Stiffness estimation of a tripod-based parallel kinematic machine

This paper presents a simple yet comprehensive approach that enables the stiffness of a tripod-based parallel kinematic machine to be quickly estimated. The approach arises from the basic idea for the determination of the equivalent stiffness of a group of serially connected linear springs and can be implemented in two steps. In the first step, the machine structure is decomposed into two substructures associated with the machine frame and parallel mechanism. The stiffness models of these two substructures are formulated by means of the virtual work principle. This is followed by the second step that enables the stiffness model of the machine structure as a whole to be achieved via linear superposition. The three-dimensional representations of the machine stiffness within the usable workspace are depicted and the contributions of different component rigidities to the machine stiffness are discussed. The results are compared with those obtained through experiments.