Performance of single-crystal Pb(Mg[sub 1∕3]Nb[sub 2∕3])-32%PbTiO[sub 3] stacked actuators with...

Performance of single-crystal Pb„Mg1/3Nb2/3…-32%PbTiO3 stacked actuatorswith application to adaptive structures

Shane C. Woodya�

2750 East WT Harris, Suite 103, Charlotte, North Carolina 28213

Stuart T. SmithUniversity of North Carolina at Charlotte, Department of Mechanical Engineering,Center for Precision Metrology, 9201 University City Boulevard, Charlotte, North Carolina 28213

Xiaoning Jiang and Paul W. RehrigTRS Technologies, 2820 E College Avenue, Suite J, State College, Pennsylvania 16801

�Received 19 March 2005; accepted 29 May 2005; published online 12 July 2005�

This article presents the performance of ultra-high-strain single-crystal piezoelectric stackedactuators using the composition Pb�Mg1/3Nb2/3�-32%PbTiO3 �PMN-32%PT�for adaptive structures�in particular for space-based applications�. Generally, dimensionally adaptive or smart structuresoften utilize piezoelectric actuators �in particular lead zirconate titanate �PZT� elements� to providehigh-frequency response motion. However, most commercial stacks are limited in range �often�0.1% strain� and the motion is further reduced at low or cryogenic temperatures for satellite-basedand many other applications. Comparatively, single-crystal actuators such as the ultra-high-strainPMN-32%PT provide greater than a factor of 4 displacement, factor of 2 strain energy density, andcryogenic displacements are comparable to room-temperature conditions for PZT actuators.Nonetheless, there are some technological and fundamental limitations, such as plate thickness,which is generally greater than 0.5 mm, low elastic modulus, and low strain at each end of thestacks. Three stack configurations with 3, 5, and 40 active layers are tested and discussed. Thisreport discusses each configuration type as a function of lost motion, obtainable strain rates, preloaddesigns, applied stiffness, stress gradients, electric fields, and bandwidth performances. The resultsobtained in this study aim to show performance and discuss the relative merits and limitations ofusing this actuator material for adaptive structures. A case study is presented for a high bandwidthsteering mirror using ultra-high-strain single crystals. Closed loop control results from theplatform’s response are briefly discussed. © 2005 American Institute of Physics.�DOI: 10.1063/1.1984974�

I. INTRODUCTION

In the 1990s, the relaxor-based single-crystal piezoelec-tric materials such as Pb�Mg1/3Nb2/3�O3–PbTiO3 �PMN–PT�were discovered, and demonstrated unusually high strains forpiezoelectric applications.1–3 In recent years, application ofthese ultra-high-strain single crystals have been explored indevelopments for underwater imaging as transducers4 andacoustic amplifiers,5 medical ultrasound,6 and adaptivestructures.7,8 As an acoustic device, compared to piezoelec-tric actuators, single crystals have exhibited 3–15 dB higheroutput power over a frequency range from 1–25 kHz. Cor-respondingly, compared to lead zirconate titanate �PZT� ele-ments, as a transducer device the single crystals have showna bandwidth increase of 20%–25% and an increase of3–5 dB in sensitivity. Still further, single crystals have ad-vantages in adaptive structures for high end performancestacked actuators. Research has indicated the stacked actua-tors provide a factor of 2 higher strain energy density, strainsexceeding 1%, which is a factor of 10 higher and, whenapplied fields are maintained below the phase transition, a

lower loss in heat dissipation due to improved hysteretic be-havior. Cryogenic applications are also favorable for singlecrystals. PZT displacements are significantly reduced atcryogenic temperatures, while the PMN-32%PT displace-ment provides comparable displacement to PZT at room-temperature conditions.

The aim of this article is to discuss investigations ofusing PMN-32%PT stacked single crystals as actuators foradaptive structures in space applications. In particular, threeactuator configurations are assessed that include stacks with3, 5, and 40 active layers. Several issues for integratingsingle crystals address the effects of mechanical compliancesbetween actuator and driven stage �lost motion�, mechanicalstiffness, avoidance of sharp stress gradients in the stack,stack boundary conditions, bandwidths, and power consump-tion �see Secs. II and III�. Finally, a case study for a faststeering mechanism using short range ultra-high-strain singlecrystals for active jitter compensation will be presented andbriefly discussed �see Sec. III�.

II. PMN-32%PT ACTUATOR PERFORMANCE

Several factors should be considered when integratingthe single-crystal actuators into closed loop control systems.a�Electronic mail: [email protected]

REVIEW OF SCIENTIFIC INSTRUMENTS 76, 075112 �2005�

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http://dx.doi.org/10.1063/1.1984974

First, power consumption and subsequent dissipation oflosses in the actuator are concerns in some systems such assatellite-based applications. An actuator’s power require-ments are dependent upon the piezoelectric compositionproperties, maximum strain, thickness of the plate elements,and operating bandwidth. Approximate equations for predict-ing the capacitance C, maximum applied voltage V, Crosssectional area A, and power P are as follows:

C =K3�T��oAn

t, �1�

V = Emaxt , �2�

P = 2�fCV2. �3�

Table I defines these terms and provides a comparisonbetween the TRS200 �high-performance PZT� and the PMN-32%PT, which are both supplied by TRS Technologies. Thetable outlines the actuator requirements for a scenario thatwould require 100 �m of motion. As shown in this table, thesingle-crystal PMN-32%PT is prepared with d33 typically be-ing in the range 1800–2200 pm V−1, a dielectric constant of5500–6500, and a maximum of 10% hysteresis. Based uponthese values, the total number of required active layers forthe single crystals is 45 in order to achieve 100 �m of mo-tion in closed loop control �after the effects of hysteresis�. Asshown, the PMN-PT stacked actuator would be scaled downin length by a factor of 4 compared to the PZT and is 14%higher in stiffness. The PZT generates higher voltage re-quirements to achieve 0.15% strain with a correspondinglyhigher capacitance load, and as a result, the applied power isgreater than 200%. As shown, the benefits clearly show asmaller stacked actuator is achievable and power require-ments are significantly less compared to the PZT stacks.

Furthermore, the stacked actuator is typically preloadedinto a mechanical system, often a carriage guided by a flex-ure, which has an inherent stiffness. The mechanical losses,which are the difference between the predicted motion for anideal electromechanical system and that obtained in practicaldesigns, are typically referred to as fractional loss of motionor sometimes simply “lost motion.”9 This can be visualizedas the increase in preload by the external flexure as the ac-

tuator applies a force to displace it. The lost motion is de-pendent upon the longitudinal stiffness of the actuator andthe flexure stiffness and can be approximated from

f =KC

�KP + KC�, �4�

where f is the lost motion, Kc is the carriage stiffness, and Kp

is the effective actuator stiffness. As the flexure stiffness ap-proaches the equivalent stiffness of the actuator, the lost mo-tion will converge to 0.5 or 50% lost motion. This is, ofcourse, undesirable; the carriage stiffness should be designedto be significantly less than the actuator stiffness.

The PMN-32%PT has clearly indicated significant per-formance improvements compared to conventional PZTcompositions �Fig. 1�. In Fig. 1�a�, an LVDT test stand ca-pable of applying prestress to the stacks was previously de-

TABLE I. Actuator comparison �PZT vs PMN-32%PT� to achieve 100 �mof motion.

Parameter TRS200 �PZT� PMN-32%PT

D33-piezoelectric constant �pm V−1� 330 2000K3�T�-relative dielectric factor 1720 5000

hysteresis �%� 30 10�-strain �%� 0.15 0.5

t-plate thickness �mm� 0.5 0.5d-Cross-sectional diameter �mm� 10 10

n-number of active layers 190 45C-capacitance �nF� 455 313

E-elastic modulus �GPa� 59 16Stiffness �N �m−1� 19 22

V-voltage �max� �kV� 1.6 1.2Applied power @ 500 Hz and 1 kV

pk-pk �kW�3.6 1.2

FIG. 1. �Color online� Overview of single-crystal performance data. �a�Cryogenic investigations with single crystals. �b� Strain versus electric fieldPMN-PT experimental analysis.

075112-2 Woody et al. Rev. Sci. Instrum. 76, 075112 �2005�


signed to fit within a helium cryostat. Strain measurementswere made point-by-point �apply voltage, record strain, re-move voltage, repeat at higher voltage� over temperaturesranging from ambient down to 30 K. At 30 K the actuatorhas a d33 equivalent to PZT-5A ceramic at room temperature.In addition to enhanced cryogenic performance, the PMN-32%PT is capable of sustaining high applied electric fieldscompared to PZT actuators. Often, PZT compositions arefundamentally limited to 20–30 kV cm−1 before breakingdown. However, the single-crystal actuators have demon-strated significant improvement compared to PZT elements�Fig. 1�b��.

An experimental study was undertaken to assess single-crystal actuators as a function of preload, stiffness, and cy-clic loading. A mechanism by which stiffness and preloadmay be readily changed and measured was designed, manu-factured, and characterized. To accomplish this goal, threeflexure mechanisms were designed and fabricated. Mecha-nism A is shown in Fig. 2�a�, wherein six leaf flexures areconstrained between a rigid frame and a central carriage. Thecenter mass platform is constrained only by the flexure ele-ments and the actuator under test. The two rigid mass com-ponents on the outer part of the mechanism connecting to thecentral carriage through the six flexures shown in mechanismA are bolted to a rigid frame. Additionally, an actuator cou-

pling interface is monolithically incorporated with the centermass and is used to contact one end of the actuator stack�Fig. 2�b��. The actuator coupling incorporates a further flex-ible element that is designed to provide compliance to ac-commodate yaw motion errors during assembly and installa-tion of the actuator. This apparatus is considered to providean adequate interface contact with the actuator stack whilehaving sufficient off-axis freedom to accommodate manufac-turing and assembly tolerances. Two secondary mechanisms�referred to as mechanisms B and C� are also used to provideincreased stiffness to the overall mechanical structure.Mechanism B, mechanism C, or a combination of both maybe mounted to mechanism ‘A’, as shown in Fig. 2�b�. Eachsecondary mechanism’s rigid mass outer elements and centermasses can be bolted to mechanism A by way of tappedholes located on mechanism A. A total of four mechanismconfigurations and stiffnesses’ may be obtained for this ex-periment, values of which are listed in Table II. The stiffnessis experimentally measured by vertically aligning the flex-ures with respect to gravity and measuring the deflection dueto an applied load. The experimental stand is designed toapply both variable preloads ranging from 50 to 400 N andapparent load stiffness values between 2 to 13 N �m−1.

A multichannel high-voltage amplifier with a high band-width response is also fabricated for this experimental study.Each amplifier channel is equipped with 0–1000 V, up to300 mA and a large signal bandwidth of 5 kHz. To assess thestacked actuator, the flexure mechanism was mounted on topof a single-axis dovetail slideway �partially shown in Fig. 2�.The slideway is rigidly clamped to a larger aluminum baseand a large aluminum block that serves as the base of theactuator is mounted in front of the slideway. The large blockcontains a second actuator coupling which has a pitch rota-tional degree of freedom with respect to the principle axes ofmotion; again, to accommodate errors in manufacture andassembly. When assembled, the stacked actuator is posi-tioned between the fixed actuator coupling �located on thelarge block� and the second actuator coupling attached to theflexure mechanism. A micrometer that is fashioned to thebase of the slideway is used to translate the mechanism intocontact with the actuator. A Michelson interferometer systemis used to detect the deflection of the mechanism when con-tact between the actuator couplings occurs. Based on theknown stiffness of each mechanism combination and deflec-tion as measured by the interferometer, the micrometer isadjusted until the desired preload is obtained. To decouplethe distortions of the slideway assembly from the measure-ment loop, the interferometric beam splitter is positioned andrigidly mounted to the top platform of the slideway. Thisconfiguration monitors the deflection of the mechanism as a

FIG. 2. �Color online� Flexure designs employed in this experiment. �a�Solid model of flexure mechanism A. �b� Typical test stand with flexures Aand B combined in series.

TABLE II. Mechanism configurations and corresponding stiffness.

Flexure configuration Stiffness along principle axis �N �m−1�

A 2.7A-B 5.9A-C 8.97

A-B-C 12.39

075112-3 Performance of single crystal PMN-32%PT Rev. Sci. Instrum. 76, 075112 �2005�


function of the force applied to the central mass. Consideringdistortions will occur on the actuator’s rigid block when aforce is applied from the slideway, one of the interferometerreference mirrors is positioned on top of the rigid block. Inthis manner, with a differential measurement from themounts on either side of the actuator, any motions due todistortion of the test apparatus are not included in the deflec-tion measurements.

In initial tests, a PMN-32%PT single-crystal stacked ac-tuator with a cross-sectional area of 5.0 mm�5.0 mm andten layers, each 0.5 mm thick, was used. Cap plates werealso placed on each end of the actuator to provide an elec-trical isolation. This test assesses the actuator’s output strainversus applied electric field �Figs. 3�a� and 3�b��. The flexureA applied an equivalent prestress to the actuators rangingfrom 2 to 16 MPa. As shown, the strain compared to thesame applied electric field substantially increased from 0.2%to 0.4% due to an increase in the prestress. Furthermore, alarger hysteresis was shown to occur for the 8 and 16 MPaprestress, which is due to a compositional phase transition.Often, a phase transition occurs as the prestress is increasedand will result in increased strain and hysteresis. Althoughthe strain is shown to increase with higher prestress, the re-

liability at these performance levels have not been assessed.To measure the same stack at a factor 4.5 higher stiffness theflexure A-B-C was used �Fig. 3�b��. As shown, the slope forthe strain versus applied electric field attenuates by approxi-mately 50% compared to an applied stiffness of 2.7 N �m−1.As a result, the fractional lost motion was determined to be afunction of preload as well as mechanical stiffness relative tothe actuator longitudinal stiffness �d33 orientation�. Clearly,the stiffness of the adaptive structure compared to the stiff-ness of the single-crystal actuator is a critical design factor,as implied by Eq. �4�.

To assess possible fatigue or aging, the actuator wassubject to a 100 N preload and cycled for a total 100�106 cycles using a Tektronix® CFG253 signal generatorand using an Insitutec HV150031 high-voltage dynamic am-plifier �Fig. 4�. The first actuator assessed was cycled from50 to 905 V at 227 Hz for five days and is referred to as thefirst cyclic test. During this experiment, it was necessary tomonitor the response of the actuator and to determine if andwhen failure occurs. To do this, an acoustic microphone ispositioned near to the actuator element and the signal fromthe microphone monitored by a Stanford SRS850 lock-inamplifier. The reference signal transmitted to the high-voltage amplifier ultimately generates an acoustic signal thatis transferred to the lock-in amplifier and is used as the ref-erence frequency. The amplitude deviation between the ref-erence and microphone signal is monitored throughout theexperiment �Fig. 4�. The first actuator was not observed tofail up to 100�106 cycles. The experiment was discontinuedafter a short period of time. Afterwards, a second stack withsimilar experimental constraints was investigated until fail-ure occurred. In Fig. 4, the second stack is referred to acyclic test number 2 and is observed to fail after more than660�106 cycles. Although further data are required, thesepreliminary tests have indicated long life is achievable undersevere constraints �high-voltage amplitudes, continuous fre-quencies, and applied stiffness�.

In a second set of tests, three types of PMN-32%PTconfigurations were evaluated. The stacks were fabricatedwith stacked disks of 10 mm diameter and 0.5 mm thickness.The configurations consisted of 3, 5, and 40 active layers,with each stack having a single, passive cap of thickness

FIG. 3. Strain vs voltage for a 5�5�5 mm3 stacked actuator. �a� Prestressto flexure A with an applied stiffness of 2.7 N �m−1. �b� Prestressed toflexure A-B-C with an applied stiffness of 12.7 N �m−1.

FIG. 4. Amplitude vs cyclic loading for two separate actuators �experimen-tal conditions included 100 N preload, 50–950 V peak-to-peak at 227 Hz�.



1.0 mm at each end �Fig. 5�a��. The initial strain tests inves-tigated single-crystal stack prototypes using an linear-voltagedifferential transformer �LVDT�-based strain measurementsystem �Fig. 5�b��. The LVDT �Schaevitz HR series, e.g.,HR050� with a 10 nm resolution was used to measure thedisplacement of the stack actuator under an applied electricfield �Fig. 6�a��. As shown, the LVDT test stand measuredthe 40 active layer actuator up to 0.35% strain at20 kV cm−1. In terms of displacement, the 40 active layeractuator extended 54 �m at 15 kV cm−1 and 69 �m under20 kV cm−1.

Following this, the stack was inserted into a circular diskcoupling flexure and preloaded to approximately 100 N. Atest stand was devised employing a flexure mechanism withan inherent stiffness of 2.7 N �m−1 �Fig. 6�b��. The stiffnessof this mechanism is a factor of 30 higher than typically usedin our adaptive structures.10 Such a high stiffness was chosento show clearly the affects of lost motion. The stacked actua-tor and preload mechanism are inserted between a rigid baseand the flexure test stand. A Lion Precision™ capacitive sen-sor with a resolution of 10 nm is mounted directly behind theflexure mechanism and collinear with the actuator. The flex-ure mechanism and capacitive sensor are both mounted ontop of a coarse slideway. The micrometer attached to theslideway is used to adjust the flexure mechanism into contactwith the stacked actuator. Once in contact, the flexuremechanism will deflect in the opposite direction of the trans-lation stage due to the reaction force from the stacked actua-tor. Based on the measured deflection after initial contact, thepreload force exerted on the stacked actuator may be esti-mated using the known inherent stiffness of the flexure teststand. In these experiments, the test stand was adjusted to a400 N preload, thereafter, the coarse slideway is rigidlyclamped. Following this, the capacitance sensor is set to zeroand actuator is cyclically ramped from 0 to 1000 V �corre-sponding to 20 kV cm−1�.

The results for the 40 active layer stack are shown inFig. 6�b�, where the maximum strain at 20 kV cm−1 was0.25%. This reduction in strain compared to the LVDT mea-surement is due primarily to the high stiffness of the me-chanical flexure in the test stand. In general, the stiffness ofan adaptive structure should be less than the actuator stiff-ness in order to minimize the effects of lost motion. Subse-quently, the 40 active layer PMN-PT is compared with a PZTstacked actuator of equivalent active length. The PZT stackis a Tokin™ actuator with a cross section of 5.0�5.0 mm2

and a length of 20 mm. The overall displacement is quotedas 18 �m, which is equivalent to 0.09%. The PZT stack istested under similar conditions of preload and applied stiff-ness. As shown, the PMN-PT generated a factor of 3 higherstrain at 0.27% compared to the conventional PZT stack at0.07%. The PZT also clearly shows a lost motion of approxi-mately 22% compared to the manufacturer’s specifications.Additionally, the PZT stack is limited to approximately15–20 kV cm−1, whereas the PMN-PT may be operated withapplied fields of up to 100 kV cm−1. Theoretically, single-plate elements have achieved significantly higher electricfields �100 kV cm−1, which is a factor of 5 higher than cur-rently measured. Currently, the stacked actuators have onlybeen assessed below 20–30 kV cm−1. However, at fields sig-nificantly higher than 30 kV cm−1 there is a phase transitionthat significantly increases the hysteresis. Nonetheless, even

FIG. 5. �Color online� �a� Photograph of the 40 and 3 active layer PMN-PTstacks. �b� LVDT setup for d33 �strain-electric field� measurement.

FIG. 6. �Color online� Comparison between PZT & PMN-PT actuators. �a�Strain vs electric field �the PZT and PMN-32%PT are measured in an “ap-plied stiffness” test stand with an inherent stiffness of 2.7 N �m−1�. �b�Photographs of the PZT and PMN-PT actuators mounted into the test stand.



at these applied fields, the PMN-32%PT provides a threetimes higher strain at 20 kV cm−1 compared to PZT ele-ments.

Results from tests on the three and five active layerstacks are shown in Fig. 7. Similar to the previous test, the

short stacks are preloaded into a flexure mechanism to ap-proximately 100 N �i.e., a pressure of 1.3 MPa� and this pre-loaded mechanism then inserted into the test stand, afterwhich there is an applied stiffness of 2.7 N �m−1 added tothe stack. The three active layer stack provided significantlyless strain compared to the 40 �see Fig. 6� and five activelayer stack �the effective d33 is only about 850 pC N−1, halfof the PMN-PT plate properties�. The three active layer stackproduced 0.15% strain compared to the five active layerswhich generated greater than 0.25% strain. This reduction instrain is due to the sharp stress gradient located at the end-cap and the PMN-PT interface, illustrated in Fig. 8. Thebonding of the active plates to the passive end-caps limits thestrain of the two end active layers due to the low Young’smodulus of single-crystal materials, causing an overall lowerstrain in the three-layer short stack. As the PMN-PT expandsin the d33 direction �vertical direction in this figure�, it cor-respondingly contracts in the lateral direction. Constraint bythe passive end-cap produces a lateral force at this interfaceand lowers the maximum strain. Several techniques may beapplied to increase the displacement output.

The impedance and phase of the stack actuator vibrationwas tested using an HP impedance analyzer to record theresonance frequency of the stack actuator, which indicatedthe actuator response time �Fig. 9�. The resonant frequencyof the stack is about 30.5 kHz, indicating the fast actuationresponse of the actuators for high bandwidth motion controlsystems. The less spurious mode also indicates a good stackassembly process without cracks or gaps in the stack.

FIG. 7. �Color online� Characterizing the three and five active layerPMN-PT stacked actuators. �a� Short stacked actuator employing five activelayers and preloaded in a flexure mechanism. �b� Strain vs applied electricfield.

FIG. 8. �Color online� Explanation of the short stacked actuators with lim-ited boundary conditions �three vs five active layers�.

FIG. 9. Resonance measurement for a 40 active layerstack.



III. ADAPTIVE STEERING MECHANISM

Steering mechanisms in satellite based applications aretypically fraught with jitter problems, which may be due toatmospheric turbulent problems.11 Jitter sources are alsofound in the pressure recovery system for high-energy lasersources.12 In recent years, high bandwidth steering mecha-nisms have been assessed and developed to actively compen-sate jitter and to thus provide a stable means for locking ontoa source.13 The ultra-high-strain single crystals are poised toprovide an optimal solution for high bandwidth actuation dueto lower power requirements, higher strain energy densities,and higher strain rates at cryogenic temperatures. As a result,the small stack actuators �five active layers� were tested in afast steering mirror with a 300 mm diameter platen servingas the mirror �Fig. 10�a��. The 300 mm diameter platenshown was preloaded on top of three short stacked actuators.The actuators were equispaced 120° and positioned at theairy point to minimize the effects of structural bending. Asensor fixture with Lion Precision™ capacitive gauges wereused to measure the displacement of the steering platen rela-tive to a fixed frame �Fig. 10�b��. A multichannel high-voltage amplifier with 300 mA, 1000 V supply and lownoise was developed in-house. The high-voltage amplifiersserved to supply voltage to the three short stacked actuators.Next, the steering structure was closed loop controlled usinga dSPACE™ digital controller with 16 bit precision AD andDA converters and 100 ksps update rates. A 300 Hz sinu-soidal with an amplitude of ±20 �rad was input into one ofthe rotational degrees of freedom �Fig. 11�a��. The corre-sponding following error using an integrator term and feed-forward algorithms was found to be ±0.5 �rad peak-to-peak�Fig. 11�b��.

In general, single-crystal stacked actuators such as thePMN-32%PT provide significant performance advantagescompared to piezoelectric actuators. This article has demon-strated that at least a factor of 2 lower power requirementsmay be achieved, greater than a factor of 3 strains may begenerated, higher displacements at cryogenic temperatures,and high bandwidth are exhibited from the ultra-high-strain

single crystals. Adaptive structures in general will benefitfrom the single-crystal actuators such as active flaps in rotor-crafts, high-speed nanopositioning systems for imaging inlife science, and high-speed positioning systems within thechip industry.

ACKNOWLEDGMENTS

The authors are grateful to the Missile Defense Agency�MDA� for providing funding under Contract No. HQ0006-04-C-7063 and to Dr. Arup Maji at the AFRL/Space VehiclesDirectorate for his technical support throughout this project.Furthermore, many of these investigations were carried outat UNC Charlotte’s Center for Precision Metrology.

1 S. E. Park and T. R. Shrout, J. Appl. Phys. 82, 1804 �1997�.2 S. E. Park and T. R. Shrout, IEEE Trans. Ultrason. Ferroelectr. Freq.Control 44, 1140 �1997�.

3 S. E. Park and W. Hackenberger, Curr. Opin. Solid State Mater. Sci. 6, 11�2002�.

4 R. J. Meyer, A. Dogan, C. Yoon, S. M. Pilgrim, and R. E. Newnham,Sens. Actuators, A 87, 157 �2001�.

5 J. F. Tressler, T. R. Howarth, and H. Dehua, Oceans Conference Record�IEEE�, 2003, Vol. 5, p. 2372.

6 T. R. Gururaja, R. K. Panda, J. Chen, and H. Beck, IEEE UltrasonicsSymposium, 1999, p. 969.

FIG. 10. �Color online� High bandwidth steering mechanism. �a� Photo-graph of platen integrated with single-crystal actuators and platform. �b�Steering structure and test stand.

FIG. 11. �Color online� Closed loop controlled response for �x at 300 Hzand ±20 �rad. �a� Response of the platform �b� following error of the plat-form.



7 W. Hackenberger, P. Rehrig, M. J. Pan, and T. Shrout, Proc. SPIE 4333,92 �2001�.

8 S. C. Woody and S. T. Smith, Rev. Sci. Instrum. 75, 842 �2004�.9 S. Smith, Flexures: Elements of Elastic Mechanisms �Gordon and Breach,New York, 2002�.

10 S. C. Woody and S. T. Smith �unpublished�.11 K. Lukas, Proc. SPIE 5240, 26 �2004�.12 R. M. Glaese, E. H. Anderson, and P. C. Janzen, Proc. SPIE 4034, 151

�2000�.13 M. R. Schulthess and S. Baugh, Proc. SPIE 2468, 206 �1995�.



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