Abstract:

：In order to achieve a thorough understanding of the stiffness characteristics of the Exechon parallel kinematic machine (PKM), an analytical kinetostatic model is proposed by using the substructure synthesis technique. The whole system is decomposed into a moving platform subsystem, three limb subsystems and a fixed base subsystem, which are connected to each other sequentially through corresponding joints. Each limb body is modeled as a spatial beam with rectangular cross-section constrained by two sets of lumped springs. The equilibrium equation of each individual limb assemblage is derived through finite element formulation and combined with that of the moving platform derived with Newtonian method to establish the governing kinetostatic equations of the system after introducing the deformation compatibility conditions between the moving platform and the limbs. The computation for the stiffness of the Exechon PKM at a typical configuration as well as throughout the workspace is carried out. Deformation of the Exechon PKM under an external load is computed by ANSYS Workbench, based on which calculation errors between the finite element method and the proposed analytical method are obtained to illustrate the high accuracy of the analytical model. The numerical simulations reveal a strong position-dependency of the PKM’s stiffness, which is symmetric about x axis in a work plane due to structural features. It is worthy mentioning that the proposed methodology of stiffness modeling in this paper can also be applied to other overconstrained PKMs and can evaluate the global rigidity over workplace efficiently with minor revisions.

Key words: Exechon, stiffness modeling, substructure synthesis, parallel kinematic machine