Micropositioning Stage Research Articles

Design of flexure-based modular architecture micro-positioning stage

As the current trend in numerous industrial domains is to miniaturise products, micro-positioning stage(MPS) capable of performing micro-manipulation and micro-assembly tasks with sub-micrometer or nanometer precision is playing an increasing important role in these fields. In addition, well performances and low cost are two emergency issues need to be addressed for widely using flexure-based MPSs. However, the design and fabrication process for MPSs at present are costly both in time and money. Especially, the designed configurations are tailored to a specific application without flexibility. Thus, the purpose of this paper is to introduce a design of precision flexure-based reconfigurable MPSs which provide better flexibility and functionality and allows to reduce the time to market significantly. To begin with, performance requirements and benefits for reconfigurable MPSs are introduced. Then, some typical modules and their functions are introduced in detail. Finally, some selective stages assembled with function modules are proposed as case studies, for the purpose of validating the benefits of reconfigurable MPSs.

Nonlinear static modeling of a tip-tilt-piston micropositioning stage comprising leaf-spring flexure hinges

Nonlinear static modeling is crucial for the design of stages with large travel ranges. However, few studies have investigated complex spatial compliant mechanisms. The present study proposes an optimization algorithm based on substructure constraint conditions to formulate the nonlinearity of the force–displacement characteristic of a tip-tilt-piston stage comprising leaf-spring flexure hinges. First, the nonlinear force–displacement characteristics of the compound basic parallelogram mechanism are derived using an optimization algorithm based on two constraint conditions (I and II). Second, the nonlinear static modeling of the tip-tilt-piston stage is conducted based on the modeling results of the compound basic parallelogram mechanism. The stage is divided into three parts, and force analyses are conducted for all three parts. The vertical displacement of the compound basic parallelogram mechanism in part 1 and the rotational angle of the rotational plate in part 2 are calculated. Subsequently, the force–displacement characteristics of the tip-tilt-piston stage are obtained based on a third constraint condition (III). A comparison of the finite element analysis results and the theoretical calculation indicates less than 4% errors. In the experimental tests conducted on the proposed stage and four compound basic parallelogram mechanisms, the displacements were evidently larger than those calculated using the finite element analysis. Therefore, a weight coefficient of the axial force w is introduced in the theoretical calculation to solve the problem of the large deviations between the experimental results and the finite element analysis results. When w is set to 1, the theoretical results are in good agreement with the finite element analysis results; when w is set to 0.05 for the tip-tilt-piston stage and 0.15 for compound basic parallelogram mechanisms, the theoretical results are consistent with the experimental results (less than 8.5% errors).

Robust μ-Synthesis With Dahl Model Based Feedforward Compensator Design for Piezo-Actuated Micropositioning Stage

In this article, a combined feedback-feedforward control design scheme is presented to enhance the tracking performance of a piezo-actuated micropositioning stage by compensating the nonlinear hysteretic behavior of the piezoelectric actuator and model uncertainties of the system. Detailed investigation of the presented control scheme is performed not only in simulation by analyzing the robust stability and robust performance but also in real-time with motion trajectories of multiple frequencies. To design the presented control scheme, first of all, the dynamic model of the system is identified from the real-time experimental data by using the recursive least squares parameter adaptation algorithm. Then, Dahl hysteresis model is considered to represent the nonlinear hysteretic behavior of the piezoelectric actuator. To deal with this hysteresis nonlinearity, Dahl feedforward compensator is designed without involving inverse model calculations to avoid any computational complexity. This feedforward compensator is then combined with $\mu $ -synthesis robust feedback controller which is designed in the presence of model uncertainties of the system. The presented control scheme ensures the boundedness of the closed-loop signals and the desired tracking performance of the considered micropositioning stage. Finally, experimental tests are conducted with motion trajectories of multiple frequencies for the validation of the control scheme. An average improvement of 95% in compensating the hysteresis nonlinearity and 80% in reducing the tracking error is achieved which demonstrates the efficacy of the presented control scheme.

Design Analysis and Optimization of Large Range Spatial Translational Compliant Micro-positioning Stage

Design Analysis and Optimization of Large Range Spatial Translational Compliant Micro-positioning Stage

Multi-feature radiation pattern measurement apparatus operative up to 67-GHz band

A multi-option, low-cost, and user-friendly radiation pattern measurement apparatus operative up to the 67 GHz millimeter-wave (MMW) band is presented in this study. The proposed apparatus is distinctly designed, with multiple parameters optimized for radiation pattern measurements at the Ka, Q, and V MMW bands. The transmit antenna, a standard gain horn, is mounted over a fixed stage. The antenna under test (AUT) is mounted on a micro-positioning stage to facilitate angular-dependent received power measurements. The positioning stage is controlled electronically, which allows precise motion along the φ-plane of the cylindrical-axis. Distinct mechanical fixtures are used to enable the mounting of the AUT at various orientations for the purpose of measuring the broadside and end-fire antenna radiation characteristics. Furthermore, polarization-dependent measurements are enabled by changing the orientation of the transmitting antenna using waveguide twists. The hardware and software components are integrated to enable the automation of the mechanical micro-positioning/rotational system and data acquisition using a vector network analyzer operating up to 67 GHz. A user-friendly graphical user interface is developed for electromechanical control, data acquisition, and post analysis of the AUTs’ radiation parameters. All the operations are sequentially connected to enable operation in a closed loop manner.

A Compound Control Based on the Piezo-Actuated Stage with Bouc–Wen Model

The piezoelectric actuator (PA) is one of the most commonly used actuators in a micro-positioning stage. But its hysteresis non-linearity can cause error in the piezo-actuated stage. A modified Bouc–Wen model is presented in this paper to describe the hysteresis non-linearity of the piezo-actuated stage. This model can be divided into two categories according to the input frequency: rate-independent type and rate-dependent type. A particle swarm optimization method (PSO) is employed to identify these parameters of the Bouc–Wen hysteresis model. An inverse model feedforward compensator is established based on the modified Bouc–Wen model. The fuzzy proportional-integral-derivative (PID) controller combined with the feedforward compensator is implemented to the piezo-actuated stage. The experimental results indicate that the proposed control strategy can compensate for the hysteresis phenomenon.

Development and Analysis for a New Compliant XY Micropositioning Stage Applied for Nanoindentation Tester System

A Compliant XY micropositioning stage is purported for situating a material sample in nanoindentation tester process. This paper aims to develop, analyze and optimize a XY compliant micropositioning stage. The working stroke of proposed XY stage is amplified by combining the four-lever and a bridge amplification mechanism. To enhance the performances of the stage, the main geometric parameters are optimized by an integration method of Taguchi method, response surface method (RSM) and genetic algorithm (GA). Firstly, static analysis and dynamic analysis are conducted by the finite element analysis in order to predict initial performances of the XY stage. Secondly, the number of experiments and the data are retrieved by combination of the finite element analysis-integrated Taguchi method. Thirdly, the effects of main design variables on the output response sensitivity are considered. Later on, mathematical model for the amplification ratio was established by the RSM. Finally, based on the mathematical equation, the GA is adopted to define the optimal design variables. The results of numerical validations are in a good agreement with the predicted results. The results depicted that the proposed hybrid approach ensures a high reliability for engineering optimization problems.

Design, Modeling, and Testing of a Novel XY Piezo-Actuated Compliant Micro-Positioning Stage.

A novel decoupled XY compliant micro-positioning stage, based on a bridge-type amplification mechanism and parallelogram mechanisms, is designed in this paper. Analytical models of the bridge-type amplification mechanism and parallelogram mechanisms are developed by Castigliano’s second theorem and a Beam constrained model. The amplification ratio, input stiffness, and output stiffness of the stage are further derived, based on the proposed model. In order to verify the theoretical analysis, the finite element method (FEM) is used for simulation and modal analysis, and the simulation results indicate that the errors of the amplification ratio, input stiffness, and output stiffness of the stage between the proposed model and the FEM results are 2.34%, 3.87%, and 2.66%, respectively. Modal analysis results show that the fundamental natural frequency is 44 Hz, and the maximum error between the theoretical model and the FEM is less than 4%, which further validates the proposed modeling method. Finally, the prototype is fabricated to test the amplification ratio, cross-coupling error, and workspace. The experimental results demonstrate that the stage has a relatively large workspace, of 346.1 μm × 357.2 μm, with corresponding amplification ratios of 5.39 in the X-axis and 5.51 in the Y-axis, while the cross-coupling error is less than 1.5%.

Multi-species micropatterning of organic materials by liquid droplet array transfer printing

Because techniques such as photolithography for inorganic materials are yet to have their equivalents for organic materials, multispecies patterning of functional organic materials at microscale resolution remains in development. This paper reports on a liquid droplet transfer printing method, that is, used for microscale patterning of multispecies materials. A transfer printing instrument is built with a multidimensional micropositioning stage, thereby enabling the technique to be used to pattern different materials on a single surface. The size range of the transferred liquid droplets can be tuned by manipulating the surface wettability and the gap between the surfaces of the sample and the stamp. The developed technique is used to prepare red–green–blue pixel patterns and microlenses integrated with color filters.

Optimum design of a large area, flexure based XYθ mask alignment stage for a 12-inch wafer using grey relation analysis

Abstract An optimum design methodology for a large area, flexure-based XYθ mask alignment stage, which can be applied to a 12-inch wafer photolithography process, was presented. The XYθ micropositioning stage consisted of a working plate with a 12-inch hole in the center, three piezo actuators, and three displacement amplifiers based on the bridge-type flexure mechanism. Grey relation analysis and orthogonal array were incorporated with finite element analysis to find optimum design conditions. The grey relation grade with weight factors was used to simultaneously optimize three objective characteristics of the micropositioning stage: the maximum stroke, deflection of the working plate, and first natural frequency. The optimally-designed stage was fabricated by wire electrical discharge machining and tested to investigate its performance. The proposed stage showed the first natural frequency of 57 Hz and the maximum stroke of 122.84 μm, 108.46 μm, 0.685 mrad in the x-, y-, and θ-direction, respectively. The resolutions in corresponding directions were 11 nm, 10 nm, and 0.5 μrad. The performance of the stage was improved by optimum design process, and the experimental results were in good agreement with the predicted ones from the finite element analysis.

State estimation of dynamic systems with sandwich structure and hysteresis

In this paper, a non-smooth observer is proposed to estimate the states of a sandwich system with hysteresis. Based on the analysis of observability of this system, a non-smooth observer is constructed. The non-smooth observer has a switchable transition matrix and contains an additional item which can switch according to the working zone of the system. By considering the suppression of model uncertainty and disturbance, the robust design of the non-smooth observer for the sandwich system with hysteresis is proposed. In the robust observer, the estimation error caused by the switched error is included as an extended disturbance and the selection of the feedback matrices of the robust observer has been converted into an optimal problem. Finally, the proposed methods are implemented to estimate the states of a micro-positioning stage with piezoelectric actuator which can be described as a non-smooth sandwich system with hysteresis. The estimations results by the non-smooth and the robust observer are superior to the conventional and the non-robust observer in the experimental case, respectively.

Design of Reconfigurable Planar Micro-Positioning Stages Based on Function Modules

Micro-positioning stages, which are capable to meet the emerging industrial trend for performing various kinds of micro-manipulation and micro-assembly tasks are the crucial tools to miniaturize the products under ultra-high precision. The current main practice is to specifically tailor a monolithic positioning stage design for one kind of micro-manipulation application. However, the design and fabrication of such a specific flexure-based micro-positioning stage are expensive in both the time and financial investment. In order to increase the flexibility and functionality of micro-positioning stages, this paper proposes a novel reconfigurable planar micro-positioning stages platform based on different function modules. A functional model-based approach is developed to divide one micro-positioning stage into a set of functionally independent sub-models, which allows flexible composition resulting in an adjustable new stage. The robustness of the proposed platform is demonstrated using some typical micro-positioning stages benchmarking cases. The effectiveness of assembly using flexible function modules is verified to show the benefits of the proposed design platform for reconfigurable micro-positioning stages.

Distributed Hammerstein Modeling for Cross-Coupling Effect of Multiaxis Piezoelectric Micropositioning Stages

Hysteresis modeling is interesting yet challenging for piezoelectric actuated systems, which are often used in micro/nano scale measurement and manufacturing equipments. However, due to its complexity, few efforts have been devoted to characterizing cross-coupling hysteresis effect of multiaxis piezoelectric micropositioning stages. To this end, a distributed Hammerstein model, composed of a cascaded connection of a static nonlinearity and a dynamic linearity, is proposed in this paper to approximate the nonlinear spatial/temporal cross-coupling effect. This model outperforms conventional piezo models, such as the Preisach model. Meanwhile, theoretical analysis is provided to guarantee the convergence of the proposed Hammerstein model. Finally, extensive experiments are conducted to verify the superiority of the proposed modeling method.

Design and analysis of translational joints using corrugated flexural beams with conic curve segments

The paper introduces a new category of corrugated flexural beams formed of serially connected conic curve segments (including elliptical, parabolic, hyperbolic) into the design of translational joints. Mohr’s integral is used to derive the small-displacement compliance analytical model of the conic curve segments. Further, the stiffness models of the translational joints are obtained using a matrix approach that sums the transformed local-frame compliance matrices of individual component segments, which are verified by taking advantages of the finite element method. The shape parameters of the translational joints are then optimized to maximize the motion range while keeping the off-axis/axial stiffness ratio above a specified limit. The optimum translational joint designs are then applied to construct 2-DOF micro-positioning stages, with experiments carried out to determine the effectiveness of design and analysis.

Investigation of a 1-DOF piezoelectric micro-positioning rotary stage

Electromagnetic motors are extensively used as actuators for high-precision rotary positioning applications; however, they can no longer satisfy continuously increasing new technical requirements, including (but not limited to) those for compactness, simple structures, high precision, and low manufacturing costs. A continuous study of a 1-DOF piezoelectric micro-positioning rotary stage, which was previously proposed by the authors and is characterised by the aforementioned criteria, is reported in this paper. The rotary stage is driven by the interaction between a cylinder-type piezoelectric transducer and a rotor, utilising resonant ultrasonic standing-wave vibrations. The results demonstrate an acceptable correspondence between the detailed numerical and experimental harmonic and modal analyses of the piezoelectric cylinder. Investigations of the motion trajectories of the contact zones and driving tips in the XZ plane indicate the suitability of the selected operational vibration mode to provide a well-defined motion of the rotary stage. The average resolution of the rotary stage is determined to be 0.25 μrad and 0.26 μrad in the clockwise and anticlockwise direction, respectively.

Analysis and optimization of 2-DOF micro-positioning stage based on flexible hinges

Analysis and optimization of 2-DOF micro-positioning stage based on flexible hinges

Design and modeling of a compliant tip-tilt-piston micropositioning stage with a large rotation range

In compliant tip-tilt-piston micropositioning stages, it is difficult to achieve a large rotation range using small air–gap voice coil actuators. With a smaller air gap, the voice coil actuators can produce a larger output force; however, the coil of the voice coil actuator touches the stator as the stage rotates. This paper presents the mechanical design, modeling and experimental tests of a novel large-angle tip-tilt-piston stage driven using four small air-gap voice coil actuators. In order to prevent the occurrence of undesired contact between the coil and stator, a compliant decoupling mechanism is introduced to minimize the transverse displacement of the coil of the voice coil actuator. An improved substructure method based on the compliance matrix is applied to calculate the rotational stiffness of the stage and transverse displacement of the coil. Lagrange’s equation is used to obtain the dynamic resonant frequencies. Based on this, an optimization procedure is proposed for determining the design parameters of the stage. The finite element analysis is performed to verify the theoretical calculation. Finally, a prototype of the stage is fabricated, and experiments are conducted to validate the feasibility of the stage. The proposed stage can achieve rotational–motion strokes of 83.18 mrad and 82.26 mrad in the working axes, for which the rotational mode frequencies are 55.45 Hz and 56.09 Hz, respectively. The motion resolution of the stage is ±6.67 μrad. The maximum transverse displacement of the coil of the voice coil actuator is 10.98 µm, which is negligible as compared to the air gap (0.38 mm) of the voice coil actuator. In summary, a tip-tilt-piston stage was designed to achieve a large rotation range using small-air-gap voice coil actuators.

Design and testing of a new 3-DOF spatial flexure parallel micropositioning stage

This paper presents the design and testing of a novel 3-DOF parallel flexure micropositioning stage for micro-scale operations. The proposed modular design can obtain the merit of high interchangeability during maintenance process. The output platform of the mechanism offers pure translational motion along X, Y, and Z axes by resorting to the flexure guiding of two parallelogram joints. Meanwhile, the output motion is decoupled by using two leaves with symmetric ellipse-shaped flexure hinges, and the platform provides isolated movement without parasitic motion. By using the bridge-type and lever-type compound amplifier, the micropositioning stage provides a large output displacement, which is over 30 times the input displacement provided by piezoelectric actuator. The enlarged displacement is translated to the orthogonal parallel mechanism by four straight beams, which provide perfect decoupling properties. In addition, the modular design principle makes it possible to adopt multiple materials to balance the performance of the actuator and decoupling flexure hinges. Analytical analysis and finite element analysis simulation are conducted to verify the fine decoupling property and large translational motion of the proposed 3-DOF parallel micropositioning stage. Moreover, a prototype is fabricated using multiple materials for experimental testing. Results demonstrate the promising performance of the developed decoupled micropositioning stage.

A decoupled flexure-based rotary micropositioning stage with compact size

This paper presents the design and analysis of a novel compact flexure-based rotary micropositioning stage driven by piezoelectric actuator. The developed stage possesses a double four-bar rotary mechanism with rotational symmetric configuration and totally kinematic decoupling, which can convert the linear motion of the piezoelectric actuator into the pure rotational motion, significantly minimizing the parasitic error at the rotation center. Based on the configuration, a single piezoelectric actuator is employed to drive the stage, avoiding actuator redundancy and large configuration size. Meanwhile, we introduce a compliant rotational guiding mechanism to enhance the rotational stiffness and dynamics of the stage. Analytical modeling and finite element analysis are adopted to facilitate the design of dimension. Finally, a prototype of the stage is manufactured and tested, which is capable of a rotational angle of [Formula: see text] with the first natural frequency of 430 Hz, whilst the well-constrained maximum center shift along the X- and Y-axis are 0.29 µm and 0.12 µm, respectively, indicating good decoupling capability. Furthermore, the compact size of [Formula: see text] is beneficial for limited working space.

Optimization of a 2-DOF micro-positioning stage using corrugated flexure units

This paper presents an analytical model that can be utilized in the design and optimization of a 2-DOF micro-positioning stage using corrugated flexure (CF) units. Stiffness components of the CF beam and the middle stage of CF stage are derived through stiffness matrix method. Numerical simulations indicate smaller length of straight segment, smaller thickness and larger number of CF units are better for maximizing the off-axis/axial stiffness ratio. Further, the dimensions of CF stage have been optimized, leading to a CF stage with higher off-axis/axial stiffness ratio and larger range of motion. The optimal result is validated by the finite element analysis (FEA) and experiments.