An X-Engine assembly includes four cylinder banks which are located on two intersecting planes with the crankshaft axis being on the line of the intersection of the two planes, and having a Double-Acting Scotch Yoke (DASY) power conversion system that couples the reciprocating motion of the pistons with the rotating crankshaft to provide pure sinusoidal piston motion. A series of DASY X-Engine configurations that satisfy even-firing for both 2-stroke and 4-stroke, and other engine cycles, achieve perfect balance with regard to vibrating forces and moments that are all zero, and all configurations have zero torsional vibration of the crankshaft resulting from the reciprocating masses.