This paper addresses the problem of generating a well-conditioned, near-optimal deterministic 3-2-1 location scheme. Given are a workpart with identified planar datum faces, each with an associated convex region of admissible locator positions, and a set of disturbing twists (resulting from the processing operations on the workpart). First, screw theory is used to identify easily implementable necessary and sufficient conditions for deterministic positioning of the workpart in a 3-2-1 locator scheme. Next, the conditioning of a location scheme is studied and combinatorial algorithms are developed for synthesizing near-optimally conditioned locator schemes. Interesting decomposition and restrictions on the search space are identified to make the synthesis procedure efficient.
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