A Study of the Geometrical Condition and a Culculatin Method for the Minimum Zone Method. The Geometrical Condition of Roundness.

Many techniques were proposed by means of optimization methods to verify the minimum zone accuracy. It is not always easy to obtain a true solution, even with long calculation time. In order to solve the problem, the geometrical condition of roundness is clarified. The geometrical condition is shown as follows: as shown in Fig. 1, if there are two points A, B on thhe inscribed circle determined by the minimum zone method, and another two points C, D on the circumscribed circle, segments AB and CD intersect each other. This paper proved this geometrical condition determined by the minimum zone roundness.