Design, Modeling, and Optimization of a Nearly Constant Displacement Reducer with Completely Distributed Compliance

This article proposes a displacement reducer based on distributed compliant mechanisms to improve the motion resolution of actuators commonly used in precision operation systems that require high-precision control and positioning, such as micro-grippers, biological manipulation, and micro-alignment mechanisms. Distributed compliance significantly diminishes its effective moving lumped mass, endowing the structure with advantages such as reduced stress concentration and an expansive range of motion. Additionally, the design incorporates an over-constraint structure through a dual-layer displacement reducer, ensuring that the reducer achieves a nearly constant reduction ratio. According to the compliance matrix method, the analytical model of the reducer is established to predict the input–output behaviors, which are verified by finite element simulations. On the basis of sensitivity analysis to structure parameters, including node positions and beam parameters, the Particle Swarm Optimization (PSO) algorithm is used to optimize the displacement reduction performance. Through finite element analysis and experimental results on the prototype, the proposed displacement reducer demonstrates a large reduction ratio of 11.03, an energy transfer efficiency of 39.6%, and a nearly constant reduction ratio with an input displacement range of 0 to 2000 µm.