A machine, such as an engine, which includes a cylinder (1), an essentially cylindrical piston (5) set on bearings and equipped with an eccentrically-set shaft (11), an inlet port or valve (8), an outlet port or valve (9), and a lever device (7), which is attached by bearings to a shaft (6) and which is intended to be in essentially tight contact with the piston (5). The cylinder (1) forms an essentially cylindrical chamber for the rotary piston (5) and a partially cylindrical chamber for the lever device (7) that moves backwards and forwards. The piston (5) is equipped, in the interior of the working chamber, with sliding-ring-type bearings (13, 14).