Method and machine for determining a shape contour on a measurement object

A coordinate measuring machine has a rotary table supporting a measurement object, a measuring head including a measuring element and a frame, on which the measuring head is arranged. The frame has first, second and third frame parts moveable relative to the workpiece holder along first, second and third movement axes, respectively. The measuring element is mounted via at least one fluid bearing, such as an air bearing, on one or more of the frame parts. The measuring head is positioned at a defined position along the first, second and third movement axes. Thereafter, the at least one fluid bearing is deactivated and the rotary table rotated around a further axis while the measuring head, using the measuring element, records current measured values. A shape contour of the object is determined on the basis of the measured values recorded while the at least one fluid bearing was selectively deactivated.