Provided is a cat-and-mouse type internal combustion engine of concentric two-rotor/six-piston type, which has a cooling chamber in its cylinder and which needs neither any lubricating oil nor any valve mechanism so that its structure is simple and compact and can be easily manufactured. Further provided are a variable correlation type crank for a constant-pressure burning (CPB) engine of a variable compression ratio, and an inertial correlation type crank for a premixed compression ignition (HCCI), thereby to realize an internal combustion engine, which matches fuels of various kinds and which has a high energy efficiency and a clean exhaust gas.