  We investigate theoretically the dynamics of a spatially symmetric
shuttle-system subjected to an ac gate voltage. We demonstrate that in such a
system parametric excitation gives rise to mechanical vibrations when the
frequency of the ac signal is close to the eigenfrequency of the mechanical
subsystem. These mechanical oscillations result in a dc shuttle current in a
certain direction due to spontaneous symmetry breaking. The direction of the
current is defined by the phase shift between the ac gate voltage and the
parametrically excited mechanical oscillations. Dependance of the shuttle
current on the dc gate voltage is also analyzed.
