用几何构造法设计可稳定切换的四连杆机械结构。
Bistable Quad-Nets Composed of Four-Bar Linkages
- 基于欧氏空间中的无穷小柔顺四边形网，通过Whiteley去平均化实现构造。
- 可在不依赖数值优化的情况下生成具有任意多链接的双稳态结构。
- 适合机械设计与可变形结构研究者，便于控制轴位置和翻转角度。
我们研究一类由空间四连杆机构组成的新型机械结构，具备双稳态特性，即存在两种稳定构型。这些结构可被解释为研究二次曲面（Study quadric）中的四边形网，并据此证明了可构建含无限多链接与关节的组装体。提出一种纯几何构造方法：从欧氏空间中无穷小柔顺的四边形网出发，应用Whiteley去平均化。该视角将问题置于离散微分几何框架内，使我们能从已知的四边形网类（如离散极小曲面）中构造双稳态结构。与多数其他双稳态结构构造方法不同，本方法无需数值优化，且可简单调控关键几何参数，如轴位置与翻转角度。
原文摘要 · Abstract (English)
We study a novel type of mechanical structures, composed of spatial four-bar linkages, that are bistable, that is, they allow for two distinct configurations. These structures have an interpretation as quad nets in the Study quadric which we use to prove existence of assemblies with an unbounded number of links and joints. We propose a purely geometric construction of such objects, starting from infinitesimally flexible quad nets in Euclidean space and applying Whiteley de-averaging. This point of view situates the problem within the broader framework of discrete differential geometry and enables the construction of bistable structures from well-known classes of quad nets, such as discrete minimal surfaces. In contrast to many other construction methods for bistable structures, our approach does not rely on numerical optimization and it allows for simple control of relevant geometric parameters such as axis positions and snap angles.
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