Dynamics of multibody systems with unilateral constraints

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. In the following, the differential-algebraic equations are transformed into a resolvable mathematical form by means of the contact laws in equation form. Ultimately we get a nonlinear system of equations for the three-dimensional contact problem with dependent constraints. For its solution, the homotopy method will be used and applied to a simple mechanical system.