Abstract: In a nutating spherical engine, improvements for increasing the seal between the rotor and the engine head comprise the provisions of a pair of minor cusps disposed on the rotor which as seen in plan view are diametrically opposed and at right angles to the major cusps of the rotor. The engine may include a rotor guide including a cam and cam follower which cause the rotor to undergo the same nutational rotation as that caused by the interaction of the rotor and cylinder head. The rotor and cylinder head may be coupled by a ball and socket, and the ball may contain a simple coupling for the drive shaft of the engine. The cam, cam follower and coupling of the engine are easily located as they are not in direct communication with the working chambers of the engine.