An arrangement measures coordinates of a workpiece and/or machines the workpiece. The arrangement has a first part and a second part that can be moved relative to the first part. The relative mobility of the first and second parts is specified in addition to a possible mobility of a probe that is optionally additionally fixed to the arrangement. The mobility of the probe is specified by a deflection of the probe from a neutral position during a mechanical probing of the workpiece for the purpose of measuring the coordinates. A measuring body is arranged on the first or second part, and at least one sensor is arranged on the other part, i.e. on the second or first part. The sensor generates a measurement signal corresponding to a position of the measuring body and thus corresponding to the relative position of the first and second part.