Hidden symmetries generate rigid folding mechanisms in periodic origami

Abstract

Significance The traditional approach to designing origami metamaterials uses particular, highly symmetric crease patterns to generate folding motions for reconfigurability. We instead consider origami sheets with periodic but otherwise generic, asymmetric triangular faces and show they exhibit nonlinear folding motions which transform sheets through two-dimensional families of cylindrical configurations, with the addition of quadrilateral faces restricting sheets to one-dimensional subsets of configurations. This leads to a topological class of mechanical modes, preventing origami from exhibiting exponentially localized floppy modes observed in other systems. These results do not depend on scale or material and hence have applications extending to architecture and robotics, but particularly to the nanoscale, where limited control over fold patterns can constrain traditional techniques.