Elastostatic stiffness modeling of overconstrained parallel manipulators

摘要

Highlights?A unified stiffness model of overconstrained parallel manipulators is proposed.?The elastostatic stiffness model is proposed based on strain energy.?The limb stiffness matrix is obtained based on Castigliano's Second Theorem.?The deformation compatibility equations are obtained using the virtual-work principle.AbstractThis paper proposes a unified method for the elastostatic stiffness modeling of overconstrained parallel manipulators. First, the constraint wrench systems of an overconstrained parallel manipulator are analyzed using screw theory. Second, the strain energy of each limb and elastic deformation of the limb end are analyzed using Castigliano's second theorem. The stiffness matrices of the limb constraint wrenches are obtained. Third, the deformation compatibility equations between the elastic deformation of the limb end and the geometric center point of the mobile platform are obtained using the virtual-work principle. Lastly, an analytical expression for the overall stiffness matrix and magnitudes of the constraint wrenches is deduced along with the balance equation of the mobile platform and deformation compatibility equations. One major advantage of this method is that the obtained stiffness matrix has a clear physical meaning and compact form. The elastostatic stiffness of a 2UPR-RPU and redundantly actuated 2UPR-2RPU overconstrained parallel manipulator are modeled to verify the proposed method. Numerical results show that the relative error between the theoretical models and finite-element analysis models obtained using commercial software is within 0.8%.]]>