Energy-Based Modeling of Tangential Compliance in 3-Dimensional Impact

This paper studies modeling of tangential compliance as two rigid bodies collide in the space. Stronge’s spring-based contact structure [13, pp. 95-96] is extended to three dimensions. Slip or stick is indicated by the tangential motion of a massless particle connected to the contact point (viewed as an infinitesimal region) on one body via three orthogonal springs. We show that the effect of tangential compliance can be analyzed using normal impulse rather than time, contrary to a previous claim by Stronge. This is primarily due to the ability of updating the elastic energies of the three springs without knowledge of their stiffnesses or length changes. The change rates, nevertheless, are computable. So are sliding velocity and tangential impulse. The latter is then integrated into impact equations and contact kinematics, making the whole system driven by normal impulse alone. Examples include a ball and a pencil bouncing on a table, and a massé billiard shot. The theory has potential impact on impulsive robotic manipulation in which the ability to deal with friction and compliance is vital for skillful maneuvers.