Dynamics of Multibody Systems Containing Dependent Unilateral Constraints with Friction

Abstract

In couplings of machines and mechanisms, backlash and friction phenomena are always occurring. Whether stick-slip phenomena take place depends on the structure of such couplings. These processes can be modeled as multibody systems with a time-varying topology. Making use of Lagrange multiplier methods with a mathematical formulation of the contact problem is very efficient for large systems with many constraints. The differential-algebraic equations of a system are transformed into a resolvable mathematical form by means of contact laws. In the following, rigid multibody systems with dependent constraints and planar friction will be considered. For the evaluation of such problems, an iterative algorithm is presented. This method is based on transformations of the kinematic secondary conditions in the form of inequalities to equations. In mathematical sense, these transformations are projections of the constraint forces on convex sets. Ultimately, we have a solvable nonlinear system of equations consisting of the differential equations of motion, the constraint equations and the projections of the constraint forces.