Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points

This article deals with the rigid body collisions of planar, kinematic 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 the energetic definitions of the coefficient of restitution. Whereas the algebraic formulation can be used to obtain solutions based on the approaches presented in Whittaker (1904) and Brach (1990). A specific example of a planar, three-link chain with two contact points is studied to compare the outcomes predicted by each approach. A particular emphasis is placed on the energy loss that results from the application of each solution scheme. The circumstances where various methods lead to identical or distinct outcomes are investigated. Most importantly, the study elaborates on the rebounds at the non-colliding ends, a phenomenon that is observed only in multi-contact collisions. The interaction of the chain with the contact surfaces at the non-colliding contact points is examined and the differences in the prediction of rebounds that arise from using various methods are investigated.