With the advent and development of precision machining and manufacturing, the necessity to ensure quality of the produced parts for their longevity has grown as fast the advances in technology. One of the ways of achieving higher product lives has been through tighter tolerances on size and form characteristics. Thus, it is imperative that designers, manufacturers and quality inspectors understand the mathematical principles guiding these dimensional and form characteristics, and further utilize them, to the greatest degree possible, in the inspection equipment and tooling. One of the greatest benefits to mankind was the invention of wheel. It is inarguably evident how much of our lives depend on machines with rotating parts. From power stations to power tools, from the smallest watch to the largest car, all contain round components. In precision machining of cylindrical parts, the measurement and evaluation of roundness (also called circularity in ASME Geometric Dimensioning & Tolerancing, GD&T Y14.5) is an indispensable component to quantify form tolerance. Based on reference circles, this paper focuses on the four modeling methods of roundness. These are (1) Least Squares Circle (LSC), (2) Maximum Inscribed Circle (MICI), (3) Minimum Circumscribed Circle (MCCI) and (4) Minimum Zone or Minimum Radial Separation Circles. These methods have been explained in the context of their implications on design applications, advantages and disadvantages. This article also explores how these multitudes of parameters are to be understood and be incorporated into undergraduate engineering curriculum, and be taught as an improved toolkit to the aspiring engineers, process engineers and quality control professionals.

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