折纸顶点分析的拉格朗日方法：多稳态性
Lagrangian approach to origami vertex analysis: Multistability
浏览论文内容
中文总结 AI 辅助
本文用拉格朗日框架降维分析折纸顶点构型空间，揭示对称约束极小值及亚稳态，并发现多数极小值在全空间扰动下失稳，为机械超材料等提供设计依据。
中文摘要 AI 辅助
研究折纸结构的多稳态性因其运动学的非线性以及难以可视化和穷举探索的高维构型空间而面临挑战。为解决这一问题，我们利用折纸的拉格朗日框架来利用对称性，并获得构型空间的降维切片。我们对具有反射对称性的六度顶点的分析揭示了随着扇形角变化其运动学空间中的拓扑转变，这对对称约束极小值的数量以及亚稳态区域的出现具有影响。这些低维切片适合穷举搜索和可视化。随后的全空间稳定性分析表明，在允许所有局部兼容扰动（包括破坏对称性的扰动）时，41个六度对称约束极小值中的18个和45个八度对称约束极小值中的14个仍然是极小值。亚稳态区域可能被仅依赖数值优化的方法所忽视，它们受到可容许运动学空间边界与折痕力学特性之间相互作用的影响。我们将分析扩展到具有更高对称性和单自由度运动学的锥状顶点，探索对称性破缺现象、组合结构及其对分支稳定性的影响。所揭示的稳定性景观在机械超材料、机械计算、基于折纸的机器人以及设计用于自展开并保持形状的结构中具有潜在应用。
英文摘要
Studying the multistability of origami structures presents challenges due to the nonlinearity of their kinematics and the high-dimensional configuration spaces that are difficult to visualize and explore exhaustively. To address this, we utilize the Lagrangian framework for origami to exploit symmetries and obtain reduced-dimensional slices of the configuration space. Our analysis of degree-6 vertices with reflection symmetry reveals topological transitions in their kinematic space as sector angles are varied, with implications for the number of symmetry-constrained minima and the emergence of metastable regions. These lower-dimensional slices are amenable to exhaustive search and visualization. A subsequent full-space stability analysis shows that 18 of 41 degree-6 and 14 of 45 degree-8 symmetry-constrained minima remain minima when all locally compatible perturbations, including those that break symmetry, are admitted. The metastable regions, which would likely be overlooked by numerical optimization alone, are influenced by the interplay between the boundaries of admissible kinematic space and crease mechanical properties. We extend our analysis to cone-like vertices with higher symmetry and one-degree-of-freedom kinematics, exploring symmetry-breaking phenomena, combinatorial structure, and their consequences for branchwise stability. The stability landscapes uncovered have potential applications in mechanical metamaterials, mechanical computing, origami-based robotics, and structures designed to self-deploy and retain their shape.
发表机构
- Air Force Research Laboratory（空军研究实验室）
机构由 AI 辅助整理，请以论文原文为准。
