Optimized Synthesis of Snapping Fixtures
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This paper deals with the following separability problem in 3D space: Given a rigid polyhedron P with n vertices, does a semi-rigid polyhedron G exist, such that both polyhedra can be transformed into an inseparable assembled state, where the fixture snaps on to P, by applying a linear force and exploiting the mild flexibility of G? If such a flexible snapping polyhedron exists, devise an efficient and robust algorithm that constructs it. In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate, we can push G towards P, slightly bending G on the way, and obtain a configuration, where G is back in its original shape, and both P and G are inseparable as rigid bodies. We define certain properties such a pair of polyhedron and its snapping fixture may possess, and prove two theorems related to the pair. We introduce an algorithm that produces a snapping fixture with such properties in O(n^5) time, if a snapping fixture exists, and an efficient and robust implementation of this algorithm.
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