Curved pleat folding for smooth wrapping

A technique is presented to minimize the packaged size of a flat sheet by folding it into a strip that can be wrapped around a hub. This is difficult to accomplish using regular straight creases, because of the thickness of the sheet. A curved crease pattern is used to address this problem of non-zero thickness. A mathematical formulation is developed in order to compute the required crease pattern for coiling a folded strip to any desired curvature, and specifically for coiling it into a tight spiral around a hub. This method is demonstrated with paper models. The crease computation algorithm is then extended to provide a folding strategy to efficiently package a square sheet around a central hub such that it can easily unfold or deploy. This development has applications particularly for deployable structures on small spacecraft.