Unified parametric modeling of origami-based tube

Existing parameterization of origami structures is based on angles, which is an inconvenience for the fabrication and calculation of the geometrical properties of an origami-engineering project. In this paper, a unified parameterization based on the dimensional parameters, including the length and height instead of the angles, is proposed. Various origami-based tubes reconstructed through the proposed parameterization process and compiled into a program are then described. Three types of tubes including non-flat foldable, locally flat-foldable, and entirely flat-foldable are systematically divided when forming a closed-loop tube, and a criterion is proposed for estimating the flat foldability of the tube. Finally, the proposed theory is validated based on physical prototypes folded using paperboard and fabricated using polymer through a blow molding process. The constructed origami-based tubes provide extensive guidance for the design of energy absorbing structures.