Abstract

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, 3 such coupled components and 3 uncoupled components are sufficient to realize any full-rank spatial stiffness matrix and that for some spatial stiffness matrices 3 coupled components are necessary. In this paper, we show how to identify the minimum number of components that provide translational-rotational coupling required to realize an arbitrarily specified spatial stiffness matrix. This number is defined 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. In addition, the relationships between the DTRC and other properties identified in previous investigations of spatial stiffness behavior are discussed.

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