A solution for folding rigid tall shopping bags

Abstract

Rigid origami is concerned with the folding of rigid thin-walled structures. The materials from which the structures are made are not allowed to deform or bend, but can rotate freely about pre-arranged creases. One of the challenges in rigid origami is the flat folding of a shopping bag with a rectangular base if the bag is made of rigid materials. The problem is not only mathematically interesting but also has practical implications as many consumer goods are packaged in box-shaped cartons or cardboard boxes. In this paper, a new crease pattern has been proposed that allows a tall box-shaped bag with a rectangular base to be rigidly folded flat. Rigid folding conditions are established, and solutions that meet these conditions are found numerically. Simulations and experiments carried out demonstrate that the solution works. The new pattern represents the first practical solution for tall bags and can lead to direct applications in the packaging industry. Moreover, the folding analysis can be used to design an automated packaging process for folding box-shaped stiff cartons.