Abstract: A sharpening machine for sharpening the cutting edges of instruments, particularly the curved inner cutting edges of dental instruments, to obtain an arbitrary wedge angle. A grinding disk is provided with both a plane surface and a radiused outer edge. A shaft extension extends above the plane of the grinding disk and serves to support the instrument as it is being sharpened. The longitudinal axis of the instrument is displaced away from the axis of rotation of the shaft extension by an offset one-half distance equal to the diameter of the shaft extension thereby determining an offset angle of the longitudinal axis of the instrument with respect to the grinding disk and thus the wedge angle of sharpening of the curved inner edge of the instrument. In order to facilitate the sharpening of the curved inner edge of the instrument, the outer edge of the grinding disk is formed with a radius shorter than the radius of curvature of the instrument.