It is well-known that there exist rigid frameworks whose physical models can snap between different realizations due to non-destructive elastic deformations of material. We present a method to measure these snapping capability based on the total elastic strain energy density of the framework by using the physical concept of Green-Lagrange strain. As this so-called snappability only depends on the intrinsic framework geometry, it enables a fair comparison of pin-jointed body-bar frameworks, thus it can serve engineers as a criterion within the design process either to avoid snapping phenomena (e.g. truss structures) or to utilize them (e.g. multistable materials). Moreover, it turns out that the value obtained from this intrinsic pseudometric also gives the distance to the closest shaky configuration in the case of isostatic frameworks. Therefore it is also of use for the kinematics community, which is highly interested in the computation of these singularity-distances for diverse mechanical devices. In more detail we study this problem for parallel manipulators of Stewart-Gough type.

中文翻译：

---

销钉连接的杆身框架的可捕捉性和奇异距离

众所周知，由于材料的无损弹性变形，存在一些刚性框架，其物理模型可以在不同的实现之间对齐。我们提出了一种通过使用格林-拉格朗日应变的物理概念，基于框架的总弹性应变能密度来测量这些捕捉能力的方法。由于这种所谓的“可捕捉性”仅取决于内部框架的几何形状，因此可以对销钉连接的车身-钢筋框架进行公平的比较，因此可以将工程师用作设计过程中的准则，从而避免发生卡扣现象（例如桁架结构）或利用它们（例如多稳态材料）。而且，事实证明，在等静力框架的情况下，从该固有伪度量获得的值还给出了到最接近的摇晃构型的距离。因此，它也可用于运动学领域，该领域对各种机械设备的奇异距离的计算非常感兴趣。我们将更详细地研究Stewart-Gough型并联机械手的这个问题。