Closed form expressions for synthesizing a spatial stiffness matrix with a parallel connection of simple springs

摘要

This article presents a method for determining closed form expressions for a minimal realization of an arbitrarily specified stiffness dominated spatial impedance through the use of a mechanism constructed of passive springs. This mechanism consists of simple springs connected in parallel where the term simple spring refers to a purely translational or purely rotational passive spring. Previous methods for synthesizing spatial stiffness matrices using a parallel connection of springs have been strictly numerical and dependent upon the chosen coordinate system. The method introduced here is based on the eigenstiffness decomposition of the stiffness matrix and has the following advantages: (i) it requires the minimum number of springs, (ii) it is independent of the choice of coordinate frame and (iii) it is the first closed form solution of its kind. These results are also applicable to realizing a spatial damping matrix.