Frustration-driven Snap-through in Snapology

Abstract

We propose a transformable modular system based on Snapology, a modular origami assembled with prismatic foldable modules connected by foldable hinges. Our Snapology system specifically employs rhombic and regular triangular modules, with all creases constrained to a single fold direction (valley or mountain). The key finding lies in exploiting geometric frustration — the inability of the system to satisfy all geometric constraints simultaneously — to achieve rapid transformation from planar to three-dimensional (3D) configurations through snapping motion. The transformation principle is programmable by controlling the activation of out-of-plane fold hinges incident on a single vertex, enabling two distinct motions: smooth motion and snapping motion. We develop kinematic models to analyze configuration spaces and elucidate the underlying transformation principles. Computational modeling and prototype fabrication validate the predicted snapping behaviors. Design explorations demonstrate various system configurations that achieve programmable 2D-to-3D transformations through controlled snapping motion. This work establishes a new paradigm for frustration-driven modular origami design, with applications in programmable matter, soft robotics, and adaptive architectural systems.