Topology optimisation of bridge input structures with maximal amplification for design of flexure mechanisms

Bridge structures are one of the two most common design elements for providing input from stroke-limited piezoelectric actuators to flexure based mechanisms for micro/nano positioning and manipulation. However, the amplification achieved by such structures is dependent on both the element geometry and the load provided by the driven mechanism. In this paper, bridge-type structures are developed which maximise the output displacement using topology optimisation, and the variation of the geometry due to changing mechanism stiffness is studied. Cost functions defined to consider the input-force to output-displacement stiffness, as well as the effective displacement due to input-stiffness losses are developed. The structures found differ substantially from the bridge designs typically employed, particularly the symmetry assumed for such designs. Furthermore, it is shown that the choice in principal output direction has a substantial impact on the achievable displacement. The results of the analysis are used to formulate a bridge structure template which can be employed within standard heuristic design methods.