Sleeve for a coordinate measuring machine

A sleeve (1) for coordinate measuring machines is presented, which has a square cross-section and is guided in its upper and in its lower regions respectively in four bearing members (3, 4, 5, 6) arranged on its four lateral guide surfaces (9, 10, 11, 12). Two further bearing members (7, 8) are located in the middle region between the upper and lower bearing members and are arranged offset by 90 DEG relative to one another. According to the invention, bearing members (5, 6, 7) which are respectively constructed in a resilient fashion are assigned to the fixed bearings (3, 4, 8) opposite thereto or offset by 90 DEG . The four corners of the sleeve (1) have a bezel (2).