Pairs of bodies with regular rigid surfaces rolling onto each other in spac
e form a nonholonomic system of a rather general type, posing several inter
esting control problems of which not much is known. The nonholonomy of such
systems can be exploited in practical devices, which is very useful in rob
otic applications. In order to achieve all potential benefits, a deeper und
erstanding of these types of systems and more practical algorithms for plan
ning and controlling their motions are necessary. In this paper, we study t
he controllability aspect of this problem, giving a complete description of
the reachable manifold for general pairs of bodies, and a constructive con
trollability algorithm for planning rolling motions for dexterous robot han
ds.