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Constructing various simple polygonal tensegrities by directly or recursively adding bars

机译：通过直接或递归添加条构造各种简单的多边形张力

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摘要

As an important type of tensegrities, polygonal tensegrities and their assemblies/variants hold various applications in, such as, architectures, robotics, and metamaterials. We here propose two methods (direct and recursive methods) to construct the topologies of simple polygonal tensegrities by directly and recursively adding bars, respectively. In the design of a simple 2n-polygonal topology using the direct method, we arrange 2n strings and 2n nodes according to the edges and vertices of simple 2n-polygon, and then add n bars between each two of un-neighboring nodes. In the same topological design using the recursive method, we construct the topology of quadrilateral tensegrity as a start, then add one bar to generate a hexagonal topology, and repeat this operation until the total number of added bars reaches n. These two methods yield exactly the same configurations, showing that the total number of simple polygonal topologies increases exponentially with the number of bars. Surprisingly, there exist almost 100 million simple 22-polygonal topologies. Finally, we validate both numerically and experimentally that each of our designed topologies can produce a stable tensegrity configuration without external loads. This work sheds light on the topological features and mechanical characteristics of polygonal tensegrities, which help broaden their application scenarios.
机译：多边形张力及其组合/变体作为一种重要的张力类型，在建筑，机器人技术和超材料等领域拥有多种应用。我们在这里提出两种方法（直接方法和递归方法），分别通过直接和递归地添加钢筋来构造简单多边形张力的拓扑。在使用直接方法设计简单的2n多边形拓扑时，我们根据简单2n多边形的边缘和顶点排列2n个字符串和2n个节点，然后在每两个非相邻节点之间添加n条。在使用递归方法的相同拓扑设计中，我们以四边形张力结构作为起点，然后添加一个钢筋以生成六边形拓扑，并重复此操作，直到添加的钢筋总数达到n。这两种方法产生完全相同的配置，表明简单多边形拓扑的总数随钢筋数量呈指数增长。令人惊讶的是，存在将近1亿个简单的22多边形拓扑。最后，我们通过数值和实验验证了我们设计的每种拓扑都可以在没有外部负载的情况下产生稳定的张力配置。这项工作揭示了多边形张力的拓扑特征和机械特性，有助于拓宽其应用场景。

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