The present invention is directed to an apparatus for grinding or polishing at least one edge of a glass substrate. The apparatus includes an air bearing support member configured to pivot about an axis of rotation with zero frictional resistance opposing said pivotal movement. A grinding unit is coupled to the air bearing support member. The grinding unit is configured to apply a predetermined force normal to the at least one edge to remove a predetermined amount of material from the at least one edge. The predetermined force is directly proportional to the predetermined amount of material and less than a normal force resulting in glass substrate breakage.