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Structural Representation of Reconfigurable Linkages

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Advances in Reconfigurable Mechanisms and Robots I

Abstract

This paper presents adjacency matrix originated three-dimensional matrix for structural representation of mechanisms by integrating binary string in the sense of displacement subgroup theory. The improved elementary matrix operation for expressing of topological transformation of metamorphic mechanism is integrated in the three-dimensional matrix representation. A novel reconfigurable eight-bar linkage employing variable-axis revolute joints is proposed and the three-dimensional matrix for each working phase is expressed to reveal the distinct geometry. The improved elementary matrix operation is used to express the topological transformation of a metamorphic eight-bar linkage and to identify the effectiveness of the operation.

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Acknowledgments

The authors thank the support of European Commission—Framework 7 Programme under grant number 270436.

Author information

Authors and Affiliations

  1. Centre for Robotics Research, King’s College London, University of London, Strand, London, WC2R 2LS, UK

    Ketao Zhang, Guowu Wei & Jian S. Dai

  2. Department of Mechanical Engineering, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Ketao Zhang & Yuefa Fang

Authors
  1. Ketao Zhang
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  2. Yuefa Fang
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  3. Guowu Wei
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  4. Jian S. Dai
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Corresponding author

Correspondence to Ketao Zhang .

Editor information

Editors and Affiliations

  1. King's College London, Western Road 17, Sutton, SM1 2TE, United Kingdom

    Jian S Dai

  2. University of Genova, Via Opera Pia 15A, Genova, Italy

    Matteo Zoppi

  3. , School of Engineering and, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom

    Xianwen Kong

Appendix

Appendix

$$ {\mathbf{BA}}_{ 1} = \left[ {\begin{array}{*{20}c} {0000} & { 1 {\text{A4}}4} & {0000} & {0000} & {0000} & {0000} & {0000} & { 1 2 {\text{C4}}} \\ { 1 {\text{A4}}4} & {0000} & {1244} & {0000} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {1244} & {0000} & {1{\text{AC}}4} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {1{\text{AC}}4} & {0000} & { 1 2 {\text{C4}}} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {0000} & { 1 2 {\text{C4}}} & {0000} & { 1 {\text{A44}}} & {0000} & {0000} \\ {0000} & {0000} & {0000} & {0000} & { 1 {\text{A44}}} & {0000} & {1244} & {0000} \\ {0000} & {0000} & {0000} & {0000} & {0000} & {1244} & {0000} & {1{\text{AC}}4} \\ { 1 2 {\text{C4}}} & {0000} & {0000} & {0000} & {0000} & {0000} & {1{\text{AC}}4} & {0000} \\ \end{array} } \right] $$
(A.1)
$$ {\mathbf{BA}}_{ 2} = \left[ {\begin{array}{*{20}c} {0000} & { 1 4 44} & {0000} & {0000} & {0000} & {0000} & {0000} & { 1 2 {\text{C4}}} \\ { 1 4 44} & {0000} & {1414} & {0000} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {1414} & {0000} & {1{\text{A4}}4} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {1{\text{A4}}4} & {0000} & { 1 4 4 4} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {0000} & { 1 4 4 4} & {0000} & { 1 4 1 4} & {0000} & {0000} \\ {0000} & {0000} & {0000} & {0000} & { 1 4 1 4} & {0000} & {1244} & {0000} \\ {0000} & {0000} & {0000} & {0000} & {0000} & {1244} & {0000} & {1{\text{AC}}4} \\ { 1 2 {\text{C4}}} & {0000} & {0000} & {0000} & {0000} & {0000} & {1{\text{AC}}4} & {0000} \\ \end{array} } \right] $$
(A.2)
$$ {\mathbf{BA}}_{ 3} = \left[ {\begin{array}{*{20}c} {0000} & { 1 1 14} & {0000} & {0000} & {0000} & {0000} & {0000} & { 1 4 4 4} \\ { 1 1 14} & {0000} & {1414} & {0000} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {1414} & {0000} & {1{\text{A4}}4} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {1{\text{A4}}4} & {0000} & { 1 1 4 4} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {0000} & { 1 1 4 4} & {0000} & { 1 1 1 4} & {0000} & {0000} \\ {0000} & {0000} & {0000} & {0000} & { 1 1 1 4} & {0000} & {1414} & {0000} \\ {0000} & {0000} & {0000} & {0000} & {0000} & {1414} & {0000} & {1{\text{A4}}4} \\ { 1 4 4 4} & {0000} & {0000} & {0000} & {0000} & {0000} & {1{\text{A4}}4} & {0000} \\ \end{array} } \right] $$
(A.3)
$$ {\mathbf{BA}}_{{{\text{m}}1}} = \left[ {\begin{array}{*{20}c} {0000} & { 1 2 {\text{A}}4} & {0000} & {0000} & {0000} & {0000} & {0000} & { 1 2 {\text{C4}}} \\ { 1 2 {\text{A}}4} & {0000} & {1214} & {0000} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {1214} & {0000} & {12{\text{A}}4} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {12{\text{A}}4} & {0000} & { 1 2 {\text{C4}}} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {0000} & { 1 2 {\text{C4}}} & {0000} & { 1 2 {\text{A4}}} & {0000} & {0000} \\ {0000} & {0000} & {0000} & {0000} & { 1 2 {\text{A4}}} & {0000} & {1214} & {0000} \\ {0000} & {0000} & {0000} & {0000} & {0000} & {1214} & {0000} & {12{\text{A}}4} \\ { 1 2 {\text{C4}}} & {0000} & {0000} & {0000} & {0000} & {0000} & {12{\text{A}}4} & {0000} \\ \end{array} } \right] $$
(A.4)
$$ {\mathbf{BA}}_{\text{m2}} = \left[ {\begin{array}{*{20}c} {0000} & { 1 2 {\text{A}}4} & {0000} & {0000} & {0000} & {0000} & {12{\text{A}}4} & { - 1 2 {\text{C4}}} \\ { 1 2 {\text{A}}4} & {0000} & {1214} & {0000} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {1214} & {0000} & {12{\text{A}}4} & {0000} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {12{\text{A}}4} & {0000} & { 1 2 {\text{A4}}} & {0000} & {0000} & {0000} \\ {0000} & {0000} & {0000} & { 1 2 {\text{A4}}} & {0000} & { - 1 2 {\text{A4}}} & {1214} & {0000} \\ {0000} & {0000} & {0000} & {0000} & { - 1 2 {\text{A4}}} & {0000} & { - 1214} & {0000} \\ {12{\text{A}}4} & {0000} & {0000} & {0000} & {1214} & { - 1214} & {0000} & { - 12{\text{A}}4} \\ { - 1 2 {\text{C4}}} & {0000} & {0000} & {0000} & {0000} & {0000} & { - 12{\text{A}}4} & {0000} \\ \end{array} } \right] $$
(A.5)

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Zhang, K., Fang, Y., Wei, G., Dai, J.S. (2012). Structural Representation of Reconfigurable Linkages. In: Dai, J., Zoppi, M., Kong, X. (eds) Advances in Reconfigurable Mechanisms and Robots I. Springer, London. https://doi.org/10.1007/978-1-4471-4141-9_13

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  • DOI: https://doi.org/10.1007/978-1-4471-4141-9_13

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4140-2

  • Online ISBN: 978-1-4471-4141-9

  • eBook Packages: EngineeringEngineering (R0)

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