Abstract: A rotor (30) is formed to include a plurality of recesses (42, 44), each of which engages a portion of a rotary piston (36, 38). The remaining portions of the rotary pistons (36, 38) project radially outwardly from the periphery of the rotor (30) to a position contiguous the inner surface of a peripheral stator wall (14). The peripheral stator wall (14) includes a plurality of endwardly projecting lobes (156, 158). The lobes (156, 158) are elongated axially of the engine and present convex surfaces of circular curvature which conform in size and shape to concave pockets (46, 48) formed in side portions of the rotary pistons (36, 38). During rotation of the rotary assembly the piston pockets (46, 48) move into and then out from a meshing engagement with the lobes (156, 158). One of the lobes (156) carries an igniter (154). An explosive lean mixture (168) is drawn into the side pocket (46) of a piston (36) as the piston ( 36) moves past an inlet opening (150).