Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects

Abstract

In order to carry out high-precision machining of aerospace structural components with large size, thin wall and complex surface, this paper proposes a novel parallel kinematic machine (PKM) and formulates its semi-analytical theoretical stiffness model considering gravitational effects that is verified by stiffness experiments. From the viewpoint of topology structure, the novel PKM consists of two substructures in terms of the redundant and overconstrained parallel mechanisms that are connected by two interlinked revolute joints. The theoretical stiffness model of the novel PKM is established based upon the virtual work principle and deformation superposition principle after mapping the stiffness models of substructures from joint space to operated space by Jacobian matrices and considering the deformation contributions of interlinked revolute joints to two substructures. Meanwhile, the component gravities are treated as external payloads exerting on the end reference point of the novel PKM resorting to static equivalence principle. This approach is proved by comparing the theoretical stiffness values with experimental stiffness values in the same configurations, which also indicates equivalent gravity can be employed to describe the actual distributed gravities in an acceptable accuracy manner. Finally, on the basis of the verified theoretical stiffness model, the stiffness distributions of the novel PKM are illustrated and the contributions of component gravities to the stiffness of the novel PKM are discussed.