Relative positioning of parts in assemblies using mathematical programming

In extending solid modeling technology to the modeling of assemblies of discrete parts, it is important to capture the position of each part in the assembly relative to the positions of its neighbors. By describing each part position in terms of relationships between various features of the part and mating features of its neighboring parts, it is possible for the solid modeling system to compute the modeling transformations needed to simulate the desired assembly configuration. In this chapter we formulate a mathematical programming approach to this problem. This approach is particularly useful in situations that arise in the solution of tolerancing problems.

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