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This research deals with the application of several algorithms to calculate the minimum zone straightness. Generally, in the evaluation of the minimum zone value of form errors such as straightness, flatness, roundness, and cylindricity, nonlinear optimization techniques are usually applied. The problem with the nonlinear technique that depends on computing algorithm is that the computing time may be prolonged. Therefore, some linear search techniques that are relatively easy to program are applied for straightness in this article. Furthermore, the problem can also be linearized by considering the characteristics of the measured profile for straightness; thus, the reduction of computing time will be achieved. Then, the problems caused by the above consideration are clarified. Consequently, the convergence criteria and comparison of results by means of several computing methods are investigated. The relationship between flatness and straightness values in some machining conditions and the comparison with the least-squares values are studied.

This article deals with the application of some nonlinear optimization techniques for minimum zone flatness. The convergence criteria of the techniques, namely the downhill simplex method and the repetitive bracketing method, are considered. The least-squares method is also applied, and subsequently the three methods are compared from the viewpoint of computational accuracy. A surface profile measuring system and a noncontact sensor are used to obtain three-dimensional data. The measured data are expressed by means of perspective mapping. Subsequently, the relationship among the above three methods is clarified according to accuracy and efficiency of the computation. Furthermore, some examples of the relationship between the manufacturing method and the flatness value, and the technique of a skilled hand are described.