Abstract: To center a tool restrained within a collet coupled to a driven portion (9) which, in turn, is coupled to a driving portion (2), and to compensate for possible axial offsets of the respective portions, a coupling element connects the driving and driven portions and two first spring elements (23, 24) are located on the driving portion, two further spring elements (31, 32) are located on the driving portions offset with respect to the first spring elements of 90 degrees. Each one of the spring elements can be adjusted with respect to a centrally located counter support portion (29, 31) by adjustment screws passing through the spring elements and bearing against the counter support, to thereby position the axis of the driven portion (9) carrying the collet, in congruence with the axis of the driving portion (2) even if there are manufacturing tolerances or other offset conditions, such as tolerances in the tool clamped in the collet.