On the stiffness and stability of Gough-Stewart platforms

This paper deals with a class of parallel mechanisms, called Gough-Stewart platforms. For these mechanisms, pre-loaded by driving forces, the stiffness matrix is derived and its basic properties are established. It is shown when the stiffness matrix becomes asymmetric, how the parametric imbalance may influence the system stability, and how the center of stiffness depends on the force pre-loading. Next, some necessary and some sufficient conditions for the stability are established in an analytical form by transforming the stiffness matrix to the center of stiffness.