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

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.