Multi-probe roundness measurement and harmonic content of Reuleaux polygons

This paper aims to clarify misconceptions present in some literature on roundness measurement related to diameter measurement and the harmonic content of Reuleaux triangles, which are sometimes referred to as shapes of constant diameter and thus implied to exhibit odd lobing. To demonstrate, the paper investigates regular Reuleaux polygons in the angular frequency domain by evaluating their harmonic components numerically. A pattern is observed in the frequency domain representation of the Reuleaux polygons, with harmonic components repeating at intervals corresponding to the number of angles in the polygon. Finally, the paper discusses the implications of mechanical filtration effects and the existence of such geometries for roundness measurement in practice, discussing the limitations of two-point diameter measurement in roundness measurement.