Fig. 1: The proposed method of defining three-dimensional runout.

In a the part in question (green) is mounted on a mandrel (blue), about which it is rotated. The four measurement positions are highlighted in red. The runout vectors of each component are then visualised. In b the runout of the mandrel is subtracted from the part, leaving the runout of the part defined only in the coordinate axes. Silhouettes of the assembly have been added to illustrate the transform. c shows how the runout vector is defined in the coordinate axes (\(\hat{r}\) and \(\hat{\theta }\)), with magnitude r and direction θ. \(\hat{z}\) is the final direction which defines the cylindrical polar coordinate system, and is normal to the plane of rotation. Finally, in d an example of the potential hardware set-up for this is shown. The part and mandrel are now mounted on a rotation stage (grey), with a sensor (orange) directed at one of the four measurement zones, with the remaining 3 zones silhouetted.