Hyperboloid Modules for Deployable Structures

Abstract

This paper presents the process used to generate hyperboloid modules for deployable structures and the general equations for their design. These units are formed by three or more rods connected at a common articulated joint. During the opening process all the rods rotate in the same direction, and at the final unfolded stage each bar sits on its adjacent bar, activating a reciprocal self-locking system. The combination of these modules creates large span structures that can be folded in compact bundles. In this paper, the geometrical relationships between the dimensions of the elements to achieve a specific maximum opening angle is established. The connectivity between units is studied, as well as the requirements to achieve the maximum compactness of the grid at the folded stage.

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References

  1. Candela, Félix, Emilio Pérez Piñero, Santiago Calatrava, Félix Escrig, and Juan B. Pérez Valcárcel. 1993. Arquitectura Transformable. Sevilla: Escuela Técnica Superior de Arquitectura de Sevilla.

  2. De Temmerman, Niels, Lara Alegria Mira, and Aline Vergauwen. 2012. Feasibility of the Universal Scissor Component (USC): Building a full-scale Deployable Dome. Journal of the International Association for Shell and Spatial Structures 53 (174): 227–236.

  3. Escrig, Félix. 2013. Emilio Pérez Piñero: Inventor of deployability. Structures and Architecture: New concepts, applications and challenges. Proceedings of the ICSA Symposium: 42–57.

  4. Escrig, Félix, and Juan B. Pérez Valcárcel. 1993. Geometry of Expandable Space Structures. International Journal of Space Structures 8 (1&2): 71–84.

  5. Fuller, Richard Buckminster. 1999. Flying Seedpod. In Your private sky. R. Buckminster Fuller. The Art of Design Science, ed. Joachim Krausser and Claude Lichtenstein, 342–343. Switzerland: Lars Muller Publishers.

  6. Gantes, Charis J. 2001. Deployable Structures: Analysis and Design. Boston: WIT Press.

  7. Hoberman, Charles. 1991. Radial Expansion/Retraction Truss Structures. Patent: US-5.024.031.

  8. Langbecker, Travis, and Faris Albermani, 2000. Foldable Positive and Negative Curvature Structures: Geometric Design and Structural Response. Journal of the International Association for Shell and Spatial Structures 41 (134): 147–161.

  9. Pérez Piñero, Emilio. 1961. Estructura Reticular Estérea Plegable. Patent: ES-266.801.

  10. Popovic Larsen, Olga. 2014. Reciprocal Frame (RF) Structures: Real and Exploratory. Nexus Network Journal 16: 119–134.

  11. Puertas del Río, Lina. 1989. Estructuras Espaciales Desmontables y Desplegables. Estudio de la Obra del Arquitecto Emilio Pérez Piñero. PhD Thesis, Universidad Politécnica de Madrid.

  12. Pugnale, Alberto, and Mario Sassone. 2014. Structural Reciprocity: Critical Overview and Promising Research/Design Issues. Nexus Network Journal 16: 9–35.

  13. Sánchez-Sánchez, José. 1996. Estructuras Desplegables de Aspas para Mallas Poliédricas Curvas. PhD Thesis, Universidad de Sevilla.

  14. Sánchez-Sánchez, José, Félix Escrig, and M.Teresa Rodríguez-León. 2014. Reciprocal Tree-like Fractal Structures. Nexus Network Journal 16: 135–150.

  15. Valcárcel, Juan B. Pérez, and Félix Escrig. 1994. Pioneering in Expandable Structures: The ‘Madrid I’ Notebook by Leonardo da Vinci. Bulletin of the International Association for Shell and Spatial Structures 35 (114): 33–45.

  16. You, Zhong, and Sergio Pellegrino. 1997. Foldable Bar Structures. International Journal of Solids and Structures 34 (15): 1825–1847.

  17. Zeigler, Theodore R. 1976. Collapsible Self-Supporting Structure. Patent: US-3.968.808.

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Correspondence to Cristina Ramos-Jaime.

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Ramos-Jaime, C., Sánchez-Sánchez, J. Hyperboloid Modules for Deployable Structures. Nexus Netw J 22, 309–328 (2020). https://doi.org/10.1007/s00004-019-00459-y

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Keywords

  • Deployable structures
  • Transformable architecture
  • Kinetic systems
  • Self-locking systems
  • Reciprocal structures