The invention relates to mechanical engineering, in particular to piston machines and mechanisms for converting the movement of the pistons thereof into shaft rotation. The technical result of the invention involves increasing the operational reliability, extending the service life, improving the specific mass and dimensional characteristics and enhancing the effectiveness of a machine. The essence of the invention is that the piston and the crank of a piston machine are interconnected by means of a hinged joint with at least a flat hinge which enables the piston to self-center along the surface of a cylinder owing to the movement of the piston with respect to the crank in any direction on a plane that intersects the longitudinal axis of the cylinder. The surfaces of the crank that take up reactive torque are constricted by rollers with synchronized toothed wheels.