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 d ifferential formulation can be used to obtain three sets of solutions based on the kinematic, kinetic, and energetic definitions of the coef ficient of restitution, whereas the algebraic formulation can be used to obtain solutions based on the approaches presented in Whittaker (19 04) and Brach (1991). A specific example of a planar three-link chain with two contact points is studied to compare the outcomes predicted b y each approach. A particular emphasis is placed on the energy loss th at results from the application of each solution scheme. The circumsta nces in which various methods lead to identical or distinct outcomes a re investigated. Most importantly, the study elaborates on the rebound s at the noncolliding ends, a phenomenon that is observed only in mult icontact collisions. The interaction of the chain with the contact sur faces at the noncolliding contact points is examined, and the differen ces in the prediction of rebounds that arise from using various method s are investigated.