The invention relates to a rotary piston machine comprising a frame, a cylinder liner rotatably supported in the frame, and a gear mechanism supported coaxially in the cylinder liner and connecting the frame, the cylinder line and the rotor, wherein the gear mechanism is located outside a working space located between the cylinder liner and rotor, and wherein the gear mechanism couples the cylinder liner and rotor for a periodically oscillating relative movement between a positive and negative rotational speed. According to the invention, the gear mechanism and the cylinder liner, together with the rotor, form a transmission having five rotational joints with the degree of freedom of 1 and a rotational/prismatic joint, wherein the gear mechanism comprises a rotational body, which is supported rotatably on the frame by means of a first rotational joint, and a connecting rod, which is rotatably connected to the rotational body by means of a second rotational joint, to the cylinder linerby means of a third rotational joint, and to the rotor by means of the rotational/prismatic joint.