Flexure Stage Research Articles

Isotropic springs based on parallel flexure stages

We define isotropic springs to be central springs having the same restoring force in all directions. In previous work, we showed that isotropic springs can be advantageously applied to horological time bases since they can be used to eliminate the escapement mechanism [7]. This paper presents our designs based on planar serial 2-DOF linear isotropic springs. We propose two architectures, both based on parallel leaf springs, then evaluate their isotropy defect using firstly an analytic model, secondly finite element analysis and thirdly experimental data measured from physical prototypes. Using these results, we analyze the isotropy defect in terms of displacement, radial distance, angular separation, stiffness and linearity. Based on this analysis, we propose improved architectures stacking in parallel or in series duplicate copies of the original mechanisms rotated at specific angles to cancel isotropy defect. We show that using the mechanisms in pairs reduces isotropy defect by one to two orders of magnitude.

Compliance and control characteristics of an additive manufactured-flexure stage

This paper presents a compliance and positioning control characteristics of additive manufactured-nanopositioning system consisted of the flexure mechanism and voice coil motor (VCM). The double compound notch type flexure stage was designed to utilize the elastic deformation of two symmetrical four-bar mechanisms to provide a millimeter-level working range. Additive manufacturing (AM) process, stereolithography, was used to fabricate the flexure stage. The AM stage was inspected by using 3D X-ray computerized tomography scanner: air-voids and shape irregularity. The compliance, open-loop resonance peak, and damping ratio of the AM stage were measured 0.317 mm/N, 80 Hz, and 0.19, respectively. The AM stage was proportional-integral-derivative positioning feedback-controlled and the capacitive type sensor was used to measure the displacement. As a result, the AM flexure mechanism was successfully 25 nm positioning controlled within 500 μm range. The resonance peak was found approximately at 280 Hz in closed-loop. This research showed that the AM flexure mechanism and the VCM can provide millimeter range with high precision and can be a good alternative to an expensive metal-based flexure mechanism and piezoelectric transducer.

Measurement of cantilever spring constant using an electrostatic sensing and actuating force measurement system

We report the measurement of the spring constant of a cantilever using an electrostatic sensing and actuating force measurement system. The force measurement system consists of three main parts: a monolithic flexure stage, a three-electrode capacitor, and a digital controller. The most important feature of the system is the utilization of the three-electrode capacitor simultaneously as a position sensor and an electrostatic force generator. This allows us to constantly adjust and maintain gap distances between three electrodes, which is critical for this design to generate precise electrostatic compensation force. The force measurement system was partly upgraded and its performance was improved. The uncertainty estimation for the upgraded force measurement system is given. By measuring the spring constant of a commercially available cantilever force sensor, we demonstrate that the force measurement system is capable of calibrating the cantilever spring constant. The spring constant of the cantilever force sensor was measured to be (2227 ± 63) mN m−1 (coverage factor k = 2), corresponding to a relative expanded uncertainty of 2.8%.

Comparison of milligram scale deadweights to electrostatic forces

This paper presents a comparison of milligram scale deadweights to electrostatic forces via an electrostatic sensing & actuating force measurement system. The electrostatic sensing & actuating force measurement system is designed for measuring force below 200 mN with an uncertainty of few nanonewton. The force measurement system consists of three main components: a monolithic flexure stage, a three-electrode capacitor for position sensing and actuating and a digital controller. The principle of force measurement used in this system is a static force balance, i.e. a force to be measured is balanced by a precisely controlled, electrostatic force. Four weights of 1 mg to 10 mg were tested in this comparison. The results of the comparison showed that there exist extra stray electrostatic forces between the test weights and the force measurement system. This extra electrostatic force adds a bias force to the measurement result, and was different for each weight. In principle, this stray electrostatic force can be eliminated by installing a metal housing to isolate the test weight from the system. In the first section, we briefly introduce the electrostatic sensing and actuating force measurement system, and then we describe the experimental setup for the comparison and the results. Finally, we give a discussion and outlook.

Precision large field scanning system for high numerical aperture lenses and application to femtosecond micromachining of ophthalmic materials.

A precision, large stroke (nearly 1 cm) scanning system was designed, built, and calibrated for micromachining of ophthalmic materials including hydrogels and cornea (excised and in vivo). This system comprises a flexure stage with an attached objective on stacked vertical and horizontal translation stages. This paper outlines the design process leading to our most current version including the specifications that were used in the design and the drawbacks of other methods that were previously used. Initial measurements of the current version are also given. The current flexure was measured to have a 27 Hz natural frequency with no load.

A two-axis in-plane motion measurement system based on optical beam deflection

Measurement of in-plane motion with high resolution and large bandwidth enables model-identification and real-time control of motion-stages. This paper presents an optical beam deflection based system for measurement of in-plane motion of both macro- and micro-scale motion stages. A curved reflector is integrated with the motion stage to achieve sensitivity to in-plane translational motion along two axes. Under optimal settings, the measurement system is shown to theoretically achieve sub-angstrom measurement resolution over a bandwidth in excess of 1 kHz and negligible cross-sensitivity to linear motion. Subsequently, the proposed technique is experimentally demonstrated by measuring the in-plane motion of a piezo flexure stage and a scanning probe microcantilever. For the former case, reflective spherical balls of different radii are employed to measure the in-plane motion and the measured sensitivities are shown to agree with theoretical values, on average, to within 8.3%. For the latter case, a prototype polydimethylsiloxane micro-reflector is integrated with the microcantilever. The measured in-plane motion of the microcantilever probe is used to identify nonlinearities and the transient dynamics of the piezo-stage upon which the probe is mounted. These are subsequently compensated by means of feedback control.

나노포지셔너 개발을 위한 테스트벤치 제작

In this study, a test-bench for developing and verifying a 1- or 2-axis nanopositioner was manufactured. Using this test-bench, adesigned and manufactured flexure stage based on an analysis can configure nanopositioning systems. A breadboard and fixture were fabricated to be equipped with various types of mechanisms and sizes of stages. The test-bench has linear encoders for calibrating sensors and verifying the orthogonality and parasitic motion of 2-axis nested-type nanopositioners. The controller was developed using LabVIEW and a TI microcontroller. A case study that exemplified the test bench for developing a nanopositioner by senior undergraduate students is shown.

Design of a precision flexural linear stage system with sub-nanometer resolution and 12-mm travel range

Precision ball-bearing-based or roller-bearing-based positioning stage systems are capable of providing a large travel range. However, it is not possible to meet requirements in sub-nanometer positioning resolution, high tilting stiffness, and microradian-level straightness of trajectory repeatability with a simple rolling element guiding system. To meet those requirements and still allow for large travel range, we have designed a novel precision flexural linear stage. It is capable of sub-nanometer positioning resolution and 12-mm travel range for synchrotron radiation instrumentation applications. The design and preliminary test results for a prototype stage system are discussed in this paper.

Design Of Feedback Controller For Non-minimum Phase nanopositioning System

One of the most important requirement of nanotechnology is precision control and manipulation of devices and materials at nanoscale i.e. nanopositioning. Nanopositioners are precision mechatronic system designed to move objects over a small range with a resolution down to a fraction of an atomic diameter. In particular, desired specifications of any nanopositioners are fast response with no or very little overshoot, large travel range with very high resolution, extremely high precision and high bandwidth. This paper presents design and identification of nanopositioning device consisting of flexure stage, piezoelectric actuator and Linear Variable Differential Transformer (LVDT) as a sensor. Open loop behavior of the nanopositioning device on the basis of time and frequency responses is studied. To improve the system characteristics feedback controllers are used. Step response and frequency response under variety of conditions are obtained to verify the effectiveness of the proposed controllers. In this paper PI and PI2 controllers are designed and system performances are investigated for different values of feedback gain. Unfortunately nanopositioners operating in closed loop achieve high bandwidth at the cost of increased sensitivity to the measurement noise and hence reduced resolution. In this paper H infinity controller is analyzed and performance of the device is studied. Then a comparative study of traditional PI and PI2 controller with H infinity controller on the basis of time and frequency response is given to show which controller is better. Simulation results for the performance analysis are carried out in MATLAB. Copyright © 2013 VBRI press.

MEASUREMENT OF CANTILEVER'S SPRING CONSTANT WITH CMS ELECTROSTATIC FORCE STANDARD

The mechanical property is one of the important parameters for evaluating micro/nano-scale materials. The measurement of micro/nano-mechanical property usually involves measurements of small displacement and force. To provide a traceable force standard in micro/nano-newton level, we have developed a force measurement system based on electrostatic sensing and actuation techniques. The system mainly consists of a monolithic flexure stage, a three-electrode capacitor and a digital controller. The three-electrode capacitor is utilized as a position sensor, and at the same time an electrostatic force actuator. The force under measurement is balanced by a compensation electrostatic force which is traceable to electrical and length standards. A commercial cantilever-type micro-force probe was used in this calibration experiment. The force probe was brought to contact with and press into the load button (a ruby sphere) of the force measurement system by a closed-loop controlled z-scanner. The spring constant was obtained from the average slope determined from measured force-displacement curves and was found to be (2.26 ± 0.01) N/m where the given uncertainty is one standard deviation. We have successfully demonstrated the calibration of the microforce probe using our self-developed electrostatic sensing and actuating force measurement system. The measured spring constant is consistent with the manufacturer's specification, and the relative standard deviation is less than 0.5%. Note from Publisher: This article contains the abstract only.

Sensitivity of freedom spaces during flexure stage design via FACT

► Identified the sensitivity of freedom spaces as an area of concern for designers. ► Showed via a case study of how a 1-DOF system may emulate a 3-DOF system. ► Quantified the sensitivity of the freedom space for the 1-DOF case study. ► Identified the design space for the 1-DOF case study. The theoretical kinematic design of flexure stages using exact constraint methods is well known. These methods, however, do not take into account practical design considerations such as non-ideal constraint behavior. It is shown via a case study that the freedom space of a one degree-of-freedom (DOF) translation stage is extremely sensitive to both the arrangement and the elastomechanic behavior of the flexural constraints. The results of the case study show that certain combinations of constraint properties and layout yield a 1-DOF system that is more accurately modeled as a 3-DOF system. A non-dimensional constraint quality metric, CQ , is introduced in this paper to help classify the system in the case study as a 1-DOF system, a 3-DOF system, or a combination thereof. This paper is a first step in showing how practical design considerations may negatively influence the kinematics of systems that were previously assumed to have been designed “correctly” using exact constraint methods.

Stable Adaptive Fuzzy Control with Hysteresis Observer for Three-Axis Micro/Nano Motion Stages

This paper considers the analytical dynamics with simplified Dahl hysteresis model for a three-axis piezoactuated micro/nano flexure stage. An adaptive controller with nonlinear dynamic hysteresis observer is proposed using Lyapunov stability theory. In the controller, a fuzzy function approximator with parameters update law is included to compensate for the identification inaccuracy, model uncertainty, and flexure coupling effects. Simulation results are used to demonstrate the control performance.

A Novel Atomic Force Microscope Control System Based on PC104 and DSP Embedded System

Abstract In order to achieve large scanning range, this article presents a new type high-speed AFM system. According to the need of rapid data transmission and operation, the AFM control system structure was composed of PC104 and DSP hardware model. Because of using a large displacement flexure stage as the sample stage, this AFM system is capable of providing a scan range of 100×100um image with 50 Hz line-scan speed. The capacitor displacement sensors are used as x-y position during AFM scan image. We realized a new scanning method based on positioning control. The scanning images are more precision and less distortion than general open-loop x-y scanning image.

Development of a metrological atomic force microscope with minimized Abbe error and differential interferometer-based real-time position control

A metrological atomic force microscope (mAFM) has been developed at LNE. It will be dedicated to traceable dimensional measurements and calibrations of transfer standards with a maximum size of 25 mm × 25 mm × 7 mm. The displacement range is 60 µm for the X and Y axes and 15 µm for the Z axis. The instrument uses four laser differential interferometers in an original Abbe-compliant arrangement to measure the position of the tip relative to the sample and to be directly traceable to the SI. The expected uncertainty for the measurement of the tip/sample relative position is 1 nm for the whole range without taking into account the tip contribution. To fulfill this specification, the design of the instrument has been optimized to minimize Abbe errors, to reduce the metrology loop length, to limit the drifts due to thermal dilatation and to improve the stability of interferometric position measurement in ambient air. To limit Abbe errors, a dedicated three-axis flexure stage has been developed to reduce parasitic rotational motion at the level of 1 µrad for the whole range. This stage is driven by piezo-actuators. The instrument controller is based on a FPGA combined with an embedded PXI controller to perform real-time control of the XYZ position. We present the design of the instrument and the very first results.

75mm stroke flexure stage for the LNE watt balance experiment

Abstract The LNE watt balance experiment aims at measuring the ratio of the Planck constant h to a standard mass m with a relative uncertainty smaller than 10−8. One step of our experiment requires to move a coil vertically inside a magnetic field along a total stroke of about 75 mm. To limit the uncertainty of our experiment, the velocity of the coil is servo-controlled at a constant value of 2 mm/s and the deviations of the trajectory from a rectilinear translation must be kept within 1 μm for straightness and within 5 μrad for yaw and pitch. These requirements must be performed along a useful stroke of 40 mm. To avoid play and friction, which are likely to perturb the feedback loop of the coil velocity, a flexure stage has been built to constrain the movement of the coil. For a 40 mm stroke, measurements show that the two straightness errors are smaller than 0.2 μm and 0.5 μm respectively, and that pitch and yaw are smaller than 4 μrad and 6 μrad respectively.

Two-Axis MEMS Lens Alignment System for Free-Space Optical Interconnect

We present a two-axis microelectromechanical systems (MEMS) lens aligner with a 260 μm × 220 μm translation range that positions a 6.35 mm lens with focal length f = 12.1 mm for alignment compensation of free-space optical interconnects (FSOIs) between computer servers separated by 50 mm spacing. Efficient ultrasonic linear piezoelectric motors (PMs) provide actuation with zero power required to hold the lens alignment. A four-channel FSOI is demonstrated with 1 × 4 vertical cavity surface-emitting laser (VCSEL) and photodiode (PD) arrays capable of 10 Gb/s transmission bandwidth. Demonstrated minimum step size of 1.68 μm is sufficient for aligning the 20 μm VCSEL spots onto the 40 μ m PD receivers. Force transmission between PMs and a silicon MEMS flexure stage is accomplished using a 1-mm steel ball bearing in a magnetic groove, providing compliance in the nondriven axis. The ball-coupling design has 15 μm backlash and induces a maximum of 8 μm of cross-axis motion.

A force measurement system based on an electrostatic sensing and actuating technique for calibrating force in a micronewton range with a resolution of nanonewton scale

This paper introduces a force measurement system recently established at the Center for Measurement Standards, Industrial Technology Research Institute for calibrating forces in a micronewton range with a resolution of a few nanonewtons. The force balance consists of a monolithic flexure stage and a specially made capacitor for electrostatic sensing and actuating. The capacitor is formed by three electrodes which can be utilized as a capacitive position sensor and an electrostatic force actuator at the same time. Force balance control is implemented with a digital controller by which the signal of the stage deflection is acquired, filtered and fed back to the electrostatic force driver to bring the flexure stage to the null position. The detailed description of the apparatus including the design of a monolithic flexure stage, principle of capacitive position sensing/electrostatic actuation and the force balance control is given in the paper. Finally, we present the results of electrostatic force calibration and the weighing of a 1 mg wire weight.

Droplet Tracking for Single Molecule Confinement

We report on a robust system for tracking femtoliter and smaller aqueous droplets in oil over tens of minutes with a few nanometers accuracy in a 150 Hz bandwidth. Tracking permits the droplet position to be maintained in the detection volume of a confocal microscope without need for physical or optical trapping, permitting detailed optical analysis of droplet contents. In addition, droplet tracks can be used to determine droplet size. As an alternative to surface attachment or liposomal confinement, we use droplets to confine individual biomolecules for study using single-molecule fluorescence trajectories. Back focal plane imaging onto a position sensitive detector (PSD), similar to the configuration frequently used to determine the position of a particle in an optical tweezer, is used to determine droplet position with respect to the confocal detection volume. Our tracking system, inspired in part by the work in Ref. (1), utilizes a dedicated microprocessor to implement a feedback loop between the PSD and a fast piezoelectric flexure stage. Motion of the stage keeps the particle in the confocal detection volume. Here we present data characterizing the system and also report on progress in using tracked droplets in single-molecule studies of RNA. 1. Desai, K. V., T. G. Bishop, L. Vicci, E. T. O'Brien, R. M. Taylor, and R. Superfine. 2008. Agnostic particle tracking for three-dimensional motion of cellular granules and membrane-tethered bead dynamics. Biophys. J. 94:2374–2384.

Test of precision weak-link stage systems with large travel range and subnanometre-scale resolution

The precision ball-bearing- or roller-bearing-based stage systems provide large travel range. However, they have difficulties in meeting subnanometre resolution, high tilting stiffness and high straightness of trajectory with a single guiding system. It is always a dream to have a compact single flexure stage to cover a large travel range with very high positioning resolution. Based on an advanced structure design with the laminar overconstrained weak-link technique, we have designed and constructed a two-dimensional linear precision weak-link stage system for nanopositioning of a specimen holder for the linear multilayer Laue lenses test setup at the Advanced Photon Source Sector 26. This system provides subnanometre resolution, coupled with subnanometre metrology at a travel range of several millimetres. The two-dimensional weak-link stage system is designed with high structure stiffness using laminar overconstrained weak-link mechanisms. In this paper we present the preliminary test results of a linear precision weak-link stage system with subcentimetre travel range and subnanometre positioning resolution.

Ultra Strengthening of Wooden Girders

Owing to the natural defects of wood, structural timber is currently used with conservative safety factors. This study investigates the use of Carbon Fiber Reinforced Polymer (CFRP) for improving the strength of structural timber. Four flexural test stages were carried out, the modes of failure of the three specimens in each stage were studied to determine and strengthen the suspected weak zone which caused the failure. It was found that the tensioned fibers of ordinary timber girders normally fail first especially at the sections containing knots. Using a strip of CFRP to strengthen tensioned fibers is a well known technology, but it will not prevent a premature failure due to horizontal shear. A strength increase of 56% was reached by the adaption of shear connectors in the form of screws. After treating tensile and shearing strengths, still testing specimens showed failure at the compressed fibers. By enhancing the compressed fibers with a steel strip, the prototype girders showed a remarkable increase in flexural strength of about 175% compared with the ordinary wooden girders having the same dimensions.