Even fitting closed curves: 2-D algorithm and assembly applications

In certain assemblies there exists a requirement for the evenness of the gap between a "peg" and a "hole." In these cases, when given a "peg" and a "hole" that must be fitted the task is to find the positioning of the "peg" such that the gap will be as even as possible. In this paper the even fitting requirement is formulated for two planar closed curves. The optimal fitting demand is Sound to be equivalent to the maximization of the minimal distance between the curves. Both convex and nonconvex curves with "tolerances" are considered and optimized. It is proven that for certain shape characteristics, fitting for evenness can be further improved by minimization of the Haussdorff distance between the curves. We demonstrate the algorithm by fitting an automobile door into a frame. The best door positioning is Sound in such a way that the variation gap is minimized according to the selected metrics.