Fixture foolproofing for polygonal parts

A modular fixture is an arrangement of fixturing elements (fixels) that locate and immobilize a workpart. A complete algorithm for designing fixtures for polygonal parts in 2-D was proposed by Brost and Goldberg (1994). The algorithm finds all fixtures consisting of three fixed-size locators and one clamp on a regular grid of holes. However, often it is possible to load the workpart into the fixture in an incorrect pose. An incorrect loading may have disastrous consequences when the part program is executed. Therefore, fixtures that permit only one pose for the loaded workpiece are very desirable. We call them foolproof fixtures. In this paper we present an algorithm that accepts a fixture design, produced by the Brost-Goldberg algorithm, and augments it by inserting in certain grid holes foolproofing pins that make the incorrect loading impossible. The algorithm is complete in the sense that it either (i) produces a solution; (ii) terminates without a solution because none exists; or (iii) detects and flags those nongeneric situations it cannot handle. (These occur rarely.) The produced set of foolproofing pins may not be minimal. However, it is not much worse than the minimal one. Experimental results and complexity analysis are provided.