Abstract: An apparatus for sharpening cutters of periodontal instruments comprises a base supported on a parallelogram formed by two carriers in which is mounted in rotary manner a grinding wheel. At the lower ends the carriers are mounted in a support plate, which is mounted by a pivot pin on a support arm of a swivel head. Below the carriers is displaceably mounted a link, which is coupled to the lower pivot pin of one of the carriers. During the rotary movement of the swivel head, the link is moved along a template, through which it is possible to adjust the angular position of the grinding wheel relative to the cutter in accordance with an eccentric relief or a bevel cut to be made. The grinding wheel is driven by a drive motor via an envelope drive, which is located in a casing, which receives all the elements of the rotating and fixed parts, with the exception of the base and the upper ends of the carriers.