President Proposal FY'96

SOLID STATE ULTRASONIC MOTORS (SSUM) DEVELOPMENT FOR MINIATURE S/C

PRINCIPAL INVESTIGATORS: Y. Bar‑Cohen, JPL, N. W. Hagood IV, MIT,

APPROVALS:

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Jovan Moacanin, Manager, Section 355

Space Materials Sci. and Eng. Section

Brian McGlinchey, Manager, Division 35

Mechanical Systems Engineering and Research Division

Earll Mumam, Chairman

Department of Aeronautics and Astronautics

Massachusetts Institute of Technology

Cambridge, Massachusetts

JET PROPULSION LABORATORY

CALIFORNIA INSTITUTE OF TECHNOLOGY

PASADENA, CALIFORNIA 91109

California Institute of Technology

FY 1995 Preseident's Fund

[ABSTRACT]{.underline}

PF #: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

[Program Title]{.underline}: Solid State Ultrasonic Motors (SSUM)
Development for Miniature S/C

[Principal Investigators]{.underline}: Nesbitt Hagood, [JPL Lead
Investigator]{.underline}: Yoseph Bar-Cohen,

[Institution]{.underline}: MIT Sect. 354, x4-7252

[Summary of Activities and Anticipated Results]{.underline}: Electric
motors are used essentially in all NASA/JPL spacecraft and instruments
to drive mechanisms and precision pointing. Electric motors have reached
a level of efficiency that it would require enormous resources to obtain
marginal improvement. The need to miniaturize spacecraft and to operate
at extrem temperatures in space is driving requirements that are
difficult to meet with current electric motor technology.

In the past few years, a new type of miniature motor has been used in
Japanese cameras and other commercial applications, which has the
desired properties of small size, high torque at zero/low speed, high
power efficiency and large holding force. Unfortunately, these motors
are not available commercially, and they have not been qualified for
space applications. MIT has investigated the motors used in Japanese
cameras, begun preliminary assessment of their potential and developed
an analytical model to optimize their performance. In this DDF, we
propose to analyze the requirements for efficient motor, to fabricate a
prototype SSUM, evaluate its performance at lower temperatures and high
vacuum, as well as define approaches for making SSUM space‑worthy.

A novel concept will be applied to the reported Japanese solid state
ultrasonic motors to increase the motor performance and simplify its
design. The prototype motor will be fabricated with the rotor serving as
the active element with the wave traveling on both surfaces of the disk,
that rotates the drive-shaft, thus doubling the driving element. The
symmetry of this drive mechanism will simplify the analysis of the motor
and improve the ability to predict the motor performance for future
optimization efforts.

Ultrasonic motors have the potential of providing higher efficiency and
torque densities than comparable electric motors. In general, they
operate at lower rpm and higher torque, thereby eliminating the need for
speed reduction associated with small high speed electric motors. Thus,
reducing the motor\'s mass, with less motor complexity and smaller
number of components that can fail. Further, the motor offers potenial
operation at low temperatures. Such a capability is needed for mosaicing
and scanning functions in missions such as PFF and for articulation of
CCD cameras and sampling tasks in Rover projects as well as perform a
wide range of other spacecraft actuation tasks.

This proposed DDF is expected to lead to in-house knowhow in producing
efficient solid state ultrasonic motors that can be space qualified.
Generally, JPL is involve in definiting the requirements for it supplier
and it is essential that we take the initiative in this area in order to
lead to commercial availability of such motors. A database of
performance criteria will be established for selection of SSUM
technology over electric motor alternatives. Further, we will explore
the formation of a USA manufacturing capability for SSUM technology.

This program will utilize the MIT model, that streamlined the design of
efficient motors, to engineer a potentially space qualifiable prototype
motor. A prototype SSUM will be developed using a novel concept and the
motor will be tested in various mechanical and thermal conditions under
vacuum. A database and performance criteria will be established for
selection of the technology as alternative to electric motors. Further,
a follow-on program joint with MIT and industry will be explored for the
development of space qualified motors.

**1. OBJECTIVE**

The objective of this DDF is to develop solid-state ultrasonic motor
(SSUM) technology as a viable alternative to electric motors with a
level of technology readiness that allows flight qualification. Further,
through the fabrication and testing of a prototype SSUM, the
requirements and design criteria will be evaluated with regards to using
the motor in space environment, i.e. low temperatures and vacuum. The
results of the DDF will be used to define follow‑on programs, for
adaptation/development of new SSUM for use in a space environment, that
will be competitive in joint NASA‑industry programs, such as the AITP.

**2. BACKGROUND**

The need to develop faster, better and cheaper NASA hardware has led JPL
to emphasize smaller spacecraft. These requirements have strained the
specifications for articulation mechanisms on current and future JPL
space missions where high precision is needed while operating at space
environment. Example of missions which require adequate articulation
include: POINTS, OSI, SONATA, PFF, AIT and various Rover programs. On
current spacecraft, rotational and translational motions are driven by
conventional electric motors. While these motors are very efficient,
they are difficult to miniaturize \[1\] and they reached a level of
efficiency that further improvement demands enormous investment. Since
deep-space missions have motor requirements that are unique, their
development in many cases is the result of JPL efforts rather than an
industry product line spin-off. JPL has a long history of working with
industry to develop improved motors for space applications.

Solid state actuators/motors, that are based on active materials (e.g.
piezoelectric, electrostrictive, magnetostrictive, etc.), are
increasingly becoming acceptable alternatives to conventional actuation
devices. As an example, for each of the three WF/PC II Articulated Fold
Mirrors a set of three pairs of electrostrictive actuators were used to
control the ray path. In this application, the articulation of the
mirror is limited to small linear displacements on the order of microns
and the operation was restricted to a very narrow temperature range
around 10oC . This recently successful NASA application of electroactive
materials for space instruments has paved the path for the application
of other more capable solid-state actuation devices.

**3. INTRODUCTION**

In the past few years, a new type of miniature motors, based on
piezoelectric materials, has been used in Japanese commercial products
such as autofocus cameras. Currently, these motors are neither available
from USA manufacturers nor space qualified. These motors, that are
identified as solid state ultrasonic motors (SSUM), offer potential
advantages in the areas of power efficiency, torque/mass ratios, compact
size and efficient force holding \[2\] (see Table 1). To form a viable
alternative with a level of technology readiness that allows flight
qualification and launch, this DDF proposes to develop a prototype
solid-state ultrasonic motor (SSUM) and evaluate the various issues
related to space application.

Generally, there are several distinctions among solid state motors as
illustrated by their functional characteristics in Figure 1. Motors can
be classified by their mode of operation (static or resonant), type of
motion (rotary or linear) and shape of implementation (beam, rod, disk,
etc.). Despite the distinctions, the fundamental principles of
solid-state actuation tie them together: microscopic material
deformations (usually associated with piezoelectric materials) are
amplified through either quasi-static mechanical or dynamic/resonant
means.

TABLE 1: Comparison of existing electromagnetic (EM) and ultrasonic (US)
motors

+---+----+-----------+--------+------+--------+------+--------+--------+
| # | Ty | De        | Manuf. | S    | N      | Mass | Torque | Peak   |
| \ | pe | scription |        | tall | o-load | (g)  | D      | effi   |
| . |    |           |        | To   |        |      | ensity | ciency |
|   |    |           |        | rque | Speed  |      | (      | %      |
|   |    |           |        |      | (rpm)  |      | Nm/kg) |        |
|   |    |           |        | (in. |        |      |        |        |
|   |    |           |        | oz)  |        |      |        |        |
+---+----+-----------+--------+------+--------+------+--------+--------+
| 1 | EM | DC,       | Ae     | 1.4  | 4K     | 256  | 0.04   | 20     |
|   |    | Brushless | roflex |      |        |      |        |        |
+---+----+-----------+--------+------+--------+------+--------+--------+
| 2 | EM | DC Brush  | Maxon  | 1.8  | 5.2K   | 38   | 0.32   | 70     |
+---+----+-----------+--------+------+--------+------+--------+--------+
| 3 | EM | AC,       | Astro  | 100  | .11K   | 340  | 2.01   | 60     |
|   |    | 3-phase   |        |      |        |      |        |        |
+---+----+-----------+--------+------+--------+------+--------+--------+
| 4 | US | Traveling | Pan    | 11   | .8K    | 70   | 1.10   | 40     |
|   |    | Wave      | asonic |      |        |      |        |        |
|   |    |           | \[12\] |      |        |      |        |        |
|   |    | \- Disc   |        |      |        |      |        |        |
+---+----+-----------+--------+------+--------+------+--------+--------+
| 5 | US | Stand.    | Kumada | 189  | .12K   | 150  | 8.80   | 80     |
|   |    | Wave      | \[8\]  |      |        |      |        |        |
|   |    |           |        |      |        |      |        |        |
|   |    | \- Rod    |        |      |        |      |        |        |
|   |    | Torsion   |        |      |        |      |        |        |
+---+----+-----------+--------+------+--------+------+--------+--------+
| 6 | US | Traveling | S      | 13   | 0.3K   | 33   | 2.70   | 35     |
|   |    | wave      | hinsei |      |        |      |        |        |
|   |    |           | \[20\] |      |        |      |        |        |
|   |    | \- Disc   |        |      |        |      |        |        |
+---+----+-----------+--------+------+--------+------+--------+--------+
| 7 | US | Traveling | Canon  | 17   | 0.08K  | 45   | 2.30   | 40     |
|   |    | wave      |        |      |        |      |        |        |
|   |    |           | \[14\] |      |        |      |        |        |
|   |    | -Ring     |        |      |        |      |        |        |
+---+----+-----------+--------+------+--------+------+--------+--------+

**SOLID STATE MOTORS**

**Quasi-static Ultrasonic/Resonance**

**Linear Rotary Standing Wave Traveling Wave**

Inchworm \[3\] Direct Drive \[5\] Linear Rotary Linear Rotary

Peristaltic \[4\] Beam \[6\] Torsional/ Oval \[9\] Disc \[11\], \[12}

Plate \[7\] Extensional Beam \[10\] Ring \[11\], \[12\]

Rim \[13\]

Figure 1: Solid state motor family tree showing distinctions between the
quasi-static and ultrasonic/resonance type motors.

Several of the motor classes, that are shown in Figure 1, have seen
commercial application in areas needing compact, efficient, intermittent
motion. Such applications include: camera auto focus lenses \[14, 15\],
watch motors \[16\] and compact paper handling \[7\]. The traveling wave
type motors are

more mature but have demonstrated peak efficiency of only 47% after
years of commercial development \[12\]. In contrast, certain standing
wave type motors have exhibited over 80% efficiency in prototype tests
\[8\]. In a significant step, Canon, the principal commercial developer
of ring type ultrasonic traveling wave motors, has recently adopted a
compact standing wave motor over its ring motor for its auto-focus-lens
product lines \[15\]. A comparison of the performance characteristics of
rotary electric motors employed in current space applications and solid
state ultrasonic motors is shown in Table 1.

In Figure 2 the operation principal of a solid state ultrasonic motor
(Traveling wave ring-type motor) is shown as an example. A traveling
wave is established over the stator surface, which behaves as an elastic
ring, and produces elliptical motion at the interface with the rotor.
This elliptical motion of the contact surface propels the rotor and the
drive-shaft conected to it. The teeth, that are attached to the stator,
are intended to improve the friction and increase the moment arm to
amplify the torque.

![](media/image1.emf){width="3.298611111111111in"
height="2.2909722222222224in"}

Figure 2: Principal of Operation of traveling wave motor.

The operation of solid state ultrasonic motors depends on friction at
the interface between the moving and non-moving elements and therefore
have limited duty cycle similar to brushless DC type motors.
Nevertheless, there are innumerable instruments and spacecraft
subsystems applications where small, intermittent motions are required
for which SSUM is well suited. The order of magnitude higher torque
density provides an attractive chracteristics especially as mission
hardware becomes increasingly miniaturized.

**4. TECHNICAL APPROACH**

The proposed program will be conducted jointly with MIT and in
cooperative relation with potential USA manufacturers (e.g. Allied
Signal, THK, etc.). MIT has previous experience with such motors and
they developed an analytical model to optimize the performance of these
type of motors. A capability to develop and evaluate the performance of
such motors at a wide range of mechanical loads, vacuum and cryogenic
conditions have been established by Division 35. The DDF efforts will be
conducted in four tasks as follows:

TASK 1: Material analysis - The materials, that are involved in an SSUM,
determine the motor efficiency and ability to operate effectively in
vacuum and cryogenic temperatures. The analytical model that was
developed by MIT will be used to establish criteria for selection of the
construction materials. Bounds of properties will be determined and
effective materials will be selected using Section 355 experience with
materials for space applications. Properties that are not documented for
potential materials will be measured using the Actuation Materials
Characterization lab that Section 355 has recently established. We
intend to apply the lessons that were learned from this lab work with
Section 382 and UCLA on the Inchworm motor, which is also a
piezoelectric device and needs to operate in cryogenic temperatures.

TASK 2: Fabrication of a prototype motor - Based on strawman
specifications of potential JPL missions, a prototype solid state
ultrasonic motor will be fabricated. This work will be conducted in
cooperation with MIT and a student will be dedicated to the fabrication
of the motor. The electronic drive will be based on instruments that are
available at the Sect. 355 Actuation Materials Characterization lab. A
novel modification to the currently reported configuration of SSUM will
be considered as shown schematically in Figure 3. A resonant traveling
wave will be induced on the rotor rather than the stator. The wave will
be transmitted on both surfaces of the rotor disk which will be
installed with teeth on these surfaces. The stator will be part of the
case that supports the motor and its interfaces with the rotor will
provide the necessary high friction. One side of the stator contact with
the rotor will be adjustable and will be pushed by a set spring to
assure the required contact with the rotor. The contact pressure between
the rotor and stator will be made adjustable to compensate for the
effect of thermal expansion changes as a function of temperature. This
proposed design will make the rotor drive mechanism symmetric and will
simplify the analysis of the motor performance.

TASK 3: Performance tests - Tests will be conducted on the prototype
motor to determine its feasibility for space applications. Tests will
include mechanical loading to measure stall torque, speed, power, force
hold capability, vibration characteristics at various temperatures down
to 120K and vacuum down to 10-8 torr. A database will be initiated using
the results of these tests and performance criteria will be determined
for selection of SSUM technology over other alternative motors. This
task will be conducted in collaboration with potential industry
partners. Some of the tests will be conducted at no-cost by the partners
(preliminary discussions of such a collaboration is currently underway
with Allied Signal).

*Thermal characteristics, design and operation*: The combination of
materials and configuration of motor components needs to be evaluated by
analysis and test to determine their temperature operating ranges, and
to define approaches for extending them to colder temperatures. Some of
the issues are related to friction, contact pressure and heat
transition. The friction and thermal heat transfer across this interface
are potentially much different in a vacuum environment. Moreover, the
clearance at the interface is a function of the temperature.

*Motor life, reliability and articulation precision*: Solid state
ultrasonic motors are expected to be limited duty cycle devices. To
develop efficient, reliable and low cost motors, the materials and
configuration of the motor components will need to be evaluated,
analyzed and tested.

The motor emission of electric and magnetic fields will be examine to
assure that they would not cause interferences to critical instruments
that are sensitive at certain frequencies. The level of emission will be
studied and ways to reduce undesirable effects will be considered.
Potential structure borne acoustic emission from the SSUM prototype may
cause a concern however the effect can be mitigated by damping, material
selection, device design for another frequency, etc.

![](media/image2.emf){width="4.367361111111111in"
height="2.326388888888889in"}

Figure 3: A Proposed Motor Design for traveling wave SSUM.

The following are some of the issues that will be addressed in this
task.

TASK 4: Evaluation of SSUM Control System - The requirements for robust
electronic/mechanical system needs to be evaluated and the performance
of the drivers vs. common instrument and spacecraft requirements for
EMI, micro‑phonics, etc. need to be determined. The design of the
electronic driver circuits and motor configurations will the analyzed to
determine the necessary modifications to reduce potential complexity
while assuring compact size and low power consumption of the drive
circuit.

**5. JPL BENEFITS**

The proposed solid state technology is expected to have a wide range of
applications for NASA once the performance database, thermal
characteristics, long term durability and quality compatibility are
determined. SSUMs potentially provide an enabling capability for compact
mechanisms which are needed for smaller, lighter, affordable and
reliable spacecraft. Their ability to operate at low temperatures,
miniaturizability and low power consumption makes them excellent
candidates for spacecraft applications.

Solid state motors and actuators can be classified by the level of
torque, force, displacement, tilt, rotation rate, and precision
requirements. Reviewing the requirements for driving mechanisms of space
system and the list in Table 1 show that they can meet current
spacecraft mechanism design requirements. With relatively simple
modifications, such motors could be used as replacement for standard
actuators on Mars Pathfinder, Rover projects, POINTS, OSI, SONATA, PFF
and AIT. On Mars Pathfinder, solid state motors can potentially be used
for the manipulation of the CCD camera mobility and soil evaluation, for
the Rover and Lander separation device to perform drive and steering and
on the APXS for deployment and pointing. Other potential applications
include thermal control louvers, camera shutters and calibration
targets.

**6. POTENTIAL SOURCE FOR FOLLOW-UP FUNDING**

Solid state ultrasonic motors have a wide range of applications for NASA
space programs and commercial products and can serve as an efficient
alternative to electric motors. Once we have a working prototype motor,
we are planning to pursue follow-on programs in collaboration with the
industry and MIT towards the development of a USA manufacturing
capability. Potential programs that will be considered include AITP,
that is funded by NASA, and other similar ones that require industry
partners.

**7. PERSONNEL**

**Dr. Yoseph Bar-Cohen** is the NDE Principal Investigator at the Jet
Propulsion Laboratory (JPL), Pasadena, CA. Since joining JPL in 1991, he
has established state-of-the-art (1) Active Materials Characterization
and (2) Nondestructive Evaluation (NDE) labs. Dr. Bar-Cohen received his
Ph. D. in Physics from the Hebrew University at Jerusalem, Israel, in
1979. He has more than 23 years experience in actuators, sensors and
NDE, including his positions at the Israel Aircraft Industry, SRL at the
Air Force Materials Laboratory and McDonnell Douglas Corporation. Dr.
Bar-Cohen co-pioneered the development of the leaky Lamb waves and the
polar backscattering for NDE of composites, and developed unique devices
that employ piezoelectric materials for which he received 4 patents. He
is the author of more than 100 publications and holds many patents. He
is also an Adjunct Professor at the University of California, Los
Angeles (UCLA).

**Dr. Nesbitt W. Hagood IV** is the Charles Stark Draper Assistant
Professor of Aeronautics and Astronautics at MIT where he previously
earned his S.B. (1985), S.M. (1988), and Ph.D. (1991) degrees. Professor
Hagood is a member of AIAA, ASME, and the SPIE. He is currently a
technical chairman in the SPIE 1994 Smart Structures and Materials
Conference and member of the editorial board on the IOP Journal of Smart
Materials and Structures. He has published material on piezoelectric
actuation in several technical journals and is currently writing a book
entitled, Piezoelectric Active Structures, to be published by Technomics
Publishing Co. in the Fall of 1993. His primary research interest is in
development of active material systems and devices. He currently holds
two patents in the area of solid state actuation and is co‑founder of a
startup company for the commercialization of active device technology.

**Mr. Gerald W. Lilienthal** received his BSME degree from the
University of Wisconsin-Milwaukee in 1981. He has 14 years of experience
in the design and development of mechanisms. Since joining the JPL in
1986, he has been responsible for the design and development of digital
scanners, precision bearing systems, spacecraft configuration design,
planetary surface sampling devices, pointing systems and other
mechanisms. Currently, he is the supervisor for the Mechanical
Components Technology Group of the Mechanical Systems Development
Section.

**Dr. Jeff Umland** received his Ph. D. from the State University of New
York at Buffalo, in 1990, where he studied active vibration control
using proof mass actuators. Dr. Umland joined JPL in 1990 as a Member of
Technical Staff in the Instrument Structures and Dynamics Group. He has
served as the lead structural technologist for the Precision Segmented
Reflector task, where he was responsible for extensive structural
testing and active structures technology demonstration, including active
damping and shape control. Currently, he is leading a piezoelectric
active member development effort for an active vibration isolation
application. He also has provided structural analysis and design support
to various JPL flight projects, including NSCAT, TOPEX, as well as Mars
Pathfinder.

**8. FACILITY**

JPL has an Actuators Characterization laboratory to measure the
electrical, mechanical (displacement) and thermal performance of
actuation materials and devices under controlled conditions. The system
is computer controlled with a 486/66MHz PC using LabView software to
allow symbolic programming. The software controls the data acquisition
(parallel or serial communication with instruments), signal processing
and display. Large number of electrical parameters can be analyzed in
the 10 Hz to 32 MHz frequency range using a Schlumbeger Impedance
Analyzer Model 1260. For the temperature control at vacuum conditions a
custom modified Janis ST-400 system is used. This system allows tests at
high vacuum up to 10-8 torr at broad temperature range from 77K to 450K.
The temperature can be controlled with an accuracy of ±0.1K. The sample
support allows testing 30 mm diameter devices with a cryostat positioner
resolution of ±25 m and 50 mm stroke. A series of electrical
feed-through and windows are available on the system to allow connection
to the impedance analyzer and proximity sensor. Further, windows are
available to assist in the sample handling as well as performing optical
test of the displacement using methods such as interferometry. The
displacement is measured with a Kaman Model KDM-7200 unit which is based
on the eddy-current method and it has a probe that provides a resolution
of 0.1 m and can be operated down to cryogenic temperatures. To activate
actuators an HP8116A Function Generator is used to drive a Burleigh High
Gain amplifier Model PZ-150M to generate up to 150V peak-to-peak 600 mA
signals. For applications, where high voltages are required, a Trek
amplifier Model 50/750 is used to generate up to ±750V and 20 mA
signals. This lab was established adjacent to the NDE lab which has
extensive state-of-the-art capabilities. The NDE lab allows the
evaluation of host materials and structures as well as determine the
integrity of actuators.

**SCHEDULE AND MILESTONES**

1 2 3 4 5 6 7 8 9 10 11 12

TASK 1: Material Analysis \<\-\-\-\-\-\-\-\-\-\--\>

TASK 2: Fabrication of a prototype motor
\<\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\>

TASK 4: Performance Tests \<\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\>

TASK 4: Evaluation of SSUM Control System
\<\-\-\-\-\-\-\-\-\-\-\-\-\-\--\>

**COST BREAKDOWN**

Totals

JPL \$50K

Cognizant labor

Paid leave and benefits

Travel

Procurement Contract - MIT \$48K

Materials

Tech. Division

Laboratory

General/Support

\-\-\-\-\-\-\-\--

Total \$98K

**REFERENCES**

1\. J. M. Hollerbach, I. W, Hunter and J. Ballantyne,\"A Comparative
Analysis of Actuator Technologies for Robotics.\" In Robotics Review 2,
MIT Press, Edited by Khatib, Craig and Lozano‑Perez (1991).

2\. A. Flynn, \"The Scoop on Ultrasonic Motors in Japan,\" Office of
Naval Research Asian Office Scientific Information Bulletin, NAVSO
P‑3580, Vol. 17, No. 2, April‑June, (1992) pp. 99‑102.

3\. Burleigh Instruments Product Catalogue, Burleigh Instruments, Inc.
Fishers, New York.

4\. \"The Application of Terfenol in Linear Motors Development,\" Proc
2nd International Conf. Giant Magnetostrictive and Amorphous Alloys for
Sensors and Applications, (1988) pp.1‑18.

5\. J. M. Vranish, D.P, Naik, J.S, Restorff, and J.P,
Toter,\"Magnetostrictive Direct Drive Rotary Motor,\" IEEE Trans, on
Mag., Vol. 27, No, 6, (November 1991) p 5335.

6\. K. Uchino, K. Kato, and M. Tohda,\"Ultrasonic Linear Motors Using a
Multilayered Piezoelectric Actuator,\" Ferroelectrics, Vol. 87, pp.
331‑334, 1988.

7\. T. Inoue, S. Takahashi, and M. Suga, \"Application of Ultrasonics to
Paper Transport Mechanisms,\" Techno, (May, 1989) pp. 4749, in Japanese,

8\. A. Kumada, \"A Piezoelectric Ultrasonic Motor.\"Japanese Journal of
Applied Physics, Vol. 24, Supplement 24‑2, pp. 739‑741, (1985).

9\. R. J Zemella, \"Design and Development of a Linear Traveling Wave
Motor,\" MIT Master\'s Thesis in Aeronautics and Astronautics. (May
1990).

10\. K. Minoru, S Ueha, and E Moru, \"Excitation Conditions of Flexural
Traveling Waves for a Reversible Ultrasonic Linear Motor,\" Journal of
the Acoustic Society of Japan, Vol, 77, No. 4, (April 1983).

11\. R, Inaba, A. Tokushima, 0. Kawasaki, Y. Ise, and H, Yoneno,
\"Piezoelectric Ultrasonic Motor,\" Proceedings of the IEEE Ultrasonics
Symposium, pp. 747‑756, (1981).

12\. \"Ultrasonic Motor\", Panasonic Technical Reference. Panasonic
Industrial Co., Division of Matsushita Electric Corporation of America,
1 Panasonic Way, Secaucus, NJ, (1987).

13 Y. Masaki, \"Vibrator and Ultrasonic Motor Employing the Same,\" U.S.
Patent 4,983,874, January 8, (1991).

14\. K. Hosoe, \"An Ultrasonic Motor for Use in Autofocus Lens
Assemblies,\" Techno. pp. 36‑41, May, 1989. in Japanese.

15\. \"Cannon Develops an 11x25mrn Miniature Ultrasonic Motor,\" Cannon,
Nikkei Mechanical, (June 1, 1992).

16\. \"Seiko Ultrasonic Micromotor Data Sheets\", Seiko Instruments
Inc., Precision Instruments Department, Consumer Products Div., 1‑9-1
Miyakubo, Ichikawa-shi. Chiba272, Japan, (1992).

17\. I. Okumura, and Izukawa.\"Vibration Wave Motor With Plural
Projection Vibrator.\" U.S. Patent 4580,073, Canon Kabushiki Kaisha,
(April 1, 1986).

18\. \"Micro Mo Miniature Drive Systems Catalog,\" Micro Mo Corp., 742
2nd Ave. South, SL Petersburg, FL, 33701,

19\. \"Mabuchi Heavy Duty Series Motor Catalog,\" Mabuchi Motor America
Corp., 475 Park Ave, (32 St.), New York, NY 10016,

20\. \"Operation Manual for The Ultrasonic Motor,\" Shinsei Corporation,
18. Kasuya 2‑chome. Setagaya‑ku, Tokyo, 157 Japan. (1989) ( in
Japanese).

21\. M. Kurosawa and S. Ueha,\"Efficiency of Ultrasonic Motor Using
Traveling Wave,\" Journal of the Acoustic Society of Japan, Vol. 44, No.
1, (1988) pp. 4046 (in Japanese).

22\. N. W. Hagood, W. H. Chung., A. von Flotow, \"Modeling of
Piezoelectric Actuator Dynamics for Active Structural Control,\" Journal
of Intelligent Material Systems and Structures, Vol, 1, No, 3, (July
1990) pp. 327‑354.

23\. B.K. Wada, J. Fanson, and E. F. Crawley, \"Adaptive Structures,\"
Adaptive Structures. AD-Vol 15, B.K. Wada (Ed.), The American Society of
Mechanical Engineers, New York, New York, (1989) pp. 1‑8.