Acta Mechanica Sinica

, Volume 27, Issue 4, pp 587–592 | Cite as

A linear complementarity model for multibody systems with frictional unilateral and bilateral constraints

  • Hai-Ping GaoEmail author
  • Qi Wang
  • Shi-Min Wang
  • Li Fu
Research Paper


The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed. For bilateral constraints, frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions. With the time-stepping impulse-velocity scheme, the measure differential equations are discretized. The equations of horizontal linear complementarity problems (HLCPs), which are used to compute the impulses, are constructed by decomposing the absolute function and the filled-in relay function. These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints, or HLCPs for frictional bilateral constraints. Finally, a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.


Coulomb friction Bilateral constraint Unilateral constraint Horizontal linear complementarity problem (HLCP) Time-stepping impulse-velocity algorithm 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of dynamics and controlBeihang UniversityBeijingChina

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