
A best fit reference line for use in partial arcs – D.J.Whitehouse
Many methods of measuring the out-of-roundness of nominally circular components or holes have been based,
for convenience, upon some form of graphical assessment in which the inspector uses a pair of compasses, a rule and a
good measure of subjective judgement. This has changed in recent years with the introduction of methods which can be
implemented in an analogue or digital form and which are based normally on a best-fit circle rather than on zonal
methods. The only practical disadvantage of this more objective approach has been its inability to cater for
components having a discontinuous circumference, such as parts with keyways, flats, etc., or parts made up of partial
arcs often encountered in the ball bearing industry. This paper justifies the use of a limacon reference line for
roundness measuring instruments and goes on to develop a general expression which enables reference lines to be fitted
to components having partial arcs or discontinuous circumferences very often met with in industry. It therefore
allows for the first time the meaningful objective assessment of the out-of-roundness or roughness of such parts.
Whitehouse, D. J. “A best fit reference line for use in partial arcs.” Journal of Physics E: Scientific Instruments 6.9 (1973): 921.