Optimization of a contact surface

The paper introduces ideas from shape optimization to multibody system dynamics. A disk rolling down a given slope is taken as a simple example, for which it is the goal of the optimization to shape the rolling contour of the disk such that it takes a minimum time to cover a certain distance. The shape of the contour is described by its radius of curvature. The governing equations of motion result from the kinematics of relative motion and the Newton–Euler formalism. Three different kinds of spirals are defined and optimized.