PCT No. PCT/SE87/00194 Sec. 371 Date Dec. 23, 1987 Sec. 102(e) Date Dec. 23, 1987 PCT Filed Apr. 23, 1987 PCT Pub. No. WO87/06451 PCT Pub. Date Nov. 5, 1987.An arrangement is used for the efficient mass production of individual bodies for the artificial rebuilding of teeth, for example. The arrangement comprises a first pair of co-rotating elements, of which the first element (1) is so arranged as to support a replica (21) of a body which is to be produced, and the second element (2) is so arranged as to support a blank from which the body is to be produced. The replica and the blank are caused to rotate synchronously about the axis of rotation (3, 4) of the respective element. In a second pair of elements a third element supports a sensing device (31) which is capable of interacting with the external contour of the replica, and a fourth element supports a tool (52) by means of which the blank is capable of being machined. The first and second pairs of elements are capable of being displaced relative to one another. The fourth element is adjustably connected to the third element (29) in such a way that the tool executes movements which correspond to the shape of the external contour of the replica sensed by the sensing device (31).