This paper reports on a novel piezo-driven, parallel-kinematic, micropositioning XY stage. This monolithic design is comprised of parallelogram four-bar linkages, flexure hinges, and piezoelectric actuators. Kinematic and dynamic analysis shows that the mechanical structure of the stage has a large work space, high bandwidth and good linearity. The stage system was run in open-loop mode to measure the step response and frequency response. The results show that the resonation frequencies of the two vibration modes are 563 and 536 Hz and the damping ratios are 0.049 and 0.0228. Two fiber optic sensors were added to the system to build a closed-loop positioning system. Linear and circular contouring performance in closed-loop mode suggests high scanning performance for such parallel-kinematic stages. The positioning resolution of the stage, limited only by the feedback sensors used, is about 20 nm.

Design analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage

Flexure hinge has been commonly used as a substitute for mechanical joints in the design of micropositioning mechanisms. However, inaccurate modeling of flexure hinges deteriorates the positioning accuracy. In this paper, a planar 3-DOF parallel-type micropositioning mechanism is designed with the intention of accurate flexure hinge modeling. For this, a preliminary kinematic analysis that includes inverse kinematics, internal kinematics, and analytic stiffness modeling referenced to the task coordinate is presented. First, the revolute type of 1-DOF flexure hinge is considered. The simulation result based on the finite element method, however, is not coincident to the analytic result. This is due to the minor axial elongation along the link direction that keeps the mechanism from precise positioning. To cope with this problem, a 2-DOF flexure hinge model that includes this additional motion degree as a prismatic joint is employed in part, and additional actuators are added to compensate for the motion of this new model. On the basis of this model, the positional accuracy is ensured. The effectiveness of this accurate model is shown through both simulation and experimentation. This paper emphasizes that the precise modeling of a flexure hinge is significant to guarantee the positional accuracy of parallel micromechanisms using flexure hinge.

https://nereus.mech.ntua.gr/courses/micro/micro_pdf/3DOF_ieee.pdf

Design and experiment of a 3 DOF parallel micro-mechanism utilizing flexure hinges

This paper presents parallel kinematic XY flexure mechanism designs based on systematic constraint patterns that allow large ranges of motion without causing over-constraint or significant error motions. Key performance characteristics of XY mechanisms such as mobility, cross-axis coupling, parasitic errors, actuator isolation, drive stiffness, lost motion, and geometric sensitivity, are discussed. The standard double parallelogram flexure module is used as a constraint building-block and its nonlinear force-displacement characteristics are employed in analytically predicting the performance characteristics of two proposed XY flexure mechanism designs. Fundamental performance tradeoffs, including those resulting from the nonlinear load-stiffening and elastokinematic effects, in flexure mechanisms are highlighted. Comparisons between closed-form linear and nonlinear analyses are presented to emphasize the inadequacy of the former. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of computational finite element analysis and experimental measurements.

/pdf/constraint-based-design-of-parallel-kinematic-xy-flexure-1s5heug9lm.pdf

Constraint-based design of parallel kinematic XY flexure mechanisms

Stiffness plays an important role in the precise performance of flexure-based ultra-precision manipulation systems. The finite element method (FEM) is currently used to determine the stiffness of the flexure parallel mechanism (FPM) with specified dimensions and free shape. This paper presents the stiffness model based on the way the flexure members are connected together in serial or parallel combinations. The modeling allows one to formulate the functional relationship between stiffness and dimensions as well as the free shape of the FPM in the design process. For illustration, stiffness matrices of a double linear spring and a three degree-of-freedom (DOF) translational flexure parallel mechanism are established. The proposed analytical model is validated by FEM model and experiments.

Stiffness modeling of flexure parallel mechanism

This paper proposes an enhanced sliding mode motion tracking control methodology for piezoelectric actuators to track desired motion trajectories. The proposed control methodology is established to accommodate parametric uncertainties, nonlinearities including the hysteresis effect, and other un-modelled disturbances, without any form of feed-forward compensation. The fundamental concept in this control strategy relies on the specification of a target performance and the formulation of an enhanced sliding mode control law based on the variable structure control approach. The control methodology ensures the convergence of the position tracking error to zero in the presence of the aforementioned conditions. The stability of the control methodology is proven theoretically and a precise tracking ability is demonstrated in the experimental study. One of the most important advantages of this control methodology is that the approach requires only a knowledge of the estimated system parameters together with their corresponding bounds and the bound of the non-linearities and disturbances in the physical realisation. Being capable of motion tracking, the proposed enhanced sliding mode control methodology is very attractive in the field of micro/nano manipulation through which high-precision piezoelectric actuation control applications can be realised.

Enhanced sliding mode motion tracking control of piezoelectric actuators

A novel three degree-of-freedom micropositioner was developed for deep ultraviolet lithography applications. The design of the micropositioner utilizes the monolithic flexural mechanism with built-in multilayer piezoelectric actuators and sensors to achieve translations in the X- and Y-axes and rotation in the /spl theta//sub Z/-axis. The compact design aims at high resolution, high stiffness, and extremely low crosstalk interference. Parametric analyses of harmonic and forced vibrations are conducted to solve the derived dynamic models for the near optimum geometry of the micropositioner. Furthermore, the error budget analysis is conducted to minimize the effects of the geometric tolerance, material variation, and hysteresis errors.

An ultra-precision XY/spl theta//sub Z/ piezo-micropositioner. I. Design and analysis

For pt I see ibid., vol. 46, no. 4 (July 1999). The performance of an ultra-precision three dimensional micropositioner using the built-in multilayer piezoelectric actuators and sensors is presented. The compact design utilizes the monolithic mechanism to achieve translation in the X- and Y-axes and rotation in the /spl theta//sub Z/ axis with high stiffness and high damping. Hysteresis, nonlinearity, and drift of piezoelectric effects are improved by incorporating the sensors in a feedback control. Experiments demonstrate that the micropositioner is capable of a 10 nm resolution over the travel range of 17.8 /spl mu/m in the X- and Y-axes and a 0.15 /spl mu/rad resolution over the range of 585 /spl mu/rad in the /spl theta//sub Z/ axis. The crossaxis interferences are within 1.14% of the full range. The results agree well with predictions by theoretical models.

Hon Chan Chien

Papers

An ultra-precision XY/spl theta//sub Z/ piezo-micropositioner. I. Design and analysis

An ultra-precision XY/spl Theta//sub Z/ piezo-micropositioner. II. Experiment and performance