LAUSR

Abstract Difficulty and complexity of stiffness modeling of parallel mechanisms will be greatly increased under considering gravity of limbs. This paper presents a general method for stiffness modeling of overconstrained parallel mechanisms under considering gravity of all moving components and external payloads. First, the expression of the end joint reaction of a limb is derived based on screw theory and special equilibrium equations. Second, an approach to stiffness modeling of a limb under its end joint reaction and own gravity is presented based on the Castigliano's second theorem associated with strain energy. Third, stiffness modeling of the whole mechanism is performed based on the static equilibrium equation of the moving platform, the base-point method and the established limb stiffness models. Finally, two typical numerical examples show that computational results obtained from the proposed method are very closed to those obtained from finite element analysis (FEA) models, illustrating the effectiveness of the proposed method.