  The dynamics of moving solids with unilateral contacts are often modeled by
assuming rigidity, point contacts, and Coulomb friction due to the simplicity
of these models. The canonical example of a rigid rod with one endpoint
slipping in two dimensions along a fixed surface (sometimes referred to as
Painlev\'e rod) has been investigated thoroughly by many authors. The generic
transitions of that system include three classical transitions (slip-stick,
slip reversal, lift-off) as well as a singularity called dynamic jamming, i.e.
convergence to a codimension 2 manifold in state space, where rigid body theory
breaks down. The goal of this paper is to identify similar singularities
arising in systems with multiple point contacts, and in a broader setting to
make initial steps towards a comprehensive list of generic transitions from
slip motion to other types of dynamics. We show that - in addition to the
classical transitions - dynamic jamming remains a generic phenomenon. We also
find new forms of singularity and solution indeterminacy, as well as generic
routes from sliding to self-excited microscopic or macroscopic oscillations.
