Is it possible to build a perpetual motion machine?

no, it would be a violation of Newtons third law...it would have to generate more energy than the energy it uses

For every action, there is an equal and opposite reaction.

I think it is. I think about satellites. The definition of a pmm is once you start it you don´t need any extra power to keep it going. Satellites don´t get any extra power after they have been launched. gravity does the rest of the work for eternity as long as no meteorite crashes intothe satellite.