  The paper focuses on synthesizing optimal contact curves that can be used to
ensure a rolling constraint between two bodies in relative motion. We show that
geodesic based contact curves generated on both the contacting surfaces are
sufficient conditions to ensure rolling. The differential geodesic equations,
when modified, can ensure proper disturbance rejection in case the system of
interacting bodies is perturbed from the desired curve. A corollary states that
geodesic curves are generated on the surface if rolling constraints are
satisfied. Simulations in the context of in-hand manipulations of the objects
are used as examples.
