Abstract: A machine measures an object of generally circular cross-section by superimposing on the subject a cylindrical coordinate system having five axes, namely a vertical measuring axis Z, three radial axes R0, R120, R240 emanating at a common point along the measuring axis Z, and a rotational axis .theta. having its center at the measuring axis Z. The machine includes an elevating unit which supports the object with its axis generally parallel to the measuring axis Z and is further capable of moving the object parallel to the measuring axis Z as well as rotationally about the measuring axis Z along the rotational axis .theta.. A measuring device monitors the linear position of the object along the axis Z while another measuring device measures the angular position of the object along the rotational axis .theta..