Stiffness modeling of compliant parallel mechanisms and applications in the performance analysis of a decoupled parallel compliant stage.

This paper investigates the stiffness modeling of compliant parallel mechanism (CPM) based on the matrix method. First, the general compliance matrix of a serial flexure chain is derived. The stiffness modeling of CPMs is next discussed in detail, considering the relative positions of the applied load and the selected displacement output point. The derived stiffness models have simple and explicit forms, and the input, output, and coupling stiffness matrices of the CPM can easily be obtained. The proposed analytical model is applied to the stiffness modeling and performance analysis of an XY parallel compliant stage with input and output decoupling characteristics. Then, the key geometrical parameters of the stage are optimized to obtain the minimum input decoupling degree. Finally, a prototype of the compliant stage is developed and its input axial stiffness, coupling characteristics, positioning resolution, and circular contouring performance are tested. The results demonstrate the excellent performance of the compliant stage and verify the effectiveness of the proposed theoretical model. The general stiffness models provided in this paper will be helpful for performance analysis, especially in determining coupling characteristics, and the structure optimization of the CPM.