Abstract: The sensing head of a coordinate measuring machine includes sensing pin combinations or sensing pins which are changeably fastened with high precision in respect to their spatial position. The receiver contains an isostatic three-point bearing against which the connecting body of the sensing pin is drawn by a pneumatically operated clamping arrangement. In the preferred embodiment the clamping arrangement consists of a suction cup and arresting elements for maintaining attachment of the receiving device to the connecting body when there is no subpressure acting upon the suction cup.