Multibody dynamics with unilateral constraints and friction. Issue 1 (December 2014) - Charles, Alexandre; Ballard, Patrick
Abstract In the view of robotics or granular media mechanics, we ask for the statement of the dynamical evolution problem for multibody systems with contacts and friction. The "event driven" approach does not allow to state an evolution problem in a systematic way: it gives a peculiar status to the instants of impact and to the contact points although they are unknowns of the problem. This matter of fact has given rise to a new approach in the frictionless case [4, 6] we generalize to the case including friction. Following to the point of view of Lagrange on the equation of the dynamics, we emphasize the systematic use of virtual powers and duality. This bias suggests to put emphasis on generalized reaction forces in the statement of the evolution problem and not on local reaction forces of the real world. This point of view allows to escape from pathologies e.g. Painlevé paradox [5] and Kane Paradox [3]. The proposed evolution problem accounts for impacts and friction in case of multiple unilateral constraints. We prove the existence and uniqueness of the solution to the associated rate problem. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)