Name
Abstract | ||
|---|---|---|
The decomposition of a linkage into minimal components is a central tool of analysis and synthesis of linkages. In this paper we prove that every pinned d-isostatic (minimally rigid) graph (grounded linkage) has a unique decomposition into minimal strongly connected components (in the sense of directed graphs), or equivalently into minimal pinned isostatic graphs, which we call d-Assur graphs. We also study key properties of motions induced by removing an edge in a d-Assur graph - defining a sharper subclass of strongly d-Assur graphs by the property that all inner vertices go into motion, for each removed edge. The strongly 3-Assur graphs are the central building blocks for kinematic linkages in 3-space and the 3-Assur graphs are components in the analysis of built linkages. The d-Assur graphs share a number of key combinatorial and geometric properties with the 2-Assur graphs, including an associated lower block-triangular decomposition of the pinned rigidity matrix which provides modular information for extending the motion induced by inserting one driver in a bottom Assur linkage to the joints of the entire linkage. We also highlight some problems in combinatorial rigidity in higher dimensions (d=3) which cause the distinction between d-Assur and strongly d-Assur which did not occur in the plane. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.dam.2013.06.004 | Discrete Applied Mathematics |
Keywords | Field | DocType |
2-assur graph,3-assur graph,central building block,kinematic linkage,unique decomposition,bottom assur linkage,entire linkage,d-assur graph,spatial linkage,minimal component,block-triangular decomposition,directed graph,strongly connected component,mechanical engineering,algorithms,decomposition | Discrete mathematics,Modular decomposition,Indifference graph,Combinatorics,Clique-sum,Chordal graph,Cograph,Graph product,Pathwidth,1-planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
161 | 18 | 0166-218X |
Citations | PageRank | References |
4 | 0.49 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Offer Shai | 1 | 41 | 7.48 |
| Adnan Sljoka | 2 | 4 | 0.83 |
| Walter Whiteley | 3 | 450 | 32.34 |