A novel rotational internal combustion engine is invented and investigated. In this engine, no eccentric rotational component is used, resulting in vibration-free operation. For this characteristics, this engine will be suitable for usage in silent environment, e.g. co-generation house plant, handy-usage and so on. The engine mainly consists of a rotor casing and two types of rotor; cycloid rotor and trochoid rotor. The shape of the cycloid rotor is characterized by epicycloid surface and lobes, and the trochoid rotor also superior-epitrochoid surface and concaves. As mentioned above, fundamental process of intake, compression, ignition, expansion and exhaust for working gas is automatically performed by the constant speed rotation of both of rotors. In this paper, first, the typical configuration including two designing procedure of the rotors are described in detail. Next the cyclic behavior of the working process is explained. Furthermore the design drawing of the prototype engine is given. The time variations of chamber volume and pressure of typical configuration of the prototype engine are estimated. Also the comparison in engine compactness and compression ratio is made for another types of engine.