An homogeneous charge compression ignition internal combustion engine comprising: a combustion cylinder, a combustion piston head movable along a piston axis within the combustion cylinder, an elongate connecting element; wherein the elongate connecting element has a first end and a second end, wherein the first end is coupled to the combustion piston head; and the engine further comprising: a compression ignition cylinder which is fluidically connected to the combustion cylinder, and a compression ignition piston moveable in reciprocating motion within the compression ignition cylinder, an actuation system for varying the timing of the compression ignition piston compared to the combustion piston head such that ignition timing may be varied according to the operating conditions of the engine, and the compression ignition piston is adapted to be moved between a bottom dead centre position corresponding to a maximum volume of the compression ignition cylinder to a top dead centre position corresponding to a minimum volume of the compression ignition cylinder during operation of the engine to create a pressure spike within the combustion cylinder thereby causing auto ignition of a fuel/air mixture within the combustion cylinder, and characterised in that the engine further comprises a track having a path, wherein the second end of the elongate connecting element is coupled to the track and the elongate connecting element is adapted to be driven by the piston as part of a power transfer mechanism for the piston; wherein the track is adapted to be moved relative to the combustion cylinder and is shaped such that, as the track moves relative to the combustion cylinder, the combustion piston head moves in reciprocating motion along the piston axis in accordance with the path of the track; and wherein the path of the track is shaped such that combustion piston head displacement is non simple harmonic with respect to displacement of the track relative to the combustion cylinder. a combustion cylinder, a combustion piston head movable along a piston axis within the combustion cylinder, an elongate connecting element; wherein the elongate connecting element has a first end and a second end, wherein the first end is coupled to the combustion piston head; and the engine further comprising: a compression ignition cylinder which is fluidically connected to the combustion cylinder, and a compression ignition piston moveable in reciprocating motion within the compression ignition cylinder, an actuation system for varying the timing of the compression ignition piston compared to the combustion piston head such that ignition timing may be varied according to the operating conditions of the engine, and the compression ignition piston is adapted to be moved between a bottom dead centre position corresponding to a maximum volume of the compression ignition cylinder to a top dead centre position corresponding to a minimum volume of the compression ignition cylinder during operation of the engine to create a pressure spike within the combustion cylinder thereby causing auto ignition of a fuel/air mixture within the combustion cylinder, and characterised in that the engine further comprises a track having a path, wherein the second end of the elongate connecting element is coupled to the track and the elongate connecting element is adapted to be driven by the piston as part of a power transfer mechanism for the piston; a compression ignition cylinder which is fluidically connected to the combustion cylinder, and a compression ignition piston moveable in reciprocating motion within the compression ignition cylinder, an actuation system for varying the timing of the compression ignition piston compared to the combustion piston head such that ignition timing may be varied according to the operating conditions of the engine, and the compression ignition piston is adapted to be moved between a bottom dead centre position corresponding to a maximum volume of the compression ignition cylinder to a top dead centre position corresponding to a minimum volume of the compression ignition cylinder during operation of the engine to create a pressure spike within the combustion cylinder thereby causing auto ignition of a fuel/air mixture within the combustion cylinder, and characterised in that the engine further comprises a track having a path, wherein the second end of the elongate connecting element is coupled to the track and the elongate connecting element is adapted to be driven by the piston as part of a power transfer mechanism for the piston; wherein the track is adapted to be moved relative to the combustion cylinder and is shaped such that, as the track moves relative to the combustion cylinder, the combustion piston head moves in reciprocating motion along the piston axis in accordance with the path of the track; and wherein the path of the track is shaped such that combustion piston head displacement is non simple harmonic with respect to displacement of the track relative to the combustion cylinder.