**JET PROPULSION LABORATORY**

Submitted to the TeleRobotic Intercenter Working Group (TRIWG)

Meeting to be held at KSC, March 1-3, 1995

**LOW MASS, COMPACT, MUSCLE-ACTUATORS USING**

**ELECTROSTRICTIVE POLYMERS (ESP)**

Yoseph Bar‑Cohen

Material Science and Engineering Section, JPL

**ABSTRACT**

Miniature actuators that are inexpensive, low mass and consume low power
are increasingly needed to support robotic requirements of NASA
missions. Flight experiment opportunities for application of such
actuators are expected to be available as early as 1998 and throughout
the early part of the next decade. Electroceramic actuators also known
as solid-state actuators are increasingly finding applications for
actuation mechanisms. The objective of this proposal is to employ
electrostrictive polymers (ESP) to develop muscle actuators in order to
demonstrate the unique and superior actuation capabilities of these
materials. The application of ESP is involved with manageable technical
challenges which will be addressed in this proposal in order to develop
breadboard muscle-actuators for space applications. The superiority of
the technology will be demonstrated in a series of rigorous terrestrial
tests including simulated space environment.

1\. **OBJECTIVES**

> 1.1 Develop a muscle-actuator as an alternative mechanism for
> articulation of miniature robots using efficient electrostrictive
> polymers (ESP). ESPs will be fabricated from polymers bearing highly
> polar pendant groups to produce a strong electrostriction effect.
> Unique actuator configurations will be considered to implement the
> large displacement that ESP materials can produce.
>
> 1.2 Conduct tests to demonstrate the viability of miniature-actuators
> driven by ESP materials to meet future NASA missions. The ability of
> ESP actuators to form a low mass, compact and low power drives will be
> demonstrated. Specifically, the goal of this proposed task will be to
> develop an ESP-actuator with 30% lower mass, 20% lower volume and 20%
> lower power requirements compared to a base line electroceramic
> Inchworm actuator.
>
> 1.3 Transfer this technology to benefit NASA spacecraft devices
> ranging from micro-manipulators, ultra-dexterous and versatile robots,
> miniature platforms, miniature adaptive optics and deployment devices.

2\. **JUSTIFICATION**

Actuation devices (motors, etc.) are used for many space applications,
including; caging and release mechanisms, antenna and instrument
deployment, positioning devices, aperture opening and closing devices,
real-time compensation for thermal expansion in space structures, etc.
Increasingly, there are requirements to reduce the size, mass and power
of actuation devices. Electroceramics (piezoelectric and
electrostrictive) offer effective, compact actuation materials to
replace electromagnetic motors and they are used to articulate
spacecraft components (e.g. WF/PC II) as well as to perform various
robotic tasks. A wide variety of such solid state devices are becoming
available and being incorporated into motors, translators and
manipulators. In contrast to electroceramics, ESPs are emerging new
active materials with capabilities that cannot be matched by the rigid
and striction-limited ceramics. ESP materials are lighter and their
potential striction capability can be at least two orders of magnitude
higher than electroceramic materials. We propose to develop an effective
muscle-actuator that is driven by an ESP material and to take advantage
of polymers' resilience and the ability to engineer their properties to
meet NASA articulation requirements.

Potentially, ESP materials can be easily mass‑produced at low cost and
in any desired shape and they can be used to build MEMS type mechanisms.
They can be designed to emulate the operation of muscles while
maintaining low mass, high toughness, no strain hysteresis, no need for
poling, provide higher electrostrictive strain constant than
piezoceramics (potentially, 2 orders of magnitude higher) and have high
inherent vibration dampening characteristics. When compared to
electromagnetic motors, the proposed muscle actuators would not require
windings and magnetic flux returns circuits and therefore would be
inherently lighter and much more compact. ESP devices are expected to
generate high torque density at low speeds allowing to eliminate the
need for speed reducing gears saving further in mass while increasing
the devices precision and reliability. The proposed drive mechanism will
have self-braking at zero-power, reducing the power requirements.
Moreover, the proposed devices can operate in multi-orientation (several
degrees of freedom) for gimbaling miniature structures and platforms

**2.1 Flight Experiment opportunities and Science Acquisition Benefits**

Various upcoming missions planned for 1998 and beyond are considering
the use of miniature robotic devices that can potentially use the
proposed technology. Such NASA missions include Mars Exploration
programs, the recently approved New Millennium initiative and others.
This proposed program would establish an alternative actuation
enabling-technology for missions that place tight restrictions on mass,
size and power.

Muscle actuator can also offer a significant advancement in assembly,
maintenance and servicing machines equipped with the functional
equivalent of hands. This technology could operate in an Extra Vehicular
Activity or Intra Vehicular Activity mode as desired. Such capabilities
can support scientific experiments which are not possible using
inefficient heavy robots.

**2.3 Robotic Applications**

Muscle actuators that are low mass and consume low power are required
for various robotic applications including: (a) End effectors with
functional characteristics and capabilities reminiscent of the human
hand (b) Arms whose capabilities and strength-to-weight ratios are
within range of corresponding biological limbs and (c) Legs which will
permit walking robots to operate with mobility significantly better than
currently available.

**3. APPROACH**

Muscle-actuator will be developed to implement the large displacement
that electrostrictive polymers can produce when subjected to an electric
field. Several muscle-actuator configurations will be tested to select
an effective mechanism of muscle-actuation using such polymers. The
characteristics of electrostrictive (ES) materials will be taken into
account in the design of the muscle-actuator. In contrast to the
piezoelectric effect, where the displacement changes linearly with the
field, electrostriction phenomena is associated with a square of the
field at low voltages and becomes linear at high voltages. The
electrostriction constant of ESP materials is negative having similar
characteristics to muscles. If there is a need to expand and contract an
ESP material it can be subjected to a DC field and the displacement will
be controlled by an AC field within the amplitude of the electric DC
field. ESP can be designed to meet elastic stiffness requirements as
needed for the muscle-actuator and an electro-mechanical analysis will
be conducted to establish design criteria for effective
muscle-actuators.

**3.1 POLYMERS ELECTROSTRICTIVE CHARACTERISTIC ENHANCEMENT CONCEPT -**

Polymers are capable of producing electrostriction which can be
significantly higher than ES-ceramics \[1- 2\]. A comparison is given in
Table 1 where polymethylmethacrylate (PMMA) polymers of different
tacticity are compared to typical ES-ceramics. The basic mechanism of
electrostriction in organic polymers involves the alignment of highly
polar pendant groups (extremely polar organic groups such as amides,
nitriles, carbonates and other groups with strong dipole moments) by the
action of an applied electric field.

TABLE 1: Electrostrictive (ES) Materials

  ------------------------- ----------------------- ----------------------
  ES Material               ES constant m^2^/V^2^   Polymer/Ceramic

  α-PMMA                    -3.7 ^•^10^-16^         Polymer

  s-PMMA                    -7.7 ^•^10^-15^         Polymer

  i-PMMA                    -1.5 ^•^10^-14^         Polymer

  PMN-PT                    6.0 ^•^10^-16^          Ceramics

  PLZT                      6.0 ^•^10^-16^          Ceramics
  ------------------------- ----------------------- ----------------------

Effective electrostriction in polymers requires a backbone and
multi-functional side chains of well characterized polar pendant groups.
Tacticity of the backbone polymer and the dielectric constant of the
polar pendant will be selected to optimize the performance of the ESP
material. A series of resins bearing high modulus (high glass transition
temperature) with polar substituents will be considered for the backbone
polymers including; poly(acylonitrile) poly(4-chlorostyrene),
poly(ethyloxazoline), poly(4-vinyl phenol) and others.

Electrostrictive materials can be fabricated with different properties
including stiffness, electrostriction constant, density, dielectric
constant, etc. To determine the required ESP material properties for an
effective muscle-actuators, the electromechanical behavior of the
material will be studied both analytically and experimentally. The
relations between the various material properties and the
muscle-actuator performance will be evaluated in this study.

**3.2 TECHNICAL APPROACH**

We are proposing to use an interdisciplinary approach to develop a low
mass, compact and low power muscle-actuator that is driven by an
efficient ESP material. We are planning to develop in parallel (a)
effective ESP materials and (b) develop an effective muscle-actuator
that is based on ESP action. Initially, i-PMMA will be used to develop
several prototype muscle actuator configuration. As better ESP materials
are being identified they will be implemented into the drive mechanism
to enhance the force or torque that the actuator produces. This program
is proposed as a three years effort and will consist of the following
tasks:

TASK 1: *FABRICATION OF AN EFFECTIVE ESP MATERIAL -* Effective ESP
material will be developed using a backbone polymer with a high
free-volume to allow easy alignment of the pendant groups in response to
an electric field activation. A polar pendant group that can create a
strong polar interaction and a backbone polymer will be chosen through
an chemical and electromechanical analysis. The mechanical properties of
the ESP will be selected as required for the specific actuator drive
configuration.

The interaction of the polar pendant groups with the electric field is
responsible for the electrostriction effect and it leads to a negative
electrostriction coefficient (see Figure 1). It also allows the
prediction of the specific chemical modifications that are required to
increase the electrostriction constant. Polymers containing highly polar
pendant groups, that interact strongly with each other upon alignment,
should have inherently better electrostriction properties. This aspect
of the ES mechanism will be implemented by selecting commercially
available research grade polymers and molding them into test specimens.
Currently, we are considering the use of styrenyl- or methacryl-
polymers as a backbone, whereas for polar pendant we are considering
nitrile (CN), carboxylates (C(O) OCH~3~), amides (C(O) NH~2~), sulphones
(S(O) ~2~ CH~3~), and ethylenecarbonates (CH ~2~ CH~2~ OC(O)O). The
results will help identifying which functional groups yield the highest
electrostriction constants.

Figure 1: A schematic description of the mechanism of rotating polar
pendant group rotating around the backbone under an applied
field.![](media/image1.emf){width="5.539583333333334in"
height="1.3270833333333334in"}

The mechanism of the pendant groups rotation is facilitated by the free
volume present in the backbone polymer \[3\], which can essentially be
viewed as the empty space between successive chains in an amorphous
polymer in which a pendant group can freely move. By chemically
modifying the polymer backbone more free space can be created to provide
the required space for the orientation of the polar pendant groups. This
can be done by adding bulky pendant groups in addition to the polar
groups that are present. For example, by changing a methacryl monomer to
an i-propyl or t-butyl monomer the resulting polymer will have chains
that cannot be packed closely together allowing the pendant groups to
freely orient themselves.

Once effective ESP materials are made they will be tested rigorously
prior to use for construction of muscle-actuators. The synthesized ESP
materials will be subjected to various thermal, electrical and
mechanical conditions to determine their actuation characteristics. High
precision displacement and force measurements will be conducted to
determine the output force/torque/displacement/strain capabilities and
conversion efficiency of the material as a function of the input
voltage. The capabilities of JPL to simulate space environments will be
used to determine the characteristics of the material.

TASK 2. *DEVELOPMENT OF MUSCLE ACTUATOR -* The requirements and
specifications for the muscle actuator will be determined in cooperation
with various JPL flight projects to establish a relevant
muscle-actuators with potential technology transfer to flight
experiment. Compact muscle actuators that employ ESP materials will be
developed to harness the high displacement at low power, mass and size
capabilities of these materials. This task will be conducted in parallel
to the development of the ESP material and as the material is improved
it will be incorporated into the actuators. To allow effective design of
the muscle, electro‑mechanical analysis will be made and the prediction
of the actuator components performance will be corroborated. Several
muscle-actuator configurations will be considered to select an effective
actuation mechanism for ESP materials. As goal for the ESP actuator
breadboard, it will be designed to have at least 30% lower mass, 20%
lower volume and 20% lower power requirements compared to an equivalent
Inchworm (Burleigh Instruments) that is driven by piezoceramics.

1: [DESIGN AN ESP TENDON-ACTUATION]{.underline} - A muscle actuator will
be designed in the form of a compact tape-drive motor as shown in Figure
2. A unit drive muscle will consist of a set of a tape and an ESP strip
actuator. To enhance the driving force capability of muscle actuator a
stack of pairs of tapes/ESP-strips will be used. A tendon will be
attached to the two ends of the drive-tape group and will serve as the
translator of the driving force to the required manipulation device
(e.g. robotic arm, walking legs, etc.). The tapes strips will have a
guiding groove in their center and a spring loaded preload screw will
provide griping force and a guide for the linear motion of the tapes.
The grooves will be ended with limiting points to serve as bounds for
the tendon total displacement. The total movement of the tendon will be
limited by the length of the drive-tapes in the compact muscle-actuator
and the distance between the limitation points.

This tape-drive ESP muscle-actuator will effectively be a linear
standing-wave motor \[4\] as shown in Figure 2b. The ESP strips will be
electroless plated to allow subjecting the ESP material to the drive
electric field. The actuation mechanism of this muscle actuator will
depend on the friction between the tapes and the ESP-strips as well as
the linear vector force that is induced by the ESP-strips acting
parallel to the tape (see Figure 2c).

![](media/image2.emf){width="3.033333333333333in" height="2.43125in"}

![](media/image3.emf){width="3.6694444444444443in" height="2.475in"}

Figure 2: Muscle actuator using multilayer tape and a traveling
standing-wave linear-drive mechanism.

A muscle-actuator will be designed in relation to the specifications
that are determined in the program initiation phase. A motor will be
fabricated and tested to determine its performance envelop and define
requirements for the ESP material . As the material is optimized the
motor efficiency will be increased. The capability of the muscle
actuator in terms of mass, power, size and actuation will be determined
and compared to reported data for electroceramic actuators. Efforts will
be made to demonstrate the capability of ESP materials as a superior
alternative to conventional actuation devices.

2: [ALTERNATIVE ESP MUSCLE ACTUATORS]{.underline} *-* Jointly with the
University of New Mexico (UNM) alternative mechanisms of
muscle-actuators will be developed and evaluated. These mechanisms will
be based on a modification of the current UNM mechanisms using effective
ESP materials that will be fabricated at JPL. For this purpose, we will
design, fabricate and test three tendon actuator configurations that
will be driven by ESP materials (using initially i-PMMA). The
configurations that will be examined include:

1.  An end-less loop tape-drive will be designed with an ESP tape
    wrapped around a pulley for rotary actuation. To induce rotary
    motion, the tape will be designed to create differential contraction
    on the opposite sides of the area of contact between the tape and
    the pulley.

2.  Linear contractile muscle-type actuator \[5\] will be designed using
    ESP tapes that will be connected at two ends of an arm similar to
    the operation of biological muscles. This muscle system will be
    configured of an ESP antagonist muscle pair. The actuator
    configuration will emulate the human skeletal system myoactuation of
    antagonistic action of muscle pairs.

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1.  A bending type ESP muscle system will be designed to operate similar
    to a bimorph actuators, as shown in Figure 3
    \[6\].![](media/image4.emf){width="3.147222222222222in"
    height="1.1201388888888888in"}

Figure 3: Schematic description of the proposed bending type ESP muscle.
The curved doted areas are showing two tendons that will act as a pair
in a bimorph configuration.

TASK 3: *DEVELOP A DEMONSTRATOR DEVICE* ‑ To demonstrate the performance
of ESP muscle-actuators we will design and fabricate a demonstrator arm
which will be driven by ESP materials. The demonstrator device will be
subjected to a series of electrical, mechanical and thermal tests to
determine the performance envelop of the actuator and to form a baseline
comparison with conventional drive mechanisms. Considering the fact that
the density of polymers is only about 30% of the density of
electroceramic materials ESP driven actuators can be expected to be
significantly lighter. Further, their two order of magnitude stronger
striction capability indicate a powerful drive mechanism. Efforts will
directed to develop force delivering capability to overcome the
limitations of polymers in terms of elastic modulus.

**3.3. LEVEL 1 DEMONSTRATION MILESTONES**

A sequence of gradually more complex tests in the terrestrial atmosphere
will drive this program and technology will be transferred incrementally
to emerging flight systems. The following describes the milestones by
tasks for this proposed program.

*[TASK 1]{.underline}: Efficient ESP Materials* FY\'96 FY\'97 FY\'98 \|

Definition of actuation specifications \-\-\--\"

Electromechanical analysis \-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\" \-\-\--\"

ES-Polymer selection and fabrication \-\-\-\-\-\-\-\--\"
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\"

Demonstration and documentation \--\" \--\"

*[TASK 2]{.underline}: Muscle Actuator*

Design muscle actuator \-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\"

Develop muscle actuator \-\-\-\-\-\-\-\--\" \-\-\-\-\-\-\-\-\-\--\"

Tests and performance-evaluation \-\-\-\--\"
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\" \-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\"

Demonstration and documentation \--\" \--\" \--\"

*[TASK 3]{.underline}: Demonstrator*

Design miniature demonstrator \-\--\"

Fabricate demonstrator \-\-\--\"

Performance envelop analysis \-\-\-\-\-\-\-\-\-\-\-\-\-\--\"

Demonstration and documentation \--\"

**4. PARTICIPANTS:**

This proposal involves a teaming between JPL, GSFC and the University of
New Mexico. Participation of industry will be explored during this
proposed program where potential match funding and cooperative
agreements will be considered. Potential companies include Burleigh
Instruments who is the manufacturer of the Inchworm linear motor with
whom the JPL Principal Investigator have conducted a similar cooperative
efforts in the Pluto-Fast-Flyby preproject phase in FY'94. The synthesis
of effective ESP materials will be made by Section 355, the design and
fabrication of the ESP muscle actuator and the demonstrator will be done
jointly with Section 345, University of New Mexico and GSFC. Section 355
will perform the electromechanical analysis and the demonstration of the
efficiency of the ESP material, the muscle-actuator and the demonstrator
device.

**5. DELIVERABLES:**

The proposed program introduces a new family of actuation technology
that supports the NASA goals of cheaper, smaller and better. It will
enable to produce new types of telerobots to enable important flight
opportunities. A methodology for the fabrication of effective ESP
materials will be developed and documented for fabrication of muscle
actuators. Effective muscle-actuators that utilize ESP materials will be
developed to establish an alternative to existing drive actuators. An
ESP-muscle actuator breadboard will be demonstrated with 30% lower mass,
20% lower volume and 20% lower power requirements compared to an
equivalent Inchworm (Burleigh Instruments) that is driven by
piezoceramics. While it maybe premature to state actual costs estimate
for the actuator but it is anticipated that this type of device will be
significantly cheaper to fabricate than its electroceramic equivalent.

**6. COMMERCIALIZATION POTENTIAL**

The low cost and mass production potential of ESPs can open a wide range
of commercial applications including actuation of mechanisms in
automobiles and consumer products. These materials can potentially be
used for active noise damping in aircraft cabinets for passengers
comfort. Artificial muscles for medical applications are another
important application of ESP actuators.

Most biological joints are controlled by antagonistic system of
contractile muscles, much the same way as our own biceps-triceps
antagonistic muscle system articulates our arms. A linear contractile
actuators built as a result of this effort can be used to manipulate
skeletal (e.g., human) systems. The UNM research team has already
experimented \[6\] with this concept designing attire, boots and gloves
that can be worn externally and actuate an internal structure such as
astronaut\'s hands, legs and feet in space or on other planets.

**7. FUNDING REQUIREMENTS**

The following describes the funding requirements for each of the member
organizations:

FY\'96 FY\'97 FY\'98

JPL \$70K \$70K \$65K

GSFC \$60K \$60K \$65K

U. of New Mexico [\$40K \$45K \$50K]{.underline}

**TOTAL** \$170K \$175K \$180K

**8. FACILITIES**

JPL has a chemistry lab to prepare the required ESP materials and to
configure ESP strips and fibers as active elements for the
muscle-actuators. Further, it has recently established an Actuators
Characterization laboratory to measure the electrical, mechanical
(displacement) and thermal performance of actuation materials and
devices under controlled conditions. A 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 a temperature
range from 77K to 450K. Actuation electronics, data acquisition and
processing hardware and software are also available and have been used
for the development of actuation technology for PFF pre-project phase.
To determine the performance of actuation mechanisms under thermal and
mechanical loads a custom designed system was purchased recently from
SATEC (expected delivery - March 95). This lab was established adjacent
to the NDE lab allows the evaluation of active materials and structures
as well as the determination of the integrity of actuators.

Goddard Space Flight center is the leading NASA flight center in
Astrophysics. As such, it is responsible for designing and building many
satellites and scientific instruments for space exploration.
Accordingly, it has extensive experience and expertise in building
electromechanical devices to support these missions, including robots.

The Intelligent Materials, Structures and Systems Laboratory at the
University of New Mexico is equipped with an IBM 7565 (white cloud)
robotic system, a 5-watt Argon laser system, computer-controlled ovens,
furnaces and ventilation hood, refrigerators and freezers, microscopes,
large chemical inventory, computer-controlled data acquisition systems,
computer-controlled signal generators, measuring devices and multimeters
as well as a two experimental setups to characterize and test artificial
muscles.

**9. PRINCIPAL INVESTIGATORS**

**Dr. Yoseph Bar-Cohen** is the Task Manager of the program. He is a
member of the Technical Staff responsible for the Advanced Actuation
Technologies at the Materials Science and Engineering Section of the Jet
Propulsion Laboratory (JPL),. Since joining JPL in 1991, he has
established state-of-the-art Active Materials Characterization and NDE
Labs. He received his Ph. D. in Physics from the Hebrew University at
Jerusalem, Israel, in 1979. He has more than 23 years experience in
areas related to sensors, active materials and NDE, including his
positions at the Israel Aircraft Industry, SRL at the Air Force
Materials Laboratory and McDonnell Douglas Corporation. He originated
the use of linear solid state motors for the articulation of the
scanning mirror of the PFF pre-project phase and is currently developing
an ultrasonic motor for the Micro Lander Dexterous Manipulator. 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).

**Paul B. Willis** is a polymer chemist in the Materials Science and
Engineering Section of the Jet Propulsion Laboratory (JPL). After
graduate work in the Polymer Science Department of the University of
Massachusetts he worked in industry doing contract research and
development for ten years prior to joining JPL in 1988. His primary
areas of interest include polymer synthesis, surface chemistry,
composites, adhesives, life analysis and applied mechanics. He has more
than twenty years experience in commercial and aerospace technologies.
He currently holds the position of Senior Research Engineer.

**Dr. Mohsen Shahinpoor** is a robotics and intelligent systems design
professor and director of Intelligent Materials, Structures and Systems
Laboratory at University of New Mexico. He holds several patents on
robotic electromechanical actuators and artificial muscle systems (see
US Patent 5,250, 167). His shape-memory alloy actuator system is
currently used by Sandia National Laboratories scientists for
intelligent dynamic shape control of large mirrors. He has also been
involved, as a research team member, in the design and fabrication of a
micro-miniaturized robotic linear actuator system (The world\'s smallest
robot) with research scientists of Edwards AFB (Dr. Wesley Hoffman) as
well as Hughes-STX (Martin Buemeister). He is a registered licensed PE
and holds a Ph.D. in Mechanical and Aerospace Engineering.

**John M. Vranish**, will be responsible for the design and fabrication
of the tendon-actuator. He is an aerospace engineer in the
Electromechanical Branch, GSFC. He holds several patents on robotic
electromechanical systems, mechanisms, and tactile proximity force
sensors, GSFC Inventor of the Year consecutively between 1992 to 1994.
His \"Capaciflector\" (capacitive reflector) sensor skin is finding
wide-spread use across NASA and industry and was successfully operated
as part of a precision robotic assembly experiment on the Shuttle
Discovery in Sept. 94 (STS64). The Capaciflector is becoming widely in
use for space applications as a fundamental sensor for robotic collision
avoidance, berthing and docking and for robot walkers. He graduated from
West Point graduate and received his MS in electrical engineering from
the George Washington University.

**10. REFERENCES**

> 1\. K. Ohara, M. Hennecke and J. Fuhrmann, Electrostriction of
> Polymethylmethacrylates, Colloid & Polymer Sci. Vol. 260, pp. 164-168
> (1982).
>
> 2\. T. Furukawa and J. X. Wen, "Electrostriction and Piezoelectricity
> in Ferroelectric Polymers," Japanese Journal of Applied Physics, Vol.
> 23, No. 9, (1984), pp. 677-679.
>
> 3\. J. M. Cowie, "Polymers: Chemistry and Physics of Modern
> Materials," Intertext, London (1973).
>
> 4\. T. Sashida and K. Takashi, "An Introduction to Ultrasonic Motors,"
> ISBN 0-19-856395-7, Monographs in Electrical and Electronic
> Engineering, Oxford University Press Inc., NY, (1993).
>
> 5\. M. Shahinpoor, G. Wang and M. Mojarrad, \"Electrothermo-Mechanics
> of Spring-Loaded Contractile Fiber Bundles with Applications to Ionic
> Polymeric Gel and SMA Actuators\", Proc. Int. Cong. Intelligent
> Materials, ICIM\'94, edited by C.A. Rogers and G.G. Wallace, Technomic
> Press, pp. 1105-1116, (1994).

6\. M. Shahinpoor and M. Mojarrad, \"Active Musculoskeletal Structures
Equipped with A Circulatory System and A Network of Ionic Polymeric Gel
Muscles,\", Pro. ICIM\'95, edited by C.A. Rogers and G.G. Wallace,
Technomic Press, pp. 1079-1085, (1995).