On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point Masses

The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal force and static friction are derived from the equations of motion for a rolling ball actuated by internal point masses that move inside the ball's frame of reference, and, as a special case, a rolling disk actuated by internal point masses. The masses may move along one-dimensional trajectories fixed in the ball's and disk's frame. The dynamics of a ball and disk actuated by masses moving along one-dimensional trajectories are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed.