The normal form of a positive semi-definite spatial stiffness matrix

A fundamental result in the theory of spatial stiffness matrices is Loncaric´s normal form. When a spatial stiffness matrix is described in an appropriate coordinate frame, it will have a particularly simple structure. In this form the 3 × 3 off-diagonal blocks of the stiffness matrix are diagonal. It has been shown that generically, a spatial stiffness matrix call be written in normal form. For example, it is fairly well known that this is possible for any positive definite spatial stiffness matrix. In this article, it is shown that any symmetric positive semi-definite matrix can also be written in normal form. As an application this result is used to design a compact parallel compliance mechanism with a prescribed positive semidefinite spatial stiffness matrix.