A new type of internal combustion engine with distinct advantages over conventional piston-engines and gas turbines in small power ranges is presented. The engine has analogies with piston engine operation, but like gas turbines it has dedicated spaces and devices for compression, burning and expansion. The engine operates on a modified limited-pressure thermodynamic cycle. The core of the engine is a nutating non-rotating disk, with the center of its hub mounted in the middle of a Z-shaped shaft. The two ends of the shaft rotate, while the disk nutates. The motion of the disk circumference prescribes a portion of a sphere. In the single-disk configuration a portion of the surface area of the disk is used for intake and compression, a portion is used to seal against a center casing, and the remaining portion is used for expansion and exhaust. The compressed air is admitted to an external accumulator, and then into an external combustion chamber before it is admitted to the power side of the disk. The external combustion chamber enables the engine to operate on a variable compression ratio cycle. Variations in cycle temperature ratio and compression ratio during normal operation enable the engine to effectively become a variable-cycle engine, allowing significant flexibility for optimizing efficiency or power output. The thermal efficiency is similar to that of medium sized diesel engines. For the same engine volume and weight this engine produces approximately twice the power of a two-stroke engine and four times the power of a four-stroke engine. The computed sea-level engine performance at design and off-design conditions in the 2 to 500 kW power range is presented.