A method for stiffness modeling of 3R2T overconstrained parallel robotic mechanisms based on screw theory and strain energy

Stiffness (or compliance) performances of three-rotation and two-translation (3R2T) overconstrained parallel mechanisms have an important influence on their applications in bio-inspired robots with precision operations. However, it is difficult to build stiffness models of the class of mechanisms due to fairly complicated structures, and an effective and efficient modeling method has not been reported. This paper presents an approach to stiffness modeling of 3R2T overconstrained parallel robotic mechanisms. First, expressions of applied wrenches exerted on limbs and joints of a mechanism under an external load are solved based on screw theory. Then, the stiffness matrix of a limb is derived by applying Castigliano's second theorem to strain energy of the limb, which is solved by introducing a strategy of structural decomposition. Third, the stiffness model of a mechanism is built based on stiffness matrices of all limbs and the principle of virtual work on the moving platform. Finally, the effectiveness of the proposed method is verified based on the fact that the computational compliance matrices are very close to those from finite element analysis (FEA) models. The proposed method can be used to build conveniently stiffness models with high accuracy for 3R2T overconstrained parallel mechanisms in precision positioning applications.