A novel design method of deployable semi-regular tessellated surfaces with plano-spherical units

Abstract

The design of movable systems gives an opportunity to create transformable designs which respond to the environmental, functional, cultural, and aesthetical needs of today's architecture. This paper proposes a method for designing a family of deployable structures which can be applied to semi-regular tessellated planar surfaces such as roofs, walls, and shading devices. The generated modular approach and adaptability provides a wide usage area and various combinations for these designs. The regular convex polygon modules are designed as a network of the triangular units. The triangular unit is designed using Bennett's overconstrained plano-spherical linkage topology. The polygonal modules are assembled to each other in one-uniform semi-regular tessellations. The assembly of adjacent regular convex polygons in each tessellation is examined to find a proper solution for no collision during deployment and to properly fit a surface without any gaps or overlaps in the deployed position. The assembly method for creating 1-DoF deployable surfaces and mobility calculations for a unit, the polygonal modules, and the assemblies are computed, and motion studies are demonstrated with CAD models and exemplified for a square module for motion tests in a prototype.