Nicolae Lobontiu

Two-axis flexure hinges with axially-collocated and symmetric notches

The paper introduces a new class of two-axis flexure hinges with axially-collocated and symmetric notches as an alternative to the existing flexure designs with serially-disposed notches. A generic formulation is developed in terms of the geometric curves defining the two notches which includes assessing the capacity of rotation, precision of rotation, sensitivity to parasitic effects, stress values, motion efficiency and shearing effects by means of compliance factors. Closed-form compliance equations are derived for a two-axis flexure hinge that is defined by two non-identical parabolic profiles. The analytical model predictions are confirmed by finite element data. A numerical comparison is made of the parabolic flexure with a constant rectangular cross-section flexure hinge in terms of several performance criteria.

Stiffness characterization of corner-filleted flexure hinges

The paper formulates the closed-form stiffness equations that can be used to characterize the static, modal, and dynamic behavior of single-axis corner-filleted flexure hinges, which are incorporated into macro/microscale monolithic mechanisms. The derivation is based on Castiliagno’s first theorem and the resulting stiffness equations reflect sensitivity to direct- and cross-bending, axial loading, and torsion. Compared to previous analytical work, which assessed the stiffness of flexures by means of compliances, this paper directly gives the stiffness factors that completely define the elastic response of corner-filleted flexure hinges. The method is cost-effective as it requires considerably less calculation steps, compared to either finite element simulation or experimental characterization. Limit calculations demonstrate that the known engineering equations for a constant cross-section flexure are retrieved from those of a corner-filleted flexure hinge when the fillet radius becomes zero. The analyti...

Two microcantilever designs: lumped-parameter model for static and modal analysis

This paper develops a lumped-parameter analytical model to enable static load-deformation and modal analysis for two microcantilever designs that can be utilized in mass detection and AFM applications. The circularly filleted microcantilever is currently utilized in several applications, whereas the elliptically filleted configuration is novel. Closed-form compliance/stiffness equations are derived for both microcantilevers in lumped form to permit design in the static regime for both long and short members. Lumped effective inertia fractions are also formulated for the two designs and used in conjunction with the lumped stiffness fractions to quantify the modal response. It is thus possible to tune the static and modal responses of these specific microcantilever designs by geometry alterations. The analytical equations are confirmed through limit calculations, finite element simulation, and experimental results available in the literature.

Modeling of nanofabricated paddle bridges for resonant mass sensing

The modeling of nanopaddle bridges is studied in this article by proposing a lumped-parameter mathematical model which enables structural characterization in the resonant domain. The distributed compliance and inertia of all three segments composing a paddle bridge are taken into consideration in order to determine the equivalent lumped-parameter stiffness and inertia fractions, and further on the bending and torsion resonant frequencies. The approximate model produces results which are confirmed by finite element analysis and experimental measurements. The model is subsequently utilized to quantify the amount of mass which attaches to the bridge by predicting the modified resonant frequencies in either bending or torsion.

Torsional stiffness of several variable rectangular cross-section flexure hinges for macro-scale and MEMS applications

The paper develops approximate closed-form equations for the torsional stiffness of several variable rectangular cross-section flexure hinges for macro-scale and MEMS applications. Specifically, corner-filleted, elliptic, parabolic and hyperbolic flexure configurations, either longitudinally symmetric or non-symmetric, are studied. The model gives the tools for a preliminary assessment of the static/modal response of flexure-based devices that deform torsionally. Several numerical simulations are conducted based on the model, which indicate that, for similar values of the geometric parameters, the hyperbolic flexure is the stiffest, followed by the parabolic, corner-filleted and elliptic configurations. The modal response is studied for a two-flexure torsional micro-mirror by sequentially considering four different pairs of longitudinally symmetric flexure designs. The results of the simulation confirm the stiffness predictions and are also in agreement with finite element analysis results.

Static Response of Planar Compliant Devices with Small-Deformation Flexure Hinges

Abstract The article presents a static load-displacement calculation procedure for planar compliant mechanisms with small-deformation flexure hinges. The approach utilizes the Castiglianos displacement theorem and enables consideration of both rigid links and flexure hinges in a unitary manner. The flexure hinges are modeled as complex springs, which are capable of elastic response to bending axial and shearing loads through corresponding compliance factors. The compliance factors are directly incorporated into the generic formulation and this feature enables implementation of various flexure configurations. This method is particularly useful in calculations of flexure-based compliant devices where the quasistatic response needs to be determined accurately. An example is studied by the proposed method and by means of finite element analysis, and the relative errors are less than 6%. Based on the same example, the errors are calculated which are induced when the model only retains the torsion-spring type compliance.

Design, Modeling, and Initial Experiments on Microscale Amplification Device

This article proposes the design of several microelectromechanical amplification devices formed of many identical microunits that are connected in a serial–parallel configuration, each being individually actuated and amplifying its own input motion. The microdevices realize the border-crossing from the micro-to the meso-scale displacement domain as they combine the micron-level individual inputs into millimeter-range output levels. The base structural unit is a flexure-based compliant device that is capable of transforming the input from a thermal actuator into an amplified displacement, about a direction perpendicular to the input one. The base unit is designed based on performance criteria, such as displacement amplification, input stiffness and output stiffness by utilizing finite element simulation, and an algorithm based on closed-form compliance equations of the incorporated flexure hinges. The microelectromechanical amplification device is monitored by means of embedded capacitive displacement sensors for the input port. The feasibility of the device design was verified through a numerical simulation and some initial experimental results are presented.

Mechanics of MEMS: a review of modeling, analysis, and design

The paper provides a review of the literature dedicated to existing modeling, analysis, synthesis and optimization tools, together with the associated design procedures for MEMS applications, by looking at the approximate analytical algorithms and finite element procedures in the static, dynamical and coupled-field domains as applied to a large compartment of compliant members and their corresponding devices. The paper gives a classification of MEMS according to their structure and another classification as a function of their function. Main architectures of compliant microdevices are also reviewed, including torsion mirrors, bending mirrors, bimorph/multimorph transducers, accelerometers, gyroscopes, scratch drives, out-of-the-plane microcantilevers, sensing devices, resonators, switches or filters. Attention is dedicated to operational means of actuation, such as thermal, electrostatic, magnetic, electromagnetic, piezoelectric or shape-memory-generated, and to their integration into the overall microsystem design. Numerical modeling techniques, such as finite or boundary element model algorithms/codes that are utilized in the analysis and design of MEMS are also presented.

Lumped-Parameter Inertia Model for Flexure Hinges

Abstract The article describes the analysis to derive the lumped-parameter inertia properties for variable cross-section flexure hinges for potential use in modeling, designing, and optimizing of these components in the resonant/dynamic range. Inertia fractions corresponding to one of the flexures 6 degrees of freedom are formulated for single-, two-, and multiple-axis flexure hinge configurations in a unitary fashion by utilizing the Rayleigh principle. Closed-form solutions are not always available for all flexure types that are defined longitudinally by means of analytical curves, but numerical integration can readily be applied to solve for the lumped-parameter inertia fractions. The model yields at limit the known inertia fractions for a constant cross-section flexure hinge. Further numerical comparison of the models predictions with finite element simulation data indicates agreement between the two approaches for the modal response of a flexure-based cantilever with tip mass.

Shape optimization of microcantilevers for mass variation detection and AFM applications

The paper proposes an analytical model-based, lumped-parameter algorithm which enables identifying a microcantilever design that will give the optimized performance with regard to stiffness and resonant frequency values in terms of a corresponding shape and its related geometric parameters. The targeted microcantilever applications are mass variation detection and atomic force microscopy (AFM) whereby the monitored system parameters are the changes in deflection and/or the natural frequency. A design set comprises several configurations, each of them being defined by analytical curves, such as straight lines, circular or elliptical arcs, and which are quantified in terms of compliances/stiffnesses and resonant frequencies by algebraic equations. The model is capable of discerning both the intensity of external excitation and the first resonant frequencies for a given microcantilever. Finite element simulation results of the static and resonant response for these microcantilevers confirm the analytical model predictions. The optimization algorithm, which is based on this model, focuses on maximizing the master bending compliance and on spacing out the first resonant frequency from the subsequent ones in order to increase the response sensitivity of the microcantilever. The model-based optimization algorithm is a relatively low-cost and sufficiently-accurate calculation procedure, which is formulated as an alternative to existing finite element simulation.