The paper is devoted to the actual topic of ensuring the movement of pistons with an infinite smallness of influence of the shear deformation of connecting rods in piston internal combustion engines with in-line arrangement of the cylinders of rotation. The article provides possessing novelty analytical dependencies of the description over the surface of an oblique open helicoid of the screw movement of a piston with the placement in a three-link crank-rod mechanism in a common plane or in parallel planes of mutually perpendicular axes of the rotation cylinder and crankshaft, of the amplitude of oscillations of forced harmonically varying through installed in accordance with the order of operation of the engine the time interval of the gases pressure force during the screw movement of the piston in the cylinder of rotation with the exception of the uncertainty of the average clearance and interference in the conjugations of sorted in a batch of the parts of the cylinder liners and pistons. Mathematical modeling of the screw motion of the piston was carried out using the program MathCAD. The proposed method of screw movement of a piston along the surface of an oblique open helicoid with the placement in a three-link crank-rod mechanism in a common plane or in parallel planes of mutually perpendicular axes of the rotation cylinder and crankshaft allows to ensure the return of connecting rod to the state of equilibrium when rearranging of the piston at the top dead center from one cylinder wall to another when passing limited by the stroke of the piston of the normalized section of its path.