A method of operating an internal combustion engine having a housing, a piston mounted in the housing for complex motion about a plurality of axes and coupled to a shaft, and wherein occur phases of compression, combustion, and expansion in the housing, and wherein, in the compression phase, air introduced through an intake port into the housing is compressed by reducing volume of a compression chamber in the housing from an initial volume to a second volume that is less than the initial volume, and in the expansion phase, byproducts of combustion expand from the second volume to a third volume that is greater than the initial volume.