Apparatus for precisely machining the surface of a workpiece comprises a rotating plate with a flat, horizontal abrasive-laden surface against which the workpiece surface is forced by gravity. The workpiece is carried on the free end of an arm pivotably supported remote from the end of the arm carrying the workpiece. Loading of the workpiece work surface can be varied by shifting weights along the length of the arm or transverse to the length of the arm. The workpiece itself can comprise a bar on which several magnetic transducing heads have been deposited. Machining the workpiece surface to a preferred position accurately defines a dimension of choice, such as the throat height of these transducers.