Quasi-static analysis of a compliant tripod stage with plane compliant lever mechanism

In nanopositioning system, the compliant tripod stages have proved to have enormous advantages for out-of-plane (z/tip/tilt) positioning in turns of compactness, simplicity in structure, and economic cost. However, most of the present-day compliant tripod stage undergo manufacturing problems due to a complicate structure, and little study has been carried out to formulate the tri-inputs and tri-outputs relationship, which is essential for precise positioning. Accordingly, this paper presents the quasi-static analysis of a novel compliant tripod stage with an equivalent plane model to achieve precise position analysis for nanopositioning. Three-plane compliant lever mechanisms and cylindrical flexure hinges with high length-diameter ratio are employed, which mitigate couple influence and enable easy fabrication via planar manufacturing processes. The spatial output motions of the compliant tripod stage are first split among inputs of the three-plane compliant lever mechanisms, where the lateral translations of the compliant tripod stage are included. Then the displacement equations of the plane compliant lever mechanism are formulated through Castigliano's second theorem. The model is further verified by finite element analysis. Finally, an experimental test system is set up and the test results validate the proposed approach.