A systematic method of generating hinged tessellations by adding hinged plates based on dual graphs

Abstract

Kinetic facades possess aesthetic expressiveness and environmental responsiveness, aligning with the principles of low-carbon architecture. Current kinetic facades primarily rely on three-dimensional movement, which are characterized by complex structures and distributed drives, resulting in monotonous form, low robustness, and high costs. This paper focuses on the design of two-dimensional kinetic facades, proposing a hinged tessellation generation method based on the duality principle. First, the paper discusses the value and principles of applying dual graphs in HT, and then proposes a method of generating HT by adding hinged plates. Then, the operation process for different tessellation types is elaborated upon. Finally, a conceptual design is proposed to illustrate the potential of this method on kinetic facades. The method proposed in this paper is applicable to all uniform tessellations and Voronoi tessellations, capable of generating an infinite variety of planar expandable structures with small spatial thickness, simple structures, stable movements. Additionally, these structures can be driven to expand by a single driving point, enabling continuous adjustment in response to the requirement. It has significant application value in fields such as architectural and decorative design, structural design, mechanical design, industrial product and graphic design.

Keywords

Hinged tessellation / Dual graph / Generative design / Kinetic facades

References

[1] Akira, N. , 1998. Home>Geometric toy.

[2] Bayar, M. , 2020. Design and computational optimization of a kinetic facade.

[3] Beatini, V. , 2015. Kinetic planar tessellations. Proceedings of International Association for Shell and Spatial Structures Symposia 2015, 1- 12.

[4] Clinton, J.D. , 1971. Advanced Structural Geometry Studies. Part 2: A Geometric Transformation Concept for Expanding Rigid Structures. Southern IllinoisUniversity,Washington D.C.. NASA Report CR-1735.

[5] Coulais, C. , Sabbadini, A. , Vink, F. , van Hecke, M. , 2018. Multi-step self-guided pathways for shape-changing metamaterials. Nature 561, 512- 515.

[6] Ding, C. , Ye, Z. , Wang, H. , 2021. Research on the shape control of deployable building skin with single-axis drive based on polar coordinate system. In: DADA2021, p. 8.

[7] Flores, A. , 2017. Hinged tilings. North American GeoGebra Journal 6 (1), 1- 12.

[8] Gazi, A. , 2010. A Method to Design Kinetic Planar Surface with Mathematical Tessellation Techniques. Izmir Institute of Technology, Turkey.

[9] Gezgin, A.G. , Korkmaz, K. , 2017. A new approach to the generation of retractable plate structures based on one-uniform tessellations. J. Mech. Robot. 9, 041015.

[10] Gray, J. , 2010. Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century. Springer Undergraduate Mathematics Series. Springer, London.

[11] Grünbaum, B. , Shephard, G.C. , 1989. Tilings and Patterns. W. H. Freeman, Company, New York.

[12] IOC , 2021. Tokyo 2020 Olympic logo, poster design & look of the games. Available at the website of the International Olympic Committee. https://olympics.com/zh/olympic-games/tokyo-2020/logo-design.

[13] Kızılörenli, E. , Maden, F. , 2023. Modular responsive facade proposals basedon semi-regularanddemi-regulartessellation:daylighting and visual comfort. Frontiers of Architectural Research 12, 601- 612.

[14] Körner, A. , Knippers, J. , Eshraghi, V. , Zolfaghari, A. , Asrar Haghighi, L. , Kalantari, M. , 2018. Arch(k)kinetic - Curved-line folding for elastic, adaptive building envelopes. In: Proceedings of IASS Annual Symposia, 2018, pp. 1-8.

[15] Moloney, J. , 2011. Designing Kinetics for Architectural Facades: State Change. Routledge.

[16] Senechal, M. , 1995. Quasicrystals and Geometry. Cambridge University Press, Cambridge.

[17] Sun, C. , Han, Y. , Wang, J. , 2022. The research and practice of computational design of the form of self-adaptive building facades. Architectural Journal (2), 1- 8.

[18] Wang, H. , 2021. A study on the type and topological transformation of tessellation regarding architectural computation design. In: DADA2020. Harbin, China.

[19] Wells, D.G. , 1991. The Penguin Dictionary of Curious and Interesting Geometry. Penguin Books. Mathematics Reference, Penguin Books.

RIGHTS & PERMISSIONS

2024 The Author(s). Publishing services by Elsevier B.V. on behalf of Higher Education Press and KeAi.