This paper provides an attempt to formulate and to solve the best mechanical alignment problem, which arises in many practical situations when a relatively expensive manufactured product does not meet design specifications and a decision is to be made for partial retreatment of the product. We define and use concepts of regular points, reference points, and referenced points for a mechanical design. These points represent important features which must be reproduced subject to tolerances, which are defined with respect to (w.r.t.) various coordinate systems. The algorithm proposed identifies candidates for reworking using minimax optimization. While the concepts introduced and the method presented resulted from a variety of approaches to solving mechanical problems in two dimensions, this class of problem can arise in other areas and further generalization is possible.

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