In this paper an analytical formulation is proposed of the Lagrangian and Cartesian stiffness matrices for parallel mechanisms with rigid bodies and elastic joints. The formulation is general, as it is based on the development of the principle of virtual work and on the definition of the stiffness matrices. A relationship is also obtained between the Lagrangian and Cartesian stiffness matrices. Each contribution to the stiffness matrices is explicitly expressed in order to gain insight into their physical meaning and mathematical nature. In the paper, three numerical examples are presented. Indeed, the stiffness matrices are calculated for three planar mechanisms. The computation method exploits the multiple closed-chain architecture in parallel architectures. For this reason, it can be performed without encountering practical difficulties.
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