Design and Construction of a Liquid-Cooled, Flexible, Permanent … · 2020. 8. 7. · Design and...

Design and Construction of a Liquid-Cooled, Flexible,

Permanent-Magnet Tubular Linear Motor Artificial Muscle

A Thesis Presented

by

Juan Antonio Woodroffe

to

The Department of Bioengineering

in partial fulfillment of the requirements

for the degree of

Master of Science

in

Bioengineering

Northeastern University

Boston, Massachusetts

April 2020

To my family, without which I wouldn’t be where I am today; my girlfriend, who tolerated having

the lab equipment set up in our kitchen for a few weeks; and all the educators of my life, who have

helped me see further.

i

Contents

List of Figures iv

List of Tables vi

Acknowledgments vii

Abstract of the Thesis viii

1 Introduction 11.1 Problem Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Understanding Biological Muscle . . . . . . . . . . . . . . . . . . . . . . 51.2.2 Biomimetic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 A Liquid-Cooled, Bendable, Permanent-Magnet Tubular Linear Motor . . 81.2.4 Ferrofluid Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 State of the Art 122.1 Quantifying the Performance of Muscle-Like Actuators . . . . . . . . . . . . . . . 132.2 Types of Muscle-like Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.1 Highly Oriented Semicrystalline Polymer Fibers . . . . . . . . . . . . . . 162.2.2 Twisted Nano-/Microfiber Yarns . . . . . . . . . . . . . . . . . . . . . . . 172.2.3 Shape Memory Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.4 Dielectric-Elastomer Actuators (DEAs) . . . . . . . . . . . . . . . . . . . 182.2.5 Stimuli-Responsive Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.6 Pneumatic Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Conventional Permanent Magnet Tubular Linear Motors . . . . . . . . . . . . . . 192.4 Bendable Permanent Magnet Tubular Linear Motors . . . . . . . . . . . . . . . . 212.5 Summary Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6 Thesis Contributions and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Theory and Initial Validation 253.1 Theoretical Models for a Single Solenoid . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

ii

CONTENTS

3.1.2 Electric Power and Heat Management . . . . . . . . . . . . . . . . . . . . 293.2 Experimental Validation of the Models . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2.1 Experimental Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.2 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2.3 Power and Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3 Generalized Model for a PMTLM . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Design and Fabrication 404.1 Overview of Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2 Overview of Electrical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.1 Circuit Board Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2.2 Arduino Motor Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 Testing, Results and Discussion 535.1 Actuator Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.1.1 Description of Data to be Collected . . . . . . . . . . . . . . . . . . . . . 535.1.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6 Conclusion 586.1 General Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.3 Limitations and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.4 Closing Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Bibliography 61

iii

List of Figures

1.1 Humanoid robots and industrial robot arms are made possible by the field of robotics,which strives to turn the cyclical, continuous motion of conventional actuators intointermittent, varying motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 The structure of biological muscle. . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Electric motors, both linear and rotary, contain analogous parts and function by the

same physics principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Final actuator design, CAD model. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Summary of muscle’s performance metrics. Figure by Mirvakili et. al. [30] . . . . 152.2 Different types of Permanent Magnet Tubular Linear Motor (PMTLM) topologies.

Figures are from Wang. et. al. [56] . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3 Different linear motors, each meant to function as muscle-like actuators. Each of

these employ different cooling strategies, core design, core topology or magneticcircuit designs. Urban et. al.’s motor serves as the most equivalent design to the oneconceived during this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1 Schematic of solenoid dimensions and desired point, P . . . . . . . . . . . . . . . . 263.2 Schematic of a magnet interacting with the solenoid. The magnetic core can be

modeled as two infinitesimally thin surfaces of opposing chargeN and S, of radius,r, and separated by distance, h. One can consider the magnetic field generated bythe solenoid at each surface separately and add them together. The South pole is ata distance ZS and the North pole is at a distance ZN . . . . . . . . . . . . . . . . . 27

3.3 Components of testing fixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4 Data processing sequence for raw force data and final comparison plot: Measured

force vs. Theoretical force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.5 Comparison plot of theoretical model for heat vs. measured data for heat. As can be

seen in the figure, the temperature rise of the coils was substantial which indicatesthat the resistance was changing over time. Because of this, the first version ofEquation 3.13 which includes the resistivity-temperature dependence of generatedheat was used with Equation 3.19 . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.1 The core of the actuator and a cross-sectional view of the ball and socket component. 414.2 Parts used in the mechanical design of the actuator and dimensions of actuator com-

ponents (coils are for illustrative purposes and not to scale). . . . . . . . . . . . . . 43

iv

LIST OF FIGURES

4.3 Coil phases and winding directions. Each letter represents a different coil. Letterswith apostrophes indicate that they are wound with the same wire, but in a differentdirection and therefore will always have a current flowing in the opposite direction.Notice as well that each individual coil of the same phase interacts with the samelocal magnetic field (as long as the core is fully inside the actuator). This means thatwhatever force is produced by the interaction of a coil, at a specific phase, and thelocal magnet is multiplied by the number of coils of that phase that are in the actuator. 45

4.4 Circuit board wiring diagram. Each of the colors represents a specific sub-circuit(or coil) that can be individually controlled in terms of magnitude (using PWM)and direction (by activating the embedded controller H-bridges). The pump canalso be controlled. Future iterations of the actuator could potentially contain embedtemperature sensors that modify the behavior of the pump when needed, similar tohow the heart changes flow rate in response to muscle activation. . . . . . . . . . . 46

4.5 Basic stepper motor control. Variations in this code can be created to make themotion more smooth by incorporating Sinusoidal PWM or to control speed by in-creasing the delay between coil activation. . . . . . . . . . . . . . . . . . . . . . . 47

4.6 Overview of the actuator fabrication process. Using the core mold, the core piecesare aligned and then epoxied. For the stator, 3D printed dividers are inserted aroundthe flexible inner tube, aligned with the actuator mold and then glued. The coils arethen individually wound into three separate phases. Sets of three (shown in brown)are going in one direction and sets of three (shown in grey) are going in the other.Once the coils are wound, the stator is inserted into the flexible outer tubing (showntransparent here) and the 3d printed end caps are placed and glued. The final step isto carefully cut out holes for the inlet and outlet tubes and glue around them to forma water-tight seal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.7 Images of the final actuator, with and without the outer flexible tube. . . . . . . . . 514.8 Close up of the final actuator. The final actuator did not incorporate the inflow and

outflow tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.1 Experimental set up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

v

List of Tables

2.1 Table summarizing the performance metrics of various muscle-like actuator tech-nologies. Notice how biological muscle is not the best in any one category, andeven has very poor performance in the stress metric relative to other actuators. How-ever, it achieves both a usable strain and strain rate (two properties that are usuallyinversely related) and, perhaps most importantly, has a bandwidth second only toDialectric-Elastomers. This allows it to be responsive, an invaluable trait when con-sidering human dexterity. Moreover, although its work density isn’t particularlyimpressive, its specific power combined with its efficiency means it can provide ac-tuation in a ”lightweight” package. This, combined with its incomparable cycle life,means it is also very durable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1 Table describing the variables used in equation 3.9 to estimate the force producedby the solenoid and magnet based on various parameters. . . . . . . . . . . . . . . 35

3.2 Table describing the variables used in Equation 3.19 to estimate the surface temper-ature of the solenoid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1 Table of performance metrics results for the actuator. . . . . . . . . . . . . . . . . 56

vi

Acknowledgments

Here I wish to thank those who have supported me during the thesis process. First andforemost my PI, Samuel Felton, who allowed me to work on a topic I was interested in even if itdidn’t exactly fit into the typical projects our lab focused on. Additionally, he was always availableto offer guidance, advice or supportive words when needed. Next I’d like to thank the membersof my lab Chang Liu, Katiso Mabulu, Marcos Oliveira and Akshay Vaidya for always helping meout when I needed it and being overall cheerful influences. Finally, I’d like to thank NortheasternUniversity for providing me with the resources and funds to pursue this research.

vii

Abstract of the Thesis

Design and Construction of a Liquid-Cooled, Flexible, Permanent-Magnet

Tubular Linear Motor Artificial Muscle

by

Juan Antonio Woodroffe

Master of Science in

Northeastern University, April 2020

Dr. Samuel Felton, Adviser

Conventional actuators are well suited for cyclical, continuous work and out match hu-man muscle in sheer power production and endurance, however, there are still many tasks - namelythose that require dexterity or variable power outputs - that they cannot do or do less effectivelythan biological muscle. Additionally, from a material perspective, current actuator technologiesare stiff and heavy which makes them likely to cause damage if they impact another object. Withrobots increasingly cohabiting alongside humans, this is a concern. Effectively addressing thesewill have a great impact on the future. In order to achieve and eventually exceed biological perfor-mance, new, muscle-like actuators are needed. A muscle-like actuator was designed by replacingthe structure of a permanent-magnet tubular linear motor (PMTLM) with soft materials or no mate-rial in places where conventional PMTLM design would call for stiff ones. Various prototypes wereconstructed and a theoretical force model, used to estimate various properties of the actuator, wasdeveloped and validated. The final actuator design incorporates only two stiff materials: the coppercoils and the core magnets. Basic testing of the actuator in order to determine quantitative perfor-mance parameters was performed. A very modest stress of .001 MPa was able to be achieved witha typical strain of about 10 % and a specific power of .0001575 kW/kg. Future iterations of theactuator could greatly improve on this performance. Regardless, its tubular shape, flexibility andeasy controllability allows for novel, parallel actuation schemes and favorable material properties.Additionally, although not used in the final design, the actuator was designed to allows for a ferro-magnetic fluid cooling system to be incorporated in order to remove heat from the coils and makethe actuator smaller and more powerful than it otherwise would be.

viii

Chapter 1

Introduction

Nature has a multitude of ingenious and unbelievable ways it creates motion. From the

microscopic rotary engine that powers the bacterial flagellum to thousands of RPM, to the spring

loaded claws of a mantis shrimp that allow it to punch with an acceleration of more than 10,000

times that of gravity, nature has made one thing clear: for the vast majority of the animals on the

planet, motion means survival. By far the most common biological creator of motion, or actuator, is

muscle. As a system, it offers several advantages over conventional actuators. Biological muscle is a

variable stiffness structure, allowing it to isometrically stabilize joints and vary overall system flex-

ibility. Its hierarchical structure allows the exact same actuation system to be used across 6 orders

of magnitude, from the micrometer to the meter scale, making it highly modular. Biological muscle

has been found to have a relatively high mechanical efficiency due to its compliant tendons capable

of storing mechanical energy, its low weight, and its high linear force generation [40]. Moreover,

its soft structure, flexibility and narrow tubular shape allows muscle to be a part of a system that

safely interacts with its surroundings and allows for parallel actuation mechanisms. Many of to-

day’s more advanced robots and machines would benefit from these features, making the creation

of an artificial muscle with comparable characteristics to biological muscle a potentially disruptive

technology. Imitating these features, however, has been exceedingly difficult using conventional

actuators. A closer look at biological muscle may suggest a way to bridge this gap. This thesis

explores the design and fabrication of a biologically inspired bendable electromechanical actuator.

1

CHAPTER 1. INTRODUCTION

1.1 Problem Background and Motivation

Humanity has successfully and to spectacular effect multiplied its ability to produce mo-

tion through out history. From manual labor to draft animals, through waterwheels and windmills, to

steam engines and electric motors, various kinds of actuators have supported our transition from no-

madic subsistence to post-industrial surplus [40]. Traditional actuators are well suited for cyclical,

continuous work and out match human muscle in sheer power production and endurance. However,

there are still many tasks that they can not do or do less effectively than biological muscle. By

themselves, they are not well suited for tasks that require intermittent, non-cyclical motion, such as

dexterously manipulating exoskeletons and prosthetics; small size, such as actuating small medical

devices [25, 29]; or variable power outputs, such as navigating robots in uneven terrain [37, 29]. All

technologies that will have a great impact on the future.

In a certain sense, the modern field of robotics was the result of acknowledging these lim-

itations and a desire to address them. Through sophisticated software, path planning, and controls,

it became possible to use traditional actuators in unconventional ways. As shown in Figure 1.1, a

great deal of progress has been made. Within the field of robotics, two main actuator types exist:

electric motors and fluid actuators [40].

(a) Atlas, by Boston Dynamics (b) Industrial Robotics Arms

Figure 1.1: Humanoid robots and industrial robot arms are made possible by the field of robotics,

which strives to turn the cyclical, continuous motion of conventional actuators into intermittent,

varying motion.

Electric motors are attractive because they offer high efficiency and torque while being

2


easily controlled. Examining these characteristics more carefully, however, limitations become

clear. Electric motors are normally built to operate towards higher rotation speeds to maximize their

efficiency. The fast rotary motion of the motors is then converted to a slower joint rotation (and

stronger torque) by using gears or other ”clockwork” mechanisms. These are often bulky, heavy,

and lower the mechanical efficiency of the system, bringing the overall maximum power output per

unit mass to below that of muscle [25]. In practice, maximum power output determines how quickly

robots can move and how much mass they can move. If one wishes to move a larger mass more

quickly one necessarily needs a bigger motor. In articulated robots using conventional design1, this

quickly becomes a problem. As the articulated arm becomes longer and incorporates more joints,

the issue of weight is compounded - the arm must rely on larger and larger actuators towards the

base in order to support the weight at the extremities.

Fluid actuators - hydraulic or pneumatic - solve many of the problems of electric motors,

but require considerable support equipment such as the fluid system, valves, and a pump [40].

Because of this, these types of systems cannot be scaled down (usually being >40kg) and generate

smoke and noise which limits their use to outdoor environments [17]. Even with the weight of all

the support equipment included, fluid actuator systems exhibit a power-to-mass ratio about the same

as that of muscle [25] during moderate use. However, for motions that require brief periods of high

power output, such as sprinting, hydraulic actuators lose efficiency since the system is continuously

shunting fluid in order to accommodate a higher actuation frequency. Pneumatic actuators do not

have this issue, but have other shortcomings such as the need for a larger pump and added modeling

complexities because of the compressibility of air.

From the material perspective both electric and, to a lesser extent, fluid actuators suffer

from a similar problem. With robots increasingly cohabiting alongside humans in confined spaces,

safety is becoming more of a concern. Current actuator technologies and the objects they actuate

are stiff and heavy which means that when they impact another object they’re more likely to damage

themselves or, because of their high inertia and stiffness, the other object. If the other object is a

human, the impact could cause injury. Much like the realization that cyclical actuators required

their own field of study - robotics - in order to create non-cyclical motion, the realization that

soft materials also offer unique benefits resulted in a relatively modern field within robotics called

soft-robotics. Much of the focus of soft robotics is in the design and study of variable stiffness

structures, bendable electronics, and of course soft actuators. Not surprisingly, biological muscle is1I.e. placing the electric motors at the joints.

3


a preeminent example in this field. In light of this, part of the motivation for creating a muscle-like

actuator stems from the fact that it is by definition soft; it tends to bend and as a result is harder

to break. Moreover, when it impacts an object it tends to deform instead of maintaining its shape

which allows the impact to be spread out over a larger area reducing the overall pressure from the

impact. This softness allows it to be more durable and interact with the world more safely.

Many of the performance problems with both electric motors and fluid actuators could be

solved by high density energy sources or pumps, by advances in materials science or by additional

improvements to the design of electric motors such as incorporating active cooling. Many of the

materials problems could be solved by similar means. These solutions are either expensive, complex

or, in the case of widely available high density energy sources or applicable materials, yet to be

discovered. The material problems are currently being investigated by the field of soft robotics and

although progress has been made [15, 14, 30], accurately imitating biological muscle is a difficult

task. As previously mentioned, software solutions, path planning and controls have allowed us to

achieve impressive feats of motion in the field of robotics using conventional actuators2, but these

solutions can only take us so far without sophisticated hardware to match it. In order to achieve and

eventually exceed biological performance and versatility, new, muscle-like actuators are needed.

1.2 Approach

The ideal actuator would have similar characteristics to biological muscle. It would be

lightweight, soft, scalable and produce a high linear force. In addition it would be highly control-

lable, in terms of actuation speed, strain and resolution, and would consume little energy. Just like

biological muscle fibers, its structure would allow its basic unit to be connected in parallel in order

to produce more force or vary stiffness when needed [23]. All these properties are made possible in

muscle by a distinct multiscale structure. Imitating this structure down to the nanometer scale would

be very difficult, but some features of the larger scales could be adapted and used in the context of

an electromechanical device, specifically a permanent-magnet tubular linear motor (PMTLM). Al-

though it is a type of electric motor, and traditionally uses rigid components, the approach was taken

that a lightweight, scalable, and bendable motor of this type could be constructed if the only stiff

parts of the actuator are the copper coils and the core magnets. Although it wouldn’t truly be a soft2Look no further than the Boston Dynamics Atlas robot: https://www.youtube.com/watch?v=

_sBBaNYex3E

4

https://www.youtube.com/watch?v=_sBBaNYex3E

https://www.youtube.com/watch?v=_sBBaNYex3E


actuator, its tubular shape and bendability would be advantageous. Moreover, it would be controlled

just as easily as a conventional electric motor and would allow for parallel actuation methods..

1.2.1 Understanding Biological Muscle

(a) Muscle’s hierarchical structure. (b) Muscle’s microscale transport system.

Figure 1.2: The structure of biological muscle.

Biological muscle has several aspects that make it particularly difficult to imitate. A key

property of muscle is that is has a hierarchical structure at many different scales (Figure 1.2a). At the

nanometer scale, biological muscles has more in common with a linear stepping motors than with

strain-based actuators [59]. As the Myosin moves along the Actin chain it brings the Z line closer

together. Muscle contraction is therefore the sum-total of the force produced by individual actin-

myosin motors. At the micrometer scale, muscle is made up of thousands of these structures, known

as Sarcomeres, arranged in series within a Myofibril. These are grouped together within a capillary-

Mitochondrion reticulum (Figure 1.2b) that brings in nutrients, produces and distributes fuel, and

removes chemical and thermal waste [40, 12]. At this point, distinct morphological characteristics

start to manifest - depending on the type of muscle fiber, the capillary-mitochondrion reticulum will

have a different structure. Slow-twitch muscles fibers, which contain less sarcomeres in parallel,

high amounts of myoglobin and mitochondrion, and a dense network of capillaries, are thinner

and appear red whereas fast-twitch muscles, which contain less of these, are wider and appear

white [43]. At the millimeter scale, muscle is made up of groups of Myofibril which are grouped

5


in parallel to form muscle fiber groups. Different individual muscle fiber have distinct functional

characteristics. Although as many as 7 types of muscle fibers have been delineated [43, 47], three

main types are usually identified. In general, fast-twitch (type IIA and IIB) muscle fibers produce

high force, but have low endurance; slow-twich (type I) muscle fibers produce low force, but have

high endurance. Most muscles have a combination of these three with subsets of ”in between” fibers.

The proportion of each type within a muscle depends on the lifestyle of the person, genetics and

the locomotive function of the muscle. At the mesocale, muscle is divided into groups of the same

muscle fiber type within a muscle fascicle. Each group is individually-controlled by motor units

that connect to the nervous system. At the macroscale, the muscle fascicles are then arranged in

parallel along the length of the entire muscle and eventually attach to the joint. The way the muscle

attaches to the joint depends largely on its locomotive function: muscles that move large amounts

of mass include series elastic elements (i.e. tendons), whereas muscles that move non-load-baring

biological structures exclude tendons [50]. These architectural features give muscle many of its

desirable functional properties.

Muscle has the ability to modulate force and strain by activating multiple muscle fibers

in parallel or multiple sarcomeres in series by a process known as recruitment [26]. At its peak,

muscle produces a normalized force of about .35 MPa, a strain of about 40% and has a maximum

specific power of about 400 W/Kg for endurance athletes [44]. In accordance to Henneman’s Prin-

ciple, as more force is needed muscle recruitment will occur from slow twitch (low force) fibers

to fast switch (high force) fibers. This provides two very important benefits: it decreases energy

expenditure by utilizing high endurance, more efficient slow-twitch muscle fibers first and only us-

ing low endurance, lower efficiency fast-twitch fibers when needed [44]. This also allows for fine

control of force at all levels of output [16]. This, along with the intrinsic efficiency of action-myosin

motors, enables muscles to have a relatively high system efficiency of 40% [26]. Muscle also has

the ability to isometrically recruit more fibers which allows it to change its stiffness by a factor of

6, from 10-60 MPa [26, 25]. This is important, for example, in the words of Madden et. al., in

catching a baseball: ”too stiff an arm will lead to a large (painful) impulse as the ball makes contact,

and provides less time to grasp the ball before it bounces back. A very compliant arm will not be

able to stop the ball. The optimum stiffness needs to be adapted to the ball mass and velocity. Such

stiffness control can be emulated in artificial actuators by fast feedback control, but at the expense

of added complexity and will only work if the actuator bandwidth is sufficient” [26]. Furthermore,

muscle has two very energy dense fuel sources available to it in the form of sugars and body fat.

Sugars, when combined with oxygen, generate about 15 MJ of energy per Kg in the form of adeno-

6


sine triphospahete (ATP). Body fat, when combined with oxygen, will generate about 37 MJ of

energy per Kg. This is an energy density more than 30 times greater than lithium ion batteries [25].

As described above, muscle also has a sophisticated integrated transport system. Because of the

microscale capillary density, fuel and waste molecules in muscle need only diffuse distances on the

order of a few micrometers in order to be delivered or removed. For this same reason, convective

heat transfer is also dramatically increased [26]. Put another way, muscle uses the extracellular fluid

surrounding muscle as a fuel delivery system, a waste disposal system and a heat removal system.

This, of course, is very economical. Furthermore, recent evidence by Glancy et. al. [12] suggest that

the mitochondrial reticulum not only produces energy, but also plays a role in actively distributing

it by way of the proton motive force; as opposed to previously held theories that suggest passive

diffusion mechanisms. This network allows for localized and quick energy distribution to locations

where the muscle needs it most. This mechanism allows muscle to move at a frequency close to 20

times a second and have a strain rate close to 500% of its length per second [12, 30]. Finally, under

ideal conditions, muscle is able to operate over billions of cycles in the case of the heart and more

than a hundred years. This, of course, is made possible by the body’s ability to regenerate itself in

situ.

1.2.2 Biomimetic Design

All of these structures and functional properties would be extremely difficult to imitate in

modern actuators. Nanoscale linear motors would require expensive and complex nanoelectrome-

chanical systems (NEMS). And a complex microscale fuel, waste, and heat transport system is just

beginning to be made possible thanks to microelectromechanical systems (MEMS). Because of this,

micrometer and nanometer scale architecture have seen less application in current muscle-like ac-

tuators [40]. Even if the actual structure can’t be achieved, however, one functional aspect of the

micrometer scale system can be imitated - the significance of removing heat from the system. At

the millimeter scale, the fact that distinct, specialized muscle fibers start to take form is also worth

investigating. At this scale, the body start to assigns specific muscle fibers groups to different ranges

of force production. The author believes that this is worth incorporating into the design of current

muscle like actuators. The premise is this: since no single actuator can operate at its optimal ef-

ficiency for all power outputs levels, our bodies use multiple ones each optimized for a specific

power output. It then places them in parallel and recruits their force contribution when needed, only

recruiting higher force, less efficient muscle fibers [44, 51] when needed. It is worth noting that this

7


arrangement only makes sense if parallel muscle fibers that aren’t being used during contraction add

a negligible amount of friction to the overall movement. It has been found that this is indeed the

case [26]. Moreover, based on this thought process it is reasonable to conclude that in order to have

a greater variety of movements (in terms of speed, endurance and force), nature must have found

this arrangement more useful than having our body contain one type of fiber which would either

be incapable of producing the range of desired movements or would produce them less effectively.

Put another way, the ”cost” of carrying around ”useless” weight when certain muscle fibers aren’t

in use (i.e. the muscle recruitment scheme) must be less than the ”cost” of having one type of mus-

cle fiber in order to produce every desired movement. In this case, cost is taken to be mechanical

efficiency of certain movements. However, it can be understood in any other number of ways, such

as the cost in terms of overall organism mass, which would ultimately necessitate a larger energy

(food) intake distinct from the one related to the mechanical efficiency of the movement or cost in

terms of produced stress - which is a function of cross-sectional area - on the muscle which would

affect how much the body needs to ”repair” that area. Overall this analysis falls into the complex

field of research that seeks to understand biological optimization strategies (which aren’t always di-

rectly based on energetic efficiency). Adequately imitating the mesoscale structure of muscle would

involve complex circuity and sophisticated controls, analogous to the body’s nervous system. At

the moment, however, this sort of hardware/software is unnecessary since they would require ade-

quate muscle like actuators to begin with. Because of actuator hardware limitations, current control

systems usually end up controlling only a single actuator per joint at most. Never mind multiple

actuators per joint and multiple force-producing-units per actuators. Finally, at the macroscale,

modern robots are starting to incorporate elastic elements in series with actuators which have been

used, for instance, in bipedal robots in order to increase mechanical efficiency [25].

1.2.3 A Liquid-Cooled, Bendable, Permanent-Magnet Tubular Linear Motor

A permanent-magnet tubular linear motor (PMTLM) is a collection of solenoids wrapped

around a cylinder which encloses a movable rod with permanent magnets aligned in alternating

and opposing directions [56]. It operates using identical physics principles as conventional electric

motors i.e. Ampere’s Law. This law relates the generated magnetic field to the current in a wire.

As current is passed through a wire, an electromagnetic field directly proportional to the amount

of current is generated which attracts a local permanent magnet towards it. In the case of conven-

tional electric motors, the arrangement of electromagnets creates a moving magnetic field along the

8


(a) Linear Tubular Electric Motor [60]. (b) Conventional Rotary Electric Motor.

Figure 1.3: Electric motors, both linear and rotary, contain analogous parts and function by the same

physics principle.

perimeter of a circle. In the case PMTLMs, the arrangement of electromagnets creates a moving

magnetic field along the inner axis of a cylinder. All other factors held equal, the stronger the mov-

ing electromagnetic field the stronger the motor. PMTLM have a number of good qualities that

would allow them to be used in place of electric or fluid actuators. They are direct drive systems

which mean they wouldn’t need a gear mechanism, they have high linear force densities and can

be employed with a servo mechanism. This in turn means that they can offer better dynamic per-

formance and improved reliability [56]. Additionally, they can have an essentially unlimited stroke

length as long as the translator/core is long enough.

In order to make the motor bendable, using Figure 1.3a as a reference, various parts had

to be changed. For instance, the magnets in the translator were spaced out and connected by a

double sided ball-and-socket joint which allowed the core to be radially flexible, but not axially.

Furthermore, a liquid cooling system was included in the final design in order to remove heat from

the coils and make the actuator smaller and more lightweight than they otherwise would be. The stiff

armature cover was replaced by a thin flexible tube which allowed liquid to flow within it and the

ferromagnetic armature slots were replaced by 3D printed elastic resin separators in order to further

decrease weight and allow cooling liquid to have direct contact with the coils. The nonferromagnetic

ring space was left empty in order to allow liquid to flow more readily and to allow the coils to bend

towards each other. The final design is shown in Figure 1.4. Further details of the approach can be

found in the Thesis Contributions and Scope section.

9


Figure 1.4: Final actuator design, CAD model.

1.2.4 Ferrofluid Cooling

Although the ferrofluid cooling system wasn’t incorporated or tested in the final design, it

was chosen as a theoretical cooling fluid of choice for several reasons that directly involve both the

intrinsic force production and heat management. The obvious reason regarding force is, although

the effect would be marginal, it would improve the magnetic circuit of the actuator. This would

allow the magnetic flux to flow more efficiently around the solenoid and produce more force from

the same current. This is due to the difference in relative permeability. Ferrofluid can have a relative

permeability up to 2.03 [27] whereas air has a relative permeability of approximately 1 [4]. Regard-

ing heat transfer, ferrofluid has excellent heat transfer properties. Ferrofluid can have a heat capacity

of 3000 J/kgK and a thermal conductivity of 2.7 W/mK whereas other liquids such as water can

have a heat capacity of 4182 J/kgK and a thermal conductivity of .6W/mK [49]. And finally, one

very interesting aspect stems from an effect called thermomagnetic convection. This effect refers

to how convective heat transfer can be ”passively” achieved using a ferrofluid in the presence of a

magnetic field. Under certain circumstances, a cyclical magnetic field causes the ferrofluid to flow

”passively” without the need for a pump. Passive convective cooling of approximately 20 to 28

Chas been achieved in applications where a .3 T magnetic field was applied at initial temperatures

of 64 Cand 87 C, respectively [3, 36, 41]. Since a magnetic field is being created along the outer

volume of the solenoids anyway, it could be used to aid in producing fluid flow. As a result less

10


energy would need to be inputted into the pump. The overall effect would theoretically save energy.

1.3 Thesis Overview

This thesis describes the motivation, design and fabrication and basic performance of a

biologically inspired bendable electromechanical actuator. It consists of 6 chapters. Chapter 1

introduces the problems found in existing conventional actuator systems used in robotics. It then

goes to describe the need for soft, flexible linear actuators with high specific force density similar

to biological muscle. The argument is made that in order to functionally imitate it, researchers

would benefit from structurally imitating it to some degree. Three aspects of biological muscle

are identified as targets for this: Muscle’s heat removal system, muscle’s specialized fibers, and

muscle’s soft, bendable structure. Only the first and last of the aforementioned are investigated in

the authors research. Chapter 2 explores the current state of the art, that is, the current state of

research on the subject of muscle like actuators. Metrics to describe the actuator performance are

chosen based on the work by Haines et. al. and Mirvakili et. al. Using these metrics, a summary

of muscle-like actuators research is given, followed by relevant research on permanent magnetic

tubular linear motors (PMTLM) and then finally bendable PMTLM research is given. Gaps in

research are identified and the contributions and scope of this thesis are given. Chapter 3 explores

the main theoretical aspects of the design of the actuator. These are mainly the force production

and the heat model. The models are then validated and generalized. Chapter 4 summarizes the

details regarding the electromechanical design and fabrication. This was done using CAD modeling,

3D printing, off the shelf parts and basic power tools. To control the final actuator, an open-loop

controller was built using an Arduino microcontroller and two DC motor drivers. Chapter 5 consists

of the testing and discussion of the final design. The performance metrics described in Chapter 2

are presented in the context of the actuator and the testing rigs that were used to measure these

are shown. The results are then presented and discussed. Chapter 6 is the conclusion of the thesis

document. It describes the general conclusions by summarizing the results and putting them in

the context of applications. The limitations of the study are discussed and potential future work to

address these limitations is described.

11

Chapter 2

State of the Art

An artificial muscle is ”any class of materials or devices that can reversibly contract, ex-

pand, or rotate due to an external stimulus” [31]. Muscle-like actuators, sometimes called artificial

muscles [14, 15, 26, 30], have tremendous appeal in terms of improved energetic performance, for

non-cyclical motion, over current actuators. Another large part of their appeal, however, also relates

to material properties. A muscle-like actuator is by definition soft; it tends to bend and as a result is

harder to break. This softness allows it to be more durable and interact with the world more safely

if the object it is actuating or itself impacts another object. Much like the realization that cyclical

actuators required their own field of study - robotics - in order to create non-cyclical motion, the

realization that soft materials also offer unique benefits resulted in a relatively modern field within

robotics called soft-robotics. Much of the focus of soft robotics is in the design and study of variable

stiffness structures, bendable electronics, and of course soft actuators. Not surprisingly, biological

muscle is the preeminent example. Like any new field soft robotics suffers from the problem of

standardization. It is often difficult to compare the performance of artificial muscles across publi-

cations because of the lack of appropriately normalized metrics [14]. Madden et. al. provide a very

good list of normalized metrics in their 2004 publication as well as a concise summary of individual

actuators technologies. Mirvakili et. al. later updated these actuator technologies in 2018, using

many of the same metrics as Madden et. al. as well as some additional ones. Their lists and metrics

will largely be drawn upon in this chapter. The same metrics, slightly modified and adapted for our

specific actuator, will eventually be used to characterize the actuator in this thesis. It includes many

familiar metrics applied to conventional actuators such as work density, specific power, efficiency,

actuation speed (in their case referred to as strain rate), bandwidth, and cycle life. Other metrics

have been added such as output strain, output stress, elastic modulus and catch-state. These metrics

12

CHAPTER 2. STATE OF THE ART

will be defined in the following section. As will be seen, different muscle-like actuators have a wide

range of performance characteristics, but none have the right combination of metrics to achieve the

performance of muscle. Additionally, as this thesis draws inspiration from an actuator that isn’t

traditionally considered a muscle-like actuator, it was felt appropriate to also include some back-

ground on the state of conventional tubular linear motors themselves as context for talking about the

state of bendable tubular linear motors research and how they compare to conventional muscle-like

actuators.

2.1 Quantifying the Performance of Muscle-Like Actuators

Muscle-like actuators have taken many forms. Because of this, it is not always easy to

quantitatively describe and compare their performances. For instance, in the words of Haines et.

al.: ”consider the popular statement that an actuator can lift X times its own weight. Although it

may lead to impressive sounding numbers, this metric conveys little useful information because it

neglects both muscle length and stroke. By cutting such a muscle in half, it would weigh half as

much, but still be able to lift the same weight, thus arbitrarily doubling the metric [14].” To this

end, it is useful to keep in mind the qualitative characteristics of muscle that we wish to imitate. As

previously mentioned an ideal muscle-like actuator would be lightweight, soft, small and produce a

high linear force. In addition it would be highly controllable, in terms of actuation speed, strain and

resolution, and would consume little energy. Madden et. al. provide a very good list of metrics that

effectively translate these qualitative characteristics into quantitative measurements. The descrip-

tions given will take on more specific mathematical definitions in Chapter 5. For now, Madden et.

al. describe the metrics as follows:

Typical stress is the typical force generated by the actuator upon excitation divided by its initial

cross-sectional area. Typical refers to the stress that is capable of being generated consistently

without potentially damaging the actuator and within the range of its typical output strain.

This metric quantifies the actuators ability to consistently produce a certain linear force and

loosely relates it to how small it is.

Peak output stress is the peak force generated by the actuator upon excitation divided by its initial

cross-sectional area. This metric quantifies the actuators maximum linear force and loosely

relates it to how small it is.

13


Typical output strain is the change in length of the actuator upon excitation, divided by its initial

length. This metric acknowledges that typically the reported strain is not generated while the

actuator is producing a ”working” or useful force. This metric quantifies the actuators strain

range within the useful force region and relates it to how small it is.

Maximum output strain is the maximum change in length that the actuator is capable of upon

excitation divided by its initial length. This metric quantifies the actuators strain range and

relates it to how small it is.

Strain rate is it is the change in typical output strain of the actuator divided by the time it took to

complete the stroke. This metric quantifies the actuation speed.

Bandwidth is a measure of how quickly the actuator will respond to a desire to change its current

state. In this context it is often expressed as the actuation frequency which causes the strain to

drop to half its low frequency amplitude [26]. In other words, for an actuator moving between

two points not very often (at a low frequency), it answers the question how high can I raise

the frequency until it only travels halfway between the two points? This metric relates to

actuation speed, but more accurately gives a measure of the response time of the system.

Energy (work) density is the output work generated by the muscle upon excitation normalised to

the volume of the actuator.

Specific Power is the output work generated by the muscle upon excitation normalised to the mass

of the actuator.

Efficiency is the ratio of output work over input energy.

Cycle life is the number of cycles the actuator can survive before failure.

Elastic Modulus is the range of isometric stiffness values that the actuator is capable of producing.

It is measured as the instantaneous stiffness multiplied by its length and divided by its cross-

sectional area.

Actuation directionality is an indication of the direction the actuator is capable of producing a

force,i.e. unidirectional or bidirectional.

Catch-state (lock-up state) If applicable, is an indicator of whether an actuator holds its actuated

state without consuming any energy. Some aquatic organisms such as mollusks exhibit a

catch-state (i.e they hold the shell locked without consuming energy) [30].

14


For reference, these metrics are summarized for various artificial muscles in Table 2.1 and are shown

for muscle in Figure 2.1 below.

Figure 2.1: Summary of muscle’s performance metrics. Figure by Mirvakili et. al. [30]

It is worth noting that this list is not exhaustive as many other additional metrics have

been published depending on the context or actuation mechanism. Moreover, much like biological

muscle, many muscle-like actuators have various metrics that are dependent on one another. For

instance, stress is in many cases dependent on strain or on velocity (analogous to the force-length

and force-velocity curves of muscles). In addition, many performance parameters such as resolution,

controllability and hysteresis aren’t even measured. As is often the case in a new field, researchers

initially aim to asses and document qualitative performance.

15


2.2 Types of Muscle-like Actuators

In the search for a true muscle-like artificial muscle, researchers have devised a multitude

of approaches. Mirvakili et. al. describe at least 14 different categories of actuator. These are:

1. Highly Oriented Semicrystalline Polymer Fibers*

2. Nanoparticle-Based Actuators

3. Twisted Nano-/Microfiber Yarns*

4. Thermally Activated Shape Memory Alloys (SMAs)*

5. Ionic-Polymer/Metal Composites (IPMC)

6. Dielectric-Elastomer Actuators (DEAs)*

7. Conducting Polymers

8. Stimuli-Responsive Gels*

9. Piezoelectric Actuators

10. Electrorestrivitive, Magnetorestrictive, and Photostrictive

11. Photoexcited Actuators

12. Electrostatic Actuators

13. Pneumatic Actuators*

14. Other Actuators

Each of these usually divide into unique subcategories based on activation mechanism, structure or

applications. This brings the overall number of unique artificial muscle actuators much higher. Ev-

idently, this research is a highly diverse and multidisciplinary, often existing at the overlap between

the fields of materials science, chemical, mechanical, electrical and bioengineering, chemistry, and

physiology. To narrow down this list, only the categories most relevant to exoskeleton and prosthet-

ics technologies, and larger scale bio-mimetic robots (marked with an asterisk) will be described in

the following section.

2.2.1 Highly Oriented Semicrystalline Polymer Fibers

Certain polymer fibers, such as polyethylene and nylon, exhibit a high degree of anisotropic

thermal expansion when their crystalline structure is oriented along along their length. This allows

the fibers to shorten about 2.5% while expanding in diameter about 4.5% [30]. This shortening

effect can further be improved by twisting the fibers into tight coils, allowing contractile actuation

up to 49% [58, 15]. Because this effect is thermally driven, various methods can be used to heat up

the fibers such as simple Joule heating, convective heating or radiation (photothermal) heating. The

16


performance of these types of actuators is usually limited by its heat transfer properties. In order to

improve this, various coatings are usually added to the fibers, but the effect of these is minimal so

efficiency and bandwidth prevent their widespread adoption.

2.2.2 Twisted Nano-/Microfiber Yarns

As opposed to the actuator above, most materials exhibit isotropic expansion when ex-

posed to a stimuli that causes a change in volume. Twisted Nano-/Microfibers Yarns are structured

in such a way that the only way to accommodate a change in diameter is by contracting along its

length [30]. This structure specifically refers to being twisted into a helix with both ends tethered

so no unwinding can occur. These types of actuators can be driven by any stimulus that causes a

change in volume in the yarn used to make them. This makes this type of actuator capable of being

thermally or swelling pressure driven. Charge injection in double layers is another, less common

form of driving these actuators and usually require more exotic materials, such as carbon nanotubes

yarns, which, at a microscopic level, contain parallel surfaces that repel each other when a voltage

is applied at the electrolete-electrode interface [2, 30, 29]. As the repelled surfaces move away from

each other the material expands in volume. This type of actuator is also limited by bandwidth and

efficiency, but additionally leaves much to be desired in terms of cycle life.

2.2.3 Shape Memory Alloys

Shape Memory Alloys (SMAs) are a class of material that can reliably and with a high

degree of precision return to their original shape, after being deformed, if subjected to a certain

stimulus such as external heat. SMAs have been used in a variety of fields, most notably in the field

of medical devices where Nickel-Titanium (Nitinol) catheters, stents, braces and active-compression

garments are commonplace [19]. The mechanism behind SMAs is explained by its metallurgical

phase transformations within a relatively narrow band of temperatures. Using certain fabrication

methods, this effect is remarkable enough to allow cycling between two shapes based on temperature

alone - at one temperature is has one shape and at another, relatively close temperature it has another

shape. Strains of about 8% are common and can be as high as 100% by using creative geometries

at the expense of lower stresses [19]. SMAs can be thermally activated by the method described

above or, more commonly because it is conductive, using direct joule heating. This method allows

SMAs to have better performance metrics during the heating cycle but still makes their performance

limited by the cooling cycle. Ultimately, this lowers their bandwidth significantly. Overall, the

17


stress produced by SMAs is unmatched by any artificial muscle but their high cost, low cycle life

and efficiency limit their use [30].

2.2.4 Dielectric-Elastomer Actuators (DEAs)

DEAs function using the force developed between two parallel surfaces subjected to a

charge difference. They can be thought of as being made up of a parallel plate capacitor with a

compliant dielectric material in between the two plates [30]. When a voltage difference is applied

across the capacitor, the two plates attempt to pull into each other, but the dialetric material serves

as a bias spring that opposes this and also prevents the circuit from shorting. In a typical device the

dialectric material compresses in height and elongates along the width and length upon activation.

Special manufacturing processes such as prestraining or introducing local stiffness variations can

cause the material to elongate or contract along preferential directions. DEAs typically require

thousands of volts to function which makes their use limited in a variety of situations despite using

extremely low currents. However, they have high bandwidth, relatively high efficiency, and produce

usable amounts of stress. An interesting example of a DEA that uses a liquid dialetric layer is the

Peano-HASEL actuator from the University of Colorado [20].

2.2.5 Stimuli-Responsive Gels

Stimuli-Responsive Gels, more commonly called hydrogels, are a well studied group of

materials that are made up of a network of cross-linked polymer chains that swell/deswell with

water when exposed to an external stimuli [30]. Their chemistry, softness, biocompatibility, high

strain and low force make them especially suitable for the biomedical device field. Applications

ranging from artificial skins [39] to drug delivery [22] have been found. They can be activated by a

multitude of stimuli including temperature, pH level, light, electric fields, or specific chemicals and

biomolecules [30]. Current performance metrics are at about 4MPa for stress values at a moderate

to slow bandwidth. Because they are well studied, it is likely that further improvements to overall

performance will be marginal moving forward.

2.2.6 Pneumatic Actuators

Pneumatic actuators are among the most popular in industry. This is due in large part

to a simple working mechanism: ”pressurization of a fluid in an expandable chamber” [30]. The

expandable chamber can take the form of a piston-cylinder or elastic deformable bladder. These

18


types of actuators usually require considerable support equipment such as the fluid system, valves,

and a pump [40]. However, even with the weight of all the support equipment included, fluid

actuator systems exhibit a power-to-mass ratio about the same as that of muscle [25] as well as a

comparable total strain, bandwidth and actuation speed during moderate use. Pneumatic actuator’s

shortcomings include the need for a large pump and added modeling complexities because of the

compressibility of air. Because of this, these types of systems cannot be scaled down and generate

smoke and noise which limits their use to outdoor environments [17].

2.3 Conventional Permanent Magnet Tubular Linear Motors

Mirvakili et. al. present another category of muscle-like actuators which they simply call

”other actuators.” Included in this category are actuators that take advantage of the Lorentz Force

or, more specifically, Ampere’s Law. They broadly define this category as any ”actuator exploiting

the force generated when an electric current interacts with an orthogonal magnetic field to produce

a mutually orthogonal force [30].” The force in these kinds of actuators is mainly limited by the

current density in their coils and by the magnetic properties of the permanent magnets within them.

A reasonable range of current density is on the order of 106A/m2 [42], but day to day technologies

are often higher than this. With a moderate amount of cooling, sustained current densities as high as

108A/m2 can be maintained [30]. Modern Neodymium (NdFeB) magnets have excellent magnetic

properties, the most relevant of which is the remanence or flux density. This property describes how

much a magnet can be magnetized before saturation. Magnetic saturation is the point at which a

further increase in the magnetic field will no longer cause a material to magnetize any further. For

Neodymium magnets, usual values range from 1 to 1.3 Tesla [38]. This puts a practical limited on

the amount of force that can be generated from an external magnetic field interacting with a certain

volume of magnet. By using cooling and high remanence magnets effectively, and incorporating

well designed magnetic circuits, permanent magnet tubular linear motors (PMTLMs) can achieve

peak stresses similar to what is produced by biological muscle. Various typologies of permanent

magnet tubular linear motors exist. These are shown in Figure 2.2. From these, various motors have

been created.

For instance, using cooling, Neodymium magnets, a well designed magnetic circuit and

a Halbach topology, Bryan Ruddy [40] designed a motor that ”generates a continuous force density

of 140 N/kg (.7 MN/m3), and has a motor constant of nearly 6 N/√W ” which is, according to

his research, ”both higher than any previously reported motor in that size class .” It also had a stroke

19


(a) Internal magnets radial magnetization topol-

ogy.

(b) External magnets radial magnetization topol-

ogy.

(c) Axial magnetization topology. (d) Halbach magnetization topology.

Figure 2.2: Different types of Permanent Magnet Tubular Linear Motor (PMTLM) topologies. Fig-

ures are from Wang. et. al. [56]

of 16mm. Although the motor is very powerful for its size, it essentially amounts to a very well de-

signed single solenoid coil which means there isn’t much control of the stroke length. Additionally,

since it uses all metal parts, the motor is rigid and cooling is accomplished by heat transfer along

metal tubes running along the coils. Expanding a similar but separate design to multiple solenoids,

Bryan Murphy [32] designed a high precision PMTLM and controller. It incorporates neodymium

magnets, a moderately well designed magnetic circuit and an axial magnetization topology. His

actuator has a maximum continuous force capacity of 26.4 N and the position resolution is 35 µm

with a stroke of 100 mm. Depending on the controller, he was able to achieve a motor rise time

of 55 ms, a settling time of 600 ms, and a 65 % overshoot for case 1 or a motor rise time of 1s, a

settling time of 2.5 s, and a .2% overshoot for case 2 at actuation speeds of almost 1.5m/s. Of sim-

ilar construction, the X-Muscle Gen. 2 by Nucleus Scientific [30] can reportedly produce 6.9 kN

(or 1.4MPa) of peak force while being 500 mm long with a stroke of 40% (200 mm). Moreover,

it can achieve sustained force densities of around 350 kN/m2 or .35 MPa , similar to biological

muscle. Based on its performance metrics and on the limited public information about it, it can be

assumed that its construction is similar to the Ruddy actuator (i.e. it incorporates active cooling,

20


neodymium magnets, a well designed magnetic circuit and a Halbach topology) arranged into a

PMTLM like the Murphy actuator. It is to say with multiple coils. In terms of raw force generation,

maximum strain, strain rate, controllability/bandwidth and other performance metrics it is clear that

conventional PMTLM hold promise. However, regarding the material properties that make artificial

muscles attractive, they are no better that electric motors.

2.4 Bendable Permanent Magnet Tubular Linear Motors

Various attempts have been made to transform stiff linear motors into bendable or flexible

linear actuators. In 2009, Ohyama et. al. verified the operation principle of a flexible linear actuator

constructed out of multiple solenoids in series with a metal wire as its core [34]. Not surprisingly,

the original flexible design had too low of a force to easily measure. This is not surprising because

ferromagnetic materials are inherently inflexible so any wire that was flexible enough for them to

use must have had a very low ferromagnetic material content and therefore a very low magnetic

permeability. They eventually remade their design using an iron rod as a core and obtained a thrust

force of 50 mN . Other performance metrics are not documented. In 2013, Takai et. al. created

a similar device. In general, the performance and architecture was not very different, however, the

idea of having individual core components connected by a flexible fiber - rather than one long metal

rod - was novel [48]. This improvement allowed the thrust force to increase to 91mN . In summary,

although serving as proofs of concept, these designs did not incorporate cooling, didn’t use strong

magnets or ferromagnetic materials efficiently, had poorly designed magnetic circuit and had no

recognizable PMTLM topology.

Alternatively, in 2012, Urban et. al. designed and built the most sophisticated of the found

flexible linear actuators and the first to have an actual (2-phase) PMTLM construction [52]. That

is to say, incorporating permanent magnets in its core. They designed it just like a conventional

PMTLM, but used a flexible material in between the core and the coils, spaced out the coils to allow

for bending, surrounded the coils with a high permeability material to improve the magnetic circuit

and separated each of the magnetic rings in the core with silicone elastomer rings. At bending radii

as low as 200 mm, the actuator could produce 7.35 N of continuous force, and for high bending

radii (i.e. essentially straight) it had a maximum holding force of around 25 N . The outer diam-

eter of their device was 30 mm, the length of the stator was 253 mm and the length of the stroke

was 115 mm. The strain rate was about .9 m/s. Overall, it had a well designed magnetic circuit,

incorporated powerful Neodymium magnets and used an axial magnetization topology. Because it

21


lacked cooling, they limited their current density to 7.4 (106)A/m2. Further improvements could

conceivably be made. In 2018, Ebrahimi et. al. designed a theoretical, solenoid-based soft actu-

ator that uses a powdered permanent magnet particles in between two solenoids [9]. Although it

doesn’t fully incorporate a PMTLM construction, they discussed in detail the mathematics of the

electromagnetic force, optimization strategies for determining solenoid parameters and the effects

of eccentric deformation on the magnetic force. One of their many theoretical model describes a

flexible solenoid actuator with an optimized design that produces a stress of .00827 MPa. This

value is low in large part because the liquid metal they use to create the coils limits their current

density and the remanence of the magnetic particles they use for the core is also low (.18 Tesla).

(a) Ohyama et. al. linear motor [34]. (b) Takai et. al. linear motor [48].

(c) Urban et. al. PMTLM [52]. (d) Ebrahimi et. al. soft actuator [9].

Figure 2.3: Different linear motors, each meant to function as muscle-like actuators. Each of these

employ different cooling strategies, core design, core topology or magnetic circuit designs. Urban

et. al.’s motor serves as the most equivalent design to the one conceived during this thesis.

22


2.5 Summary Table

Technology ActuatorTypical

Stress (MPa)

Typical Strain

(% of length)

Strain rate

(%/s)

Bandwidth

(Hz)

Work Density

(kJ/m3)

Specific Power

(kW/kg)

Efficiency

(%)Cycle life

Mammals [26] 0.1 20 500 20 8 50 40 > 109Biological Muscle

Hummingbird [57] 0.1 20 500 80 – 75 – > 109

Nylon-6,6 [15] 22 @10% 33 @ 15 MPa <1 7.5 2.48 kJ/kg 27.1 =< 1 (1.2) 106

Nylon-6 [15] 8.4 @ 12% 49 @ 1 MPa <1 – – – =< 1 (1.2) 106

Nylon-6,6 [15] 38 @ 10% 24 @ 15 MPa <1 5 – – =< 1 (1.2) 106

Highly Oriented

Semicrystalline Polymer

Fibers (twisted coils)Polyethylene [15] 15 MPa 16 @ 15 MPa <1 2 2.63 kJ/kg 5.26 =< 1 –

MWCNT [11] 88 @ 1% 1 @ 88 MPa 1 1 1.1 920 10 <5000

MWCNT/wax-coiled [24] 84 9.5 @ 5.5 MPa 120 20 1.36 27900 2 (1.4) 106

Niobium NW/wax [31] 20 @ .24% .24 @ 20 MPa 1 5 48 10 2 –

Twisted Nano-/

Microfiber Yarns

Spider-silk dragline [1] 80 2.5 1 << 1 500 130-190 – –

Thermally driven SMAs [53] 700 8 300 3 1000 50 5 –Shape Memory Alloys

Ferromagnetic SMAs [33, 46] 1 6 10000 1000 100 – <16 300 to 107

Silicone [8, 21, 35, 45] 0.3 120 34000 1400 10 5 25 107Dielectric-Elastomer

Actuators (DEAs) VHB [8, 21, 35, 45] 1.6 380 450 10 150 3600 30 107

Stimuli-Responsive Gels Polymer Hydrogels [7, 13] 4 90 @ 4 MPa – 0.5 460 – – –

Pneumatic [54, 6] 3.4 15 1590 6 @ 4% 0.5 10 19.1 > 100, 000Fluid Actuators

Hydraulic [5, 28] 0.753 43.5 4347 – 596 – 53.3 –

Ruddy actuator [40] .7 16 mm – – 11.2 – – –

Murphy actuator [32] 26.4 N 100 mm 1.5 m/s 100 – – – –Conventional PMTLM

X-Muscle [30] 1.4 40 – – – – – –

Ohyama actuator [34] 50 mN – – – – – – –

Takai actuator [48] 91 mN – – – – – – –

Urban actuator [52] .01 115 mm .9 m/s – 4.72 – – –Bendable PMTLM

Ebrahimi actuator [9] .00827 – – – – – – –

Note: Words in bold represent the largest value in the column. Also, some values were not found for the normalized

units so other, non-normalized units were used for the comparison

Table 2.1: Table summarizing the performance metrics of various muscle-like actuator technolo-

gies. Notice how biological muscle is not the best in any one category, and even has very poor

performance in the stress metric relative to other actuators. However, it achieves both a usable

strain and strain rate (two properties that are usually inversely related) and, perhaps most impor-

tantly, has a bandwidth second only to Dialectric-Elastomers. This allows it to be responsive, an

invaluable trait when considering human dexterity. Moreover, although its work density isn’t par-

ticularly impressive, its specific power combined with its efficiency means it can provide actuation

in a ”lightweight” package. This, combined with its incomparable cycle life, means it is also very

durable.

23


2.6 Thesis Contributions and Scope

From the published research it is clear that there is room for improvement in the design of

bendable PMTLM. To reiterate, broadly speaking the variables that can be adjusted when designing

the PMTLM can be the magnetic circuit, the cooling and the core. Additionally, the general topology

of the core and coils can also be varied as shown in Figure 2.2. Urban et. al. will be used as the

basis for comparison. Regarding the magnetic circuit, Urban et. al. utilize a well designed magnetic

circuit both in structure and in chosen materials so not much is to be improved there. As they

correctly note, ”the design of the iron circuit has an enormous influence on the characteristic force

curve” [52]. However, in theory a properly designed magnetic circuit can be traded-off in favor

of a higher current density in order to achieve an equivalent force as long as proper cooling is

implemented. By avoiding using the stiff, bulky and heavy materials that makeup the magnetic

circuit, the material properties of the overall actuator could be improved. In terms of cooling, the

Ruddy actuator explores convective heat transfer to cool the coils, but it does not implement it

directly unto the coils. Since the coils have insulation anyway, it should be conceivable to directly

cool the coils by flowing a cooling fluid directly on them. Moreover, if this cooling fluid had

favorable magnetic permeability properties (to improve the magnetic circuit) as well as favorable

heat transfer properties it would make sense to use it. Ferrofluid could serve as such a fluid. Finally,

in terms of the core design, Urban et. al. lose valuable surface area (which will be shown to affect

force in the next chapter) by using magnetic rings instead of solid cylinders and add unnecessary

complexities to the system by using elastomeric magnet spacers. An improved design would hold

the magnets together in such a way that they would be axially stiff, but radially be flexible, allowing

the overall system to still maintain flexibility.

As mentioned, various avenues incorporating many different fields can be used to explore

and attempt to imitate the structure of muscle in the context of artificial actuators and robotics.

Given all these, the contributions of this thesis are:

1. A bendable and soft structure.

2. A direct contant, convective heat transfer ferrofluid cooling system.

3. A novel magnetic core design that is axially stiff, but radially flexible.

It is worth specifying that the main purpose of this thesis is to illustrate the approach,

possible design, fabrication and basic testing of the actuator. Given this, extensive data regarding

the actuator’s performance was not collected.

24

Chapter 3

Theory and Initial Validation

In order to design the PMTLM, which consists of multiple solenoids in series, first theo-

retical force and heat models for one solenoid interacting with one permanent magnet were derived

and experimental data was collected. Next, the theoretical models were compared to the experimen-

tal data in order to validate the models. Finally, once they were established as accurate, they were

extended to include a PMTLM geometry.

3.1 Theoretical Models for a Single Solenoid

Ampere’s Law relates the generated magnetic field to the current in a closed loop. As

current is passed through the loop, an electromagnetic field directly proportional to the amount of

current is generated which attracts a local permanent magnet towards it. Under most circumstances,

Ampere’s law is mathematically difficult to accurately apply unless the object in question has a

high degree of symmetry. Ebrahimi et. al. use a simpler law, the Biot-Savart law, since it is more

mathematically accessible. Much of the theoretical analysis done in this section is based on the

work they did. Once a formula for the magnetic field created by a solenoid is established, the

force on the magnetic core is derived using the charge model. Because a solenoid is inherently an

electromagnetic system, there are also electrical aspects to be considered such as power and heat.

The equations describing these properties are shown.

3.1.1 Force

Undergraduate textbooks generally approximate the strength of an electromagnetic field

along the central axis of the coils using formulas that depend on their geometry. For instance, the

25

CHAPTER 3. THEORY AND INITIAL VALIDATION

magnetic field of an electromagnet where L>> R is approximated with the following formula [42]:

Bz =µNI

l(3.1)

Where N /l is the turn density, I is the current and µ is the relative permeability of the material in

the core. The relative permeability of the material quantifies how strongly or efficiently a material

attracts magnetic fields towards it. Certain materials, such as iron, have a very high relative perme-

ability. The mathematical analysis will usually not go much beyond that and formulas that apply to

other geometries are usually excluded even in textbooks geared towards engineering students [42].

Ebrahimi et. al. provide a detailed derivation of a more complete formula for all coil geometries

that describes the force from a single solenoid imparting a magnetic field on a permanent magnet

core. Some of the key steps of their derivation will be shown here, interpreted and then modified

for our specific geometry. For further details on their derivation, refer to their 2018 paper [9].

Starting with the Biot-Savart Law, they derive the following equation for the magnetic

field generated by a single solenoid at a point P with a distance z from the center of the solenoid:

Bz =µ0NI

2l

(l/2)− z√(z − l/2)2 +R2

avg.

+(l/2) + z√

(z + l/2)2 +R2avg.

(3.2)

where µ0 is the permeability of free space,N is the number of turns, I is the current flowing through

the wire, l is the length of the solenoid, z is the distance from the center of the solenoid to point

P , and Ravg. is the radius of the solenoid (more accurately the average radius when accounting for

multiple coil windings). These dimensions are illustrated in Figure 3.1. They then use the charge

Figure 3.1: Schematic of solenoid dimensions and desired point, P .

model of electrostatics to calculate the applied force on the magnet. This is expressed by equation

3.3:

F =

∫vρmBdv +

∮sσmBds (3.3)

26


where ρm = −5 ·M, is the equivalent volume charge density in units of A/m2 and σm = M · n,

is the equivalent surface charge density in units of A/m. The magnetization, M, is the net magnetic

moment per unit volume in the permanent magnet. In a certain sense, this constant expresses the

magnetic field strength and direction for every point in the magnet. It can be calculated using

equation 3.4:

M = Br/µ0 (3.4)

where Br is a material property called remanence or flux density in units Tesla, T . Remanence or

flux density describes how much a material can be magnetized before being saturated. n is the unit

surface normal vectors, which represent the locations and directions of the vectors perpendicular to

each of the magnet surfaces. Because the magnetic material has a uniform magnetization along its

length, the volume charge density, ρm, equals 0, which eliminates the first integral. This leaves only

the surface integral. Of the three distinct surfaces of the magnet – the two ends and the radial surface

– only the two end surfaces need to be considered since the magnetic fields along the radius surfaces

cancel each other out [9]. As a result of the unit surface normal vectors, the two ends end up having

equal, but opposite direction magnetization when one solves for the surface charge density, σm.

This means that ultimately, a cylindrical magnetic core can be treated as two magnetic monopole

surfaces (i.e infinitesimally thin) with an area equal to the cross-sectional area of the magnet and

of opposing charge, rigidly attached and separated by a distance equal to the length of the magnet,

h. This concept is illustrated by Figure 3.2. The interaction between the magnetic core and the

Figure 3.2: Schematic of a magnet interacting with the solenoid. The magnetic core can be modeled

as two infinitesimally thin surfaces of opposing charge N and S, of radius, r, and separated by

distance, h. One can consider the magnetic field generated by the solenoid at each surface separately

and add them together. The South pole is at a distance ZS and the North pole is at a distance ZN .

27


solenoid then becomes one described by the vector subtraction of the magnetic fields generated by

the solenoid at the two surfaces. If we consider the South pole is at a distance ZS and the North pole

is at a distance ZN , as in Figure 3.2, from the center of the solenoid we can calculate the magnetic

field at two arbitrary points on each surface using Equation 3.2. This would yield equations 3.5 and

3.6 which represent the magnetic field on points on the south and north pole respectively.

BS =µ0NI

2l

(l/2)− ZS√(ZS − l/2)2 +R2

avg.

+(l/2) + ZS√

(ZS + l/2)2 +R2avg.

(3.5)

BN =µ0NI

2l

(l/2)− ZN√(ZN − l/2)2 +R2

avg.

+(l/2) + ZN√

(ZN + l/2)2 +R2avg.

(3.6)

For convenience, the previous equations were modified in terms of z, the distance from the center

of the magnet to the center of the solenoid, and h, the length of the magnet using the substitutions:

ZN = z − h/2 and ZS = z + h/2. Performing the vector subtraction, Btotal = BS − BN , with

these substitutions ultimately yields:

Btotal =µ0NI

2l

[(l/2)− z − h/2√

(z + h/2− l/2)2 +R2avg.

+(l/2) + z + h/2√

(z + h/2 + l/2)2 +R2avg.

− (l/2)− z + h/2√(z − h/2− l/2)2 +R2

avg.

− (l/2) + z − h/2√(z − h/2 + l/2)2 +R2

avg.

](3.7)

The order of the vector subtraction is determined by the direction of the current in the coil or by the

direction the magnetic core is inserted. Applying all these considerations to Equation 3.3, one can

solve for the force on the magnetic core.

F =

∮sσmBtotalds = BtotalM

∫ r

0

∫ 2π

0rdrdθ = Btotal

Brµ0πr2 (3.8)

It is worth noting that the πr2 terms simply represent the cross-sectional area of the magnets which

indicates that these equation can be used for ring shaped cores as well as long as the appropriate

substitution is made. Substituting in Equation 3.7 for the total magnetic field, Equation 3.8 becomes:

F(z) =NIBrπr

2

2l

[(l/2)− z − h/2√

(z + h/2− l/2)2 +R2avg.

+(l/2) + z + h/2√

(z + h/2 + l/2)2 +R2avg.

− (l/2)− z + h/2√(z − h/2− l/2)2 +R2

avg.

− (l/2) + z − h/2√(z − h/2 + l/2)2 +R2

avg.

](3.9)

28


In summary, Equation 3.9 gives the force as a function of distance z, as measured from the center of

a cylindrical magnet with certain properties/dimensions to the center of a cylindrical solenoid with

certain properties/dimensions. For the magnet these are: length, h, radius, r (or cross-sectional area)

and magnetic remanence or flux density, Br. For the solenoid these are: the number of turns,N , the

current going through the wire, I , the length of the coil, l and the average turn radius, Ravg., which

will be explained below.

The average turn radius is a parameter that takes into account how the circumference of

the solenoid changes as the turn density, N/l, increases. In other words, for a multilayered coil of a

fixed length and certain inner diameter, increasing the number of turns will always increase the outer

radius, ro, and consequently the average radius of the solenoid. This parameter can be estimated,

based on the work by Schimpf [42], using the equation:

Ravg. =Na

2lλ+ ro (3.10)

Where the new variables a and λ represent the cross sectional area of the wire and the circle packing

density respectively. This latter variable, λ, takes into account that round wire can only be wound so

tightly and therefore has, for instance, a maximum value of π/√

12 = .907 for a lattice arrangement

or a value of π/4 = .785 for a grid arrangement [42]. The average turn radius plays an important

part in electrical power and heat related calculations and will be described in more detail in the next

section. For convenience, Equation 3.11 for the number of turns is also given.

N =λl(Ro−Ri)

a(3.11)

3.1.2 Electric Power and Heat Management

Various engineering trade-offs can be considered when thinking about the electrical power

consumed by the solenoid. Many of these trade offs are due to the fact that most circuits are driven

by a constant voltage. For instance, as more turns are added to the coil and the wire becomes

longer, the electrical resistance will increase and the current will decrease in accordance to Ohm’s

Law, V = IR, where V is the applied voltage and R is the electrical resistance. As a result,

the magnetomotive force per length of wire produced by the solenoid will decrease. For solenoids

consisting of a single layer, the two effects – an increasing number of turns and a decreasing current

– exactly cancel each other out [42]. In other words, given a constant voltage, adding (or removing)

turns decreases (or increases) current in such a way that the total magnetomotive force remains

constant. Because of the behavior described by the average turn radius, however, the two effects

29


don’t exactly cancel each other once a multilayered solenoid is considered. Equation 3.10 indicates

that, everything else held equal, adding more turns to the coil will eventually increase Ravg. which

will have a secondary affect of reducing the magnetomotive force [42]. Another, more significant

trade-off, becomes evident when one considers the effect of various thicknesses (cross sectional

areas, a) of copper wire. A thicker wire means more current can be run through the coil without

heating (i.e. it has a lower resistance per unit length of wire, γ), but it also means less turns can fit

per unit length of coil. Schimpf and N. Ebrahimi et. al. explore these trade off more deeply in their

2013 and 2018 publications.

In terms of heat management, coil dimensions also play a role especially when consider-

ing convective and conductive heat transfer. In order to build a powerful electric motor one would

ideally run as much current through the thinnest wire possible, but because these are electric device

one is limited by Ohmic/Joule heating in the amount or duration of current that one can provide. To

facilitate a higher current one would need to extract heat from the coils. Since convective heat trans-

fer is directly related to the amount of surface area that is available to extract heat from, presumably

there is a trade-offs between the coil design that has the most surface area (and thus allows for the

best heat transfer properties) and the coil design that has the best intrinsic magnetic field properties.

Moreover, in order to increase conductive heat transfer between the layers of the coil, one would

want to keep the coils packed as tightly as possible (i.e. would want λ, the circle packing density,

to be high). Although λ ultimately doesn’t have a strong influence on the intrinsic strength of the

magnetic field generated by the solenoid, it exerts a strong influence on the conductive heat transfer

properties of the coil since the air in between the layers provides a considerable amount of thermal

resistance as compared to copper. For reference, the thermal conductivity of copper is 401 WmK vs.

.0263 WmK for air [18]. Ruddy et. al. explored these thermal trade-offs in their 2012 publication

[40]. A less detailed exploration in order to illustrate some of the factors that need to be considered

will be presented here.

Conservation of energy states that the energy that is stored,Est, within an electrical circuit

(which causes it to have a certain temperature) is equal to the energy generated, Eg, minus the

energy that escapes, Eout. Interpreted as a rate equation, the rate at which an object heats up (or

stores energy) is given by:

Eg − ˙Eout = Est (3.12)

For an electrical circuit such as a solenoid, the energy generated, Eg is described by the

30


equation for Joule/Ohmic heating:

Eg = I2prLwire

a= I2Rwire (3.13)

Where pr describes the resistivity of copper, itself a function of temperature defined by the equation

pr = prt[1+α(T−Trt)] (where α is the thermal coefficient of resistivity), and a describes the cross-

sectional area of the wire. For convenience, since coils are often wound using American Wire Gage

(AWG), an equation that gives the area, a, inm2 as a function of Wire Gage Number, AWG, can be

used: a = 1.2668(10−8)9236−AWG

19.5 . An equation for Lwire, which describes the length of the wire,

can be found at the end of this section. Because the goal is to extract enough heat energy where

the temperature of the wire isn’t changing over a wide range, the overall resistance-temperature

dependence will be ignored and the second form of Equation 3.13 is used. The energy that escapes

is the sum of convective, conductive and radiation heat transfer. Neglecting heat removal due to

radiation (because it usually makes up a small part):

˙Eout = Aosh(T − Tfluid) +Aiskeff.T − Trt

x(3.14)

Where the first group of terms are factors having to do with convective heat transfer: Aos is the

area of the outer surface of the coil exposed to the flowing fluid, h is the convective heat transfer

coefficient, T is the present temperature of the coils and Tfluid is the temperature of the fluid. The

second group of terms are factors having to do with conductive heat transfer: Ais is the surface

area of the coils not exposed to the flowing fluid, keff. is the effective thermal conductivity of

all the material between the surfaces of the coil and the surroundings, Trt is the temperature of

the surroundings, and x is the thickness of the material. The internal energy (energy stored) in a

uniform material is described by its specific heat capacity. This number determines the amount of

energy that must be ”stored” within a certain amount of a specific material in order for it to reach a

certain temperature. As a rate, it is described by the following:

Est =d

dt(ρdV cT ) =

dT

dt(ρdV c) (3.15)

Where ρd is the density of the material, V is the volume, c is the specific heat capacity and T is the

present temperature. Putting these equations together, the energy balance becomes:

dT

dt(ρdV c) = I2Rwire −Aosh(T − Tfluid)−Aiskeff.

T − Trtx

(3.16)

Solving for the heating rate, Equation 3.16 becomes:

dT

dt=I2Rwire −Aosh(T − Tfluid)−Aiskeff. T−Trtx

ρdV c(3.17)

31


Equation 3.17 describes the instantaneous rate at which a solenoid is heating at a certain period in

time given a current, certain coil dimensional and material properties, and certain fluid properties. It

assumes a very modest increase in temperature since the temperature-resistance dependence of the

heat generated in the coils is not included.1 Additionally, it neglects the interaction between internal

heat generation/transfer and λ, the circle packing density as well as increased thermal resistance due

to contact resistance. These effects would likely play a significant part in determining keff.. Exam-

ining the equation allows one to draw insight about the system. For instance, as one would expect,

as the temperature, T , increases the energy leaving the system through convective and conductive

heat transfer increases and eventually matches the energy generated. This causes a steady state tem-

perature where dTdt = 0. Additionally, the opposing incentives regarding heat are now quantified.

On one hand, based on Equation 3.9, the output force is linearly related to the amount of current, on

the other hand, based on Equation 3.17, the generated heat is exponentially related to the current. In

order to reconcile this relation the Rwire of the wire must be kept low which implies that it is more

efficient to use thicker wires. Obviously, as mentioned above, the heat transfer coefficient h needs

to be as high as possible in order to mitigate the energy generation. Furthermore, material with a

high thermal conductivity, keff., would ideally be used. The equation can then be integrated to find

an equation that gives the temperature of the coil, T , as a function of time.

T =

(I2Rwire −Aosh(T − Tfluid)−Aiskeff. T−Trtx

ρdV c

)t (3.18)

Solving for T ultimately yields:

T (t) =I2Rwiret+AoshTfluidt+Aiskeff.Trtt/x

pdV c+Aosht+Aiskeff.t/x(3.19)

Equation 3.19 gives the approximate temperature rise of a single coil generating Ohmic/Joule

heating with certain conductive and convective heat transfer properties.

Equations for finding the length of the wire, Lwire, used in the coil and the electrical

resistance, and Rwire of the solenoid is found fairly straightforwardly using Equation 3.10 for the

average radius (Ravg.) and the resistance per unit length, γ:

Rwire = Lwireγ =prLwire

a(3.20)

Lwire = 2πRavg.N =Rwirea

pr(3.21)

1In order to correct for this, the first version of Equation 3.13 could be used while making the appropriate substitutionusing the equation for resistivity-temperature dependence and Ohm’s law.

32


It is worth specifying at this point that the parameters Ravg., N and λ must be estimated from

measured or true values. This can be done by first obtaining a true value for the resistance of the

wire, Rwire, and using this value to calculate a true length for the wire, Lwire, using latter version

of Equation 3.21. Next, one must guess at a value for λ (a reasonable guess is .6) and plug it into

Equation 3.11 and plug that result into Equation 3.10. Using the resulting estimates, one plugs the

values back into the first version of Equation 3.21 and tweaks the λ estimate until the estimated

length matches the true length.

3.2 Experimental Validation of the Models

Having valid theoretical models allows one to make predictions about the performance of

different designs and iterate on those predictions in order to make it better. Two different models

were validated:

1. The force model, which states that we have a way of predicting what the force on the magnet

will be based on the characteristic parameters of the coil and magnet.

2. The electric power and heat model, which states that we have a way of predicting what the

temperature of the coil will be based on the coil dimensions, input voltage and heat transfer

behavior.

3.2.1 Experimental Set-Up

A fixture was built using 3D printed parts to allow a solenoid to be attached to a MultiTest

2.5i tensile tester. This test allowed the measurement of force as a function of distance from the

solenoid at different voltages. While the test was taking place, a J-type thermocouple was attached

to the surface of the solenoid to measure the surface temperature. The data from the thermocouple

was amplified by an Adafruit MAX31856 Universal Thermocouple Amplifier and logged using an

Arduino microcontroller and the software RealTerm.

33


(a) Experimental set-up. (b) 3D printed parts.

(c) Close up of thermocouple and top half with the

magnetic core attached.

(d) Wiring diagram for the thermocouple. Image

from Adafruit.

Figure 3.3: Components of testing fixture.

3.2.2 Force

In order to test the accuracy of the model in predicting force, Equation 3.9 was used

with the values shown in Table 3.1. The raw data was collected, processed to account for friction,

34


smoothed and normalized to center it at 0mm. A moving average filter was used to smooth the data

with a window size of 15 and a value of 1 for the ”a” coefficient. Finally, as shown in Figure 3.4, the

measured and theoretical data were plotted against each other. Qualitatively, the agreement seems

to be strong initially, but deviates as time goes on. This can be readily explained by the confluence

of heat and friction. The initial discrepancy is within the range of the collected friction which could

explain the low 3 and 4 V values. Moreover, these measurements were collected while the system

was heating up. As will be seen in the following section, the change in temperature was substantial

which indicates that the change in current due to a higher resistance was substantial as well. The

fact that the force decreases (evident by non-equivalence of the global maximum and minimum) is

consistent with a coil that is heating up. Overall, the force model succeeds in predicting what the

force on the magnet will be based on the characteristic parameters of the coil and magnet.

Type of Property Description Variable Value Unit

MaterialRemanence or residual

flux densityBr 1.37 T

Geometric Length of solenoid* l .01 m

Length of magnet h .003175 m

Radius of magnet r .0031550 m

Inner radius of the coil* Ri .00512 m

Wire gauge* AWG 30 n/a

Measured/Assumed

Voltage* V 3, 4 & 5 V

Resistance in wire* Rwire 1.6 Ω

Circle packing density* λ .5955 n/a

Outer radius of the coil* Ro .00625 m

Calculated Number of turns N 132 n/a

Current I 1.8750, 2.5 & 3.125 A

Average radius Ravg. .0057 m

Length of wire Lwire 4.7198 m

Wire cross sectional area a 5.0927(108) m2

*Note: Properties marked with asterisks are used to obtain the calculated

properties.

Table 3.1: Table describing the variables used in equation 3.9 to estimate the force produced by the

solenoid and magnet based on various parameters.

35


Figure 3.4: Data processing sequence for raw force data and final comparison plot: Measured force

vs. Theoretical force.

36


3.2.3 Power and Heat

In order to determine the accuracy of the heat model, Equation 3.19 was used. However,

because the temperature change was significant, the first version of Equation 3.13 was used in the

generated energy term of Equation 3.19 to account for the resistivity-temperature dependence. The

equation was then solved for T using the software Mathematica. Using the values in Table 3.2,

the variables for convective heat transfer h, effective thermal conductivity, keff. and thickness of

conduction material, x were varied until they approximated the measured data. The results are

shown in Figure 3.5. As can be seen, the match is not very accurate although the temperature at

at 17 seconds is relatively close. This could be due to any number of reasons including the highly

simplified nature of the equation as well as poor contact between the thermocouple and the coil

when collecting the data. Overall, this indicates that the model needs to be modified in order to

better match the data. Once this is done, the two equations can be explored in order to determine

the best actuator design.

Type of

PropertyDescription Variable Value Unit

Material

Thermal coefficient of resistivity α .00393 n/a

Resistivity at room temperature prt 1.724(10−8) Ωm

Specific heat capacity c 385 J/kgK

Density ρd 8933 kg/m3

GeometricLength of solenoid* l .1 m

Wire gauge* AWG 30 n/a

Measured/Assumed

Voltage V 3, 4 & 5 V olts

Convective heat transfer

coefficienth 10 W/m2C

Effective thermal conductivity keff. .2 W/C

Thickness of conduction material x .0025 m

Temperature of the fluid Tfluid 23.41 C

Room temperature Trt 23.41 C

Outer radius of the coil* Ro .00625 m

Calculated

Outer surface areas Aos .00393 m2

Inner surface area Ais .00322 m2

Length of wire Lwire 4.7264 m

Volume of copper v 2.393(10−7) m3

Wire cross sectional area a 5.0927(108) m2

Note: Asterisks represent variables that were used to find values of measured variables.

Table 3.2: Table describing the variables used in Equation 3.19 to estimate the surface temperature

of the solenoid.

37


Figure 3.5: Comparison plot of theoretical model for heat vs. measured data for heat. As can be seen

in the figure, the temperature rise of the coils was substantial which indicates that the resistance was

changing over time. Because of this, the first version of Equation 3.13 which includes the resistivity-

temperature dependence of generated heat was used with Equation 3.19

.

3.3 Generalized Model for a PMTLM

The generalized model for the expected force from the actuator depends on the control

circuit that is implemented. A control circuit that recruits only one coil to ”pull” the magnet nearest

to it (effectively functioning like a stepper motor) would end up having a force that is the sum of the

number of magnets in the core and the force that each magnet is producing, based on its position,

when it interacts with the nearest coil. The actuator was designed in such a way that every magnet

position, relative to the nearest coil, looks the same for every magnet. This will be described in more

detail in the next chapter. This ultimately means that the total force (specifically holding force) of

the actuator is simply Equation 3.22 times the number of magnets, M in the core.

38


F(z) =MNIBrπr

2

2l

[(l/2)− z − h/2√

(z + h/2− l/2)2 +R2avg.

+(l/2) + z + h/2√

(z + h/2 + l/2)2 +R2avg.

− (l/2)− z + h/2√(z − h/2− l/2)2 +R2

avg.

− (l/2) + z − h/2√(z − h/2 + l/2)2 +R2

avg.

](3.22)

In summary, Equation 3.22 gives the force as a function of distance z, as measured from

the center of a cylindrical magnet with certain properties/dimensions to the center of whatever coil

is being activated in the actuator. For the magnet these are: length, h, radius, r (or cross-sectional

area) and magnetic remanence or flux density, Br and number of magnets, M . For the solenoid

these are: the number of turns, N , the current going through the wire, I , the length of the coil, l and

the average turn radius, Ravg..

The equation for heat would be more complex to apply accurately for the final actuator

design. As fluid flows through the actuator, it well heat up causing the coils towards the outlet to

be hotter than the coils towards the inlet. These means that the temperature of each coil will be

different and, for large temperature difference, the force produced by each coil will be different.

However, a reasonable approach to obtaining the average temperature of each coil would be to

multiply the generated heat by the number of coils in the actuator (thereby affecting the Eg term),

using an average heat value for the Tfluid and by making the appropriate surface area adjustments.

This value could be estimated empirically by measuring the temperature at the inlet and outlet of

the actuator. Ultimately, Equation 3.19 becomes:

T (t) =M(I2Rwiret+Aosh(Toutlet − Tinlet/2)t+Aiskeff.Trtt/x)

pdV c+Aosht+Aiskeff.t/x(3.23)

39

Chapter 4

Design and Fabrication

Electric motor components can in general be divided into the rotor, stator and armature.

The rotor is the part that moves or rotates, the stator is the part that is stationary and the armature

is the part that contains the coils. Depending on the design, the armature may be the same as the

stator or the rotor. The PMTLM designed in this thesis will be divided into the same components.

In our case, the rotor will be referred to as the core and the stator (the same as the armature) will

still be called the stator. First, the mechanical design of the core will be described followed by the

design of the stator. Then the electrical aspects will be described in general and details about the

circuit design and arduino motor control code will be shown. The fabrication portion will describe

what was accomplished using a combination of 3D printed components and off the shelf parts and

how they were put together.

4.1 Overview of Mechanical Design

The core design consists of permanent magnets placed in alternating and opposing di-

rections with 3D printed double sided ball and socket joints holding them together. The two com-

ponents were held together by GFlex 650 Toughed Epoxy. This type of epoxy was used not only

because it would bond well with plastic and metal, but also because it is toughed meaning that it

is not brittle. This allows the core to handle large accelerations without snapping. The 3D printed

ball and socket joint is made of PLA. It is 6.36 mm (.25 inches) in diameter and 12.8082 mm (.5

inches) in length. The middle stem was made as thick as possible in order to maximize strength, but

to still allow an approximately 45rotation from the middle axis. It was designed to be printed all in

one piece with a single, small support column holding the ball in place within the socket. Because

40

CHAPTER 4. DESIGN AND FABRICATION

this support column is small and much weaker it can be broken once the part is printed by rotating

the socket. The permanent magnet is a disk shaped, through thickness, Nickel plated, Neodymium

N52 grade magnet. It has a maximum temperature tolerance of 80 Cand a flux density of 1.48 T .

It has the same dimensions as the ball and socket joint: 6.36mm diameter and 12.8082mm length.

Figure 4.1: The core of the actuator and a cross-sectional view of the ball and socket component.

The stator/armature design is more complex as it requires more steps and includes the

winding and spacing of the coils. As was painfully found out through many different design itera-

tions in this thesis, if the winding and spacing of the coils aren’t correct the core will not properly

commute (move smoothly and in the desired way). This usually manifested itself as twitching with

low force. The stator consists of a flexible inner tube, elastic 3D printed coil dividers, insulated

copper wire, a flexible outer tube, elastic 3D printed end caps, and tubing for the inlet and outlets of

the cooling fluid.

The flexible inner tube is Smooth-Flow Tygon tubing. It has a Durometer 70A hardness

rating with a bend radius of 1.25 in, and a temperature tolerance of approximately 50 C. Its inner

diameter is 7.93 mm and its outer diameter is 11.1125 mm which results in a its wall thickness of

1.58 mm. This material was chosen because it is reasonably soft and flexible, but not so much that

it looses shape easily or is not strong. Additionally, Tygon has favorable material properties which

resists buildup or absorption. Ideally the wall thickness would have been thinner and the inner

diameter would have been closer to the diameter of the magnet (in order to increase magnetomotive

force), but this size was readily available through McMaster-Carr so it was chosen. The elastic

3D printed coil dividers and end caps are made out of FormLabs Elastic Resin. This material

is meant to imitate silicone and was chosen because it makes manufacturing easier while having

adequate material properties. For instance, it has a Shore hardness of 50A, an ultimate tensile

41


strength of 3.23 MPa, an elogation of 160%, a temperature tolerance of at least 60 Cs and and

good solvent compatibility for a variety of substances including water and many types of oils. The

dividers have an outer diameter of 15.875 mm and an inner diameter of 11.1125 mm. This gives

a total annulus area of 100.94 mm2. With the current design, the surface area of the front face

of the divider is 51.9572 mm2 which means that the effective diameter reduction is about 50%

whenever the fluid flows through a divider (excluding the coils). Although this represents a high area

reduction, this should have a minimal effect on the overall heat conduction especially considering

that they are 1.905 mm thick and spaced out 6.561 mm from each other. The end caps are printed

with three 1.2 mm diameter holes to allow the copper wires to go through. These can then be

glued shut. The copper coils are wound using NEMA 1000 MW-35C certified, 24 AWG motor

winding wire rated for a temperature of approximately 200 C. It has a polyester base coat and

a polyamideimide topcoat which gives it ”superior chemical resistance to most common solvents

and refrigerants” [10]. At their tested conditions, this allowed the wire to be submerged in harsh

chemicals such as 5% sulfuric acid, petroleum naphtha, 3toluene, and acetone for 24 hours with

minimal damage. The coils are 6.561 mm long and wound directly around the flexible inner tube

until they are approximately 15.5 mm in diameter. This radius allows an annulus area of 9.1 mm2

with the coils, which means an inlet and outlet tube with an inner radius of 1.71 mm2 must be

used to satisfy mass continuity. The outer tube of the actuator is made out of a High-Temperature

Silicone Rubber tube with a hardness of 50A. It is flexible, with a bend radius of 2.25 inches and

a temperature tolerance up to approximately 200 C. It also has good solvent compatibility which

allows it to maintain its properties over time even in the presence of certain liquids. Additionally, if

the insulated copper wire losses insulation the rubber provides a degree of protection. It has an inner

diameter of 15.875 mm and an outer diameter of 19.05 mm. Ultimately, the actuator has a total

diameter of 19.05 mm or .75 inches. The inlet and outlet tubes are made from the same material

with smaller dimensions. For reference, parts and dimensions of the stator are shown in Figure 4.2.

42


(a) Cross-section of the

coil dividers.

(b) Flexible inner tube with dividers and some coils.

(c) Actuator end caps. (d) Final actuator put together.

(e) Dimensions of various parts of the coil. All units are in mm.

Figure 4.2: Parts used in the mechanical design of the actuator and dimensions of actuator compo-

nents (coils are for illustrative purposes and not to scale).

43


4.2 Overview of Electrical Design

The actuator essentially functions as a stepper motor where each coil that is activated

attracts the nearest magnet to it. This is then done in sequence to allow the core to move in steps

along the actuator. There are three coils in the motor, A, B and C which are wound in the same

direction. A magnet with the necessary magnetisation direction to be attracted to coil A when a

current is flowing through it will also be attracted to B and C as long as a current flows in the same

direction. Because the magnets have alternating and opposite magnetizations, in order to have the

next magnet in the core be attracted to coils A, B and C, the current direction must be switched. An

H bridge allows one to do this. This process can be visualized more effectively using Figure 4.3.

Additionally, as seen in the Theory section of this document, controlling the voltage (current) allows

one to control the force produced by the interaction of one coil and one magnet. In order to allow

the actuator to be more versatile, the circuit needs to allow the voltage to be changed easily for each

individual coil of the motor. Pulse Width Modulation (PWM) allows one to do this. Given all this,

electrical components with embedded H-bridges, that allowed for PWM and for the control of at

least 3 individual sub-circuits were chosen. Two Cytron 10A Dual Channel Bi-directional DC Motor

Drivers along with an Arduino micro-controller were chosen as the main electronic components of

the actuator. Each Cytron driver allows two individual sub-circuits (phases) to be connected to it.

Each one can be individually controlled in terms of both magnitude (through PWM) and direction.

Furthermore, the continuous current capacity without cooling is 10 A with up to 10 seconds of 30

A peak currents for each channel. The Arduino micro-controller was chosen because it is capable

of outputting several PWM signals that can be used with the drivers. One of the outputs of the

Cytron drivers was used to control the fluid pump. A peristaltic pump was used in order to avoid

any complications that might arise due to direct contact with the pumping fluid and the interaction

of the ferrofluid nanoparticles and a regular pump shaft. A INTLLAB 12 V DC, 170 460 mL/min

Peristaltic Liquid Pump was chosen.

44


Figure 4.3: Coil phases and winding directions. Each letter represents a different coil. Letters

with apostrophes indicate that they are wound with the same wire, but in a different direction and

therefore will always have a current flowing in the opposite direction. Notice as well that each

individual coil of the same phase interacts with the same local magnetic field (as long as the core is

fully inside the actuator). This means that whatever force is produced by the interaction of a coil, at

a specific phase, and the local magnet is multiplied by the number of coils of that phase that are in

the actuator.

45


4.2.1 Circuit Board Design

Figure 4.4: Circuit board wiring diagram. Each of the colors represents a specific sub-circuit (or

coil) that can be individually controlled in terms of magnitude (using PWM) and direction (by

activating the embedded controller H-bridges). The pump can also be controlled. Future iterations

of the actuator could potentially contain embed temperature sensors that modify the behavior of the

pump when needed, similar to how the heart changes flow rate in response to muscle activation.

46


4.2.2 Arduino Motor Control

Figure 4.5: Basic stepper motor control. Variations in this code can be created to make the motion

more smooth by incorporating Sinusoidal PWM or to control speed by increasing the delay between

coil activation.

47


4.3 Fabrication

A combination of 3D printed components and off the shelf parts were used to manufacture

the actuator. The steps are summarized in Figure 4.6. First the core needs to be built. The core uses

a 3D printed, PLA, double sided ball and socket joint designed on SolidWorks and printed on a

PRUSA i3 Mk3 at .05mm layer height and 100% infill; a mold for aligning the parts (also designed

on SolidWorks and printed on a Prusa, with .15 mm layer height and 15% infill); and the magnets.

Print several ball and socket joints, depending on how long the core will be, and remove from the

Prusa. The ”ball” of the printed joint has an internal support that holds it against the socket, it

must be broken in order for the socket to be radially flexible. While the joint internal supports are

being broken, the mold can be set to print. Once the mold is done printing, with all the materials in

hand, place the mold on a metal (ferromagnetic) surface in order to facilitate aligning the magnets

in alternating and opposing directions. If this is not done the magnets will push away from each

other when placed. Place the ball and socket joints into the alignment ridges of the mold. Lightly

sand the ends of the magnets, wipe them down well with some cloth, put a small amount of Gflex

650 Toughed Epoxy and place them on the mold in the proper orientations. Push them against each

other. The epoxy will take 7 to 10 hours to fully cure.

Next, the stator must be built. The stator consists of a flexible inner tube, elastic 3D

printed coil dividers, insulated copper wire, a flexible outer tube, elastic 3D printed end caps, and

tubing for the inlet and outlets of the cooling fluid. The flexible inner tube is an off the shelf

component that must be cut depending on how long the intended actuator will be. Refer to Figure

4.2 for dimensions. Based on the intended length, a number of dividers must be printed. These were

printed from elastic resin on Formlabs printers 1. In accordance with Formlabs post processing, they

must be washed for 20 minutes in fresh IPA and then cured for 20 minutes at 60 C. Once the post

processing is done the supports must be cut off. While the dividers are being made, the actuator

alignment mold must be printed. This is printed the same way as the core alignment mold. Put the

flexible inner tube through the dividers and place the tube into the alignment mold. Once aligned,

glue the dividers to the tube. Next, the coils are wound. Coils A, B and C are wound in the same

direction, the next three coils are wound in the opposite direction using the wires from coils A, B

and C, respectively. This pattern is continued throughout the entire length of the actuator in between

all the dividers. Make sure to keep extra length of wire along the ends to make the circuit. Once1Unfortunately this version had to have stiff 3D printed parts since access to a formlabs 3d printer was not possible

due to the Covid pandemic

48


this is done cut the rubber tube to a proper length, about 13 mm from each divider end. Push the

actuator into the rubber tube, pull the copper wires through the end cap holes and glue the caps to

the rubber tube. Insert some glue into the wire holes to seal them. Carefully cut two small slits in

the sides of the rubber to insert the inlet and outlet tubing. Glue around the hole to make sure there

is a proper seal.

49


Figure 4.6: Overview of the actuator fabrication process. Using the core mold, the core pieces are

aligned and then epoxied. For the stator, 3D printed dividers are inserted around the flexible inner

tube, aligned with the actuator mold and then glued. The coils are then individually wound into

three separate phases. Sets of three (shown in brown) are going in one direction and sets of three

(shown in grey) are going in the other. Once the coils are wound, the stator is inserted into the

flexible outer tubing (shown transparent here) and the 3d printed end caps are placed and glued.

The final step is to carefully cut out holes for the inlet and outlet tubes and glue around them to

form a water-tight seal.

50


Figure 4.7: Images of the final actuator, with and without the outer flexible tube.

51


Figure 4.8: Close up of the final actuator. The final actuator did not incorporate the inflow and

outflow tubes.

52

Chapter 5

Testing, Results and Discussion

General tests were performed to evaluate the performance of the actuator in light of the

metrics discussed in Chapter 2. These metrics will be given a mathematical definition in this section

and a description of the experimental set up necessary to obtain the information will be illustrated.

The results will then be shown, summarized and discussed. Unfortunately, the initial test of the

actuator resulted in structural damage due to overheating so values are much lower than they could

have potentially been.

5.1 Actuator Tests

As previous mentioned, Madden et. al give a very good list of metrics for quantifying

the performance of muscle-like actuators. They are meant to quantify how much force, and at what

range, the actuator is capable of producing normalized to its size. How quickly it can actuate, how

responsive it is, and how much force it can produce normalize to its weight; how energetically

efficient it is, how many cycles can it withstand, its elastic modulus, its directionality and its catch-

state. Some of these metrics were used to get a general idea of the performance of the actuator. The

ones that were used along with the experiments to obtain them, are mathematically described below.

Detailed tests were not able to be carried out because of a lack of equipment, but approximate values

were determined.

5.1.1 Description of Data to be Collected

Typical output stress (σa): the average force, Fa, generated by the actuator upon excitation

in the range of ”useful” force divided by its initial cross-sectional area, Ai, at rest. Because the

53

CHAPTER 5. TESTING, RESULTS AND DISCUSSION

average force is used, it is acknowledged that it is likely that the force varies as a function of strain.

σa =FaAi≡MPa (5.1)

Peak output stress (σp): the peak force, Fp, generated by the actuator upon excitation divided by its

initial cross-sectional area, Ai, at rest.

σp =FpAi≡MPa (5.2)

Typical output strain (εt): the change in length, Lt, of the actuator upon excitation in the range

where it provides ”useful” force, divided by its initial length, Lit, when fully elongated. Because

this metric states a condition of ”useful” force, it is obtained from the Typical Output Stress data.

εt = 100∆LtLit≡ % (5.3)

Maximum output strain (εm): the change in length,Lm, of the actuator upon excitation divided by

its initial length, Lim, when fully elongated.

εm = 100∆LmLim

≡ % (5.4)

Strain rate (R): is it is the change in typical output strain of the actuator divided by the time it took

to complete the stroke, s.

Rs =εts≡ %/s (5.5)

Energy (work) density Ed: the output work generated by the actuator upon excitation in the typical

range, normalised to the volume, Vt, of the actuator at the typical initial length.

Ed =Fa∆LtVt

≡ kJ/m3 (5.6)

Specific Power (Ps): the output of power in the typical range normalized to the weight of the

actuator, W .

Ps =Fa∆LtWs

≡ kW/Kg (5.7)

Efficiency : the ratio of output work over input energy (energy in any form).

η = 100EoutEin

≡ % (5.8)

54


5.1.2 Experimental Setup

The set up was meant to determine how much force the actuator was capable of producing.

The actuator was programmed to have a repeatable motion within a narrow range and then the scale

was slowly pulled back until the pull out force was achieved. This value was used as the typical

force. To determine the peak output stress, an additional test was performed to see if the actuator

was capable of lifting its own weight by simply inverting the actuator vertically, holding the core

and raising the current until the stator was able to reliably cycle within the narrow motion range

while supporting itself. This was chosen as the peak force. Performance metrics were then derived

from this information.

Figure 5.1: Experimental set up.

55


5.2 Results

Variable Values

Weight, W 80grams Typical Initial Length, Lit 205.3mm

Stator Length 158.572mm Maximum Initial Length, Lim 281.63mm

Friction force, f .4 < f < 1 ∆Lt 21mm

Peak Force, Fp .8N ∆Lm 245mm

Continuous Force, Fa .3N Cross sectional area, Ai 285.023mm2

Volume, Vt 45196.66mm3 Stroke time, s .5s

Performance Metrics Results

Metric Result Note

Typical Stress (MPa) .001052

Was measured with all the magnets in the stator. In reality

a ”useful” force could be determined to be with only 3 magnets

in the stator.

Peak Stress (MPa) .002806

Was chosen to be when enough force was produced to reliably

lift itself. In reality a peak force could be much higher since the

power supply can only output 5A, but the motor drivers can handle

peak currents of 30A for 10 seconds.

Typical Strain (% of length) 10.229 Assuming all the magnets are in contact with a coil.

Maximum Strain (% of length) 86.99Assuming the strain occurs from last magnet in contact with the

first coil to the first magnet in contact with the last coil.

Work/Energy Density (kJ/m3) .1393 Used just the volume of the stator from end cap to end cap.

Specific Power (kW/kg) .0001575 Mechanical Power was determined by Work/stroke time

Efficiency (%) .2133Calculated by taking Mechanical Power and

dividing by Electrical Power (VI).

Table 5.1: Table of performance metrics results for the actuator.

5.3 Discussion

As can be seen, the performance of the actuator was below anything that was described

in Table 2.1 in the Literature Review section. There are a variety of reasons for this. First, and

most important, the actuator was tested after it had experienced damage. When the actuator was

first turned on, it was tested with a high current (approximately 5 Amps) running through it. This

caused it to heat up substantially. Because of this, the flexible inner tube, which has a temperature

tolerance of approximately 50 C, was damaged. The damage caused it to contract and deform

with bumps on the inside which increased friction. As can be seen in Table 5.1, the friction in the

actuator was anywhere from .4 to 1 N. This negatively effected performance. Future testing of the

actuator was done with a much lower current (< 2Amps). Obviously, as was determined in the

56


theory section, a lower current is linearly related to a lower force. With the proper materials, and by

actually implementing the cooling that the actuator was built for, at least 10 times the continuous

force could reasonably be achieved and even higher peak forces could be achieved by running the

30 amps (for a maximum of 10 seconds) that the drivers are built for. Secondly, as can be seen

in Figure 4.5, the Arduino code that controls the actuator was very simple. Simpler code means

the created motion is simple and not optimized. By considering factors such winding inductance

and back-EMF generated by the moving core, the actuator can further be improved especially when

moving more quickly.

Addressing specific metrics, various comments are worth mentioning. In general, unfor-

tunately, the data could not be appropriately collected during this work. Ideally, data to create a

force-length curve (similar to that of muscle) would have been obtained. With the curve in hand, a

proper force threshold could have been determined. Anything below this threshold would not have

been considered a part of the typical stress. The average of the leftover data would have been taken

and this force would have been used as the Typical Stress. The Peak Stress of the actuator repre-

sents the maximum force that the actuator can produce. Because it is known that the drivers can

sustain 30 Amps of current, a similar exercise could have been done for the peak stress. Using the

force-length curves, the typical and maximum strains could have been determined more accurately.

Overall, many improvements can be made in future iterations.

57

Chapter 6

Conclusion

Nature uses soft materials frequently and stiff materials sparingly.

— Vogel 1995, Better Bent than Broken [55]

Aircraft can fly just fine without resorting to flapping their wings.

— Unknown

6.1 General Conclusion

This thesis presents the need for a new kind of muscle-like actuator based on the various

benefits that this kind of actuator would provide. The ideal actuator would be highly controllable, in

terms of actuation speed, strain and resolution, and would consume little energy. In general, it would

have tremendous appeal in terms of energetic performance, for non-cyclical motion, over current

actuators and would have favorable material properties. The argument was made that imitating some

aspects of biological muscle would be a worthwhile approach in accomplishing this. The identified

aspects to imitate include its repeating structure, its heat removal system, its specialized fibers,

its linear elastic elements and its bendable structure. A PMTLM was designed and constructed

which incorporates a bendable structure, a heat removal system and a new core design for PMTLM.

The actuator underwent basic testing which unfortunately indicated less-than-favorable performance

parameters which could be greatly improved in future iterations.

58

CHAPTER 6. CONCLUSION

6.2 Applications

Unfortunately, with the current performance metrics, not many useful applications exist

that aren’t better served by other actuators. If single actuator performance is improved, however,

reasonable applications could include the actuation of bio-mimetic robotics or prosthetics. Addi-

tionally, by using this type of actuator parallel actuation schemes could be explored while taking

advantage of the favorable material properties. Finally, if properly miniaturized, this type of actuator

(or PMTLMs in general) could be used to actuate small medical devices.

6.3 Limitations and Future Work

The actuator in this research could have been improved in a variety of ways. Firstly, by

using an inner flexible tube made out of a higher temperature tolerance material (at least a tolerance

greater than 90 C). Secondly, improving the code and electric circuit to account for inductance

and back-EMF, and implementing micro-stepping in order to make the actuator more efficient and

move more smoothly. Thirdly, unlike DC motors, the current consumption of stepper motors is

independent of load and they constantly draw maximum current. As such, they tend to become hot

and are not very efficient since they draw power even without doing work. Incorporating a catch-

state would be an interesting project. Forth, investigating various optimized geometries in order

to imitate the various specialized muscle fibers that biological muscle incorporates would also be

novel and worthwhile. And finally, in regards to the design, using a Hallback array coil arrangement

in order to focus the magnetic field and square winding wire instead of circular wire would improve

performance.

6.4 Closing Thoughts

Big picture, these results and others like it ultimately lead to the question: Is it worth

creating an artificial muscle in order to imitate its function? The two quotes above in a certain sense

illustrate competing perspectives. As was continuously stated throughout this document, there are

various benefits to be had - both mechanical and material - in creating an artificial muscle. In terms

of mechanics, conventional electric motors could just as well be improved with cooling and higher

energy density sources are an area of ongoing research. Ultimately, if the goal is to create torques

about joints, there is no approach more simple and straightforward than simply putting an electric

59

CHAPTER 6. CONCLUSION

motor in it. Similarly if the goal is to fly from point A to B, aircraft can do it just fine without

resorting to flapping their wings. Other considerations held equal - energetic, durability, comfort,

ease of manufacturing, etc.- the simpler approach is always best. Alternatively, there is a reason

nature uses soft materials frequently and stiff materials sparingly. As much of folk wisdom suggests,

it is better to bend rather than to break. Much of the natural world lives and develops by this mantra.

It would be hard to imagine some version of a conventional electric motor (or any current actuator

for that matter) that was able to bend significantly without breaking or be used in such a diverse

range of environments and size scales. Biological muscle has achieved this. Any environment

where humans are present alongside robots - increasingly more and more environments - would

benefits from the existence of an actuator of this kind. In the future these kinds of actuators may

safely power the robotic assists that take care of the young or elderly, or work alongside astronauts

in exploring the universe.

60

Bibliography

[1] Ingi Agnarsson, Ali Dhinojwala, Vasav Sahni, and Todd A Blackledge. Spider silk as a novel

high performance biomimetic muscle driven by humidity. Journal of Experimental Biology,

212(13):1990–1994, 2009.

[2] Ray H Baughman, Changxing Cui, Anvar A Zakhidov, Zafar Iqbal, Joseph N Barisci, Geoff M

Spinks, Gordon G Wallace, Alberto Mazzoldi, Danilo De Rossi, Andrew G Rinzler, et al.

Carbon nanotube actuators. Science, 284(5418):1340–1344, 1999.

[3] V Chaudhary, Z Wang, A Ray, I Sridhar, and RV Ramanujan. Self pumping magnetic cooling.

Journal of Physics D: Applied Physics, 50(3):03LT03, 2016.

[4] Bernard Dennis Cullity and Chad D Graham. Introduction to magnetic materials. John Wiley

& Sons, 2011.

[5] Michael De Volder, Jan Peirs, Dominiek Reynaerts, Johan Coosemans, Robert Puers, Olivier

Smal, and Benoit Raucent. Production and characterization of a hydraulic microactuator.

Journal of Micromechanics and microengineering, 15(7):S15, 2005.

[6] Michael De Volder and Dominiek Reynaerts. Pneumatic and hydraulic microactuators: a

review. Journal of Micromechanics and microengineering, 20(4):043001, 2010.

[7] Kosmas Deligkaris, Tadele Shiferaw Tadele, Wouter Olthuis, and Albert van den Berg.

Hydrogel-based devices for biomedical applications. Sensors and Actuators B: Chemical,

147(2):765–774, 2010.

[8] Mihai Duduta, Robert J Wood, and David R Clarke. Multilayer dielectric elastomers for fast,

programmable actuation without prestretch. Advanced Materials, 28(36):8058–8063, 2016.

61

BIBLIOGRAPHY

[9] Nafiseh Ebrahimi, Paul Schimpf, and Amir Jafari. Design optimization of a solenoid-based

electromagnetic soft actuator with permanent magnet core. Sensors and Actuators A: Physical,

284:276–285, 2018.

[10] Essex Group, Inc. Essex GP/MR-200 Product Data Sheet, 2008.

[11] Javad Foroughi, Geoffrey M Spinks, Gordon G Wallace, Jiyoung Oh, Mikhail E Kozlov, Shaoli

Fang, Tissaphern Mirfakhrai, John DW Madden, Min Kyoon Shin, Seon Jeong Kim, et al.

Torsional carbon nanotube artificial muscles. Science, 334(6055):494–497, 2011.

[12] Brian Glancy, Lisa M Hartnell, Daniela Malide, Zu-Xi Yu, Christian A Combs, Patricia S

Connelly, Sriram Subramaniam, and Robert S Balaban. Mitochondrial reticulum for cellular

energy distribution in muscle. Nature, 523(7562):617, 2015.

[13] Rinaldo Greiner, Merle Allerdissen, Andreas Voigt, and Andreas Richter. Fluidic microchemo-

mechanical integrated circuits processing chemical information. Lab on a Chip, 12(23):5034–

5044, 2012.

[14] Carter S Haines, Na Li, Geoffrey M Spinks, Ali E Aliev, Jiangtao Di, and Ray H Baugh-

man. New twist on artificial muscles. Proceedings of the National Academy of Sciences,

113(42):11709–11716, 2016.

[15] Carter S Haines, Marcio D Lima, Na Li, Geoffrey M Spinks, Javad Foroughi, John DW Mad-

den, Shi Hyeong Kim, Shaoli Fang, Monica Jung De Andrade, Fatma Goktepe, et al. Artificial

muscles from fishing line and sewing thread. science, 343(6173):868–872, 2014.

[16] Elwood Henneman. The size-principle: a deterministic output emerges from a set of proba-

bilistic connections. Journal of experimental biology, 115(1):105–112, 1985.

[17] Jemin Hwangbo, Joonho Lee, Alexey Dosovitskiy, Dario Bellicoso, Vassilios Tsounis, Vladlen

Koltun, and Marco Hutter. Learning agile and dynamic motor skills for legged robots. arXiv

preprint arXiv:1901.08652, 2019.

[18] Frank P Incropera, Adrienne S Lavine, Theodore L Bergman, and David P DeWitt. Funda-

mentals of heat and mass transfer. Wiley, 2007.

[19] Jaronie Mohd Jani, Martin Leary, Aleksandar Subic, and Mark A Gibson. A review of shape

memory alloy research, applications and opportunities. Materials & Design (1980-2015),

56:1078–1113, 2014.

62

BIBLIOGRAPHY

[20] Nicholas Kellaris, Vidyacharan Gopaluni Venkata, Garrett M Smith, Shane K Mitchell, and

Christoph Keplinger. Peano-hasel actuators: Muscle-mimetic, electrohydraulic transducers

that linearly contract on activation. Science Robotics, 3(14), 2018.

[21] Roy D Kornbluh, Ron Pelrine, Qibing Pei, Seajin Oh, and Jose Joseph. Ultrahigh strain re-

sponse of field-actuated elastomeric polymers. In Smart Structures and Materials 2000: Elec-

troactive Polymer Actuators and Devices (Eapad), volume 3987, pages 51–64. International

Society for Optics and Photonics, 2000.

[22] Sang Cheon Lee, Il Keun Kwon, and Kinam Park. Hydrogels for delivery of bioactive agents:

a historical perspective. Advanced drug delivery reviews, 65(1):17–20, 2013.

[23] Richard L Lieber. Skeletal muscle adaptability. i: Review of basic properties. Dev Med Child

Neurol, 28(3):390–7, 1986.

[24] Marcio D Lima, Na Li, Monica Jung De Andrade, Shaoli Fang, Jiyoung Oh, Geoffrey M

Spinks, Mikhail E Kozlov, Carter S Haines, Dongseok Suh, Javad Foroughi, et al. Electri-

cally, chemically, and photonically powered torsional and tensile actuation of hybrid carbon

nanotube yarn muscles. science, 338(6109):928–932, 2012.

[25] John D Madden. Mobile robots: motor challenges and materials solutions. science,

318(5853):1094–1097, 2007.

[26] John DW Madden, Nathan A Vandesteeg, Patrick A Anquetil, Peter GA Madden, Arash Tak-

shi, Rachel Z Pytel, Serge R Lafontaine, Paul A Wieringa, and Ian W Hunter. Artificial muscle

technology: physical principles and naval prospects. IEEE Journal of oceanic engineering,

29(3):706–728, 2004.

[27] Daniel Mayer and Petr Polcar. A novel approach to measurement of permeability of magnetic

fluids. Przeglad Elektrotechniczny, 88(7):229–231, 2012.

[28] Michael A Meller, Matthew Bryant, and Ephrahim Garcia. Reconsidering the mckibben mus-

cle: Energetics, operating fluid, and bladder material. Journal of Intelligent Material Systems

and Structures, 25(18):2276–2293, 2014.

[29] Tissaphern Mirfakhrai, John DW Madden, and Ray H Baughman. Polymer artificial muscles.

Materials today, 10(4):30–38, 2007.

63

BIBLIOGRAPHY

[30] Seyed M Mirvakili and Ian W Hunter. Artificial muscles: Mechanisms, applications, and

challenges. Advanced Materials, 30(6):1704407, 2018.

[31] Seyed M Mirvakili, Alexey Pazukha, William Sikkema, Chad W Sinclair, Geoffrey M Spinks,

Ray H Baughman, and John DW Madden. Niobium nanowire yarns and their application as

artificial muscles. Advanced Functional Materials, 23(35):4311–4316, 2013.

[32] Bryan Craig Murphy. Design and construction of a precision tubular linear motor and con-

troller. PhD thesis, Texas A&M University, 2004.

[33] STEVEN J Murray, MIGUEL Marioni, SM Allen, RC Ohandley, and Thomas A Lograsso. 6%

magnetic-field-induced strain by twin-boundary motion in ferromagnetic ni–mn–ga. Applied

Physics Letters, 77(6):886–888, 2000.

[34] Kazuhiro Ohyama, Yasushi Hyakutake, and Hitoshi Kino. Verification of operating princi-

ple of flexible linear actuator. In 2009 International Conference on Electrical Machines and

Systems, pages 1–6. IEEE, 2009.

[35] Qibing Pei, Marcus A Rosenthal, Ron Pelrine, Scott Stanford, and Roy D Kornbluh. Multi-

functional electroelastomer roll actuators and their application for biomimetic walking robots.

In Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EA-

PAD), volume 5051, pages 281–290. International Society for Optics and Photonics, 2003.

[36] Lakshita Phor and Vinod Kumar. Self-cooling by ferrofluid in magnetic field. SN Applied

Sciences, 1(12):1696, 2019.

[37] Robert Playter, Martin Buehler, and Marc Raibert. Bigdog. In Unmanned Systems Technology

VIII, volume 6230, page 62302O. International Society for Optics and Photonics, 2006.

[38] Juha Pyrhonen, Tapani Jokinen, and Valeria Hrabovcova. Design of rotating electrical ma-

chines. John Wiley & Sons, 2013.

[39] Andreas Richter and Georgi Paschew. Optoelectrothermic control of highly integrated

polymer-based mems applied in an artificial skin. Advanced Materials, 21(9):979–983, 2009.

[40] Bryan Paul Ruddy. High force density linear permanent magnet motors:” electromagnetic

muscle actuators”. PhD thesis, Massachusetts Institute of Technology, 2012.

64

BIBLIOGRAPHY

[41] Claudio Scherer and Antonio Martins Figueiredo Neto. Ferrofluids: properties and applica-

tions. Brazilian Journal of Physics, 35(3A):718–727, 2005.

[42] Paul H Schimpf. A detailed explanation of solenoid force. International Journal on Recent

Trends in Engineering & Technology, 8(2):7, 2013.

[43] Wayne Scott, Jennifer Stevens, and Stuart A Binder-Macleod. Human skeletal muscle fiber

type classifications. Physical therapy, 81(11):1810–1816, 2001.

[44] Nicholas P Smith, Christopher J Barclay, and Denis S Loiselle. The efficiency of muscle

contraction. Progress in biophysics and molecular biology, 88(1):1–58, 2005.

[45] Peter Sommer-Larsen, Guggi Kofod, MH Shridhar, Mohammed Benslimane, and Peter

Gravesen. Performance of dielectric elastomer actuators and materials. In Smart Structures

and Materials 2002: Electroactive polymer actuators and devices (EAPAD), volume 4695,

pages 158–166. International Society for Optics and Photonics, 2002.

[46] Alexei Sozinov, AA Likhachev, N Lanska, and Kari Ullakko. Giant magnetic-field-induced

strain in nimnga seven-layered martensitic phase. Applied Physics Letters, 80(10):1746–1748,

2002.

[47] Robert S Staron. Human skeletal muscle fiber types: delineation, development, and distribu-

tion. Canadian Journal of Applied Physiology, 22(4):307–327, 1997.

[48] Asuka Takai, Nouf Alanizi, Kazuo Kiguchi, and Thrishantha Nanayakkara. Prototyping the

flexible solenoid-coil artificial muscle, for exoskeletal robots. In 2013 13th International Con-

ference on Control, Automation and Systems (ICCAS 2013), pages 1046–1051. IEEE, 2013.

[49] Chittin Tangthieng, Bruce A Finlayson, John Maulbetsch, and Tahir Cader. Heat transfer

enhancement in ferrofluids subjected to steady magnetic fields. Journal of Magnetism and

Magnetic Materials, 201(1-3):252–255, 1999.

[50] Bret W Tobalske and Andrew A Biewener. Contractile properties of the pigeon supracora-

coideus during different modes of flight. Journal of Experimental Biology, 211(2):170–179,

2008.

[51] Brian R Umberger, Karin GM Gerritsen, and Philip E Martin. A model of human muscle

energy expenditure. Computer methods in biomechanics and biomedical engineering, 6(2):99–

111, 2003.

65

BIBLIOGRAPHY

[52] Christian Urban, Richard Gunther, Thomas Nagel, Rene Richter, and Robert Witt. Develop-

ment of a bendable permanent-magnet tubular linear motor. IEEE Transactions on Magnetics,

48(8):2367–2373, 2012.

[53] Allan Joshua Veale and Shane Quan Xie. Towards compliant and wearable robotic orthoses:

A review of current and emerging actuator technologies. Medical engineering & physics,

38(4):317–325, 2016.

[54] Rino Versluys, Kristel Deckers, Michael Van Damme, Ronald Van Ham, Gunther Steenackers,

Patrick Guillaume, and Dirk Lefeber. A study on the bandwidth characteristics of pleated

pneumatic artificial muscles. Applied Bionics and Biomechanics, 6(1):3–9, 2009.

[55] S Vogel and N Jakesevic. Better bent than broken. Discover, 16(5):62–67, 1995.

[56] Jiabin Wang, Geraint W Jewell, and David Howe. A general framework for the analysis

and design of tubular linear permanent magnet machines. IEEE Transactions on Magnetics,

35(3):1986–2000, 1999.

[57] Douglas Warrick, Tyson Hedrick, Marıa Jose Fernandez, Bret Tobalske, and Andrew

Biewener. Hummingbird flight. Current Biology, 22(12):R472–R477, 2012.

[58] Sang Yul Yang, Kyeong Ho Cho, Youngeun Kim, Min-Geun Song, Ho Sang Jung, Ji Wang

Yoo, Hyungpil Moon, Ja Choon Koo, Hyouk Ryeol Choi, et al. High performance twisted and

coiled soft actuator with spandex fiber for artificial muscles. Smart Materials and Structures,

26(10):105025, 2017.

[59] Felix E Zajac. Muscle and tendon: properties, models, scaling, and application to biomechan-

ics and motor control. Critical reviews in biomedical engineering, 17(4):359–411, 1989.

[60] Amir Hosein Zamanian and Edmond Richer. Identification and compensation of cogging and

friction forces in tubular permanent magnet linear motors. In ASME 2017 Dynamic Systems

and Control Conference, pages V002T04A003–V002T04A003. American Society of Mechan-

ical Engineers, 2017.

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