Stiffness analysis of a Stewart platform-based parallel kinematic machine

Stiffness is one of the important considerations in the design of Stewart platform based parallel kinematic machine (PKM). In most stiffness models of PKMs, the machine frames are thought of rigid bodies. In this paper, an approach is presented to establish the stiffness model of a Stewart platform-based PKM, considering the deformation of the frame. The deformation of legs and the frame is considered as kinematic parameter errors of Stewart platform. According to the differential error model, the machine structure is decomposed into two subsystems: the parallel links subsystem and the machine frame subsystem. The stiffness matrix of each subsystem is established respectively, assuming that the other one is a rigid structure. By linear superposition of the two subsystems, the stiffness model of the machine structure is obtained. A finite element analysis (FEA) model is used to simulate the physical structure. The FEA results are compared to those derived from a mathematical model, and the comparison shows the validity of this approach.