Abstract: An arrangement for controlledly removing material from an effective surface of a workpiece includes a mounting member which is mounted on a support for movement relative thereto at least in and opposite to a predetermined direction toward and away from the effective surface and a working member which is caused to rotate relative to the mounting member about a rotational axis that extends substantially normal to the predetermined direction. A pressing force acting in the predetermined direction is applied to the mounting member so that successive regions of an outer circumferential surface of the working member which is centered on the rotational axis act on a predetermined zone of the effective surface of the workpiece during the rotation of the working member with local pressures dependent on the magnitude of the pressing force and sufficient to remove material from the workpiece.