Flexure-based Stage Research Articles

An XYZ parallel nanopositioning stage with hybrid damping

It is well known that lightly damping linear dynamics of a piezo-hysteresis-compensated flexure-based stage severely limits its motion control bandwidth. To address it, a novel damped XYZ parallel flexure-based nanopositioning stage (3⊥(P⊥K∥K), P for prismatic, K for Cardan or Universal) with hybrid passive damping, which is composed of shearing–squeezing hinge damping and in-band damping by graded local resonators (GLRs), is presented. The dynamic modeling and optimization design are implemented based on the maximization of motion amplification ratio, first-order natural frequency, and inverse in-band H2 norm of frequency response function (FRF). The optimized GLR module has distributed dynamic characteristics. The approximate motion decoupling is verified by Jacobin matrix analysis and experiments. The static/scanning-frequency dynamic experiments and step/triangular trajectory tracking control with the low-order controllers for all-hinge damping and hybrid damping stages are implemented. The experimental results indicate the small crosstalks due to hybrid passive damping, as the static crosstalks in X-to-Z and Y-to-Z are 0.293% and 0.276%, respectively, and the dynamic crosstalks in X-to-Z and Y-to-Z are 0.922% and 0.910%, respectively. The capability of improving positioning precision and expanding control bandwidth by hybrid damping only with a low-order controller is also validated experimentally.

Damped two-axis axially collocated flexure hinge.

Broadband motion control in flexure-based stages can benefit from passive damping enhancement at their flexible structures. This paper develops a damped two-axis axially collocated (2-AC) flexure hinge with damping-enabling hybrid inserts and analytically derives its loss factor model based on hybrid (empirical and analytical) compliance modeling and shearing damping modeling. The analytical loss factor model is verified by finite element analysis. It is seen that the geometric parameters of the diameter and slope angle of the insert are sensitive to the hinge's loss factor based on the theoretical loss factor model, especially in low-frequency and resonant zone. The actual experiments and finite element simulation indicate that embedding the hybrid inserts into the 2-AC flexure hinge can improve the damping performance of the hinge.

Design of a flexure-based parallel XY micropositioning stage with millimeter workspace and high bandwidth

This paper presents the design of a flexure-based parallel XY micropositioning stage with millimeter workspace and high bandwidth. The large range micropositioning requires the workspace of flexure-based stage to reach millimeter level. Meanwhile, the structural bandwidth of the flexure-based stage with large range is relatively low, which limits the scan rate and is required to be improved. A novel parallel mechanism is implemented to improve the structural bandwidth of the millimeter level flexure-based XY stage by removing redundant mass. The coupling between the working axes is reduced by a decoupler based on circular hinges. The mechanical performances of the designed XY stage are analyzed by theoretical models and verified by finite element analysis (FEA). Experimental results indicate that the designed XY micropositioning stage is capable of achieving millimeter workspace as well as a relatively high resonance frequency compared with other millimeter level flexure-based XY stages.

A Damped Decoupled XY Nanopositioning Stage Embedding Graded Local Resonators

Lightly damping linear dynamic characteristics of a flexure-based stage mainly limit control bandwidth when its piezo-actuating hysteresis is well compensated. In this article, a novel damped decoupled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">XY</i> nanopositioning stage embedding graded local resonators (GLRs) is developed and optimized based on the maximization of motion range and first-order natural frequency. The modal damping strengthening mechanism of local resonant metastructures is analyzed based on the built dynamic model. The GLRs embedded in the working platform has different dynamic parameters, which are optimized based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> norm. The motion decoupling is guaranteed by the designed hybrid flexure-guided mechanism while strengthening the Z-direction supporting stiffness. The static/ scanning-frequency dynamic experiment and trajectory tracking control with a propotional-integral-derivative (PID) controller is implemented. The experimental results indicate that maximum motion crosstalk is 0.69%, and validate the effectiveness of improving the linear dynamics of the stage and expanding control bandwidth.

Design, Fabrication, and Testing of a New Compact Piezo-Driven Flexure Stage for Vertical Micro/Nanopositioning

This paper presents the design of a new compact one-degree-of-freedom (1-DOF) compliant stage driven by a piezoelectric actuator (PEA) for micro/nanopositioning in the vertical direction. An orthogonal compound bridge-type amplifier is introduced to amplify the displacement of the PEA. It significantly reduces the height of the stage and leads to a compact design. By analytical modeling of the mechanism, the design variables are determined, which are then optimized via the multiobjective genetic algorithm based on the finite-element analysis. Simulation results show that the 1-DOF stage is able to provide the maximum displacement of $181.18~\mu \text{m}$ in theory, which is more than $12\times $ the input displacement of PEA. Payload test results indicate that the stage can support a maximum load of about 80 N. Comparison study reveals that the presented vertical positioning stage offers a more compact structure than existing ones. A prototype is fabricated for experimental studies, and the deviation between the experimental and simulation results is discussed in detail. Moreover, closed-loop performance test exhibits a resolution of 10 nm for the developed vertical positioning stage. Note to Practitioners —The motivation of this paper is to devise a compact flexure-based stage, which can be mounted on the top of an XY stage for constructing a hybrid type of XYZ stage dedicated to micro/nanopositioning applications. Such a design scheme provides a more flexible solution than serial- and parallel-kinematic designs. In order to fulfill the design requirement and to improve the compactness and output directionality of the stage, a series of design processes is conducted. The design parameters are optimized and the optimal design leads to the stage dimension of 58 mm $\times20$ mm $\times15.5$ mm (length $\times $ width $\times $ height), which offers a motion range of $97.32~\mu \text{m}$ as verified by the experimental study. In consideration of the motion range and physical size, the proposed stage offers a more compact structure than available designs. Experimental results demonstrate the fine performance of the developed prototype stage for vertical micro/nanopositioning.

Design and characterization of a two-axis, flexure-based nanopositioning stage with 50 mm travel and reduced higher order modes

Long range, high precision, XY stages have a multitude of applications in scanning probe microscopy, lithography, micro-AM, wafer inspection and other fields. However, finding cost effective precision motion stages with a range of more than 12 mm with a precision better than one micron is a challenge. This study presents parametric design of the two XY flexure-based stages with a travel ranges of up to 50 mm and sub-micron resolution. First, the fabrication and testing of a two-axis double parallelogram flexure stage is presented and the results obtained from FEA and experimental measurements are shown to be in good agreement with the analytical predictions for this stage. A modified stage design with reduced higher order modes and same range, is also presented. This modified design is shown to be capable of achieving an open loop resolution of 100 nm with a travel range of greater than 50 mm. Higher order modes of the modified stage have been shown to be shifted from 25 Hz in the double parallelogram flexure (DPF) stage to over 86 Hz in the modified DPF stage making it much simpler to design a high speed (>10 Hz) controller for the modified stage.

Design and quasi-static characteristics study on a planar piezoelectric nanopositioner with ultralow parasitic rotation

This paper presents a particular mechanism design which is inherently inclined to have no parasitic rotation. The flexure-based stage comprises symmetric flexure guiding mechanism and two piezoelectric stack actuators. The layout of the stage is evaluated by finite element analysis, and the results indicate that the proposed design exhibits ultralow parasitic rotation. A prototype of the stage is then fabricated, and its performance is tested. Experimental results show that the stage has a stroke of 500μm×500μm and the crosstalk is less than 1%. The maximum parasitic rotation is ±1.2 arcsec at a stroke of 500μm.

A parallel alignment device with dynamic force compensation for nanoimprint lithography

Nanoimprint lithography is a nano/micro patterning technology to fabricate functional devices by pressing a template with predefined structures on a substrate. Uniformity of the force distribution between the contacting surfaces should be ensured to produce features with high fidelity. In this paper, a parallel alignment device with the abilities of dynamic force distribution control is developed. By adopting a spherical air bearing held with a 5-degree-of-freedom flexure-based stage, wedge errors between the template and the substrate can be eliminated passively without friction when an imprint force is applied. Since the vertical imprint force is mainly supported by the spherical air bearing, the device is very suitable for high force applications, without causing damage to the delicate compliant stage or precision degradation. Besides, the force distribution of the imprint process is measured, based on which dynamic force compensation is performed by actuating the compliant stage actively. Five-hundred-nm-period grating structures are transferred successfully with the device and proofs effectiveness of the device.

A single-mask thermal displacement sensor in MEMS

This work presents a MEMS displacement sensor based on the conductive heat transfer of a resistively heated silicon structure towards an actuated stage parallel to the structure. This differential sensor can be easily incorporated into a silicon-on-insulator-based process, and fabricated within the same mask as electrostatic actuators and flexure-based stages. We discuss a lumped capacitance model to optimize the sensor sensitivity as a function of the doping concentration, the operating temperature, the heater length and width. We demonstrate various sensor designs. The typical sensor resolution is 2 nm within a bandwidth of 25 Hz at a full scale range of 110 µm.