Abstract: A self-supporting hand-held grinding device (10) for beveling the edges of a part having a compound contoured surface includes a frame (12) having a flat triangular-shaped base (22) and an integrally formed arm (24) with a cylindrical flange (26) projecting from the arm (24) to which is attached a grinding tool (14). The longitudinal axis of the cylindrical flange (26) is oriented such that the longitudinal axis X of the grinding tool (14) tilts away from the longitudinal axis (W) of the base (22) by an angle, .alpha., lying in the range of 5.degree. to 8.degree., and preferably at 7.5.degree.. Three legs (46) are attached to the base (22) by a retaining nut (58) and are adjusted in height by backing off a knurled locking nut (60) and turning the shaft by means of an adjusting nut (68). A foot (48) having a socket (52) is pivotally mounted to the ball-shaped supporting end (50) of each leg (46 ).