Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points

This article deals with the rigid body collisions of planar kine matic chains with an external surface while in contact with other surfaces. Two solution procedures that cast the impact equations in differential and algebraic forms are developed to solve the general problem. The differential formulation can be used to obtain three sets of solutions based on the kinematic, kinetic, and energetic definitions of the coefficient of restitution, whereas the algebraic formulation can be used to obtain solu tions based on the approaches presented in Whittaker (1904) and Brach (1991). A specific example of a planar three-link chain with two contact points is studied to compare the out comes predicted by each approach. A particular emphasis is placed on the energy loss that results from the application of each solution scheme. The circumstances in which various methods lead to identical or distinct outcomes are investigated. Most importantly, the study elaborates on the rebounds at the noncolliding ends, a phenomenon that is observed only in multicontact collisions. The interaction of the chain with the contact surfaces at the noncolliding contact points is examined, and the differences in the prediction of rebounds that arise from using various methods are investigated.