"Golden Ratio Yoshimura" for Meta-Stable and Massively Reconfigurable Deployment

Yoshimura origami is a classical folding pattern that has inspired many deployable structure designs. Its applications span from space exploration, kinetic architectures, and soft robots to even everyday household items. However, despite its wide usage, Yoshimura has been fixated on a set of design constraints to ensure its flat-foldability. Through extensive kinematic analysis and prototype tests, this study presents a new Yoshimura that intentionally defies these constraints. Remarkably, one can impart a unique meta-stability by using the Golden Ratio angle to define the triangular facets of a generalized Yoshimura. As a result, when its facets are strategically popped out, a ``Golden Ratio Yoshimura'' boom with $m$ modules can be theoretically reconfigured into $8^m$ geometrically unique and load-bearing shapes. This result not only challenges the existing design norms but also opens up a new avenue to create deployable and versatile structural systems.