Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method

Although stiffness analyses of specific parallelogram-type parallel manipulators (PTPMs) have been presented by several researchers, an algebraic expression is still needed to obtain the stiffness of a general PTPM. To address this issue, this paper uses a strain energy method considering the compliances of the mobile platform, the limb and the actuator of a PTPM. In this method, the deformation of the mobile platform, which has typically been ignored by many researchers, is integrated in the total deformation of the PTPM. After comparison with a FEA method, it is found that the proposed algebraic method is a comparable alternative to the FEA method to be used in the pre-design stage. Additionally, a new stiffness index is proposed to evaluate the stiffness property. Compared with other stiffness indices, the new index uses virtual work to unify the units of translation and orientation and relates the index value to the direction of the wrench experienced by a parallel manipulator in a task. With this index, the resistance of a PTPM to deformation under a given wrench can be measured easily.