  A mechanical system is presented exhibiting a non-deterministic singularity,
that is, a point in an otherwise deterministic system where forward time
trajectories become non-unique. A Coulomb friction force applies linear and
angular forces to a wheel mounted on a turntable. In certain configurations the
friction force is not uniquely determined. When the dynamics evolves past the
singularity and the mechanism slips, the future state becomes uncertain up to a
set of possible values. For certain parameters the system repeatedly returns to
the singularity, giving recurrent yet unpredictable behaviour that constitutes
non-deterministic chaotic dynamics. The robustness of the phenomenon is such
that we expect it to persist with more sophisticated friction models,
manifesting as extreme sensitivity to initial conditions, and complex global
dynamics attributable to a local loss of determinism in the limit of
discontinuous friction.
