  In this paper, we study under which conditions the trajectories of a
mechanical control system can track any curve on the configuration manifold. We
focus on systems that can be represented as forced affine connection control
systems and we generalize the sufficient conditions for tracking known in the
literature. The sufficient conditions are expressed in terms of convex cones of
vector fields defined through particular brackets of the control vector fields
of the system. The tracking control laws obtained by our constructions depend
on several parameters. By imposing suitable asymptotic conditions on such
parameters, we construct algorithmically one-parameter tracking control laws.
The theory is supported by examples of control systems associated with elliptic
hovercrafts and ellipsoidal submarines.
