Computational modeling methods for deployable structure based on alternatively asymmetric triangulation

Abstract

Asymmetric triangulation is an interesting method combined with concentric pleating to obtain a 3D shape without stretching or tearing. There exists some geometric properties in the process of folding to help realize extension and contraction, which can be used in parametric modeling of different regular polygons. To facilitate design and modeling, adequate computational modeling methods are indispensable. This paper proposes a new mathematical idea and presents a feasible way to build the parameterized models in the digital environment of Rhinoceros, utilizing the Kangaroo plugin in Grasshopper. Designers can directly observe the models' kinematic deployment and calculate the folding efficiency. It is concluded that the tendencies of folding efficiency in different regular polygons are not the same. To realize rigid folding, each polygon has a limited folding angle.