Quantifying the complexity of folding origami membranes

This paper presents a preliminary quantitative model to analyze the complexity or difficulty of folding origami structures from flat membranes. Extensive efforts have realized intricate origami patterns with desired functions such as mechanical properties, packaging efficiency, and deployment behavior. However, the complexity associated with the manufacturing or folding of origami patterns has not been explored. Understanding how difficult origami structures are to make, and how much time they require to form is crucial information to determining the practical feasibility of origami designs and future applications such as robotic origami assembly in space. In this work, we determine this origami complexity metric by modeling the geometric properties and crease formation mechanics of the origami structure, from which it outputs crease and pattern complexity values and a prediction of the time to complete the pattern assembly, based on the characteristics of the operator. The model is experimentally validated by fabricating various Miura-ori origami paper models.