Programming sequential deployment of origami via kinematic transition fronts

• 成果类型: Article
• 署名作者: Imada, Rinki; Tachi, Tomohiro
• 署名单位: Japan Aerospace Exploration Agency (JAXA); Institute of Space & Astronautical Science (ISAS); University of Tokyo
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.2615468123
• 发表日期: 2026-09-15
• 页码: e2615468123
• 关键词: transition fronts; origami; sequential deployment; discrete dynamical systems; heteroclinic orbits; TENDRIL PERVERSION; waves

摘要

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.