Abstract: A self-limiting method and apparatus for deburring or rounding sharp edges. Structures which basically comprise a skin which is a surface of revolution with a plurality of upstanding ribs in a pattern forming pockets often have sharp edges on the sides of the ribs, formed by chemical milling or machining operations, with the edges lying along lines substantially parallel to the skin. It is necessary to deburr or round over these sharp edges without damaging or deforming the ribs or skin. To accomplish this, the structure is mounted on a fixture which permits the structure to be rotated around its axis of rotation while the axis is tilted at selected angles. The fixture is positioned above a hopper containing hard, small balls (usually steel). An elevator mechanism lifts the balls to a dispenser above the fixture which has appropriately located slots above the sharp edges to be rounded. Balls are allowed to fall through the slots onto the sharp edges and adjacent areas.