The clamping apparatus comprises a clamping chuck and a work piece carrier releasably connected thereto. The clamping chuck is provided with a central opening for receiving a clamping pin attached to the work piece carrier. The central opening of the clamping chuck has a conical inserting portion, and the clamping pin has at ldeast one surface portion corresponding in shape to the conical inserting portion, or several surface portions for aligning the clamping pin in X- and/or Y-direction. The clamping chuck comprises a clamping mechanism for clamping the clamping pin. The top of the clamping chuck is provided with at least one surface portion serving as a Z-stop member. The clamping pin is dimensioned such that, prior to activating the clamping mechanism, a gap exists between the flat bottom surface of the work piece carrier and the surface portion of the clamping chuck serving as a Z- direction stop member. The clamping pin and/or the region around the central opening of the clamping chuck is/are adapted to be elastically deformed upon activation of the clamping mechanism to further pull in the clamping pin into the central opening and simultaneously the work piece carrier towards the surface portion serving as a Z-direction stop member until the flat bottom surface of the work piece carrier rests on the surface portion of the clamping chuck serving as a Z-direction stop member. |