Modeling Of Compliant Displacement Amplifier Based On A Generalized Model For Conic Flexure Hinges

The performance of flexure-based mechanisms is highly dependent on the characteristics of flexure hinges; therefore, the design of flexure hinges is of practical importance. There are two chief aspects to consider when designing flexure hinges for a flexure-based mechanism, namely, the cutout profile selection and the parameter design of flexure hinges. Because the two aspects are theoretically independent, and there are no clear-cut guidelines for selection of the cutout profile, flexure hinge design is always performed first by selecting a certain type of flexure hinge based on the designer’s experience, and then designing the parameters using the corresponding design equations. This situation prohibits designers from confidently and consistently finding the most suitable hinge designs. The generalized flexure hinge model, with one set of design equations which includes multiple types of conic flexure hinges, effectively combines the aspects of cutout profile selection and parameter design into one.Based on a generalized model for conic flexure hinges, this dissertation investigates the kinetostatics and dynamics modeling, stress and multi-objective optimization of the bridge-type displacement amplifier, considering the cutout profile and parameters of flexure hinges, and other parameters of the mechanism. The main works include:(1) By utilizing the generalized equation for conic curves in polar coordinates, a generalized model for conic flexure hinges is proposed, and it brings elliptical arc, parabolic, and hyperbolic profiles together. Based on the hypothesis of the small deflection beam, all the elements in the compliance matrices for conic flexure hinges are deduced. The kinetostatics model of the bridge-type displacement amplifier, comprehensively considering the cutout profile and parameters of flexure hinges, and other parameters of the mechanism, is established. On the basis of the generalized conic flexure hinge model, effects of the cutout profile of flexure hinges and geometric parameters of the mechanism on the performance of the mechanism are manifested.(2) Based on the force-based finite element method, the derivation of the exact displacement shape function of flexure hinges is developed by using the Unit Load method, and equations of the consistant mass matrix are derived. The dynamical equations of conic flexure hinges are established, and the effect of the cutout profile and geometric parameters of flexure hinges on the natural frequency is analyzed, based on the generalized conic flexure hinge model.(3) Dynamic models of the bridge-type displacement amplifier are derived by employing Lagrange’s equation, respectively based on the pseudo-rigid-body-model(PRBM) method and the flexible multibody dynamic(FMD) model method. The research, concerning the effect of the cutout profile of flexure hinges and geometric parameters of the mechanism on the natural frequency of the mechanism, is carried out.(4)The stress distribution in conic flexure hinges under loads in plane is investigated, and the equation of the maximum nominal stress is provided. According to the distortion energy theory, the strength criterion of flexure hinges is given. Using the ratio of the radius of curvature of the stress concentrating feature to the minimum thickness as the only fitting variable, generalized equations for both the bending and tension stress concentration factors are obtained for conic flexure hinges, through fitting the finite element results. And equations for the maximum stress of conic flexure hinges and the displacement amplifier are derived, with the stress concentration in consideration.(5) According to the usability principle, the materials selection criterion is the failure resisting force indexes of flexure hinges on the premise of the natural frequency. Material selections of flexure hinges are analysed based on the Ashby charts, and some kinds of materials which suitable for manufacturing flexure hinges are provided.(6) Comprehensively considering static and dynamic performances and the stress condition, the evaluation function of the amplification mechanism is constructed and parameters optimizations of the mechanism are carried out. The prototype, according to the optimized results, is manufactured. The experiment platform is set up, and the amplification ratio of the prototype is tested. Results of the experiment and the finite element simulation verify the correctness of the theoretical model.