Programming sequential deployment of origami via kinematic transition fronts

TL;DR

This paper presents a systematic framework for programming sequential origami deployment using kinematic transition fronts modeled as heteroclinic orbits, enabling controlled shape change through geometric constraints.

Contribution

The authors develop a novel design approach linking heteroclinic orbits in dynamical systems to origami transition fronts, allowing programmable sequential deployment.

Findings

Asymmetric crease coupling produces nonlinear recurrence relations.

Recurrence relations can be designed to generate heteroclinic orbits for sequential deployment.

Shape programming is decoupled from propagation behavior through invariance exploitation.

Abstract

Propagating transition fronts, in which local interactions sequentially trigger state changes, are widely observed across natural, biological, and engineered systems. While such propagation has been engineered using energy-driven instabilities, front propagation governed purely by geometric constraints remains underexplored and lacks a general design framework. In particular, how to program sequential deployment in origami through such kinematic propagation remains an open challenge. Here, we develop a systematic design framework for kinematic transition fronts based on their correspondence with heteroclinic orbits in discrete dynamical systems. Focusing on strips of developable and flat-foldable degree-4 origami vertices, we show that asymmetric coupling between adjacent creases produces nonlinear recurrence relations whose composition generically gives rise to heteroclinic orbits connecting developed and flat-folded states, enabling domino-like sequential deployment. We further show that macroscopic shape can be programmed independently of propagation behavior by exploiting invariances in the recurrence relation, and illustrate the approach through a representative thick-panel origami prototype. These results enable programmable sequential deployment in origami via transition fronts, while also establishing a general framework for kinematic transition fronts in geometrically constrained systems.