Roundness: A closed form upper bound for the centroid to minimum zone center distance by worst-case analysis

The minimum zone tolerance (MZT) meets the ISO 1101 definition of roundness error: it determines two concentric circles that contain the roundness profile and such that the difference in radii is the least possible value. This article provides theoretical evidence that the minimum size of the neighborhood of the centroid containing the minimum zone center is pi E-1(C), where E-C is the roundness error related to the centroid, which can be evaluated in closed form. The implications of such linear estimating are twofold: (i) locating the part center with a given tolerance, e.g. for manufacturing tasks, such as handling (peg-hole) or machining (centering) and (ii) providing a search area for minimum zone center-based algorithms, such as metaheuristics (GA, PSO, etc.).