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 efficiency 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 cylinder surface 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. Side bearing elements are mounted on the interacting parts of the body and the crank; furthermore, the connection between the opposite parts of the crank and the coupling elements is designed in such a way that the movement of one part of the crank with respect to the opposite part thereof is limited in the direction away from the axis of rotation of the shaft along the reciprocating motion of the crank in order to ensure a specified distance between the contact surfaces of the working bearing elements of the crank when the machine is in operation. Furthermore, a preliminary load is created between the contacting surfaces of the working bearing elements and rollers.