In prior art, an additional radial inward movement that is performed in accordance with a rotating cam disk is imparted on the grinding disk in order to relief-grind the cutting teeth and the chamfer of taps and the cutting teeth of thread formers. The invention relates to a cam disk (11) which can be rotated about an axis A and is provided with a control cam (12). Said control cam (12) forms a group of curves according to a large number of possible undercut contours on the grinding teeth of the tap or thread former, which are to be relief-ground. In order to obtain a specific undercut contour on a cutting tooth, a limited angle of rotation alpha is selected from the control cam (12). Said area is mechanically, optically, or electronically scanned by means of a scanning device (13). To this avail, the cam disk (11) performs an oscillating rotary movement only above the selected section of the control cam (12) (arrow indicating the direction of rotation 15). Relief-grinding of the cutting tooth is completed once a fore-and-aft movement has been performed, and the grinding disk returns to the starting position thereof. The result of the scan is transmitted to an electronic control device via a signal line (14).