An investigation of reference criteria used in roundness measurement

The minimum zone, minimum circumscribing and maximum inscribing references (here grouped as 'bounding references') used in the measurement of roundness are investigated. Their behaviour is studied by formulating their definitions mathematically as optimisation problems. The advantages of limacon references, both for accuracy under practical measurement conditions and for computational convenience, are investigated and the relationships between these and circular references are discussed. The formulation leads to the development of efficient algorithms (which can be given simple geometric interpretations) for determining these references. The approach adopted is also believed to give a new insight into the interpretation of data derived from roundness measuring instruments with radius suppression.