Design of Deployable Membranes Using Conformal Mapping

Abstract

This paper proposes a new method for designing the crease patterns of deployable membranes that can be wrapped up compactly. The method utilizes conformal mapping and the origami folding technique. The mapping of the flow with circulation can be used to control the angles between the fold lines, produce elements of the same shape, and maintain regularity of the fold lines. The proposed method thus enables the systematic and efficient design of complex patterns based on simple ones. The proposed method was successfully used to produce the patterns of Nojima and other extended new patterns of deployable membranes consisting of discrete equiangular spirals. The patterns were wrapped and used to form pillars such as regular polygonal, rectangular, and diamond pillars. Toward the industrial application of the proposed method, this paper also discusses pattern design for spacesaving storage and to reduce the effect of thickness when using versatile materials.