Translationally acting tool module for finishing, comprising a) at least one finishing element (12, 34, 48, 54) having a pressing stroke, b) at least one pressing force system for influencing a pressing force from the at least one finishing element (12, 34, 48, 54) on a workpiece surface to be worked, and c) drive means for driving the at least one finishing element (12, 34, 48, 54), d) the at least one finishing element (12, 34, 48, 54) being arranged on at least one translation unit (19, 43, 61, 81, 91, 92) which is driven and linearly guided by means of the drive means, further comprising e) at least one transmitting device, arranged in the translation unit (19, 43, 61, 81, 91, 92) or in at least one of the translation units (19, 43, 61, 81, 91, 92) and intended for transmitting a force onto the finishing element (12, 34, 48, 54) or onto at least one of the finishing elements (12, 34, 48, 54), the transmitting device being - a pressure transmitting device, which comprises a piston-cylinder system and is operated by fluid pressure, or - an electrically operated force transmitting device, characterized by f) a machine interface for connection to a machine, in particular a machine tool or a robot, g) the drive means comprising conversion means for converting a rotational movement of a machine element into the linearly guided translational movement of the at least one translation unit (19, 43, 61, 81, 91, 92), h) the machine interface being set up for connection to a spindle (14, 93) and the conversion means being provided for converting a rotation of the spindle (14, 93). a) at least one finishing element (12, 34, 48, 54) having a pressing stroke, b) at least one pressing force system for influencing a pressing force from the at least one finishing element (12, 34, 48, 54) on a workpiece surface to be worked, and c) drive means for driving the at least one finishing element (12, 34, 48, 54), d) the at least one finishing element (12, 34, 48, 54) being arranged on at least one translation unit (19, 43, 61, 81, 91, 92) which is driven and linearly guided by means of the drive means, further comprising e) at least one transmitting device, arranged in the translation unit (19, 43, 61, 81, 91, 92) or in at least one of the translation units (19, 43, 61, 81, 91, 92) and intended for transmitting a force onto the finishing element (12, 34, 48, 54) or onto at least one of the finishing elements (12, 34, 48, 54), the transmitting device being - a pressure transmitting device, which comprises a piston-cylinder system and is operated by fluid pressure, or - an electrically operated force transmitting device, characterized by - a pressure transmitting device, which comprises a piston-cylinder system and is operated by fluid pressure, or - an electrically operated force transmitting device, characterized by f) a machine interface for connection to a machine, in particular a machine tool or a robot, g) the drive means comprising conversion means for converting a rotational movement of a machine element into the linearly guided translational movement of the at least one translation unit (19, 43, 61, 81, 91, 92), h) the machine interface being set up for connection to a spindle (14, 93) and the conversion means being provided for converting a rotation of the spindle (14, 93).