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Unformatted text preview: ary and sufficient condition for a well-constrained assembly of N parts is that the sum of edge weights is 3(N - 1), and that for each cycle in the graph with Nc nodes, the sum of weights is 3(Nc - 1) and there is exactly one edge of weight 2 and one edge of weight 1 (a cycle with three edges of weight 2 results in a non-linear system of six equations with no general solution). The above conditions are a special case of the Grübler equation for planar mechanisms [Erdman, 1997]. Well-constrained assembly graphs have two important properties: 1. When two parts are connected by a chain of edges of weight 3, their relative position is determined link by link, where each link is solved as in Section 2.2. Such a chain of parts can be regarded as a single rigid part, because any rigid transformation on the parts as a group preserves the relation constraints. 72 Y. Ostrovsky-Berman and L. Joskowicz Fig. 4. (a) Infeasible instance of the mechanism when vertices v1,v2,v3,v4 of P3 and v5,v6 of P4 vary in 1mm from...
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