Determinate synthesis of symmetrical, monolithic tip-tilt-piston flexure stages

This paper mainly deals with the determinate design/synthesis of a class of symmetrical and monolithic flexure mechanisms. Each is composed of six identical in-plane wire beams with uniform square cross sections. These flexure stages can provide three out-ofplane tip-tilt-piston motions for applications in high-precision or miniaturization environments. A generic symmetrical structure is proposed at first with a group of defined parameters considering constraint and noninterference conditions. Normalized static analytical compliance entries for the diagonal compliance matrix of a generic structure are derived and symbolically represented by the parameters. Comprehensive compliance analysis is then followed using the analytical results, and quick insights into the effects of parameters on compliances in different directions are gained. Case studies without and with actuation consideration are finally discussed. As a second contribution, a physical prototype with three actuation legs is monolithically fabricated (using computer numerical control milling machining), kinematically modeled, and experimentally tested, which shows that the desired out-of-plane motion can be generated from the in-plane actuation.