  We investigate theoretically the non-linear dynamics of a coupled
nanomechanical oscillator. Under a weak radio frequency excitation, the
resonators can be parametrically tuned into a self-sustained oscillatory
regime. The transfer of electrons from one contact to the other is then
mechanically assisted, generating a rectified current. The direction of the
rectified current is, in most unstable regions, determined by the phase shift
between the mechanical oscillations and the signal. However, we locate
intriguing parametrical regions of uni-directional rectified current,
suggesting a practical scheme for the realization of a self-powered device in
the nanoscale. In these regions, a dynamical symmetry breaking is induced by
the non-linear coupling of the mechanical and electrical degrees of freedom.
When operating within the Coulomb blockade limit, we locate bands of
instability of enhanced gain.
