The clamping apparatus comprises a first coupling element and a second coupling element that can be releasably attached thereto. The first coupling element is provided with four at least partially conical centering pins that are adapted to engage four grooves correspondingly arranged on the second coupling element. Both coupling elements have stop surfaces serving as Z references, cooperating upon clamping together the two coupling elements to determine the position of the second coupling element with regard to the first coupling element in Z-direction once they are clamped together. The centering pins are, in relation to the grooves, designed such that each centering pin rests only on one flank of the associated groove. Thus, a gap remains between the centering pin and the other flank of the groove. Out of the overall eight groove flanks of the four grooves, the centering pins rest on in each case two pairs of diametrically opposite flanks, while they do not rest on the two further pairs of oppositely located flanks.

A coupling device with two coupling members, which are to be connected coaxially together, and a tension rod, which penetrates the first coupling member and is to be coupled with the second coupling member. To minimize the effect of the cross forces on the positioning of the second coupling member, it is provided that the end, facing the head of the tension rod, penetrates into a passage borehole of the second coupling member with a radial clearance; and a connector, resting against a shoulder of the second coupling member, can be attached to the end, thus resulting in radial clearance between connector and second coupling member. Furthermore, a connector is described whose periphery has a contour, which prevents a turning action inside the coupling member, whereby the connector can also be moved in the coupling member and exhibits an axial contact surface, which is adequately small to enable a swivelling motion without generating a counteracting moment of flexion.