  We analyze here the minimal conditions for directional motion (net flow in
phase space) of a molecular motor placed on a mirror-symmetric environment and
driven by a center-symmetric and time-periodic force field. The complete
characterization of the deterministic limit of the dissipative dynamics of
several realizations of this minimal model, reveals a complex structure in the
phase diagram in parameter space, with intertwined regions of pinning (closed
orbits) and directional motion. This demonstrates that the mirror-symmetry
breaking which is needed for directional motion to occur, can operate through
an internal degree of freedom coupled to the translational one.
