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  • symmetry-06-00516

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Symmetry adapted Assur decompositions

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Symmetry adapted Assur decompositions. / Nixon, Anthony; Schulze, Bernd; Sljoka, Adnan et al.
In: Symmetry, Vol. 6, No. 3, 27.06.2014, p. 516-550.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Nixon, A, Schulze, B, Sljoka, A & Whiteley, W 2014, 'Symmetry adapted Assur decompositions', Symmetry, vol. 6, no. 3, pp. 516-550. https://doi.org/10.3390/sym6030516

APA

Nixon, A., Schulze, B., Sljoka, A., & Whiteley, W. (2014). Symmetry adapted Assur decompositions. Symmetry, 6(3), 516-550. https://doi.org/10.3390/sym6030516

Vancouver

Nixon A, Schulze B, Sljoka A, Whiteley W. Symmetry adapted Assur decompositions. Symmetry. 2014 Jun 27;6(3):516-550. doi: 10.3390/sym6030516

Author

Nixon, Anthony ; Schulze, Bernd ; Sljoka, Adnan et al. / Symmetry adapted Assur decompositions. In: Symmetry. 2014 ; Vol. 6, No. 3. pp. 516-550.

Bibtex

@article{8683118a22454999af805f38013f71bf,
title = "Symmetry adapted Assur decompositions",
abstract = " Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.",
keywords = "Assur decomposition, pinned framework , forced symmetry , symmetric infinitesimal motion , isostatic graph , gain graph , orbit matrix",
author = "Anthony Nixon and Bernd Schulze and Adnan Sljoka and Walter Whiteley",
note = "This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.",
year = "2014",
month = jun,
day = "27",
doi = "10.3390/sym6030516",
language = "English",
volume = "6",
pages = "516--550",
journal = "Symmetry",
issn = "2073-8994",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "3",

}

RIS

TY - JOUR

T1 - Symmetry adapted Assur decompositions

AU - Nixon, Anthony

AU - Schulze, Bernd

AU - Sljoka, Adnan

AU - Whiteley, Walter

N1 - This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PY - 2014/6/27

Y1 - 2014/6/27

N2 - Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.

AB - Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.

KW - Assur decomposition

KW - pinned framework

KW - forced symmetry

KW - symmetric infinitesimal motion

KW - isostatic graph

KW - gain graph

KW - orbit matrix

U2 - 10.3390/sym6030516

DO - 10.3390/sym6030516

M3 - Journal article

VL - 6

SP - 516

EP - 550

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 3

ER -