Analytical Formulation of the Classical Friction Model for Motion Analysis and Simulation

Abstract

Starting from a precise definition of friction torque when velocity vanishes that distinguishes the case of instantaneous zero crossing from that where the velocity is zero over a time interval, this paper proposes a compact analytical formulation of the classical discontinuous friction model that is useful for motion analysis. A finite state machine that allows a numerically robust computation of motion equations when velocity vanishes or motion restarts is then defined. Simulation results show that the discontinuous model can be seen as an asymptotic approximation, infinitely fast, of a recently proposed continuous, dynamic friction model.