Abstract: A rotary engine wherein a piston is moving within the inside of a cylindrical housing describing its geometrical center or shaft a hypocycloid while the remaining points are generated by a circumference gyrating in the inside of a hypocycloid. The piston is formed by a cylindrical drum with projecting radial vanes. The drum is supported by a crank mechanism which includes a first crank rotatable about the crankshaft and a second crank eccentrically rotatably supported on the first crank. The drum is rotatably supported on the second crank, and a pinion associated with the second crank meshingly reacts with a stationary crown gear, whereby the drum moves along said hypocycloidal path.