A flat-foldable equiangular spiral folding pattern inspired by sunflowers for deployable structures

Flasher origami pattern has been widely utilized to improve the stowage efficiency of deployable structures. Nevertheless, flasher origami cannot be folded fully flat, and they still have great potential for optimization in terms of storage volume and folding creases. In this paper, a flat foldable equiangular spiral folding pattern inspired by the sunflower disk is introduced. Then, a parametric design method for this equiangular spiral crease diagram is introduced in detail. Subsequently, a kinematic model of the equiangular spiral folding pattern is established based on the kinematic equivalence between rigid origami and spherical linkages. A simulation of the developed model demonstrates that the equiangular spiral folding pattern can be folded flat. Using the folded ratio as an evaluation index, the calculated results and experiments show that the equiangular spiral crease pattern can yield fewer creases and improve stowage efficiency in comparison to flasher origami pattern. Equiangular spiral folding pattern can save a considerable amount of space and provide a new approach to spatially deployable structures.