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. 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.
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