Spatial stiffness realization with parallel springs using geometric parameters

This paper investigates the synthesis of a spatial stiffness matrix using simple line springs. A new algorithm is developed, which enables the selection of constituent springs based on their positions and directions. The constraining space of the line springs is then investigated. It is shown that an isotropic stiffness matrix, in general, can be split into the sum of two rank-3 stiffness matrices. The three line springs of the first matrix can be selected to pass through any arbitrary points in space, while the three line springs of the second stiffness matrix lie on a quadric surface, which is usually a hyperboloid of one sheet.