Abstract: A piston engine has at least one cylinder and one piston, a crankshaft and gearing apparatus that has a set of two or more traveling gears fixed together which are rotating on a crank that belongs to: 1) either the crankshaft itself, 2) either an extended part of the crankshaft, or 3) to an auxiliary shaft which is geared to the said crankshaft. One of the traveling gears is of irregular design and travels in a periodical way against a non-rotating internally toothed ring. The second traveling gear is of regular form and meshes with a rotating output ring, which in turn drives an output shaft which can be used as an output instead of the regular crankshaft and provides an alternate non regular pattern of piston displacement relative to output shaft rotation. The gearing apparatus provides a volume expansion rate in the cylinder which is conducive to efficient combustion.