICAL ANALYSIS AND EXPERIMETNAL VERIFICATION FOR PAINLEV碋 PARADOX[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 37-44. DOI: 10.6052/0459-1879-12-316
Citation: Zhao Zhen, Liu Caishany, Chen Bin. THEORETICAL ANALYSIS AND EXPERIMETNAL VERIFICATION FOR PAINLEV碋 PARADOX[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 37-44. DOI: 10.6052/0459-1879-12-316
shu

THEORETICAL ANALYSIS AND EXPERIMETNAL VERIFICATION FOR PAINLEV碋 PARADOX

  • 1.

    School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

  • 2. College of Engineering, Peking University, Beijing 100871, China

Funds: The project was supported by the National Natural Science Foundation of China (11172019, 11132001) and Fanzhou Youth Research Foundation (20110501).
  • Received Date: November 08, 2012
  • Revised Date: November 20, 2012
    Graphical Abstract
    • Abstract
  • Painlevé paradox may appear in multi-rigid-body systems subjected to Coulomb’ friction. No solution or multiple solutions make the systems inconsistent or indeterminate. It is worth investigating how the subsequent motions of the systems in inconsistent states evolve since the actual systems will always move on. The theoretical analysis and the experimental verification are carried out to confirm the tangential impact in the inconsistent case of the systems. The characteristic of the stick motions are confirmed during tangential impact.
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    • References (10)
  • 1 Painlevé P. Sur les Lois du Ffrottement de Glissement. C R Hebd Seances Acad Sci, 1895, 121: 112-115 (in French)
    2 Brogliato B. Nonsmooth Mechanics, Models, Dynamics and Control. London: Springer-Verlag London Limited, 1999
    3 姚文丽, 徐鉴. 考虑奇异性的平面多刚体系统冲击问题理论解. 振 动工程学报, 2009, 22(1): 65-69 (Yao Wenli, Xu Jian. Theoretical dynamical impact solution on planar multi-rigid-body systems considering singularity. Journal of Vibration Engineering, 2009, 22(1):65-69 (in Chinese))
    4 Song P, Kraus P, Kumar V, et al. Analysis of rigid-body dynamic models for simulation of systems with frictional contacts. Journal of Applied Mechanics, 2001, 68: 118-128
    5 Shivaswamy S. Modeling contact forces and energy dissipation during impact in mechanical systems. [PhD Thesis]. Ann Arbor MI: UMI, 2002
    6 Zhao Z, Chen B, Liu CS. Impact model resolution on Painlevé paradox. Acta Mechanica Sinica, 2004, 20(6): 659-660
    7 Zhao Z, Liu CS, Chen B. The Painlevé paradox studied at a 3D slender rod. Multibody Syst Dyn, 2008, 19: 323-343
    8 Genot F, Brogliato B. New results on Painlevé paradoxes. Eur J Mech A/Solids, 1999, 18: 653-677
    9 Liu CS, Zhen Z, Chen B. The bouncing motion appearing in a robotic system with unilateral constraint. Nonlinear Dynamics,2007, 49 (1-2): 217-232
    10 Zhao Z, Liu CS, Ma W, et al. Experimental investigation of the Painlevé paradox in a robotic System. J Appl Mech, 2008, 75(4):041006
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