On the stability conditions for a class of parallel manipulators

This paper deals with the stability of a class of planar parallel mechanisms, called unifunctional manipulators. For this problem the stiffness matrix of the mechanisms is derived, and its basic properties are analyzed. Necessary and sufficient conditions for the stability are established in an analytical form by transforming the stiffness matrix to the center of stiffness. Next, at the level of force planning, the problem of stable force distribution is formulated. It is shown that an unstable force distribution can be stabilized by a simple control law if the mechanism is not in a singular configuration. Finally, conditions of the feedback stabilizability in singular configurations are established and illustrated on simple examples.