Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel
Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel
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DOI：
10.1115/1.2829309
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发表时间：
1998-12
影响因子：
3.3
通讯作者：
Shuguang Huang;J. Schimmels
中科院分区：
文献类型：
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作者：
Shuguang Huang;J. Schimmels
本文讨论了任意空间刚度矩阵的综合问题。我们以前已经表明，一个任意的刚度矩阵不能实现与传统的平移弹簧和旋转弹簧（简单的弹簧）并联连接，无论使用的弹簧数量或其连接的几何形状。为了实现具有并联连接的弹簧的任意空间刚度矩阵，需要耦合平移和旋转分量的弹性装置。具有这些特性的装置在这里被定义为螺旋弹簧。两个这样的设备的设计示出。我们发现，存在一些刚度矩阵，需要3个螺旋弹簧，其实现和不超过3个螺旋弹簧需要实现满秩空间刚度矩阵。此外，我们提出了两个程序的任意空间刚度矩阵的合成。用一个过程，任何秩为m的半正定矩阵都可以用m个弹簧实现，其中所有弹簧都可以是螺旋弹簧。另一种方法是用6个弹簧实现任意正定矩阵，其中螺旋弹簧不超过3个。
In this paper, the synthesis of an arbitrary spatial stiffness matrix is addressed. We have previously shown that an arbitrary stiffness matrix cannot be achieved with conventional translational springs and rotational springs (simple springs) connected in parallel regardless of the number of springs used or the geometry of their connection. To achieve an arbitrary spatial stiffness matrix with springs connected in parallel, elastic devices that couple translational and rotational components are required. Devices having these characteristics are defined here as screw springs. The designs of two such devices are illustrated. We show that there exist some stiffness matrices that require 3 screw springs for their realization and that no more than 3 screw springs are required for the realization of full-rank spatial stiffness matrices. In addition, we present two procedures for the synthesis of an arbitrary spatial stiffness matrix. With one procedure, any rank-m positive semidefinite matrix is realized with m springs of which all may be screw springs. With the other procedure, any positive definite matrix is realized with 6 springs of which no more than 3 are screw springs.