通过运动学转变前沿编程折纸的顺序展开
Programming sequential deployment of origami via kinematic transition fronts
AI总结：
本文提出基于异宿轨道对应关系的运动学转变前沿设计框架，通过非对称耦合实现折纸多米诺式顺序展开，并独立编程宏观形状。
摘要：
传播中的转变前沿（其中局部相互作用顺序触发状态变化）在自然、生物和工程系统中被广泛观察到。虽然这种传播已通过能量驱动的失稳实现工程化，但纯粹由几何约束控制的前沿传播仍未被充分探索，且缺乏通用的设计框架。特别是，如何通过这种运动学传播在折纸中编程顺序展开仍是一个开放的挑战。在此，我们基于运动学转变前沿与离散动力系统中异宿轨道的对应关系，开发了一个系统性的设计框架。聚焦于可展开且可平折的四阶折纸顶点的条带，我们展示了相邻折痕之间的非对称耦合产生非线性递推关系，其组合通常产生连接展开态和平折态的异宿轨道，从而实现多米诺骨牌式的顺序展开。我们进一步表明，通过利用递推关系中的不变性，宏观形状可以独立于传播行为进行编程，并通过一个代表性的厚板折纸原型展示了该方法。这些结果通过转变前沿实现了折纸的可编程顺序展开，同时也为几何约束系统中的运动学转变前沿建立了一个通用框架。
英文摘要：
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.
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