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

TL;DR

This paper derives the normal and static friction forces on a rolling ball actuated by internal point masses, analyzing how internal mass movements influence contact forces and slip prevention.

Contribution

It introduces a novel derivation of contact forces for internally actuated rolling bodies and explores their dynamics through numerical simulations.

Findings

Derived explicit formulas for normal and static friction forces.

Identified minimum static friction coefficients to prevent slippage.

Validated dynamics through numerical simulations.

Abstract

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.