On the Motion of a Set of Spheres Between Two Parallel Planes

Abstract

The motion is investigated of the centers of a set of identical spheres in rolling contact with two plane, parallel surfaces having general, coplanar motions. This motion is shown to be a rigid-body motion (which we call cage-plane motion). General properties of the motion are derived. Next the nature of the cage-plane motion is investigated in the case of input-plane motions, which are generated mechanically. The results reduce to the known special cases and indicate that the element (cage) usually regarded only as a spacer in ball bearings has a general motion, which is both versatile and potentially useful.