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Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review
Assur decompositions of direction-length frameworks. / Nixon, Anthony.
Graphs and Combinatorial Optimization : from Theory to Applications : CTW2020 Proceedings. ed. / Claudio Gentile; Giuseppe Stecca; Paolo Ventura. Cham : Springer, 2020. p. 131-143 (AIRO Springer).Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review
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TY - CHAP
T1 - Assur decompositions of direction-length frameworks
AU - Nixon, Anthony
PY - 2020/11/9
Y1 - 2020/11/9
N2 - A bar-joint framework is a realisation of a graph consisting of stiff barslinked by universal joints. The framework is rigid if the only bar-length preserving continuous motions of the joints arise from isometries. A rigid framework is isostatic if deleting any single edge results in a flexible framework. Generically, rigidity depends only on the graph and we say an Assur graph is a pinned isostatic graph with no proper pinned isostatic subgraphs. Any pinned isostatic graph can be decomposed into Assur components which may be of use for mechanical engineers in decomposing mechanisms for simpler analysis and synthesis. A direction-length framework is a generalisation of bar-joint framework where some distance constraints are replaced by direction constraints. We initiate a theory of Assur graphs and Assur decompositions for direction-length frameworks using graph orientations and spanning trees and then analyse choices of pinning set.
AB - A bar-joint framework is a realisation of a graph consisting of stiff barslinked by universal joints. The framework is rigid if the only bar-length preserving continuous motions of the joints arise from isometries. A rigid framework is isostatic if deleting any single edge results in a flexible framework. Generically, rigidity depends only on the graph and we say an Assur graph is a pinned isostatic graph with no proper pinned isostatic subgraphs. Any pinned isostatic graph can be decomposed into Assur components which may be of use for mechanical engineers in decomposing mechanisms for simpler analysis and synthesis. A direction-length framework is a generalisation of bar-joint framework where some distance constraints are replaced by direction constraints. We initiate a theory of Assur graphs and Assur decompositions for direction-length frameworks using graph orientations and spanning trees and then analyse choices of pinning set.
KW - Assur decomposition
KW - Assur graph
KW - Bar-joint framework
KW - Direction-length framework
KW - Pinned framework
KW - Rigid graph
U2 - 10.1007/978-3-030-63072-0_11
DO - 10.1007/978-3-030-63072-0_11
M3 - Chapter (peer-reviewed)
SN - 9783030630713
SN - 9783030630744
T3 - AIRO Springer
SP - 131
EP - 143
BT - Graphs and Combinatorial Optimization : from Theory to Applications
A2 - Gentile, Claudio
A2 - Stecca, Giuseppe
A2 - Ventura, Paolo
PB - Springer
CY - Cham
T2 - 18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
Y2 - 14 September 2020 through 16 September 2020
ER -