Time-stepping for multibody dynamics with friction-affected bilateral constraints

The dynamics of multibody systems with friction-affected bilateral constraints is essentially different from those of smooth multibody systems. In this paper, general modeling and numerical methods for this kind of friction-affected system are given. Each friction-affected bilateral constraint is modeled by splitting it into two unilateral constraints opposite to each other. The constraint equalities are replaced with complementarity inequalities to avoid the absolute value terms in the dynamic equations. A linear complementarity problem time-stepping scheme is presented for simulation that does not suffer from the difficulties of enumeration (known as Delassus’ problem). The algorithm has the advantage that it needs no detection for stick-slip transition when neglecting the difference between the static and kinetic friction coefficients. Our method is carried out in an example to analyze the nonsmooth nonlinear behavior of a typical mechanism.