Worm gears are special gears consisting of a worm wheel and a worm. Worm gears can be produced in different ways, depending on the size of the transmission, the number of courses, the pitch angle of worm profile, the number of units produced, the purpose of application, etc. As cylindrical worm gears we consider the cylindrical worms with globoid gears, globoid worm with globoid worm gear and globoid worm with cylindrical worm gearing. This paper deals with the evolvent worm whose curve of the tooth side in the front plane is evolvent. The production of worm with an optimal profile for optimal meshing conditions is an increasingly frequent focus of worm gear manufacturers. The problem of designing the tool cutting edge can be divided into several steps. This article deals with the problems of optimum design of a tool shape for the production of worms; and the problems of calculating the coordinates of the transition cutting edge shape, and thus the path of grinding wheel for sharpening the tool cutting edge shape are solved. By grinding tool of grinding machine we can complete the worm shape and also sharpen the cutting edges of tools for production of worm surface. The problems of calculation of the coordinates are solved with regard to the functioning of the KON 250 CNC grinding machine logic.