Abstract: A rotary engine including a static toroidal cavity having an inlet port for introducing fuel and air to the cavity and an outlet port for exhausting products of combustion from the cavity. A first power train including a first output shaft and a second power train including a second output shaft are located partially within the cavity and able to rotate in the first direction. A plurality of pistons are positioned around a perimeter of the toroidal cavity and between the first and second power trains. The plurality of pistons are movable with respect to the cavity and include a first set of pistons connected to rotate with the first power train and a second set of pistons connected to rotate with the second power train. The plurality of pistons defining a plurality of chambers therebetween.