Design and modeling of single-axis, flexure-hinge type, micro-positioning stages

A general approach for design and modeling of single-axis, notch flexure-hinge type, translational micro-positioning stages is presented in this dissertation. The objective is to develop design equations that can accurately predict the behavior of such stages especially the "lost motion" due to hinge stretching, without performing finite element modeling. General design equations for obtaining the stiffness and the displacement of these stages are developed in this thesis. The development of these equations is based on a static analysis of a general configuration of a single-axis, translational, flexure-hinge type, piezo-driven micro-positioning stage using a multi-lever structure. The displacement ratio between the input and output motions of one of the levers, plus the stiffness at either end of this lever are obtained based on the analysis. The overall displacement and stiffness of the micro-positioning stage are then obtained by cascading the individual results from every lever. The developed equations include the effects of the flexure hinge bending and stretching. A novel low profile, vertical motion micro-positioning stage was designed by using the developed equations. The stiffness and displacement of this stage are predicated by these equations, which are compared to the stiffness and displacement directly obtained from the finite element modeling of the same micro-positioning stage. The comparison shows that the two methods give similar results (within 3.1% for displacement and 1.3% for stiffness), which implies that finite element modeling verification in micro-positioning stage design is not necessary when analytical design equations are used. A prototype of the novel micro-positioning stage was fabricated by conventional machining and EDM. The stage is driven by a piezo electrical translator mounted inside the micro-positioning stage. The experimental results show that the measured stiffness and displacement of the stage are within 10% of the values predicted by the developed equations.