108 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 24, NO. 1, FEBRUARY 2015

Millimeter-Scale Traveling Wave RotaryUltrasonic Motors

Ryan Q. Rudy, Gabriel L. Smith, Don L. DeVoe, and Ronald G. Polcawich, Member, IEEE

Abstract— Bidirectional rotary motion of a millimeter-scaletraveling wave ultrasonic motor is demonstrated using solution-deposited thin-film lead zirconate titanate and wafer-scalemicroelectromechanical system fabrication techniques. Rotationspeeds of a motor 3 mm in diameter have been characterizedup to 2000 r/min as a function of voltage, phase, and fre-quency, with power consumption less than 4 mW. Frequencycharacterization shows no nonlinear behavior, while phase char-acterization shows that motion can be generated with a singlesource drive. Furthermore, imprint in the piezoelectric responsewas exploited to achieve higher speeds, starting voltages lowerthan 4 V, and demonstration of a 2-mm diameter motor upto 1730 r/min. Design and fabrication of the motors are alsopresented. [2013-0032]

Index Terms— Micromotors, piezoelectric films, traveling wavedevices, PZT ceramics.

I. INTRODUCTION

ULTRASONIC motors, known for their compact size andhigh torque at the macro-scale, can be reduced in size

by an order of magnitude through the use of microfabrica-tion techniques, opening the door to new high-performancerotary actuators at the millimeter scale and below. In thepresent work we use thin-film lead zirconate titanate (PZT)and microelectromechanical system (MEMS) fabrication tech-niques to create a millimeter-scale traveling wave ultra-sonic motor (TWUM). Our previous work includes report ofbi-directional rotor motion as described in [1], while standingand traveling wave characterization is described in [2]. Beyondpreviously published work, the authors present here enhancedmotor performance leveraging the imprint characteristics ofthe PZT thin films, further characterization of rotor speed as afunction of actuation voltage, frequency, and phase offset, andthe demonstration of a 2 mm diameter TWUM. To the authors’knowledge, this motor represents the smallest demonstrated

Manuscript received January 30, 2013; revised March 27, 2014; acceptedApril 7, 2014. Date of publication June 4, 2014; date of current versionJanuary 30, 2015. The work of R. Q. Rudy was supported by the Science,Mathematics, and Research for Transformation (SMART) Program. SubjectEditor K. F. Bohringer.

R. Q. Rudy is with the Sensors and Electron Devices Directorate, U.S. ArmyResearch Laboratory, Adelphi, MD 20783 USA; and also with the MechanicalEngineering Department, University of Maryland, College Park, MD 20742USA (e-mail: ryan.q.rudy.ctr@mail.mil).

G. L. Smith and R. G. Polcawich are with the Sensors and Electron DevicesDirectorate, U.S. Army Research Laboratory, Adelphi, MD 20783 USA(e-mail: gabriel.l.smith.12.civ@mail.mil; ronald.g.polcawich.civ@mail.mil).

D. L. DeVoe is with the Mechanical Engineering Department, Universityof Maryland, College Park, MD 20742 USA (e-mail: ddev@umd.edu).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2014.2317778

traveling wave ultrasonic motor to date and the only successfuldemonstration of a TWUM using wafer-scale microfabrication.

Advantages of TWUMs include high torque output, lowspeed operation without the need for reducing gears, compactprofiles, and quiet operation [3]. Despite these beneficialcharacteristics, miniaturization of TWUMs has largely stalleddue to limited manufacturing precision associated with existingfabrication approaches [4]. The application of monolithicMEMS fabrication techniques to the challenge of TWUMdevelopment provides a new approach to achieve high pre-cision and high accuracy features, through photolithographicpatterning of piezoelectric films and surface and bulk micro-machining of silicon substrates. Ultrasonic actuation has beenpreviously realized with thin-film PZT combined with MEMSfabrication techniques [5].

Beyond TWUMs, alternative motor technology, such aselectromagnetic motors and electrostatic motors, does notscale well to the millimeter domain. Electromagnetic motorefficiency drops quickly with decreasing size and the largecoils required pose miniaturization problems [6]. Electrostaticmotors function well at the micrometer-scale, however largevoltages are necessary to operate the motor and torques arerelatively low compared to TWUM [7].

Much work has been done in the field of TWUMs. Fol-lowing Sashida’s invention of the first TWUM in 1983 [8],the technology was quickly commercialized for use incamera auto-focus mechanisms [9] and wrist watches [10]. Theoriginal motivation for the invention of the TWUM, creating amechanical hand highlighting the high torque and compactnessof the motor, was recently realized as reported in [11].

While many macro-scale TWUMs, have been developed fora wide range of applications, ultrasonic motors at the millime-ter scale reflect a more recent development in the field. Muchof the initial innovation in this area was reported by Flynn [12],and the present work shares several attributes with the workin [12] including the use of thin-film piezoelectric actuationand established traveling wave stator designs. In contrast to thework in [12], Flynn reported only uni-directional rotation withno definitive explanation provided as to why bi-directionalrotation could not be achieved (fabrication asymmetries pre-venting two required standing waves at the same frequency aresuggested as a possible cause) [13]. This work demonstratesbi-directional operation, unlike [13], with speeds almost tentimes higher than reported in [13].

Other ultrasonic piezoelectric motor research of noteincludes Uchino’s 1.6 mm diameter, 4 mm long motor whichboasts impressive motor characteristics and a simple design

1057-7157 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

RUDY et al.: MILLIMETER-SCALE TRAVELING WAVE ROTARY ULTRASONIC MOTORS 109

Fig. 1. This exploded view of one embodiment of the conceptual motorshows the silicon stator with PZT deposited and patterned, which is electricallyconnected through copper posts in the center. The stator teeth amplifythe surface motion and frictionally couple to the rotor, which is made ofelectroplated copper.

consisting of only 4 components [14]. Differences betweenUchino’s motor and this research, include the thin profile ofthe current work (500 μm thick with 450 μm inactive substratewhich can be thinned), parallel batch production enabled byMEMS fabrication processing, and arguably more applicationflexibility with an ease of integrating a variety of rotors.Piralta et al. have also recently reported on a millimeter scaleTWUM [15], however this is a non-contact ultrasonic motorallowing for high speeds. These non-contact ultrasonic motorsare unable to produce large torques as described in [16].Muralt created a standing wave ultrasonic motor, which usesthin-film PZT, however the design of the motor only enabledunidirectional motion, whereas the current work producesbi-direction motion [17]. Tang et al. have also recently reporteda standing wave magnetoelastic ultrasonic motor capable ofbi-direction rotation using different actuation frequencies [18].The main novelty in [18] appears to be the wireless drive,however it appears that motor speed and torque are much lowercompared to piezoelectric ultrasonic motors.

Macro-scale TWUMs have been shown to exhibit nonlinearresonance effects which can result in sudden stoppage dueto catastrophic jumps in the frequency response [19]. Forthis reason, frequency characterization was performed on themillimeter-scale TWUM to investigate this effect.

This article will detail the speed characteristics of a thin-film TWUM as a function of actuation voltage, frequency,and phase offset. Torque-speed characteristics of a motor arereported, as well as enhanced motor performance leveragingthe imprint characteristics of the PZT thin films, a review thefabrication process, and an analysis of the center anchor motordesign.

II. MOTOR CONCEPT & DESIGN

A. Conceptual Design

The conceptual design of this small-scale TWUM utilizeschemical solution deposited thin-film PZT with a Zr/Ti ratio of52/48 at an approximate thickness of 1 μm. Integrated batch

Fig. 2. A micrograph of the 3mm diameter stator shows the gold bond padsfor wirebonding, segmented platinum electrodes on PZT for actuation, andhandle wafer etch holes for backside vapor HF release of the buried oxide.

fabrication of stator and rotor components will be realizedthrough a PZT on silicon-on-insulator (SOI) stator wafer andmulti-layer electroplated copper rotors. An exploded view ofthe conceptual design is shown in Fig. 1.

In this design, the bottom center fixed disk, or stator,vibrates and waves propagate about the disk. The columnsprotruding from the stator, called stator teeth, act to amplifysurface motion to increase speed. The rotor moves when thestator teeth frictionally couple to the rotor. It is proposed thatthese stator teeth, as well as the rotor, can be fabricated using amulti-layer electroplating process currently under developmentand beyond the scope of this paper.

B. Proof-of-Concept Motor

In order to demonstrate the feasibility of the conceptualdesign outlined above, proof-of-concept motors were created.A micrograph of a fabricated 3 mm diameter stator componentis shown in Fig. 2. A proof-of-concept system was assembledto demonstrate the motor and to investigate motor character-istics. A 2 mm diameter proof-of-concept motor is shown inFig. 3. To the authors’ knowledge, this 2 mm diameter motorrepresents the smallest traveling wave motor reported in theliterature. In this prototype, stator teeth are omitted and wirebonds to the center are used to make electrical connection.Rather than electroplated copper, the rotor is made of siliconand is manually positioned on the stator before wire-bonding.

C. Operating Principle

In a TWUM, a propagating elastic wave travels throughthe stator and creates elliptical motion at the surface of thestator. This elliptical surface motion is then coupled to therotor through friction. The motion is rectified by intermittentcontact with the rotor, allowing the stator surface points toapply force in only one direction while tracing the ellipticalorbit. This operating principle is illustrated in Fig. 4.

This propagating elastic wave is often excited using piezo-electric materials (e.g. PZT), which strain when exposed to an

110 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 24, NO. 1, FEBRUARY 2015

Fig. 3. A micrograph of the 2 mm diameter proof-of-concept motor displaysthe assembled motor with gold wires bonded to the stator through the centerhole of the rotor.

Fig. 4. Illustration of operating principle of the TWUM is shown.The traveling wave creates elliptical motion at the surface of the stator. Thismotion is frictionally coupled to the rotor causing rotation.

electric field. The traveling wave is excited by simultaneouslyexciting two standing waves separated in space and phase butoccurring at the same frequency. Two orthogonal resonancemodes are often used because resonance amplification pro-duces large out-of-plane deflections which correlate to bettermotor characteristics. The two orthogonal resonance modesare excited 90° out of phase. These two modes combine tocreate a traveling wave, by the trigonometric identity in (1).

sin(nθ) sin(ωt) + cos(nθ) cos(ωt) = cos(nθ − ωt) (1)

In this equation, n is the number of nodal diameters, θ isthe angular polar coordinate, ω is the actuation frequency,and t is time. Through finite element modeling and laserDoppler vibrometry, the modal response was modeled andcharacterized as detailed in [2]. The B13 mode was chosenfor the proof-of-concept system to allow for three points tocontact the rotor during operation.

An important aspect of creating the traveling wave isgenerating two orthogonal modes out of phase. Generally, theout of plane resonance modes in disks are orthogonal to their

Fig. 5. This laser Doppler vibrometry measurement shows the standing waveshape. The electrode sets A and B are highlighted. Vibrometry data shows thatwhen electrode A is active, anti-nodes of the resonance mode are collocatedwith the actuation region. The orthogonal mode is excited when electrode Bis active.

degenerate counterparts, and the location of the nodal diameteris arbitrary as the disk has infinite lines of symmetry. In prac-tice, small imperfections in the disk fix the nodal diametersof the disk in certain locations. In order to excite orthogonalvibration modes out of phase, it is necessary to demonstratecontrol of the nodal lines of the excited vibration modes. Thiswas achieved in the prototype stator by segmenting the topPt electrode so that the point of largest vibration, or anti-node, of the disk would align with the region of active PZT.This is shown experimentally by laser Doppler vibrometry inFig. 5, where electrode A is active and the anti-node alignswith the active electrode. With two sets of electrodes that canindependently excite orthogonal resonance modes (labeled asA and B in Fig. 5), two electrical signals with a 90° phaseoffset can be used to create a traveling wave. Six of twelveregions were driven, because operation voltages in thin-filmPZT are above the coercive voltage, and bipolar operationwould re-pole the material.

III. FABRICATION

Traditional small-scale TWUMs produced usingmacro-scale manufacturing techniques are bounded in size dueprecision and accuracy limitations inherent in the fabricationprocess. Using photolithographic processing and MEMSfabrication techniques these limitations are circumvented anda millimeter-scale TWUM becomes realizable. To demonstratethe rotary motion, stators were fabricated using the processflow described in [2]. Details of the PZT deposition processcan be found in [20]. Once the stator components are released,the device die are attached to a package using double-sidedKapton tape. A silicon rotor, fabricated using deep reactiveion etching, is then placed onto the stator and gold wirebondsfrom the package are brought through the center of the rotor

RUDY et al.: MILLIMETER-SCALE TRAVELING WAVE ROTARY ULTRASONIC MOTORS 111

Fig. 6. Experimental results show speed and power as a function of actuationvoltage for the 3 mm diameter motor. Error bars on rotational speed representstandard deviation [1].

Fig. 7. (a) Rotation speeds of the 3 mm diameter motor as a function ofpeak actuation voltage for positive and negative bias shows that higher speedsand lower starting voltages can be obtained by operating with negative bias.(b) Power consumption of the 3 mm diameter motor under negative bias islower than under positive bias and trends linear above 5V.

and attached to the stator electrodes. These wirebonds servetwo purposes: bringing electrical signal to the stator andconstraining the lateral motion of the rotor.

IV. RESULTS AND DISCUSSION

A proof of concept motor with a stator 3 mm in diameterand 30 μm thick was used to characterize the motor speedbehavior. In this stator, the B13 resonance mode occurs at252.2 kHz. The 500 μm thick silicon rotor is made using deepreactive ion etching. The rotor is manually positioned on thestator and the assembled motor is wirebonded to a 24-pin dualin-line package. Two 252.2 kHz sinusoidal electrical signals

Fig. 8. Rotation speed as a function of phase for the 3 mm diameter motorshows a smooth but nonlinear response. The zero speed crossing occurs at anon-zero phase offset, demonstrating that traveling waves may be generatedwithin the stator using input signals with no phase offset.

0-Vp, where Vp is the peak actuation voltage, are deliveredto the device, offset by 90° in phase. Fig. 6 shows the speedand power consumption as a function peak actuation voltageas reported in [1].

Observations from other PZT based MEMS devices fabri-cated at the US Army Research Laboratory [5] highlighteda degree of imprint in the piezoelectric response of the finaldevices. The imprint creates a preferred bias operation for thedevice such that one polarity bias can create larger strainsthan the opposite polarity [21]. For TWUMs, a negativebias applied to the top Pt electrode results in a larger straingeneration. As a result, the increased out of plane deflection inthe stator increases the speed of operation at a given voltageand also decreases the required starting voltage of the motor.Speed and power consumption as a function of voltage forthe proof-of-concept motor is plotted in Fig. 7, showing thesmaller starting voltage and higher speeds under a negativebias voltage. This also shows that input voltage can be usedto control motor speed.

Characterization of motor speed as a function of phase wasalso performed and is shown in Fig. 8. Phase control has beenused in macro-scale TWUMs to allow for a slow start and stop,although this is accomplished at a lower efficiency [22]. Oneinteresting note is that the zero speed crossing occurs at a non-zero phase, and by extension the rotor moves when the phaseoffset between the two excitation signals is zero. Furthermore,the rotor moves when only one set of electrodes is active. Thisbehavior is likely due to small imperfections in the disk whichserve to split the degenerate resonance frequencies, resultingin a natural phase offset between the orthogonal modes ata specific drive frequency. This natural phase offset can beexploited to create a single source TWUM as described in [6].A frequency split of 190 Hz (0.08%) was measured in a similardevice using laser Doppler vibrometry.

Rotation speed as a function of frequency has also beencharacterized and is shown in Fig. 9. Frequency control canalso be used to control motor speed, however it is often notused in macro-scale motors because researchers have notedthat the motor suddenly stops when gradually decreasingthe frequency. Sattel attributes this to a catastrophic jumpdue to non-linear dynamics and shows Duffing-like behaviorexperimentally [19]. Sattel argues that the catastrophic jump

112 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 24, NO. 1, FEBRUARY 2015

Fig. 9. The speed-frequency relationship for the 3 mm diameter stator,shown here, does not exhibit any significant nonlinearities typically observedin macro-scale motors.

Fig. 10. Torque as a function of speed for the 2 mm diameter motor isplotted here, both calculated using high speed video capture to measure angleover time.

causes a sudden decrease in deflection, which drops belowthe level required for motion. Because this Duffing behaviorexists in macro-scale motors, temperature change can shift theresonance frequency, leading to a catastrophic jump duringoperation. To avoid this catastrophic jump, macro-scale motorsmust operate away from the peak resonance condition, reduc-ing the performance of the motor. Contrary to what is observedin macro-scale motors, there is no softening resonance curveobserved in these micro-scale motors for either the statorcomponent or the motor. This allows the motor to operateat peak resonance condition without concern for the suddenstop seen in their macro-scale counterparts.

A separate 2 mm diameter motor was used to characterizethe torque performance as a function of speed as shown inFig. 10. A starting torque of 2.6 nNm was calculated usinga high speed camera by monitoring the change in angleover time during the start-up phase, determining the angularacceleration and multiplying by the rotational inertia of therotor according to the equation, τ = αI, where τ is thetorque, α is the angular acceleration, and I is the rotationalinertia of the octagonal rotor [23]. It should be noted that themotor torque could be greatly increased by providing a larger

normal force beyond merely the self-weight of the rotor. Theseefforts, exploiting negative bias voltages, have demonstratedthe operation of a 2 mm diameter motor up to 1730 RPM.To this point, no performance degradation due to frictionalwear has been observed. Further miniaturization was preventedbecause of mode mismatch, however with a design change, itis expected that millimeter diameter and smaller TWUMs canbe successfully created using this process.

Further reduction of the ultrasonic motor size scale isdesirable for applications demanding high torque output ina sub-millimeter form factor. As noted previously, smallerstators did not operate as designed due to mode mismatch,with orthogonal modes occurring at different frequencies.This prevents the creation of the traveling wave because theidentity requires two standing waves at the same frequency.Furthermore, the anti-nodes of the mode shape are not local-ized to the active electrode as described in Section II C,but instead the anti-nodes are set somewhere between theactive electrodes. The simplest explanation is that there isa component in the system which is changing the modalstiffness or mass so that the resonance frequencies shift and thenodal lines are fixed by this component rather than the activeelectrodes.

To identify this component, it is important to note a numberof factors. First, all 1 mm diameter stators showed similar fre-quency offset and similar nodal line locations. This systematicconsistency suggests that the problem is likely not random andalso not material defect related. Therefore it is essential toexamine the design of the stator to identify possible sourcesof this problem. Second, the modal shift is present only forsmall diameter devices, whereas larger diameter devices showno problems. Finite element simulations during the designphase showed that smaller devices are more affected by theanchor condition than larger devices. Finally, upon examiningthe design, the backside release holes, shown in Fig. 11 (a),are varied in size and shape near the anchor portion so asto create a circular anchor, which would prevent any modemismatch.

The large holes align to the anti-nodes of the experimentallyobserved lower frequency modes suggesting that the largerholes reduced the stiffness for deflections coincident with theseholes, thus dropping the resonance frequency for that mode.These observations lead to the next question – how does thesize of the hole affect the stiffness of the structure? To remindthe reader, the holes are etched through the approximately500 μm thick handle wafer to open the buried oxide to avapor HF etch, while maintaining the structural integrity ofthe handle wafer silicon. It is suggested that a larger volumeof the gas is delivered through the large etch holes, and thusthe etch front progresses faster in the vicinity. The faster etchrate would leave a hexagonal anchor which would create themodal mismatch observed experimentally. This argument isillustrated in Fig. 11 (b).

The buried oxide etch-front, usually visible using infraredimaging, cannot be observed in this case because the throughwafer holes prevent sufficient contrast to observe the etch-front. Although the buried oxide etch-front is not easilyobservable, the argument that asymmetric etching of the buried

RUDY et al.: MILLIMETER-SCALE TRAVELING WAVE ROTARY ULTRASONIC MOTORS 113

Fig. 11. (a) This shows the photolithographic pattern used to etch the handle wafer for vapor HF release. Note the holes of various sizes at the center.(b) This illustration of the simulated etch front progression (gray lines) shows asymmetric etching leading to a non-circular anchor. (c) This new designalleviates problems with uneven etching during vapor HF release due to size of etch hole. (d) This illustration of the simulated etch front progression (graylines) shows a significantly more symmetric center anchor, which should allow for smaller devices to function without mode-splitting.

oxide creates modal mismatch seems to hold weight as alikely explanation. Assuming this is the problem, Fig. 11 (c)shows a possible design solution which uses holes that areall approximately the same area, allowing the etch front toprogress at the same rate. The resulting etch progression andanchor condition are shown in Fig. 11 (d). Furthermore, withthis design any etching asymmetries caused by the twelveholes near the anchor will be matched by the twelve regionsof excitation, thus eliminating mode mismatch problems thatwere observed under the previous design. This design prob-lem emphasizes that these motors can be quite sensitive toboundary conditions. Because of this sensitivity to boundaryconditions, the design of the motor must be done carefully,ensuring that modal mismatches are avoided or mitigatedwhenever possible.

V. CONCLUSIONS

This work has shown enhanced speed performance andsmaller functional TWUM than previously reported. With an

applied normal load, it is expected that these motors willproduce useful torque, which would open new avenues foractuation at the millimeter scale. Furthermore, simple controlis enabled through near-linear voltage-speed characteristic,slow-start drive is enabled by phase control, and non-linearinstability does not appear to be a problem. A design problemwas also presented, displaying the necessity for high preci-sion manufacturing, careful design, and much thought whenminiaturizing such devices.

Many challenges remain in making a small scale motorwith useful torque using MEMS fabrication techniques. Themost prominent of these challenges is applying a normalload, to increase frictional coupling between stator and rotor,without creating excessive drag between the rotor and otherstationary components. Normal load is important for high-torque applications because the normal load is directly relatedto the frictional force at the stator surface. Off-the-shelfbearings, which can serve this function at the macro-scale,are not available for such small motors, so a different solutionmust be devised.

114 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 24, NO. 1, FEBRUARY 2015

Twenty years have passed since Flynn noted that, “buildingmass-producible useful-torque-producing micromotors will behard” [13]. Accomplishing this challenge remains difficult,however progress has been made in demonstrating a previouslyelusive bi-direction traveling wave ultrasonic motor usingwafer-scale manufacturing, and future work could lead touseful motors for small scale and low power applications.

ACKNOWLEDGMENT

The authors would like to thank Joel Martin, Brian Power,and Luz Sanchez of the US Army Research Laboratory forfabrication support.

REFERENCES

[1] R. Q. Rudy, G. L. Smith, D. L. DeVoe, and R. G. Polcawich,“Traveling wave ultrasonic motor using thin-film piezoelectrics,” inProc. Solid-State Sens., Actuators, Microsyst. Workshop, Hilton Head,SC, USA, Jun. 2012, pp. 417–420.

[2] G. L. Smith, R. Q. Rudy, R. G. Polcawich, and D. L. DeVoe, “Inte-grated thin-film piezoelectric traveling wave ultrasonic motors,” Sens.Actuators A, Phys., vol. 188, pp. 305–311, Dec. 2012.

[3] K. Uchino, “Piezoelectric ultrasonic motors: Overview,” Smart Mater.Struct., vol. 7, no. 3, pp. 273–285, 1998.

[4] K. Uchino and J. R. Giniewicz, Micromechatronics. New York, NY,USA: Marcel Dekker, 2003, pp. 417–430.

[5] G. L. Smith et al., “PZT-based piezoelectric MEMS technology,”J. Amer. Ceram. Soc., vol. 95, no. 6, pp. 1777–1792, 2012.

[6] S. Ueha and Y. Tomikawa, Ultrasonic Motors: Theory and Applications.New York, NY, USA: Oxford Univ. Press, 1993, pp. 6–7.

[7] T. Morita, “Miniature piezoelectric motors,” Sens. Actuators A, Phys.,vol. 103, no. 3, pp. 291–300, 2003.

[8] T. Sashida and T. Kenjo, An Introduction to Ultrasonic Motors.New York, NY, USA: Oxford Univ. Press, 2003, pp. 5–12.

[9] T. Maeno, T. Tsukimoto, and A. Miyake, “The contact mechanism ofan ultrasonic motor,” in Proc. IEEE 7th Int. Symp. Appl. Ferroelectr.,Jun. 1990, pp. 535–538.

[10] A. Iino, K. Suzuki, M. Kasuga, M. Suzuki, and T. Yamanaka,“Development of a self-oscillating ultrasonic micro-motor and itsapplication to a watch,” Ultrasonics, vol. 38, no. 1, pp. 54–59, 2000.

[11] I. Yamano and T. Maeno, “Five-fingered robot hand using ultrasonicmotors and elastic elements,” in Proc. Int. Conf. Robot. Autom.,Barcelona, Spain, 2005, pp. 2673–2678.

[12] A. M. Flynn, “Piezoelectric ultrasonic micromotors,” Ph.D.dissertation, Dept. Electr. Eng. Comput. Sci., Massachusetts Inst.Technol., Cambridge, MA, USA, 1995.

[13] A. M. Flynn et al., “Piezoelectric micromotors for microrobots,”J. Microelectromech. Syst., vol. 1, no. 1, pp. 44–51, Mar. 1992.

[14] S. Cagatay, B. Koc, P. Moses, and K. Uchino, “A piezoelectricmicromotor with a stator of ϕ = 1.6 mm and l = 4 mm using bulkPZT,” Jpn. J. Appl. Phys., vol. 43, no. 4R, pp. 1429–1433, 2004.

[15] S. Piratla, M. Pandey, and A. Lal, “Nanogap ultrasonic actuator fornon-contact control of levitated inertial sensor rotor,” in Proc.Solid-State Sens., Actuators, Microsyst. Workshop, Hilton Head, SC,USA, Jun. 2012, pp. 82–85.

[16] C. Zhao, Ultrasonic Motors: Technologies and Applications.Berlin, Germany: Springer-Verlag, 2011, pp. 327–340.

[17] P. Muralt et al., “Fabrication and characterization of PZT thin-filmvibrators for micromotors,” Sens. Actuators A, Phys., vol. 48, no. 2,pp. 157–165, 1995.

[18] J. Tang, S. R. Green, and Y. B. Gianchandani, “Miniature wire-less resonant rotary motor actuated by lithographically micromachinedmagnetoelastic foil,” in Proc. Solid-State Sens., Actuators, Microsyst.Workshop, Hilton Head, SC, USA, Jun. 2012, pp. 86–89.

[19] T. Sattel, “Dynamics of ultrasonic motors,” Ph.D. dissertation, Dept.Mech. Eng., Technische Univ. Darmstadt, Darmstadt, Germany, 2002.

[20] L. M. Sanchez et al., “Optimization of PbTiO3 seed layers and Ptmetallization for PZT-based piezoMEMS actuators,” J. Mater. Res.,vol. 28, no. 14, pp. 1920–1931, 2013.

[21] J. Lee, C. H. Choi, B. H. Park, T. W. Noh, and J. K. Lee,“Built-in voltages and asymmetric polarization switching in Pb(Zr,Ti)O3thin film capacitors,” Appl. Phys. Lett., vol. 72, no. 25, pp. 3380–3382,1998.

[22] F. Giraud, B. Semail, and J.-T. Audren, “Analysis and phase controlof a piezoelectric traveling-wave ultrasonic motor for haptic stickapplication,” IEEE Trans. Ind. Appl., vol. 40, no. 6, pp. 1541–1549,Nov./Dec. 2003.

[23] J. A. Myers, “Handbook of Equations for Mass and Area Properties ofVarious Geometrical Shapes,” U.S. Naval Ordnance Test Station, ChinaLake, CA, USA, NAVWEPS Rep. 7827, 1962.

Ryan Q. Rudy received the B.S.E. degree and theM.S.E. degree in mechanical engineering from theUniversity of Michigan, Ann Arbor, MI, in 2009and 2010, respectively. Since 2010, he has beenpart of the MEMS and Microfluidics Laboratory atthe University of Maryland, College Park, where heis pursuing the Ph.D. degree with the support ofthe SMART Program. His current research interestsinclude millimeter-scale robotic actuators with aspecific focus on rotary traveling wave ultrasonicmotors.

Gabriel L. Smith received B.S. and M.S. degreesin mechanical engineering from the University ofMaryland, College Park, in 1999 and 2002, respec-tively. He has worked in MEMS design for thepast 15 years with the U.S. Naval Surface WarfareSystems, U.S. Army Armaments Research Devel-opment and Engineering Center, and U.S. ArmyResearch Laboratory. He currently holds six U.S.patents with three patents pending, and has authoredseven journal and conference papers on MEMSdevices.

Don L. DeVoe is a Professor of Mechanical Engi-neering at the University of Maryland, College Park,with affiliate appointments in the Department ofBioengineering and Department of Chemical andBiomolecular Engineering. He received his Ph.D.degree in Mechanical Engineering from the Uni-versity of California, Berkeley, with a focus onpiezoelectric MEMS. His current research interestsinclude thermoplastic microfluidic technology, andpiezoelectric microsystems leveraging advanced thinfilm and bulk piezoelectric materials. Dr. DeVoe

serves the microsystems community as an Associate Editor for the JOURNAL

OF MICROELECTROMECHANICAL SYSTEMS. He is a Kavli Fellow of theNational Academy of Sciences, and a recipient of the Presidential Early CareerAward for Scientists and Engineers from the National Science Foundation foradvances in microsystems technology.

Ronald G. Polcawich (M’07) is a staff researcherin the Micro & Nano Materials & Devices Branchof US Army Research Laboratory (ARL), Adel-phi, MD. He received a B.S. in Materials Scienceand Engineering from Carnegie Mellon University(1997), and M.S. degree in Materials from PennState University (1999), and a Ph.D. in Materi-als Science and Engineering from Penn State Uni-versity (2007). He is currently the team lead forPiezoMEMS at ARL with a focus on developingsolutions for RF systems and mm-scale robotics. He

currently holds 8 patents, has 10 patent applications pending review, and hasauthored over 70 articles and two book chapters on fabrication and design ofpiezoelectric MEMS devices using PZT thin films. Additionally, Dr. Polcawichreceived the 2012 Presidential Early Career Award for Scientists and Engineers(PECASE). Dr. Polcawich is an elected member of the IEEE FerroelectricsCommittee, and an elected member of the IEEE Ultrasonics, Ferroelectrics,and Frequency Control (UFFC) Administrative Committee (AdCom) for 2014-2016.