Nonlinear Analysis of the Singularity of Multi-Rigid-Body Systems with One-Point Frictional Contact

摘要

This study performs a dynamic analysis of a multi-rigid-body system with one-point frictional contact. The linear complementary problem (LCP) theory is applied to obtain a general criterion, which can identify the singularity induced by non-ideal geometrical constraints in a multi-rigid-body system. The small normal flexibility at the frictional contact point is proposed to discuss the property of the singularity and to determine solutions of the systems when the singularity arises. The stability of the solutions is analyzed. When the small normal flexibility fails to obtain the finite solutions, a velocity jump is introduced at frictional contact point and an analytical expression is deduced to find a proper value of the jump. The results show that the solutions of the system can be computed continuously. It implies that the scheme provides in the present paper is valid when the singularity occurs in the multi-rigid-body system.