Stiffness modeling of some 4-DOF over-constrained parallel manipulators with various constrained wrench forms

Abstract

This study aims to build a unified stiffness model of three 4-degree of freedom (DOF) over-constrained parallel manipulators (PMs), which comprise a novel PM with four constrained forces, a PM with four constrained torques, as well as a PM with two constrained forces and two constrained torques. First, with the geometrical conditions as a starting point, a research is discussed on the constrained wrenches and kinematics analysis of the three PMs. Second, oriented to different constrained wrench forms in the three over-constrained PMs, the wrenches directly causing deformations are determined based on the deformation and force decomposition method, and the correlations between the wrenches and their corresponding deformations are explored according to the material mechanics. Third, all of the above analysis, combined with the virtual work principle of deformed body and the static balance principle, a unified stiffness model which is suitable for the three 4-DOF over-constrained PM with various constrained wrench forms is established. Lastly, an integrated finite element (FE) simulation model of the three PMs is built to verify the correctness of the analytic stiffness model. This study proposes a general and straightforward approach to solve the stiffness problem of 4-DOF over-constrained PMs with various constrained wrench forms.