In this paper, the synthesis of the stiffness matrices that can be realized with “simple springs” connected in parallel to a single rigid body is presented. The expression “simple spring” is used to refer to the set of elastic relations associated with passive translational springs and rotational springs.
We have previously identified the realizable sub-space of stiffnesses achieved with simple springs and provided a procedure to synthesize an arbitrary full-rank stiffness matrix within this realizable subspace. In this paper, an optimization routine is used in conjunction with the synthesis procedure to obtain alternate sets of springs that better satisfy practical design considerations. The procedure presented here requires no more than 7 simple springs to realize any simple spring realizable stiffness.