International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

This study treats a study oriented to the basic synthesis of the conic convolute helicoid. On the base of the elaborated mathematical model, the written equations show a theoretical possibility, depending on the basic geometrical characteristics of the designed conic convolute worm, to generate the active flanks of the helical teeth as parts of these conical convolute helicoids. Analytical dependences of the cross-section and the axial section of the conic convolute surfaces are obtained. These relations, as well as the performed studies of the graphic images of these sections, precede the process of constructing the algorithms for computer synthesis and design of these conic helical surfaces. The realized studies of the graphic images of these sections are the basis of the algorithms for computer synthesis and design of these conical helical surfaces. The appearance of singular points on these surfaces is examined, which is of particular importance for their technological synthesis. Based on the developed algorithm, a computer program for the synthesis and visualization of conic helical surfaces is realized and illustrated.