Development of a passive compliant mechanism for measurement of micro/nano-scale planar three DOF motions

This paper presents the design, optimization, and computational and experimental performance evaluations of a passively actuated, monolithic, compliant mechanism. The mechanism is designed to be mounted on or built into any precision positioning stage which produces three degree of freedom (DOF) planar motions. It transforms such movements into linear motions which can then be measured using laser interferometry based sensing and measurement techniques commonly used for translational axes. This methodology reduces the introduction of geometric errors into sensor measurements, and bypasses the need for increased complexity sensing systems. A computational technique is employed to optimize the mechanism’s performance, in particular to ensure the kinematic relationships match a set of desired relationships. Computational analysis is then employed to predict the performance of the mechanism throughout the workspace of a coupled positioning stage, and the errors are shown to vary linearly with the input position. This allows the errors to be corrected through calibration. A prototype is manufactured and experimentally tested, confirming the ability of the proposed mechanism to permit measurements of three DOF motions

Modeling and tracking control of a novel XYθz stage

A XYθz stage is designed and experimentally tested. This developed stage is driven by three piezoelectric actuators (PZTs) and guided by a flexure hinge based mechanism with three symmetric T-shape hinges. It was manufactured monolithically by using wire electrical discharge machining technology. In addition, considering the both electrical and mechanical characteristics, a third-order dynamic model of the 3-DOF system has been established to investigate the relationship between the input voltage and the output displacement of the entire system. The parameters of the third-order dynamic model were estimated by using the system identification toolbox. Furthermore, decoupling control is also proposed to solve the existed coupling motion of the stage. In order to compensate the hysteresis of PZT, the inverse Bouc-Wen model was utilized as a feedforward hysteresis compensator. Finally, extensive experiments were performed to verify the good decoupling and tracking performances of the developed stage

Design and control of a 6-degree-of-freedom precision positioning system

This paper presents the design and test of a6-degree-of-freedom (DOF) precision positioning system, which is assembledby two different 3-DOF precision positioning stages each driven by three piezoelectric actuators (PEAs). Based on the precision PEAs and flexure hinge mechanisms, high precision motion is obtained.The design methodology and kinematic characteristics of the6-DOF positioning system areinvestigated. According to an effective kinematic model, the transformation matrices are obtained, which is used to predict the relationship between the output displacement from the system arrangement and the amountof PEAsexpansion. In addition, the static and dynamic characteristics of the 6-DOF system have been evaluated by finite element method (FEM) simulation andexperiments. The design structure provides a high dynamic bandwidth withthe first naturalfrequency of 586.3 Hz.Decoupling control is proposed to solve the existing coupling motion of the 6-DOF system. Meanwhile, in order to compensate for the hysteresis of PEAs, the inverse Bouc-Wen model was applied as a feedforward hysteresis compensator in the feedforward/feedback hybrid control method. Finally, extensive experiments were performed to verify the tracking performance of the developed mechanism

Design and control methodology of a 3-DOF flexure-based mechanism for micro/nano-positioning

A 3-DOF (X–Y–θZ) planar flexure-based mechanism is designed and monolithically manufactured using Wire Electro-Discharge Machining (WEDM) technology. The compact flexure-based mechanism is directly driven by three piezoelectric actuators (PZTs) through decoupling mechanisms. The orthogonal configuration in the x and y directions can guarantee the decoupling translational motion in these axes. The rotational motion and translational displacement in the x direction can be decoupled by controlling the piezoelectric actuators in the x axis with the same displacement values in same and opposite motion directions, respectively. The static and dynamic models of the developed flexure-based mechanism have been developed based on the pseudo-rigid-body model methodology. The mechanical design optimization is conducted to improve the static and dynamic characteristics of the flexure-based mechanism. Finite Element Analyses (FEA) are also carried out to verify the established models and optimization results. A novel hybrid feedforward/feedback controller has been provided to eliminate/reduce the nonlinear hysteresis and external disturbance of the flexure-based mechanism. Experimental testing has been performed to examine the dynamic performance of the developed flexure-based mechanism

Development of compliant mechanisms for real-time machine tool accuracy enhancement using dual-servo principle

Ph.DDOCTOR OF PHILOSOPH

Design and computational optimization of a flexure-based XY nano-positioning stage

This thesis presents the design and computational optimization of a two-axis nano-positioning stage. The devised stage relies on double parallelogram flexure bearings with under-constraint eliminating linkages to enable motion in the primary degrees-of-freedom. The structural parameters of the underlying flexures were optimized to provide a large-range and high bandwidth with sub-micron resolution while maintaining a compact size. A finite element model was created to establish a functional relationship between the geometry of the flexure elements and the stiffness behavior. Then, a neural network was trained from the simulation results to explore the design space with a low computational expense. The neural net was integrated with a genetic algorithm to optimize the design of the flexures for compactness and dynamic performance. The optimal solutions resulted in a reduction of stage footprint by 14% and an increase in the first natural frequency by 75% relative to a baseline design, all while preserving the same 50mm range in each axis with a factor of safety of 2. This confirms the efficacy of the proposed approach in improving stage performance through an optimization of its constituent flexures.Mechanical Engineerin

Mechatronic Design, Dynamics, Controls, and Metrology of a Long-Stroke Linear Nano-Positioner

Precision motion systems find a broad range of application in various fields such as micro/nano machining tools, lithography scanners, testing and metrology machines, micro-assembly, biotechnology, optics manufacturing, magnetic data-storage, and optical disk drives. In this thesis, an ultraprecision motion stage (nano-positioner) is designed and built based on the concept of a low-cost desktop precision micro machine tool. Linear positioning performance requirements of such a machine tool are used as design objectives. The nano-positioner’s mechatronic design is carried out in such a way to integrate different components towards high performance in terms of high dynamic range, high feedrate, servo accuracy, and geometric accuracy. A self-aligning air-bearing/bushing arrangement is employed for frictionless motion with infinite theoretical resolution, as well as reduced assembly costs and footprint. The air discharge from the air bearings/bushings are also utilized for assistance in the removal of heat dissipated from actuator coils. A voice coil actuator (VCA) is chosen for continuous, non-contact operation, and designed from scratch. A number of dimensional variables of the cylindrical VCA are set according to required forces, motion range, production/assembly tolerances, magnet availability, leakage flux, etc. The remainder of variables is determined according to two novel optimization objectives defined independent of the coil wire gauge, which separately aim for maximum stage acceleration capacity and minimum heat generation per generated force. The actuators are operated in a complementary double configuration for control simplicity which allows for a straightforward and robust design for controller stability. Controller design is carried out at current control and position control levels. Current frequency response of the voice coil actuators is obtained, and they are observed to possess additional high frequency dynamics on top of the expected first order lumped resistance and inductance model. These are attributed to the eddy currents in the stator structure. A closed loop bandwidth of better than 907 [Hz] is achieved using the integrator plus lead current controller. The position controller is designed using the identified overall plant which includes the moving body, current dynamics and the force response. The lead-lag position controller is tuned at 450 [Hz] cross-over frequency and 40 [deg] phase margin. The control error during the tracking of a step trajectory filtered at 40 [Hz] is found to vary between ±5 [nm], indicating a 4 million dynamic range over the 20 [mm] stroke length. Dynamic Error Budgeting (DEB) method has been used to resolve the components of the error, and the largest contributor is found to be the sensor noise. The actual positioning error, which is an ideal signal excluding sensor noise is estimated using the same methodology and disturbance models, and it is found to be 0.680 [nm] root-mean-square (RMS). For the trajectory following case, experiments are carried out with and without a compensation scheme for encoder quadrature detection errors. The compensation is observed to reduce the ±45 [nm] control error to ±15 [nm]. For the assessment of stage performance and the verification of design choices, modal testing and laser interferometric metrology have been applied to the linear nano-positioner. For modal testing, two independent methods are used and their predictions are compared. In the first method, a graphical approach, namely the peak-picking method, is employed to identify modal parameters (natural frequency and damping ratio) and mode shapes. In the second method, a modal testing software package is used to identify the same using automated algorithms. The first mode, which is the most critical one for controller design, is identified at 65 [Hz] as a roll mode, followed by horizontal, vertical, and pitch modes at 450, 484, and 960 [Hz], respectively. The geometric errors of the system are identified using laser interferometric measurements, using various optical setups for linear and angular components. An error budget is formed using these results, together with the estimated thermal errors and servo errors. The accuracy of the stage is determined to be ±5.0 [μm], which had a ±1.1 [μm] non-repeatable component. In the future, the controller structure can be enhanced with an additional pole beyond the crossover frequency, in order to suppress unnecessary oscillations of the control effort signal around the set point due to the encoder noise transmitted to the controller input. Using an estimation of air bearing pitch stiffness from the catalogue values for normal stiffness, the roll mode was predicted at 672 [Hz]. The much lower natural frequency for that mode identified in modal testing (65 [Hz]) can be attributed to the shortcomings of the estimation method, primarily the neglect of the distortion of the supporting air cushion at the bearing interface due to out of plane rotations. In the future, experimental data can be obtained to characterize the air bearing pitch stiffness more accurately. It was observed that the preferred compensation scheme for the encoder quadrature detection errors is unable to match third and fourth harmonics of the encoder measurement error sufficiently. In the future, better compensation methods can be investigated for an improved match. During laser interferometric measurements, measurement uncertainty due to laser beam misalignment and air turbulence were inferred to be high. In the future, better ways to align the laser with the optics, as well as methods for improved assessment and compensation of environmental effects can be investigated

Design, modelling and characterization of a 2-DOF precision positioning platform

This paper presents the mechanical design, parameter optimization and experimental tests of a 2-degree-of-freedom (DOF) flexure-based precision positioning platform, which has great potential application in many scientific and engineering fields. During the mechanical design, the leaf parallelogram structures provide the functions of joint mechanisms and transmission mechanisms with excellent decoupling properties. The dynamic model of the developed positioning platform is established and analysed using pseudo rigid body model methodology. A particle swarm algorithm optimization approach is utilized to perform the parameter optimization and thus improve the static and dynamic characteristics of the positioning platform. The prototype of the developed 2-DOF positioning platform has been fabricated using a wire electric discharge machining technique. A number of experimental tests have been conducted to investigate the performance of the platform and verify the established models and optimization methodologies. The experimental results show that the platform has a workspace range in excess of 8.0×8.0 μm with a stiffness of 4.97 N/µm and first-order natural frequency of 231 Hz. The cross-axis coupling ratio is less than 0.6%, verifying the excellent decoupling performance

Creative design and modelling of large-range translation compliant parallel manipulators

Compliant parallel mechanisms/manipulators (CPMs) are parallel manipulators that transmit motion/load by deformation of their compliant members. Due to their merits such as the eliminated backlash and friction, no need for lubrication, reduced wear and noise, and monolithic configuration, they have been used in many emerging applications as scanning tables, bio-cell injectors, nano-positioners, and etc. How to design large-range CPMs is still a challenging issue. To meet the needs for large-range translational CPMs for high-precision motion stages, this thesis focuses on the systematic conceptual design and modelling of large-range translational CPMs with distributed-compliance. Firstly, several compliant parallel modules with distributed-compliance, such as spatial multi-beam modules, are identified as building blocks of translational CPMs. A normalized, nonlinear and analytical model is then derived for the spatial multi-beam modules to address the non-linearity of load-equilibrium equations. Secondly, a new design methodology for translational CPMs is presented. The main characteristic of the proposed design approach is not only to replace kinematic joints as in the literature, but also to replace kinematic chains with appropriate multiple degrees-of-freedom (DOF) compliant parallel modules. Thirdly, novel large-range translational CPMs are constructed using the proposed design methodology and identified compliant parallel modules. The proposed novel CPMs include, for example, a 1-DOF compliant parallel gripper with auto-adaptive grasping function, a stiffness-enhanced XY CPM with a spatial compliant leg, and an improved modular XYZ CPM using identical spatial double four-beam modules. Especially, the proposed XY CPM and XYZ CPM can achieve a 10mm’s motion range along each axis in the case studies. Finally, kinematostatic modelling of the proposed translational CPMs is presented to enable rapid performance characteristic analysis. The proposed analytical models are also compared with finite element analysis