The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms
The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms
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DOI：
10.1115/1.1434273
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发表时间：
2002-03
影响因子：
1.7
通讯作者：
Shuguang Huang;J. Schimmels
中科院分区：
文献类型：
--
作者：
Shuguang Huang;J. Schimmels
空间弹性行为由6X6正定矩阵（空间刚度矩阵）或其逆矩阵（空间柔度矩阵）表征。以前，空间刚度矩阵的结构和它的实现使用一个平行的弹性系统已经解决。本文将这些结果扩展到使用串行机构的空间柔度矩阵的分析和实现，并确定了与并联和串联弹性机构相关的空间刚度和柔度的对偶性。我们表明，空间柔度矩阵可以分解成一组秩为1的柔度矩阵，每个矩阵可以实现一个弹性关节的串联机构。为了实现一般的空间顺应性，串联机构必须包含耦合沿沿着/围绕轴的平移和旋转运动的关节。空间柔度矩阵的结构可以用一个六关节串联弹性机构唯一地解释，该机构的几何形状由柔度矩阵的特征螺旋分解得到。空间柔性行为及其实现的串联机构的分析所获得的结果进行了比较，空间刚度行为及其实现的并联机构。
Spatial elastic behavior is characterized by a 6X6 positive definite matrix, the spatial stiffness matrix, or its inverse, the spatial compliance matrix. Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism and identifies the duality in spatial stiffness and compliance associated with parallel and serial elastic mechanisms. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 compliance matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.