A Poisson-based formulation for frictional impact analysis of multibody mechanical systems with open or closed kinematic chains

Analysis of frictional impact in a multibody mechanical system requires a f riction model capable of correct detection of all possible impact modes suc h as sliding, sticking, and reverse sliding. Conventional methods for frict ional impact analysis have tither shown energy gain or nor developed for jo inted mechanical system, and especially not for closed-chain multibody syst ems. This paper presents a general formulation for the analysis of impact p roblems with friction in both open- and closed-loop multibody mechanical sy stems. Poisson's hypothesis is used for the definition of the coefficient o f restitution, and thus the energy gains inherent with the use of Newton's hypothesis are avoided. A canonical form of the system equations of motion rising Cartesian coordinates and Cartesian momenta is utilized. The canonic al momentum-balance equations are formulated and solved for the change in t he system Cartesian momenta using an extension of Routh's graphical method for the normal and tangential impulses. The velocity jumps are calculated b y balancing the accumulated system momenta during the contact period. The f ormulation is shown to recognize all modes of impact; i.e., sliding, sticki ng, and reverse sliding. The impact problems are classified into seven type s, and based on the pre-impact system configuration and velocities, express ions for the normal and tangential impulses are derived for each impact typ e. Examples including the tip of a double pendulum impacting the ground wit h some experimental verification, and the impact of the rear wheel and susp ension system of an automobile executing a very stiff bump are analyzed wit h the developed formulation.