Abstract: The present invention discloses a rotary engine having a cylindrical stator with a plurality of radially arranged cylinders each having a piston, a shaft is rotatably mounted co-incident with the longitudinal stator axis, and an orbitor having a cylindrical interior encompasses the stator. Sequentially phased reciprocation of the pistons is transmitted to the orbitor which orbits about the shaft axis in a "polishing-cloth" motion without rotation or revolution of the orbitor. A gear mechanism converts the orbital motion of the orbitor to rotation of the shaft.