Dynamics of multi-rigid-body systems under non-smooth constraints and linear complementary problems

Abstract

The objective is to combine the dynamical problem of multi-rigid-body systems under non-smooth constraints with linear complementary problem (LCP). For multibody systems under unilateral constraints, according to their unilateral property, the laws governing such situations can be formulated to a complementary problem. But for multibody systems under bilateral constraints with friction, it becomes more difficult to formulate the complementary conditions because normal contact force is no longer non-negative. The complementary conditions are derived by introducing new parameters according to the property of rigid bilateral constraints in a completely general way, so that the fundamental problem of multi-rigid-body systems with frictional bilateral constraints can be solved as a mixed problem of DAE and LCP. The example shows the realized process and possible singularity and validates the LCP formulations given in this paper indirectly.

Keywords:

• Linear complementary problem
• Multi-rigid-body systems
• Bilateral constraints
• Unilateral constraints
• Friction
• Non-smooth constraints

Acknowledgements

The authors are grateful for the support of the Outstanding Young Scientists Foundation under grant No. 10625211, Chinese state natural science fund 10532050 and 10472083, and Science development funds of Shandong University of Science and Technology 05g017.