Mathematical techniques for geometrical detection of contact within multibody systems

Abstract

Within a multibody dynamics algorithm, the occurrence of contact events is checked at each time integration step, being the contact forces computed, together with other existing forces, and then introduced into the Newton-Euler equations of motion as external generalized forces. In general, the evaluation of these contact forces relies on constitutive laws, which have to be selected according to the material’s nature of the contacting bodies (from linear elastic to nonlinear dissipative models). Prior to the calculation of the contact forces, a geometrical detection of the contact is required. This is not a trivial task and it depends on two key factors: (i) mathematical representation of the contact geometries and, (ii) proximity queries and simulation parameters. In this work, an overview of the most used techniques for the geometrical detection of contact is presented, given a special attention to the application field of multibody system dynamics.