Prediction and control of slip-free rotation states in sphere assemblies

TL;DR

This paper investigates how assemblies of touching spheres can reach slip-free rotation states through friction, providing analytical predictions for bipartite assemblies and experimental methods to control these states with minimal input.

Contribution

It introduces a theoretical framework for predicting slip-free states in sphere assemblies and demonstrates a simple control method via experiments.

Findings

Final slip-free states are independent of friction strength.

Analytical prediction of states for assemblies with four degrees of freedom.

Experimental control of rotation states by manipulating only two spheres.

Abstract

We study fixed assemblies of touching spheres that can individually rotate. From any initial state, sliding friction drives an assembly toward a slip-free rotation state. For bipartite assemblies, which have only even loops, this state has at least four degrees of freedom. For exactly four degrees of freedom, we analytically predict the final state, which we prove to be independent of the strength of sliding friction, from an arbitrary initial one. With a tabletop experiment, we show how to impose any slip-free rotation state by only controlling two spheres, regardless of the total number.