When used as input to the algorithm in ostrovsky

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online