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.
