IEEE ICIA 2010 Conference Proceeding

Proceedings of the 2010 IEEE International Conference on Information and Automation June 20 - 23, Harbin, China

Design of a Compliant XY Stage with Embedded Force Sensor for Micro-Scale Positioning Qiaokang Liang1, 2, Dan Zhang3,

Quanjun Song1 and Yunjian Ge1

1

3

Institute of Intelligent Machines, Chinese Academy of Sciences 2 Department of Automation, University of Science and Technology of China, Hefei, Anhui, China {Qiaokang.Liang & Dan.Zhang}@uoit.ca Abstract— This paper presents the development of a micro-scale positioning device based on two degrees of freedom (DOF) plane compliant parallel mechanism, which is featured by piezo-driven actuators and flexure joints, integrated force/torque sensor that capable of delivering 2-DOF motions with high precision and providing real-time force/torque or position information for feedback control. With optimization design, the proper parameters of the proposed structure and flexure joints are chosen. The stage possesses high precision and resolution, configurational simplicity and compactness. And the embedded sensor possesses the advantages such as, isotropic and high sensitivity. Index Terms –Flexure mechanism, micro-scale positioning, piezoelectric actuation, optimization design.

I. INTRODUCTION

M

ICRO positioning equipments with high resolution position feedback are apparatus used to physically interact with a sample under a microscope, where a level of precision of movement is necessary that cannot be achieved by the unaided human hand. It has been developing widely and rapidly as its potential applications in various fields such as optical fiber alignment, micro device assembly and patch clamp experiments in biological research [1]. The design of a proper micro-scale precise positioning device requires interdisciplinary discipline integrating machine design, material science, compliant mechanism, detecting techniques and control theory. Parallel mechanisms are novel robotic architectures that offer unprecedented dexterity, rigidity and precision when interacting with the environment. Therefore, more and more micro equipments are made of hybrid and parallel structures to acquire perfect performance. However, conventional parallel mechanisms always suffer from errors such as backlash, friction. Recently, some researchers use the flexure joints instead of conventional rigid joints to remove the friction at joints and backlash. Y.J. Choi designed a large displacement precision XY positioning stage by using cross strip flexure joints [2], which actuated by a linear motor and can provide large-motion rage. A flexure-based XY parallel micromanipulator, which is featured with monolithic parallel-kinematic architecture, flexure hinge-based joints, and piezoelectric actuation, was presented by Y. Li [3]. Yuen

978-1-4244-5704-5/10/$26.00 ©2010 IEEE

Canada Research Chair in Robotic & Automation Laboratory, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, ON L1H 7K4, Canada {qjsong & yjge}@iim.ac.cn

Kuan Yong presented a flexure-based, piezoelectric stack-actuated XY nanopositioning to combine the ability to scan over a relatively large range (25μmX25μm) with high scanning speed [4]. Unfortunately, most of the existing micro positioning devices have no real-time force or position feedback which is crucial to in any closed-loop positioning systems [1-7]. Therefore, XY stage with integrated force sensor for micro-scale positioning, which could increase the accuracy Anti-Jamming Performance, requires further research. In this paper, we are dedicated to design a novel device with integrated force sensor and actuators based on parallel mechanism, which could be used as a micro-scale operating platform in micro manipulations. In section 2, the architecture of the 2-DOF XY stage is briefly described. Then in section 3, the Finite Element Analysis (FEA) and optimization design were performed using ANSYS. Then in section 4, the integrated sensor was introduced and force and position feedback was delivered. Finally, section 5 concisely concludes this study. II. ARCHITECTURE DESCRIPTION Figure 1 represent the designed 2-DOF piezoelectric stack-actuated stage based on flexure joints and elastic beams. The stage consists of two piezoelectric stack actuators that provide the acquired input displacements and forces alone X-axis and Y-axis, respectively; amplifying section that connect the actuators and the output stage and amplifies the displacements provided by actuators, mobile platform as the output stage and elastic beams connect the amplifying sections and the mobile platform. The stage adopts flexure hinges at all joints and has identical kinematic structure alone X-axis and Y-axis. When the limb in amplifying section of X-axis is driven by the PZT actuator with a displacement d and a force F whereas the limb in amplifying section of Y-axis remains un-driven, the limb will rotate around the left end and the right end therefore will apply the output stage with amplified displacement d’ and decreased force F’: ο݀’ ൌ

ୖାୖଵ ୖ

൉ ο݀

1494

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(1)

‫ ܨ‬ൌ

ୖ ୖଵାୖ

൉

Mz. While for planar applications, only in-plane components Fx, Fy, and Mz have substantive effects on the flexure operation. Therefore, the corresponding deformations are two translations, ୶ ǡ ୷ and one rotation, ୸ , which can be found as:

(2)

୶ǡ୊୶ ୶ ൥୷ ൩ ൌ ቎ Ͳ ୸ Ͳ

Ͳ ୷ǡ୊୷ ୸ǡ୊୷

Ͳ ୷ǡ୑୸ ቏ ൥ ൩ ୸ǡ୑୸

(4)

where ௜ǡ௝ are termed influence coefficients represents the deformation produced at i by a unit load applied at j, which together make up the compliance matrix [C]. According to the principle of reciprocity presented in [8], the in-plane generic compliance equations are: ୶ǡ୊୶ ൌ

ଵ ‫ܫ‬ ாఠ ଵ

The eight elastic beams will be deformed and the mobile platform will move along X-axis with the decoupled displacement d. For extremely small deflections, the equation for the maximum deflection under this case can be expressed as:

-

݀ൌ

ସሺோଵାோሻ

൉

ி௟య ଵଽଶா௃

ଵ

൤

ଶሺଶ௥ା௧ሻ

൨ ܽ‫݊ܽݐܿݎ‬ටͳ ൅

ாఠ ඥ௧ሺସ௥ା௧ሻ

ସ௥ ௧

െ

గ ଶ

(5)

3 2 2 8r ( 44r +28rt+5t ) ½ °2 ( 2r+t ) +t+ ° 2 2 t ( 4r+t ) 12 3 °° °° 4 3 2 2 I2 = cy,Fy = ® ( 2r+t ) t ( 4r+t ) ª-80r +24r t+8 ( 3+2 ) r t º ¾ E 4E ( 2r+t ) ° «¬+4 (1+2 ) rt 3 +t 4 »¼ ° °+ ° 5 5 t ( 4r+t ) °¯ ¿°

Fig. 1 CAD model of the stage based on flexure joints.

ோ

ൌ

8 ( 2r+t )

4

t

(3)

5

( -6r +4rt+t ) arctan 2

( 4r+t )

2

1+

4r

12 24r 2 I3 = 3 Eω Eωt 3 ( 2r + t )( 4r + t ) 2 2 ªt ( 4r + t ) ( 6r + 4rt + t ) º » ×« 4 r « +6r ( 2r + t ) 2 t ( 4r + t )arctan 1 + » «¬ t »¼

c y,Mz =

where E is Yong’s modulus, J is the moment of inertia and ݈ is the length of the elastic beams. Desired displacement value of the output stage could be derived by choosing relevant dimensions of the amplifying section and driving forces of actuators.

୸ǡ୑୸ ൌ

(6)

t

5

ଵଶ ୉ ସ

ൌ

ୡ౯ǡ౉౰ ୰

(7)

(8)

Where is the constant cross-sectional width, E is the Young’s Modulus of the joint material, t is the thickness of the thinnest portion of the joint, r is the radius of the circle.

Fig. 2 Schematic representation of the 2-DOF stage with PZT actuators.

Fig. 3 Cross-sectional profile of adopted circular flexure joint.

The coordinate and the dimensions of the adopted circular flexure joint in this study are illustrated in figure 2. The generic loading and deformations at end has six-dimensional components: one axial load, Fx; two shearing forces, Fy, Fz; one torsional moment, Mx; and two bending moments, My, 1495 Authorized licensed use limited to: University of Groningen. Downloaded on August 02,2010 at 12:06:18 UTC from IEEE Xplore. Restrictions apply.

B. Dynamic analysis

III. FINITE ELEMENT ANALYSIS AND OPTIMIZATION DESIGN

Fig. 4 Deformation occurred on the stage under one-dimensional force.

A. Static analysis In order to verify the structural behavior of the stage, finite element analysis (FEA) via software ANSYS was performed. An area force is applied on the specified area which contacts with the PZT actuator along the specified direction. Figure 4 shows the deformation occurred on the stage under one-dimensional force Fx = 100N. It is clear that the motion under single-dimensional force is decoupled and in micro scale. The system performs as a completely decoupled positioner in X-axis and a pure 590μm displacement was occurred on the platform. And the maximum positive and negative strains are located at the ends of elastic beams. In addition, as the structure is symmetrical, the result of the FEA under the other dimensional force is equivalent, the deformation and distributions of the elastic normal strain are identical. Figure 5 shows the deformation occurred on the stage under two-dimensional force Fx = Fy = 100N. It is obvious that the designed structure can deform and move alone both axes simultaneously.

Fig. 6 The first six mode shapes of the stage

When subjected to the applied loads or displacements, the compliant stage actually behaves dynamically. So we made a modal analysis via ANSYS to confirm that the sensor has a good dynamic performance such as vibration characteristics (natural frequencies and mode shapes), which are important parameters in the design of a structure for dynamic loading conditions. Figure 6 shows the result of the modal analysis, first six mode shapes of the proposed stage. We apply a fixed support to lower surface of the base, and specify the number of frequencies of interest for the first six natural frequencies without any damping condition. Finally, we get the first six natural frequencies, shown in Table I, which are helpful in understanding how the sensor vibrates. It shows that the first and second modes are the result of actuation with respect to the X- or Y-axis and are separate from modes of twisting and Z-axis.

Mode Nature Frequency (Hz)

TABLE I THE FIRST SIX NATURE FREQUENCY 1 2 3 4 1231.4

1236.1

2448.5

3109.6

5

6

3734.1

4047.2

Fig. 5 Deformation occurred on the stage under two-dimensional force.

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C. Optimization design We pose the mechanism design as a multi-objective optimization based on Design of Experiments (DOE) approach provided by software ANSYS, which can capture the behavioral changes due to parameter variations, optimize a set of goals for quantities such as stress and deflection and get the most optimal values of the parameters. In this study, we chose the design parameters to be the thickness of the thinnest portion of the joint, t, the radius of the circle, r, the length l and thickness t1 of the elastic beams subject to following bounds: 0.1mm t 1mm, 3mm r 5mm, 25mm l 35mm, 1 mm t1 3mm,

the PZT actuators to produce force and control the stage with that. In PZT actuators, force generation is always coupled with a reduction in displacement. And the maximum force a PZT actuator can generate depends on its stiffness and maximum displacement. At maximum force generation, displacement drops to zero. The maximum force a PZT actuator can generate in an infinitely rigid restraint as follow [9]: ‫ܨ‬௠௔௫ ൌ ݇௉ ‫ ڄ‬ο‫ܮ‬଴

where ݇௉ is the PZT actuator stiffness [N/m], and ο‫ܮ‬଴ is the maximum nominal displacement without external force or restraint [m]. While in actual applications, the PZT actuator is always against a finitely rigid restraint. Then the force under such application can be generated is:

with the objectives:

‫ܨ‬௠௔௫ ൌ ݇௉ ‫ ڄ‬ο‫ܮ‬଴ ቀͳ െ

500 mm/mm ε 1000 mm/mm e y dmax 0.1mm where ε is the elastic strain occurred on the elastic beams, e and y are the von Mises stress and the yield stress of the material of the stage, and the dmax is the maximum deformation occurred on the stage. The first objective can make sure the elastic beams, which will be used as elastic element of the force sensor, works within the elastic limit and have enough elastic strain to sensing the applied forces. And the second objective is to make sure the stage has a good linearity. At last, the third objective is in regard to the stability of the stage. At last, the software captures the optimal value of the design parameters: t = 0.549 mm, r = 4.32 mm, l = 28.77 mm, t1 = 2.67mm. IV. ACTUATORS Compliant stages are actuated for positioning or applying an external load on the objects. Significant actuator design parameters are: accuracy, range of motion, degree of freedom, band width (settling speed to a desired position) and linearity [1]. For the desired accuracy, we apply closed-loop control to decease the effect of the repeatability, linearity, creep and mechanical, electrical and thermal noises. The proposed system adopts PZT actuators to actuate the stage. In most applications, PZT actuators are used to produce displacement. However, in our study, it is hard to accurately control the displacement as part of the displacement generated by the PZT actuator will be lost due to the elasticity and complicated mechanism structure of the stage. So we use

(9)

௞ು ௞ು ା௞ೞ

ቁ

(10)

where ݇௦ is the stiffness of external stage, which can be calculated by the compliant mentioned above. By considering the resonance frequency and travel range of the stage, we select a PZT actuator P-888.30 of Physik Instrument Co., Ltd, whose technical specifications are shown in Table II.

Dimensions [mm] 10×10×13.5

TABLE II TECHNICAL PARAMETERS OF THE PZT Nominal Resonant Stiffness displacement frequency [N/ μm] [μm/100V] [kHZ] 11 ±20% 267 90

Blocking force [N/120V] 3500

V. SENSORS The integration of sensing and compliant mechanisms has received much less attention than has actuation. However, the function of precise detection of the deformation or force/torque is quite important to improve the operating performance of the stage. Actually, the distributed nature of static strain on the compliant stage is amenable to traditional force/torque sensing schemes. Therefore strain gauges can be used on the structure and will be sensitive to the displacements and external loadings. The sensor embedded in the compliant stage can be used as not only the feedback to the closed-loop operation of the PZT actuators but also the force/torque or deformation sensor to detect the external loadings. Strain gauges are very sensitive devices and are used with an electronic measuring unit. When the gauges are bonded to the surface, they undergo the same strain as the member surface. The resistance strain gauges are normally made parts of measuring circuits so that the changes in their resistances can be measured. The purpose of the strain gauges and bridge circuits is to convert the force and moment applied on the stage with enough sensitivity and little coupling to a voltage proportional to the strain. The orientation, the position of strain gauges arranged on the elastic elements should be determined based on the stress and strain analysis of the elastic force-sensing elements [10, 11].


To convert the change in resistance due to strain to a voltage proportional to strain a measuring circuit is used. As the Wheatstone bridge has performance such as high sensitivity, wide measurement range, simple circuit, high precision, it can meet the requirement commendably. According to the strain analysis and the arrangement scheme of strain gauges, the Wheatstone bridges connection mode of this embedded sensor is determined, as shown in Fig.10. The two groups of the strain gauges are all connected to full-bridge circuits, in which every bridge arm is a strain gauge. Fig. 7 The elastic normal strain occurred on the elastic beams when the stage subjects the force along X-axis

The positions conducive for strain gauges to detect strain, as shown in Fig.7 and Fig. 8, are the ends of the elastic beams. So, we select the inner ends the central beams to arrange the strain gauges to detect the axial strains in X-axis or Y-axis direction arose by Fx and Fy.

Fig. 10 bridge connection of the strain gauges.

When the sensor is bearing the tangential force Fx and the temperature of its environment changes, the resistances of strain gauges will change correspondingly: οோభ ோభ οோర ோర οோఱ ோఱ

Fig. 8 The elastic normal strain occurred on the elastic beams when the stage subjects the forces along X- and Y-axis simultaneously.

As shown in Fig.9, we arrange strain gauges R1, R2, R3, R4 on central elastic beams along the radial direction as group x to detect the tangential force Fx, strain gauges R5, R6, R7, R8 on the other two central elastic beams along the radial direction perpendicular to group x as group y to detect the tangential force Fy.

ൌെ

οோమ

ൌെ

οோయ

ൌ

ோమ

ோయ

οோల ோల

ൌ

ൌሺ

οோభ

ሻ ோభ ఌ

൅ ሺ ሻ௧

ൌሺ

οோమ

൅ ሺ ሻ௧

οோళ ோళ

ሻ ோమ ఌ

ൌ

οோఴ ோఴ

οோ ோ

οோ ோ

οோ

ൌ ሺ ሻ௧ ோ

(11) (12) (13)

So the output of x Group Bridge is: ௎ οோభ

οܷ௫ ൌ ቀ ସ

ோభ

െ

௎

οோభ

ସ

ோభ

ൌ ൬ʹ ቀ

οோమ ோమ

൅

οோర ோర

ቁ െ ʹቀ ఌ

െ

οோమ ோమ

οோయ ோయ

ቁ

ቁ ൰ൌ ఌ

௎௄ ସ

ሺʹߝଵ ൅ ʹȁߝଶ ȁሻ

(14)

where K is the sensitivity coefficient of the strain gaugesˈand οோ ߝ is the elastic strain of the membrane, ሺ ೔ሻఌ means change ோ೔

rate of the resistance of the strain gauge Ri due to strain οோ variation, ሺ ೔ ሻ௧ means change rate of the resistance of the ோ೔

Fig. 9 strain gauges arrangement on the elastic beams.

strain gauge due to temperature variation. In a word, the strain gauges arrangement and bridge connection scheme mentioned above can determine the magnitude of a force applied to the stage without coupling. If the strain gauges are located in the perfect places, it can allow each axial force to generate output voltage of bridge circuit on the corresponding axial direction. For example, when bearing the tangential force Fx, the sensor should only have output


voltages of group X. Therefore, the force sensor can directly get the force value through measuring the output voltage of bridge circuit on each axis. In addition, the sensor features hardware temperature compensation to stabilize its sensitivity over temperature. And this compensation method optimizes the accuracy over a range approximately from -50 to +80 degrees Celsius. VI. CONCLUSION This study has endeavored in designing a novel two-dimensional flexure hinges based XY stage with embedded force sensor for micro-scale positioning. The main sensitive dimensions are chosen by optimization design to ensure the stage have a good performance. And the design possesses configurational simplicity and compactness. After added close-loop control with the force feedback provided by the embedded sensor, the stage can provided completely decoupled displacement along X- or Y-axis with high precision and resolution. ACKNOWLEDGMENT This work is financially supported in part by the National 863 Project under Grant No. 2006AA04Z244 and National Nature Science Foundation of China under Grant No. NSFC60874097, NSFC60910005. The authors gratefully acknowledge Jun Ma, Yijun Wang, Wenfa Ya and Yuping Sun (Institute of Intelligent Machines, Chinese Academy of Sciences) for their great technological supports. The first author gratefully acknowledges the financial support from the China Scholarship Council, Ministry of Education of the P.R.C. and Innovation Program of USTC, and the second author appreciates the financial support from the Canada Research Chairs program.

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