Abstract: A valve-free engine of 4n (4, 8, 12, etc.) cylinders comprises a fixed inner assembly comprising a pair of sun gears, a fixed outer assembly comprising fore and aft elements and a rotatable intermediate assembly. Each outer assembly element has an intake port and an exhaust port spaced circumferentially and offset from intake port and exhaust port of the outer element. Eight (or 4n) pairs of planetary gears rotate about the sun gears to control the in and out movement of pistons within a plurality of cylinder heads in a controlled pattern so that the distance of each diametrically opposite piston from the fixed inner assembly changes constantly and equally. The cylinder heads support piston cylinders along axes that are oblique to radii from said fixed shaft at a constant angle to said radii that is constructed and arranged to propel its piston in the direction of rotation of the intermediate assembly.