Proposed solution to eliminate pitch fluctuation in case of conical screw surface machining by apex adjustment

In case of conical worm production by conventional thread grinder, the fluctuation in angular velocity causes thread error. One possible way to eliminate the pitch error at the conical screw surface machining by shaft displacement is to design a drive pin that provides a constant pitch. In the course of our research, the examination of the machining of the conical worm surfaces by apex adjustment to eliminate the pitch fluctuation problem was carried out as a generalization of studies simulated with trigonometric relations in a particular case. The investigation was continued in a constructive geometric way with the aim of exploring universal mathematical relations in explicit forms in the mathematical kinematic model instead of the point series of the driver pin creator curve calculated in a given occurrence. The developed method makes exact design of the correct threading possible as a function of angular rotation in motion transfer under the given technology conditions, and thus expands the mathematical toolbar for innovative engineering design. Here we introduce the constructive geometric path supported by the algebraic toolbar, which also required affine and projective geometric relations in developing a solution that meets freely chosen expectations.