  The interplay of synchronization and topological band structures with
symmetry protected midgap states under the influence of driving and dissipation
is largely unexplored. Here we consider a trimer chain of electron shuttles,
each consisting of a harmonic oscillator coupled to a quantum dot positioned
between two electronic leads. Each shuttle is subject to thermal dissipation
and undergoes a bifurcation towards self-oscillation with a stable limit cycle
if driven by a bias voltage between the leads. By mechanically coupling the
oscillators together, we observe synchronized motion at the ends of the chain,
which can be explained using a linear stability analysis. Due to the inversion
symmetry of the trimer chain, these synchronized states are topologically
protected against local disorder. Furthermore, with current experimental
feasibility, the synchronized motion can be observed by measuring the dot
occupation of each shuttle. Our results open a new avenue to enhance the
robustness of synchronized motion by exploiting topology.
