Modelling of Compact Folding/Wrapping of Flat Circular Membranes

(Folding Patterns of Equiangular Spirals)

Abstract

We describe the folding/wrapping methods of thin flat circular membranes using folding patterns prescribed by combining two groups of spirals. By using both folding conditions at nodes and continuous conditions of equiangular spiral fold lines in the membranes, two kinds of folding patterns have been analytically designed: (1) folding patterns consisting of pseudo-equiangular spirals (zigzag spirals) and equiangular spirals, and (2) folding patterns consisting of two groups of equiangular spirals. The applicability of the present folding/wrapping methods to circular membranes has been verified by manufacturing paper and very thin metal sheet samples.