To solve problems that needs and the importance of the improvement of fuel consumption and the use of alternative fuel instead of fuel such as gasoline, diesel oil or the like are increased, demands of an internal combustion engine based on a fuel mixed with impurities and residual incombustible matters after combustion without being limited to high-quality fuel are increased, and conventional reciprocating engines and some types of rotary engines do not fulfil the demands due to the clogging of incombustible matters in discharging exhaust gas or the like.

The rotary engine is formed in a structure in which each stroke is performed in a separate compartment in a housing, and a rotary head and a partitioning valve are installed in the housing so that all the exhaust gas and the residual matters are discharged. In addition, the engine is formed so that a groove is formed in a rotor, and by opening/closing of an opening/closing valve which is opened and closed in the housing via an opening/closing gear, an opening/closing gear shaft, and a coupling bar which are installed in the groove, an output can be obtained so that the expanding action of a gaseous matter in combusting is received only in a rotating forward direction. In addition, the engine is formed in a structure so that a ratio of volumes of spaces of intake, compression, combustion, and exhaust can be set in a wide range according to the combination of a compression ratio and the volume of the expansion space by changing a shape of the groove of the grooved rotor installed therein, and the engine can be used for a variety of kinds of fuel.