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.
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