Folding a flat rectangular plate of uniform-thickness panels using Miura-ori

Abstract

In the realm of space technology, aerospace solar arrays are conventionally employed as efficient means of energy harvesting. The solar arrays need to be packaged in a payload capsule before launch and unfold as a standard rectangle with uniform thickness and a flat surface in orbit. In this paper, we introduce a novel methodology for folding a standard rectangular plate with uniform thickness and a flat surface based on Miura origami. Importantly, these plates can be unfolded with a single degree of freedom after a special design. The package direction is defined by analyzing the distinct characteristics of wave creases and straight creases. To achieve motion equivalence, different lengths of tape spring hinges are used along the package direction, while door hinges are employed at the wave crease. In order to address the motion interference problem during folding and maintain structural stability, constraints are derived, and a discrete nonlinear optimization model is established. The particle swarm optimization algorithm is used and improved to enhance convergence performance and computational efficiency. According to the calculation results, the corresponding folding plates were made, and the folding process and results are consistent with zero-thickness origami. These findings suggest that the proposed thick-panel origami method not only achieves efficient optimization of the geometric design but also preserves the essential characteristics of traditional zero-thickness origami. To aid designers, some key design recommendations based on the parameter analysis are provided for enhancing the deployment ratio.