Drawing on screw theory and engineering mechanics, a mathematical theory for automatic configuration of machining fixtures for prismatic parts is developed. There are two parts in the theory: analysis and synthesis. The following functions of fixtures are analyzed: deterministic workpiece location, clamping stability, and total restraint. The synthesis of fixtures includes the determination of locating and clamping points on workpiece surface and the determination of clamping forces. The theory deals with the general case of 3-dimensional parts, polygon support (as opposed to three-point support), and multiple machining operations.

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