Abstract: A center lapping apparatus for precisely lapping center holes in opposite ends of the workpiece prior to outside diameter grinding of the workpiece includes a conical lapping stone and a dressing apparatus that supports a dressing stone for periodically dressing the lapping stone. Movement of the dressing stone during any dressing operation is confined to a plane in which an axis of symmetry of the lapping stone lies. A spring loaded pin disposed in a movable head of the dressing apparatus has a slightly tapered end which precisely fits in a stationary hole of a mounting bracket about which the movable head pivots. The tapered end of the spring loaded pin ensures that the dressing stone can always be returned to precisely the same position for a dressing operation despite wear of the spring loaded pin. A precise flat surface of the moveable head slides against a precision flat surface of the stationary plate during pivoting of the movable head.