A coordinate measuring machine for determining spatial coordinates on a measurement object has a frame structure on which a probe head is arranged. The probe head has a probe head sensor system, a body part and a coupling part which can move relative to the body part. The frame structure is designed to move the probe head relative to the measurement object. The probe tool has at least one stylus for making contact with the measurement object, and also has a rotating plate. The stylus is coupled to the coupling part by means of the rotating plate, such that it can rotate. At least one roll motion projection is formed on the body part. The rotating plate can be rolled along this roll motion projection by means of a movement of the coupling part in order to set a defined orientation of the stylus.