Treatment of impact with friction in planar multibody mechanical systems

Frictional impact analysis of multibody mechanical systems has traditionall y relied on the use of Newton's hypothesis for the definition of the coeffi cient of restitution. This approach has in some cases shown energy gains in herent in the use of Newton's hypothesis. This paper presents a general for mulation, consistent with energy conservation principles, for the analysis of impact problems with friction in any planar multibody mechanical system. Poisson's hypothesis is instead utilized for the definition of the coeffic ient of restitution. A canonical form of Cartesian momentum/impulse-balance equations are assembled and solved for the changes in the momenta using an extension of Routh's graphical method for the normal and tangential impuls es. Impulse process diagrams are numerically generated, and the Cartesian v elocity or momenta jumps are calculated by balancing the accumulated system momenta during the contact period. This formulation recognizes the correct mode of impact, i.e., sliding, sticking, and reverse sliding. Impact probl ems are classified into seven cases, based on these three modes and the con ditions during the compression and restitution phases of impact. Expression s are derived for the normal and tangential impulses corresponding to each impact case. The developed formulation is shown to be an effective tool in analyzing some frictional impact problems including frictional impact in a two-body system, an open-loop system, and a closed-loop system.