A Classification of Spatial Stiffness Based on the Degree of Translational–Rotational Coupling
A Classification of Spatial Stiffness Based on the Degree of Translational–Rotational Coupling
复制标题
基于平动-旋转耦合程度的空间刚度分类
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Schimmels
中科院分区：
文献类型：
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作者：
Shuguang Huang;J. Schimmels
以前，我们已经表明，要实现任意的空间刚度矩阵，需要将翻译和旋转行为沿着/大约轴绕一个轴的弹簧组件。我们表明，三个这样的耦合组件和三个未耦合的组件足以实现任何完整的空间刚度矩阵，并且对于某些空间刚度矩阵，需要三个耦合组件。在本文中，我们展示了如何识别提供的最小组件数量，这些组件数量提供了实现任意指定的空间刚度矩阵所需的翻译 - 旋转耦合。我们基于此数字建立了空间刚度矩阵的分类，我们称之为翻译旋转耦合（DTRC）的程度。我们表明，刚度矩阵的DTRC由空间刚度映射唯一确定，并通过评估空间刚度矩阵的特征性来获得。确定了每个类的拓扑特性。此外，讨论了先前对空间僵硬行为的研究中发现的DTRC与其他属性之间的关系。
Previously, we have shown that, to realize an arbitrary spatial stiffness matrix, spring components that couple the translational and rotational behavior along/about an axis are required. We showed that, three such coupled components and three uncoupled components are sufficient to realize any full-rank spatial stiffness matrix and that, for some spatial stiffness matrices, three coupled components are necessary. In this paper, we show how to identify the minimum number of components that provide the translational-rotational coupling required to realize an arbitrarily specified spatial stiffness matrix. We establish a classification of spatial stiffness matrices based on this number which we refer to as the degree of translational-rotational coupling (DTRC). We show that the DTRC of a stiffness matrix is uniquely determined by the spatial stiffness mapping and is obtained by evaluating the eigenstiffnesses of the spatial stiffness matrix. The topological properties of each class are identified. In addition, the relationships between the DTRC and other properties identified in previous investigations of spatial stiffness behavior are discussed.