(57) A method and apparatus for sharpening knives, blades, and the like utilizing a rotating displaceable abrasive disk where the abrading force on the knife cutting edge facet in parallel contact with the surface of the disk perpendicular to its axis of rotation is controlled by a biasing means such as a spring or equivalent, the position of the cutting edge facet on the disk is established by two appropriate stops contiguous to the disk and the angle between the principal plane of the disk and the face of the knife is controlled precisely so as to accommodate knives of different thickness and shape. Magnetic means to control the angle are claimed. Methods and apparatus include sequential steps that utilize one or more orbiting abrasive surfaces together with an abrasive disk sharpener where in each step there is a guide, preferably magnetic, to control the sharpening angle and where the angle is progressively greater in those sharpening steps where the orbiting abrasive elements are employed. Also claimed are means in a disk sharpener to prevent accidental contact of the face of the blade with the moving abrasive surface.