The article shows the possibility of designing and manufacturing using multi-coordinate grinding and sharpening machines with CNC for workable worm mills for machining straight-slotted slots. Screw backing provides the necessary values of the rear side corners, and the ability of CNC machines to achieve the required accuracy and manufacturability of the tool. The lack of such tools consists in the increase of the diametrical sizes in comparison with the classically used ones. A positive effect when using the principles of screw backlash is the shaping of the cutting edges of the teeth in a checkerboard pattern, which significantly reduces the cutting forces. The use of techno-logical 3D models as a result of the design allows, at the design stage, to evaluate the arising design flaws and to make the necessary corrective actions into the initial data of the tool.