Development of an Exo-Limb for People with Lower-Leg Injuries
Team Lead:
In Collaboration with:
Michael Villavecer
Victor Lopez
Team Members:
Volunteer Assistant:
Bryan Holloway
Justin Chin
Salar Nosratabadi
Larry Tlilayatzi
Gaby Martinez
Mentored by:
Jason Taylor
Dr. Scott Lynn
CALIFORNIA STATE UNIVERSITY, FULLERTON
College of Engineering and Computer Science
Mechanical Engineering Department
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Table of Contents
List of Figures………………………………………………………………………………………………………3
List of Tables………………………………………………………………………………………………………. 5
Acknowledgements…………………………………………………………………………………………….. 6
Abstract……………………………………………………………………………………………………………… 7
Project Background…………………………………………………………………………………………….. 9
Problem Statement & Objectives…………………………………………………………………………27
Proposed Conceptual Design………………………………………………………………………………31
Update Design ………………………………………………………………………………………………......42
Project Management…………………………………………………………………………………………..45
References…………………………………………………………………………………………………………55
Appendix…………………………………………………….……………………………………………………..56
ABET Requirement…………………………………………………………………………………………….59
2
List of Figures
Figure 1 – Comparison between Texas A&M’s design and CSUF ’12-’13 design…..9
Figure 2 – Comparing the gait with the devices to the gait without them…..……….10
Figure 3 – The gait cycle…………………………………………………………………………..………11
Figure 4 – The reference planes of the human body………………………………………….12
Figure 5 – Time spent on each limb during the gait cycle……………………………….….12
Figure 6 – The Freedom Leg……………………………………………………………………………13
Figure 7 – The iWalk Free……………………………………………………………………………….14
Figure 8 – The Flexleg……………………………………………………………………………………..15
Figure 9 – A passive dynamic walking robot…………………………………………………….18
Figure 10 - Stability Diagram of four bar linkage with instant center………………...21
Figure 11 - Comparisons of the natural walking gait vs. four bar, six bar linkage.22
Figure 12 - The parameter of natural walking gait with 20 percent error………….23
Figure 13 – A prosthetic leg from Össur…………………………………………………………..26
Figure 14 – Underarm crutches……………………………………………………………………….27
Figure 15 – Functional Block Diagram……………………………………………………………..31
Figure 16 – Morph Chart…………………………………………………………………………………33
Figure 17 – Pugh charts for the body attachment sub-assembly………….....................33
Figure 18 – Pugh charts for the knee joint sub-assembly………………………………….34
Figure 19 – Pugh charts for the foot material…………………………………………………...34
3
Figure 20 - The motion path of the first trial of the four bar linkage design idea..35
Figure 21 - The motion path of the second trial of the four bar linkage idea………36
Figure 22 – The motion path after several trial of the four bar linkage idea……….37
Figure 23 – The overall system and leg attachment subsystem……………………....…38
Figure 24 – The knee joint subsystem…………………………………………………………......39
Figure 25 – The foot subsystem………………………………………………………………………40
Figure 26 – Knee Support Sub-Assembly …………………………………….……………..….....42
Figure 27 - Four-bar Linkage Design 1……………………………………………………………..43
Figure 28 – Four-bar Linkage Design 2……………………………………………………….….....44
Figure 29 – Work Breakdown structure……………………………………..……………….….....45
Figure 30- Hydraulic Press Break …………………………………………………………………….48
Figure 31- Ultra-Low Profile Shoulder Screw…………………………………………………….49
Figure 32- Static and Fatigue testing ……………………………………………………..….……….50
Figure 33 – Surveying Results from 16 Students…………………………………………………51
Figure 34 - Overall project gantt chart……………………………………………………………….56
4
List of Tables
Table 1 – Foot Clearance of common prosthetic devices………………………………........24
5
Acknowledgements
We would like to give a special thank you to Dr. Nina Robson and Jason Taylor for
their generous help and support.
6
Abstract
The goal of the Exo-limb project is to engineer a device for people with below the
knee injuries such as athletes or anyone with a busy life that cant afford to lose the
freedom of their hands. Engineering a mechanical device that helps people with an
injury live a normal life is motivating. It is challenging to find a simple, cheap, and
well working design and is something completely different from anything else.
The objectives of the project are to create a purely mechanical, hands free
walking device that mimics the natural walking gait of a human. It must safely
support a user of 200lb’s with a safety factor of 3 and also be adjustable and
comfortable to the user. In order to meet these requirements we have incorporated
4bar linkage into the knee mechanism and combined it with lightweight
construction. The 4 bar linkage will mimic the natural teardrop shape the trajectory
of the human ankle follows through the walking gait. Carbon fiber, polypropylene,
and aluminum are combined to achieve a lightweight and comfortable device.
The biggest struggle for the device was mimicking the natural teardrop shape of
the ankle. This is also critical, as it will make the user feel like they are using their
own leg and not a hand’s free crutch. Using a simple hinge for the knee mechanism
has a flat crescent shaped trajectory and will feel unnatural and hard to use. The 4
bar linkage follows a similar teardrop shape and will closely mimic the natural
swing of the ankle.
The Exo-limb device is designed for people with lower leg injuries that want to
continue to live their life without their injury getting in the way of their day-to-day
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tasks. The Exo-limb will be lightweight, easy to use, comfortable, and natural
feeling. By using simple four bar mechanics the device can be used by an injured
user with ease.
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Project Background
Project History
Texas A&M came up with a design mechanism based on the double pendulum
linkage of the knee. It was able to support 261% walking load and was capable of
346% descending stairs. The problems were that it was not successful to keep the
walking balance since it had to be mounted to outside of the leg and did not mimic
the natural walking ankle trajectory of a teardrop shape.
Figure 1 – Comparison between Texas A&M’s design and CSUF ’12-’13 design.
The senior design team at California State University Fullerton 2012-2013 came up
with a new design of hand free crutch called P.A.W.D. It was a self locking passive
assisted walking device that was equipped with a pre-determined bending angle
system helped by two springs and belts, suspenders, and straps for the body and leg.
It was extremely successful to simulate the natural walking tear shape trajectory,
however it was uncomfortable and hard to mount due to the position of the
mounting.
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Figure 2 – Comparing the gait with the devices to the gait without them.
Literature Review
Biomechanics
In order to design a device that mimics the natural walking gait, we had to
review the basic principles of biomechanics.
We specifically focused on the
principles of human dynamic walking as it relates to the gait cycle. The gait cycle
consists of two main sequences: the stance phase and the swing phase. During the
stance phase, the leg in focus is planted on the ground while the opposite leg moves
through the air. During the swing phase, the leg in focus moves through the air and
the opposite leg is planted on the ground supporting the person. These two phases
can be broken down into several sequences. The stance phase begins with heelstrike, then moves to flat foot, then to mid-stance, and finally to heel off. Following
that, the swing phase begins with toe-off, then mid-swing, and finally back to heel
strike. This process can be seen in the diagram of figure 3.
The human walking gait is a complex process that takes place in three
dimensions. Motions in the three coordinate systems are referenced to planes of the
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human body in the standard anatomical position. They are the frontal plane, the
transverse plane, and the sagittal plane. They can be seen in figure 4.
Figure 3 – The gait cycle.
For this project, we decided to focus on constraining the motion profile to
two degrees: the x- and y- coordinates along the sagittal plane. This was done to
simplify calculations, and it doesn’t drastically differ from using 3-dimensional
coordinates since motion in the frontal plane during the gait cycle is minimal.
The stance phase of the gait cycle corresponds to single-limb support. For
this reason, we had to make sure that the stability of the user during this phase
produced optimal results to ensure the safety of the person using the device. Also,
because the device requires some fine motor skills to operate correctly, we intend
for users of the device to be between the ages of 16-60. In later sections, stability of
different mechanisms will be compared.
The swing phase is the most active dynamic phase. We used a 2-D motion
tracking software package called Kinovea to track the position of a person’s ankle,
knee, and hip. By gathering and analyzing the data from the motion tracking
software, we were able to determine the coordinates of the natural human walking
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gait. This data will allow us to compare the gait of a person using the device to that
of a person walking naturally.
Figure 4 – The reference planes of the human body.
Due to the cyclic nature of the gait cycle, the processes are repeatable for
each side of the body. In essence, when the left side undergoes stance phase, the
right side undergoes swing phase and vice versa. There is also a period of time
when both legs are in contact with the ground at the same time. This can be seen in
figure 5. From that figure, we can see that the stance phase makes up 62% of the
total cycle and the swing phase is 38% of the total cycle.
Using the motion tracking software enabled us to compare the natural
walking gait to the gait of a person using a hands-free crutch. With this in mind, we
decided to do a comparative analysis of some previously designed hands-free
crutches and some products that are already out on the market.
Figure 5 – Time spent on each limb during the gait cycle.
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Current Devices
The current devices out in the market aim to assist people with lower leg
injuries. The three devices that we will discuss are the Freedom Leg, iWalk Free and
the FlexLeg devices. The common feature in all three devices is that it is attached to
the thigh and the foot is in a fixed position.
Figure 6 – The Freedom Leg.
The Freedom Leg boasts many features and benefits to their product. The
device has an adjustable length of the brace to give control of the weight on the
injured leg. One can walk safely with zero weight on the injured foot, ankle, knee or
lower leg. Freeing of the hands helps accomplish all normal day to day tasks without
assistance. Use of the upper leg muscles on the injured leg is still exercised to reduce
the atrophy of the upper leg muscles normally associated with extended periods of
off-loading which can significantly reduce rehabilitation time. Stairs can easily be
climbed because hand rails can be used. It is made of composite materials so that it
is light weight.it is attached to the thigh via a thigh cuff. The device needs to be fitted
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dependent on the brace size, the inseam of the leg, and the strap length, the
circumference of upper thigh. It can be used by anyone in need. The device typically
falls under L2136 code which is for a pre-fabricated knee-ankle-foot-orthosis
(KAFO).
It is intended to be used when a patient needs a “greater ability to
ambulate independently”. The code does not require pre-authorization and the
Freedom Leg fits the definition well.
It is sold for the retail price of $449.
Complaints have been reported to be that it is uncomfortable and expensive.
The iWalk Free is the other device that we that we took a look at. We
purchased it and tried it out for a bit to evaluate it. The iWalk boasts a hands free
design that has a knee platform that evenly and comfortably distributes your weight
across the shin. It is used as a peg leg that is adjustable accordingly to height. Three
straps hold the thigh and shin into place.
Figure 7 – The iWalk Free.
The iWalk Free offers enhanced mobility, greater comfort, ability to manage
daily activities and remain independent, improved motor function, personal safety,
and ability to exercise emotional wellbeing, potential for reduction in muscle
atrophy, strength and bone density loss, potential for shortened rehabilitation time.
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The device part lists is as follows: upper assembly, knee platform, lower assembly,
support tubes, clamp bolt, nut and straps. This device can be used on both legs by
turning the “foot” around
The Flexleg offers a medical device similar to the iWalk Free but offers a flexible foot
which is supposed to add a more natural feel. FlexLeg is specifically designed to
interface directly with the upper leg and knee such that it acts as an interim lower
leg, allowing a user to walk and move normally. The FlexLeg acts as your lower leg
would, and can walk up and down stairs, inclines, and other terrain. FlexLeg is light
weight and designed to allow for easy movement through tight spaces and pivoting
from one side to another without losing balance. The foot has been designed to be
both light and strong and comes in one of four weight ranges to ensure a more
custom fit. The foot uses Vibram® tread at the bottom of each foot to provide the
right amount of grip and cushioning to feel secure and relaxed to navigate everyday
tight spaces and uneven terrains such as a row of chairs, grass, or a sidewalk curb. It
is also designed to be used without the straps for short periods of time. The Flexleg
is a class 1 medical device registered with the FDA.
Figure 8 – The Flexleg.
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All the devices are static, meaning they do not have moving parts. These devices’
trajectory of the “foot” is flat giving them an unnatural feeling. The flat trajectory of
the device is the cause of the devices uncomfortableness. It has also been
experienced that they are tiresome and expensive. All of these combined lead to a
change in design. A dynamic and more ergonomic device which can mimic the
natural walking gait.
Passive Walking Robots
The class of robots known as passive-dynamic walkers was introduced in the
late 1980’s by Tad McGeer.
McGeer took the development of airplanes as an
inspiration, noting that the Wright brothers first mastered gliding before adding
energy for powered flight. McGeer successfully designed both a straight-legged and
a kneed version of a two-dimensional robot that was capable of walking down a
range of shallow gradients in a smooth and graceful manner without actuation. The
walker was constrained against falling over sideways by using two pairs of legs and
walked essentially as if it were using 6 a pair of crutches. Since McGeer, more
complex passive-dynamic walkers have been made, including 3D bipedal walkers
that incorporate knees and arms.
Passive-dynamic walkers are a class of robots that can walk down a ramp
stably without actuators or control due to the mechanical dynamics of the robot.
Using a passive-dynamic design as the basis for a powered robot helps to simplify
the control problem and maximize energy efficiency compared to the traditional
joint-angle control strategy. This thesis outlines the design of a knee for the robot
known as Toddler, a passive-dynamic based powered walker built at the
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Massachusetts Institute of Technology. An actuator at the knee allows the robot to
bend and straighten the leg, but a clutch mechanism allows the actuator to
completely disengage so that the leg can swing freely. The clutch operates by using a
motor to rotate a lead screw which engages or disengages a set of spur gears.
Control of the knee is accomplished by utilizing the robot’s sensors to determine
whether or not the knee should be engaged. The engagement signal is then fed
through a simple motor control circuit which controls the motor that turns the lead
screw.
Since passive-dynamic walkers rely on gravity to power them, actuators
must be added to them before they can walk on flat surfaces. By adding a small
number of actuators to a few degrees of freedom, it is possible to capitalize on
energy efficiency as well as to allow the dynamics of the system to simplify the
control problem. A project led by Russ Tedrake of the Seung Lab at the
Massachusetts Institute of Technology successfully actuated a simple straightlegged passive-dynamic walker. The robot that they developed was named Toddler,
and can be seen in Figure. Two other powered robots based on the passive-dynamic
design were built around the same time, one at Cornell University and one at Delft
University of Technology in the Netherlands. Toddler is unique in the sense that he
uses a reinforcement learning algorithm to teach itself to walk. While most walking
robots would require too many trials to successfully utilize a reinforcement learning
algorithm to learn to walk, the simplified required control due to the passive
dynamic design along with some clever programming by Dr. Tedrake allow for
Toddler to learn to walk from a blank slate in about twenty minutes.
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Toddler is actuated by four servos, two on each ankle. The hip joints are
completely passive and the arms are simply mechanically coupled to the opposite
leg. If the servos are commanded to hold rigidly at the neutral position, Toddler
simulates passive-dynamic walking and can walk down a ramp without any control.
Toddler walks by rocking side to side on his curved feet in order to obtain foot
clearance. With each 7 step, Toddler rocks onto one leg, lifting the opposite leg off
the ground. The lifted leg is free to swing forward like a pendulum and take a step.
Toddler then rocks onto this leg, allowing the other leg to swing forward and repeat
the process. In the purely passive mode, Toddler requires gravity to provide the
energy for the walking motion. He is capable however of using his ankle actuators to
put energy back into the system instead of relying on gravity, which allows him to
walk on the flat.
Figure 9 – A passive dynamic walking robot.
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Four-Bar Linkages
In America, there are more than 200 lower limb prosthetics available for the
injury’s person to use. Even though they are fall into two categories that are singleaxis knees and polycentric knees. Hinge joint is one of the examples for single-axis
knee and rotates about its only axis which will only create the arc shape at the angle
joint. On the other hand, four bar linkage is one the examples of the polycentric
knees that have advantages over the single hinge joints are easier to mimic the
natural walking gaits, stability at the stance-phase, and foot clearance and easy to
manufacture since linkage are simplest design. We will use steel material in four bar
linkage design because the most impact force happen at the stance phrase on the
four bar linkage knee. In addition, we also consider about the cheaper cost of
material with the best quality to stand when the load bearing is on the four bar
linkage design.
Stability at the Stance-phase
Stability of the four bar linkage can be determined by the relationship
between the load line and the instant center of the rotation from the four bar linkage
react to the ground reaction force vector. First, determined the load line that related
to the stability of the four bar linkage. The position and direction of the load line can
only be determined by reaction force from the ground that acting on the force plate
to measure the ground force vector with respect to the body weight that is applying
at the hip joint. When the heel contact happened in Figure 10 (a), the amputee is
exerting the body weight at the hip joint and the ground reaction force that are
acting on the ground. The load line can be drawn by connecting the two force
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vectors. In this case, the two reaction force will create knee to bend and make the
amputee feel insure and collapse in Figure 10 (c). It is not the right location for the
load line. In this case, the load line is exerting a moment about the hip joint in
counter-clockwise direction at Figure 10 (c) to prevent the knee from bending and
make the amputee feel secure and stable. When superimposing two diagram of heel
contact at (a) and Push off at (c), it would give the standing phase at (b). As shown in
diagram (b), the cross-hatched area represents an area where the instant center can
be located within the boundary to be stable and ability to initiate knee flexion when
push off happen.
The instant center of rotation is always located at the intersections that drew
from the extension lines of the two linkages. It can also be imagined that a
temporary hinge joint that connecting the shank and thigh section at the instant
center. Not like single hinge joint, the four bar linkage changes the location of
instant center depending on the knee flexion happen during the swing phase and
stance phases which are heel contact and push off. The four bar linkage to be stable
the instant center of four bar linkage’s knee must be posterior to the load line during
the stance phase. During the swing phase, the four bar linkage’s knee is stable
because there is no load bearing happening to the amputees and there is no force
that acting on the amputee’s leg to be unstable. It is also important to be aware that
changing the linkages of the four bars and the fixed pivot point are playing a
tremendous roles in stability of the four bar linkage’s knee. Changing those might
affect the stability of the four bar linkage’s knee. As seen in Figure 10 (a), the instant
center is posterior to the load line which is stable position without requiring the hip
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extension moment. In diagram (c) at the push off stance, the instant center is also
posterior to the load line to be stable but it is not possible for the amputee to initiate
knee flexion with the help of the hip moment. It would lead to the problem of
causing at knee flexion. We can adjust this problem by using the torsional spring to
help improve the knee flexion happen in push off phase. The diagram (b) is the
superimposed of diagram (a) and (c) to show the instant center can be lie within the
boundary of the cross-hatched zone. On the other hand, the hinge joint can only be
stable at the directly above the load line.
Figure 10 - Stability Diagram of four bar linkage with instant center.
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Mimicking natural walking Gait and parameter
According to Journal of Rehabilitation Research & development, the article
was conducted with the same procedure for the six bar linkage and the four bar
linkage design. The error that happens in the four-bar linkage vs. natural walking
gait is 6.71 percent error in ankle joint trajectories whereas the six bar linkage give
1.96 percent error only. We consider that six bar linkage is the best option for us to
design to achieve the requirement goal of the Mimicking natural walking gait. The
reason that we chose the four bar linkage is that six bar linkage is more complex and
harder to design within the shorter period of time that we have to have the walking
prototype for our design.
Figure 11 - Comparisons of the natural walking gait vs. four bar and six bar linkage.
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We were able to achieve to parameter of the natural walking gait using the
motion capture system at the kinesiology department with the help of Dr. Scott
Lynn. By using the parameter of natural walking gait, we are trying to achieve the
goal of within 20% error margin of the natural walking gait.
Figure 12 - The parameter of natural walking gait with 20 percent error.
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Foot clearance
The four bar linkage’s knee are nonlinear when walking and instant center
changes as position of the shin changes and create acceleration vary relative to
position. Since the human knee is nonlinear when walking, four bar linkage’s knee is
possible to design the characteristic related to the human knee that would give us a
teardrop shape. Whereas the hinge joint knee is a linear design that can only create
constant motion profile when walking with them. It would be harder to get the tear
drop shape. Here is the comparison of four bar linkage knee vs. the hinge joint knee
toe clearance comparison below. It can definitely able to say that the existing
current devices using four bar linkage knee were at least give twice the amount of
single axis knee device.
Table 1 – Foot Clearance of common prosthetic devices.
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Prosthetic Devices
Many different people become in need of a prosthetic limb. Most common
amputation in both civilian and military populations is the lower extremity
amputation of the leg.
Because of this the technology and development of
prosthetic limbs has became increasingly popular as the demand is there.
Prosthetic limbs are used with amputees who want to live a normal life again and
function efficiently in this fast paced world we live in today. We are a product of our
surroundings in this ever-evolving world and the ability to live it to the fullest extent
is the dream of many. We now see amputees and other disabilities of all types who
are proving that they can function and live as a part of this world with or without
the same amount of limbs as the rest of us. With this kind of demand there is now
reason to develop prosthetic limbs for all different purposes and not just to replace
a limb. Much technology has gone into developing prosthetic limbs that move just
as a natural limb does in order for the user to feel so comfortable they forget that it
is even there.
For the lower limb prosthetics, designs are currently utilizing
technology that makes for very comfortable, efficient, and effective designs.
One of the main company’s ahead of the industry in the prosthetics is Össur
America, based out of Aliso Viejo, Ca. They have been researching and developing
prosthetic limbs for years now and has had very successful results. One of their
main technical prosthetic limbs is seen below. This is an example of what kind of
measures are being taken in order to design a prosthetic limb for people with the
ultimate goal of mimicking the lower limb of a human.
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Figure 13 – A prosthetic leg from Össur.
Devices like this are much more complex then something of the Exo-limb
project. According to an article “there are several pathways to certification, and it is
important for each MTF to ensure that its prosthetics are appropriately certified.
ABC
requires
that
prosthetic
education
be
obtained
from
institutions
accredited…(Kapp, 563)
The Exo-limb could be a much more complex device like that of the exotic
lower prosthetic legs from Ossur, but there is a large cost that goes with something
like that. A prosthetic limb will ideally be worn for the length of your life and needs
to function just as a normal limb would. In order to achieve this comes a high
expense that a simple design as the Exo-limb does not have. The typical advantages
of Body-Powered Devices are lower initial cost, lighter, easier to repair, and offer
better tension feedback to the body, according to the Amputee Coalition of America
(PROSTHETIC DEVICES, 46).
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Problem Statement & Objectives
Leg injury is a major disruption in everyday’s life. At the moment, there are
only two options of recovery are: cast, crutches. Crutches widely used because they
are simple, cost effective, but at the same time very uncomfortable. We in Exo-limb
design team believe that people should have the opportunity to live life to its fullest
potential.
Figure 14 – Underarm crutches.
There are thousands of prosthetic & orthotic devices on the market that help
people live without limitations but they are painful, debilitating, exhausting, clunky,
unnatural, expensive and uncomfortable. Forearm crutches, wheelchairs, and
scooters are great, but still require use of the hands and mostly can’t get over
obstacles such as stairs.
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Project Objectives
The main objective is to development a hands-free crutch alternative for
people with knee and below knee injuries. The prototype should mimic the natural
human walking gait to provide a comfortable stride while reducing stress and
fatigue in the non-affected leg. It is desired that the hands free crutch design should
be attached to the body in order to allow it being used with a knee injury and lower
leg injury.
Materials should be chosen with the lowest cost and highest strength in
mind; The crutch needs to be constructed out of the lightest and strongest material.
Depending on the target cost of the crutch, many different materials will be
considered anywhere from plastic to carbon fiber.
The overall cost of the design is targeted to be as low and affordable as
possible, but also as effective, comfortable, usable, and convenient as possible; as a
comparison, current product costs anywhere between $250-$1500 depending on
quality and design, so we want to shoot for something that is most cost effective, but
also with the most advanced design and quality.
The type of person that should be able to use the design should be physically
capable and have no prior medical conditions or issues with walking or balancing;
the entire public will not be able to use the crutch. People who are obese, have
problems balancing or walking, or have particular medical conditions will be
excluded from using this crutch. In general, athletes, adults 18-60, and anyone else
who meets the criteria will be targeted to use the device. And finally the design
should be passive or fully mechanical.
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It is also intended to improve stability by providing additional points of
contact the walking aid provides both additional support and a wider range of stable
center of gravity positioning.
Furthermore, reducing lower-limb loading by directing load through the
arms and the walking aid, lower impact and static forces are transmitted through
the affected limbs. And finally for the ease generating movement, the walking aid
and arms can substitute for the muscles and joints of the spine, pelvis and/or legs in
the generation of dynamic forces during walking.
Some detailed objectives are included but not limited to: The X and Y position
of the Exo-limb’s pseudo-ankle in the sagittal plane must be within 20% of the user’s
ankle trajectory without the device, The Exo-limb must score higher than 3 on all
questions on the Likert scale questionnaire from at least 5 different users. The Exolimb must not deform or break when a 600 lb load is applied. Lastly the pseudo-foot
subsystem must not deform or break before 300,000 cyclic loads of 150 lbs.
Test Objectives
The test series for the Development of an Exo-limb for People with Lower
Leg Injuries includes motion analysis and user surveys for comfortability. These
tests will help to determine if the performance criteria based on the A-Specs were
met. Motion analysis software will be used to track and compare the kinematics of
the proposed design with the natural walking gait of the user. The software package
entitled Kinovea will be used to determine the positions of the ankle, knee, and hip
joints.
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From this data, the leg angles can be determined. The user survey on
comfortability was developed during the project planning stage. This survey will be
used to determine the baseline user preference on topics such as stability,
functionality, and safety. They will be compared to other crutch devices developed
at Texas A&M and in the 2012-2013 school year senior design project at California
State University, Fullerton.
Testing took place during the Spring 2014 semester at California State
University, Fullerton in the CIM lab.
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Proposed Conceptual Design
The block diagram illustrates below how the subsystems work in conjunction
with each other. The strapping, padding and rigid support are all features that will
be a part of the body attachment to the thigh. The knee assembly is comprised a
linkage mechanism by which the natural gait of the human walk is achieved. There
were several ways to do this. But ultimately attaching a coupler to the linkage
projected the gait down to the where the human foot would be. The lower leg is
comprised of an adjustable height extender and a flexible foot. All of the subsystems
will work in conjunction with each other to produce a natural and comfortable
human walk.
Figure 15 – Functional Block Diagram
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Requirements, design projections, and margin. The requirement for our
device extend from performances to constraints of the device. Some which cannot
be measure numerically but has to be scored by users. First The X and Y position of
the Exo-limb’s pseudo-ankle in the sagittal plane must be within 20% of the user’s
teardrop-shaped ankle trajectory without the device. This means that a walking gait
that matches the human walking gait perfectly. The device also has to be hands free
to enable to user to have mobility and be able to perform daily tasks. The device
must not severely limit the capabilities of the user. The user must also be
comfortable using the device for extended periods of time. The Exo-limb must be
given a 3 out of 5 score in all areas when scored by actual users in a test
administered by the design team which involves the categories of comfort ability,
natural feel, weight, and fatigue. The device must also be a purely passive
mechanical system with no actuator or motors. This ensures that design and
simplicity will keep costs down. The device must also be able to safely support a
200 pound person and must also be adjustable to fit different sized users. In the end
keeping the price of the device down is our design strategy. We want to design an
Exo-limb for the masses. Choosing materials that are low cost will ensure that it isn’t
expensive to manufacture. In turn, this should keep the retail price down. Our device
will be well below other surveyed devices that retail well above $200. The build and
design of the device and the material should also ensure that the length of time that
the device is useable is worth the amount the end user pays for it.
Our design approach suggested by our collaborator was that the knee trajectory
played no importance to whether the walking gait felt natural. Only the tractor of
32
the foot was of importance. That being said we focused on how we can achieve the
trajectory of the foot. We wanted a low cost device so we limited ourselves to
materials that were cost effective and achieve the same goal. We also did this for
weight because we need a design that was light weight. We took into consideration
the possible torques that can be produced in the leg by the placement of the device.
These are the functions that we are aiming to achieve and the possible means by
which these functions can be achieved. From these, the infeasible were discarded
and the feasible were put into a Pugh chart (weighted and non-weighted)
Function
Simulate Walking Gait
Means
4 Bar Linkage w/ 4 Bar Linkage w/
Coupler Ext
Inverter
6 Bar Linkage
Hinge Joint
Peg-Leg
Cam System
Hydraulic
Adjustable (Height)
Locking Pin
Clamp/Slide
Screw
Button Lock
Tension Rod
Mechanism
Adjustable Strap
Attachment
Nylon Straps
Elastic
Velcro
Mold
Rope/Mesh
Support 200 lb
Carbon Fiber
Steel
Aluminum
PVC
ABS
Attach to User
Knee Support
Glute
Hip
Shoulder Strap
Thigh
Ambi-functional
Dedicated Left Symmetric Foot
and Right Feet
Design
Lower back
Calf
Reversible
Design
Figure 16 – Morph Chart.
The body attachment pugh chart takes into consideration the comfort, support,
adjuastibility and removability. In the weighted chart comfort and support were
given the majority of the weight. In both charts the thigh and knee were rated the
highest rated in both charts so a knee and thigh combo was choosen.
33
Figure 17 – Pugh charts for the body attachment sub-assembly.
Knee joint mechanism Pugh chart took into consideration the mimic of the natural
walking gait, stability, simplicity and manufacturability. The non-weighted charts
produced a tied score for the peg leg design and the four bar linkage. In the
weighted design where the mimicking of the natural walking gait and stability. In
this chart the four bar linkage excelled above the rest so it was chosen.
Figure 18 – Pugh charts for the knee joint sub-assembly.
The pugh chart for the foot material took into consideration strength, flexibility,
cost, and weight. In the non-weighted chart carbon fiber scored the highest amongst
the materials taken into consideration. Cost is the biggest drawback. In the weighted
34
chart flexibility and cost is weighted the most. In this chart the carbon fiber also
scored the highest.
Figure 19 – Pugh charts for the foot material.
We design the four bar linkages in SolidWorks Cad Design software to
simulate the motion path profile to be able to achieve the requirement of the
mimicking the natural walking gait. At figure 20: the snap shot of the four bars
linkage is our first trial of the design idea come to our mind how the four bar linkage
can give us the motion path. When two linkages are extended maximum, it is about
25 degree forward and backward knee flexion which is pretty much relate to normal
walking angle of 20 degree forward and 25 degree knee flexion on the backward
motion during the swing phrase. In this design, it doesn’t require the stopper at the
swing since two linkages are line up together parallel and lock up together when the
swing happened in forward motion.
35
Figure 20 - The motion path of the first trial of the four bar linkage design idea.
On the second trial, we change the length, position, fix joint, and add the
coupler to guide us how to achieve the natural walking gait to achieve the tear drop
shape motion profile at the angle joint when walking. As a result, we get the
irregular ellipse shape of the motion profile.
Figure 21 - The motion path of the second trial of the four bar linkage design idea.
36
After several trial of changing the length, position and fix joint, we were able
to achieve closer to the teardrop shape with the help of our professor Dr. Robson. In
this motion path trial, we just simulate the four bar linkage alone. For the mimicking
natural walking gait, there is the rotational and translational movement of the thigh
and the foot at the stance phrase plays a big role on natural walking gait motion
profile that give tear drop shape. During the break, we will try to optimize the
design and try to simulate the dynamic motion path to achieve the teardrop shape.
The teardrop shape of the normal walking gait is range between 3 ft to 4.5 ft. With
our design, it can be able to achieve by connecting the leg extension on the joint of
the coupler. The leg extension part is the multiplier of the tear drop shape.
Figure 22 – The motion path after several trial of the four bar linkage design idea.
Illustrative Drawings of System and Subsystem
The Exo-limb system that we design is based off of simple mechanical
systems and components. Together they will make an Exo-limb device that is very
natural feeling, comfortable, practical, and easy to use.
The three important
subsystems of the design are the attachment to body, the knee, and the lower leg.
37
By using designs that take these three aspects into consideration, our Exo-limb
device will prevent people with lower leg injuries from being help back in their
everyday lives. Although not everyone is qualified to use a device of this nature, a
good part of the society will be able to take advantage of this device.
A very important aspect of our device is that it is lightweight and rigid. By
using materials such as carbon fiber and aluminum for the majority of our support
and weight bearing structures, we are able to create a good balance between a
device that is lightweight, yet strong. This is important because the more weight
that exists in the system, the more energy it will take to use it. This means that the
user would become tired quickly and not be able to function with it for an extended
period of time. As you can see from the figure below, our design utilizes aluminum
tubing for the main support and structure of the device. This aluminum piping
makes the device easy to manufacturer as well as cost effective and readily
available. There are no complicated processes for the assembly of the device and
the techniques used to manufacture it are simple. The upper device would only
require the use of cutting, bending, and drilling where as the lower part of the
device might require some machining for the adjustability of the lower leg.
38
Figure 23 – The overall system and leg attachment subsystem.
The subsystem for the leg attachment part of the device also needs to be
comfortable to the user. One of the biggest complaints of any user of a standard
crutch device is that it is uncomfortable and cannot be used for extended periods of
time. With the combination of the polypropylene padding and the curvature of the
leg attachment structure, the device will have an overall comfortable design. With
the curvature of the lower leg platform close to that of a typical user, the leg
attachment can be worn tightly to the lower leg without it pointing unnecessary
points of pressure in any area of the leg. This is important, as the device needs to
feel confident to the user. If the attachment cant be tightened to the leg without
causing some sort of pain, than it might be worn loosely with the user and would not
feel as natural as it should be. The adjustability of the nylon straps also makes for a
more comfortable attachment to the users leg. Having the device fit closely and
naturally to the body is just as important as a good pair of snug, well-fitted boots
being worn all day by somebody. On top of comfort and adjustability, the leg
attachment subsystem should also be easy to get into and easy to take off. If the
39
device is difficult or complicated to mount, than it will not be used as often as it
could be. We want this device to be convenient to the user in as many ways
possible. This is why we use nylon straps with easy to snap connections for the
critical points of attachment to the lower leg.
Figure 24 – The knee joint subsystem.
The most important subsystem of our device is the knee mechanism. This is
what determines how easy the device is to use and how natural it will feel when
being used. Through the motion of the natural human walking gait, the ankle of the
person rides a teardrop-like shape. In order to make this device feel as natural as
your own foot below you, this natural teardrop shape needs to be mimicked. In
order to do so we incorporated the use of four-bar linkage to the knee mechanism.
This is necessary as the use of a hinge joint would give a crescent-shaped motion
and be almost 1 dimensional. By incorporation the four-bar linkage instead of a
hinge joint, the teardrop shaped motion can be achieved. The lengths of the fourbar linkage can also be adjusted or custom fitted for the user in order to fine-tune
40
the natural swing of the device as your walking. Using this four-bar linkage also
helps keep the foot from dragging as it is being swung through the walking gait.
Figure 25 – The foot subsystem.
The last subsystem of our device is the lower leg. The lower leg is adjustable
for people of different height and constructed of aluminum and carbon fiber. The
lower leg also consists of a carbon fiber foot manufactured by Ossur. This carbon
fiber foot has been designed to mimic the natural feel and motion of a weight
bearing foot while keeping weight to a minimum and strength to the maximum. The
carbon fiber foot has a similar range of motion as a natural foot and also has similar
curvature. These aspects both help to make the device as a whole feel very realistic
and natural, which is the ultimate goal of the entire Exo-limb device.
41
Updated Design
The updated design for the Exo-Limb project relatively followed the same
path of the original prototype and first design. The idea was to incorporate a fourbar linkage deign into a comfortable, stable and adjustable knee frame. The foot was
expected to be lightweight with a realistic flex and feel of a natural foot. The foot
used in the final design was a donation from our collaborator at Ossur and was
exactly what we were looking for on our system.
Figure 23 shows the final prototype design before the manufacturing of the
actual design begun. Certain thing had to be changed in order to make this design
easily manufacturable. The knee support frame constructed from bent aluminum
sheet metal that was laser cut on a CNC mill. The final assembly was then welded
for rigidity and strength. Later the frame would be lined with Velcro for removable
padding that make the knee support much more comfortable. Nylon adjustable
straps were also added with eyelets riveted to the support frame.
Figure 26 – Knee Support Sub-Assembly
42
The four bar linkage consisted of two main designs seen below in Figure 27
and Figure 28. The linkage design is a very important mechanism of the Exo-limb
for it is what gives the ability to mimic the natural motion path of a human leg. By
adjusting dimensions of the four bar linkage and increasing or decreasing start and
stop points of the system. Bolts were used to create the starting/stopping posts for
the linkages as they swing through the motion.
Both linkage designs were
constructed from 11-gauge stainless steel material that was also laser cut and bent.
Shoulder bolts were used for the bearing posts of the linkages and shims and Teflon
washers were used to control slop in the linkages. This is important as the linkage
plays an important roll in the stability, feel, and comfort of the Exo-limb.
Figure 27 – Four-bar Linkage Design 1
The linkage seen in Figure 28 was based off of a computer model that
mimicked the desired motion path of the human leg.
The model had the
mathematics and profile that was needed, but in the real system felt very unstable.
The leg attachment sat in front of the linkages and created a torque on the entire
system at certain points when pressure was applied. In order to gain stability of the
43
linkage system, it was necessary to keep the leg attachment in the middle of the
linkage system.
Figure 28 – Four-bar Linkage Design 2
As good as the results of the updated design were, there is still much room
for improvement.
The attachment for the lower leg to the “y-shaped bars”
connecting to the linkage needed to be hardened to prevent torsion and bending.
Rigid supports could have also been used in order to reinforce the subsystem. As all
of the weight in transferred through these y-bars and lower leg attachment knuckle,
strength and rigidity is required for these components in order to gain that
stable/confidant feel. A damping control system should also be incorporated into
the design in order to help control and track that motion path that was desired
throughout the walking motion.
44
Project Management
Team Structure
In order to work as efficiently as possible, we split up tasks according to the
individual strengths of each team member. The diagram of figure 26 shows the
work breakdown structure of the entire project. Having a small group enabled us to
also work on different elements of the project, but the individuals listed under each
category are the ones responsible for that subject. Michael Villavecer worked on
project management materials. This included scheduling, developing project goals,
and a general oversight of the entire project. Justin Chin was responsible for
research in biomechanics, four bar linkages, stability, passive dynamic walking, and
prosthetic devices. Salar Nosratabadti was responsible for analysis of the design.
This included comparative analysis of current devices and measurements related to
the natural walking gait. He was also responsible for Finite Element Analysis of
major structural components.
Figure 29 – Work Breakdown structure
45
Larry Tlilayatzi headed the design of the project. This included mechanical
design of structural and dynamic components, tolerances, fits, and material
selection.
Bryan Holloway was responsible for CAD drawings.
This included
modeling and renderings of the device using SolidWorks 2013. Michael Villavecer
was also responsible for testing, which included developing a test plan and
designing of test structures for static loading and fatigue analysis of the device. This
aspect of the project will be completed during the Spring 2014 semester.
Our mentors for this project are Jason Taylor and Dr. Scott Lynn. Taylor is a
Senior Project Manager at Össur America.
prosthetic and orthotic devices.
They are a company that makes
He helped us with managing the project,
scheduling, design, testing, and other elements related to the project. Dr. Lynn is a
professor of Kinesiology at California State University, Fullerton. He is also in
charge of the biomechanics laboratory that we used to obtain natural walking gait
data.
Dr. Robson and Hart Roussel are the advisors for the project.
Dr. Robson
provided guidance during the course of the semester and also helped on the motion
profile analysis using four-bar linkages. Hart Roussel helped the team look for funds
to support the project.
He had initially contacted a potential sponsor from
Sunnycrest Living Facility in Fullerton who was interested in sponsoring the project.
Ultimately, they decided not to support the project. Roussel was able to secure
$3000 from the Dean’s office to fund our project.
46
Project Scheduling
The schedule for Fall 2013 is shown in the appendix. The beginning of the
semester included forming teams, selecting a project, selecting a team leader,
performing a detailed literature review, finding a mentor, and developing project
goals. Presentations were given every two weeks to provide advisors and other
teams updates on the project.
During the project-planning phase, a schedule,
Statement of Work, Work Breakdown Structure, A-Specs, work plan, budget, and
project proposal were drafted. Following the project-planning phase, we spent most
of the semester on developing designs for the leg attachment, knee joint, and foot
sub-assemblies. The knee joint in particular was a major focus because it is the
main component responsible for mimicking the natural walking gait. We developed
several designs that included using a hinge joint, a four-bar linkage, and several
other linkage designs. We developed a bill of materials after finalizing the design of
the Exo-Limb. The final weeks of the semester were spent preparing for the final
presentation and report.
47
Manufacturing Process
In order to have a functional design we limited ourselves to using 11 gauge 304
stainless steel sheet metal for the four bar linkage knee joint mechanism. The rest of
the design utilized 5052 aluminum alloy. The drawings were produced for all parts.
Because the need for the use of a complex piece not easily manually fabricated, the
four bar linkage mechanism was produced using an out of house Laser Cutting
Machine. For the bottom of the four bar linkage, the bend was produced using an out
of house hydraulic Press Brake. An inner bend radius equal to the thickness of the
metal was used to not induce excessive stress.
Figure 30 – Hydraulic Press Break
For the rest of the device, 5052 aluminum alloy was used for its malleability. We
started with raw aluminum alloy sheet metal. The correct dimensioned rectangular
flat patterns were cut using the manual shear. All locations of the holes were
marked using a height gauge, then marked once again using a center punch. Quarter
inch holes were drilled using a manual drill press for higher accuracy. The manual
48
press break was used to bend all aluminum pieces to correct angles. A manual slip
roll was then used to add a radius to the sheet metal for the pieces which make shin
and thigh contact. Two aluminum tubes were used to attach the platform to the foot.
Holes were drilled with half inch spacing. In order to drill holes accurately a V-block
and drill press was used. All holes were marked using a height gauge and center
punch. The device was put together using 0.25” stainless steel nuts and bolts. The
four bar linkage knee mechanism could not utilize the standard hardware we were
using due to high friction. Instead 0.25” 18-8 stainless ultra-low profile shoulder
screws with corresponding ultra-low profile nuts were used to assemble all moving
parts together. Additionally, to make sure the nets would not come loose we added
Loc-Tite to the nuts in place.
Figure 31 – Ultra-Low Profile Shoulder Screw
49
Results of testing
In order to test the device in real world situations, a few tests were conducted for
rigidity, reliability, and conformability. Several simulations were run using
SolidWorks Simulations to determine the mechanical performance of the key
structural components. The tests included a static load simulation of 300 lb, which
the device passed with the minimum amount of component’s displacement.
Furthermore the fatigue test was performed for up to 1,000,000 cycles (which was
based on the research showing an average American taking about 5000 footsteps
per day, knowing average ankle recovery time for people with lower leg injury being
7 weeks, multiplying those numbers, getting around 245,000 footsteps during
recovery time). The Exo-limp withstood the fatigue test by showing no signs of
cracks or failure.
Picture of Static and Fatigue testing
Figure 32 –
50
As the last test, 16 students were asked to put on all four devices (Exo-limp, Texas
A&M, CSUF 2013, iWalk free) and walk on them for 5 minutes and score the devices
based on stability, comfort, natural, and safe criterias in the scale of 1 to 5. Exo-limp
scored higher than Texas and CSUF ’13 designs in all 4 categories and the highest
among all in comfort, however and iWalk free was slightly superior in safety and
stability.
Figure 33 – Surveying Results from 16 Students
51
Project Deliverables
For this project, we developed several design requirements and goals that we intend
to meet. In our Statement of Work, we describe these goals and requirements and
have a detailed description of what we intend to deliver at the end of the Spring
2014 semester. The Statement of Work includes:
4.0 General. Development of an Exo-limb for People with Lower Leg Injuries
4.1 Introduction. Designed to assist walking or otherwise improve the mobility
of people with mobility impairments.
4.2 Objectives. Low overall cost; high effectiveness, comfort, usability.
4.3 Scope. The objectives of the design are to:
Improve stability; by providing additional points of contact the walking aid
provides both additional support and a wider range of stable centre of gravity
positioning.
Reduce lower-limb loading; by directing load through the arms and the walking
aid, lower impact and static forces are transmitted through the affected limbs.
Ease Generating Movement; the walking aid and arms can substitute for the
muscles and joints of the spine, pelvis and/or legs in the generation of dynamic
forces during walking.
4.4 Place of Performance/Hours of Operation. California State University of
Fullerton, Mechanical Engineering Department, Monday through Thursday
8:00am – 11:00am. The contractor shall visit this location every Thursday.
52
4.5 Period of Performance. Duration of this task is from 09/01/13 through
5/16/14. This project may be incrementally funded, which may result in
extensions to the end date of this project.
4.6 Privacy Act. Work on this project may require that personnel have access to
Privacy Information. Personnel shall adhere to the Privacy Act, Title 5 of the U.S.
Code, Section 552a and applicable agency rules and regulations.
4.7 Personal Service. The client has determined that the use of contract satisfies
the requirement in the best interest of the government, economic and other factors
considered, and this task order is not being used to procure personal services
prohibited by the Federal Acquisition Regulation (FAR) Part 37.104 titled
“Personal services contract”.
4.8 Security. This project is considered to be “Unclassified”.
4.9 Costs. As part of the Cost Proposal, the contractor shall provide a breakdown
of any costs or other direct costs (ODCs) in the Cost Proposal. The contractor
shall provide any anticipated travel costs, if known, to include: origination;
destination; number of trips; number of persons; and a breakdown of lodging,
meals, transportation and related costs. Actual expenses are limited by the
Government Travel Regulations and must be pre-approved by the client.
4.10 Status Reports. Status reports must be submitted monthly.
4.11 Delivery Instructions. All deliverables shall be delivered to the client no
later than 5/16/14.
4.12 Procedures for Payment. Billing and payment shall be accomplished in
accordance with the contract. The contractor’s invoice will be for one week for
53
services performed in the previous week. The contractor may invoice only for the
hours, travel and unique services. Invoices submitted for payment must be
accompanied by a copy of the government’s tax document(s) (i.e. DD250 or
similar form) accepting the covered services. Failure to comply with the
procedures outlined above may result in your payment being delayed.
In addition to the Statement of Work, we developed several project objectives that are
called A-Specs. These include:
1. Mimicking the natural walking gait
a. The x- and y- position of the Exo-limb’s pseudo ankle in the sagittal
plane must be within 20% of the user’s teardrop-shaped ankle
trajectory without the device.
2. The device must be hands-free
3. The device must be comfortable for the user
4. The device must be a purely mechanical system with no motors or actuators
other than the natural movement of the human body
5. The device must safely support a 200 lb person
a. Using a safety factor of 3, the Exo-limb must not fail when a 600 lb
load is applied
6. The device must be adjustable to fit different sized users
54
References
Kapp, Susan, and Joseph A. Miller. "LOWER LIMB PROSTHETICS." Car of the Combat
Amputee. N.p., n.d. Web.
"PROSTHETIC DEVICES." Amputee Coalition of America. N.p., n.d. Web. 12 Dec. 2013.
Vaughan, Davis, & O’Connor. Dynamics of Human Gait. Kiboho Publishers. 1999
Whittle, Michael. Gait Analysis: An Introduction, Second Edition. Oxford: ButterworthHeinemann, 1996.
Rose, Jessica; Gamble, James. Human Walking, Second Edition. Baltimore: Williams
and Wilkins, 1994.
McGill University. Molson Medical Informatics Project. (1999). Normal gait. Retrieved
March 18, 2002, from
http://sprojects.mmi.mcgill.ca/gait/normal/movie2.asp
Gard, Steven A. “The influence of Four-Bar Linkage Knees on Prosthetic Swing-Phase
Floor Clearance” Web. 19 Dec. 2013<
http://www.oandp.org/jpo/library/1996_02_034.asp>
Greene, Michael P. “Four Bar Linkage Knee Analysis” Web. 19 Dec. 2013
http://www.oandplibrary.org/op/pdf/1983_01_015.pdf
Jin, Dewen and el “Kinematic and dynamic performance of prosthetic knee joint
using six-bar mechanism” <
http://www.rehab.research.va.gov/jour/03/40/1/jin.html>
Radcliffe, C.W. “Four-bar linkage prosthetic knee mechanisms: kinetics, alignment
and prescription criteria” Web. 19 Dec. 2013
http://www.me.berkeley.edu/faculty/radcliffe/ISPO1994vol18pp1591731.pdf
55
Appendices
Project Schedule
Exo Limb Project - Gantt Chart
8/22
9/5
9/19 10/3 10/17 10/31 11/14 11/28 12/12
Current Date
Team formation
Pick a project
Literature Review
Develop project goals
Find a mentor
Bi-Weekly Report 1
Bi-Weekly Report 2
Bi-Weekly Report 3
Bi-Weekly Report 4
Bi-Weekly Report 5
Bi-Weekly Report 6
Project Planning
Develop a project schedule
Write Statement of Work (SOW)
Develop Work Breakdown Structure (WBS)
Develop A-Specs
Create a rough budget
Obtain lab keys
Project Proposal
Work Plan
Design Development
Knee Joint Research & Analysis
Leg Attachment Design Iteration 1
Knee Joint Design Iteration 1
Foot Design Iteration 1
Leg Attachment Design Iteration 2
Knee Joint Design Iteration 2
Foot Design Iteration 2
Bill of Materials
Prepare Final Report
Testing & Manufacturing Schedule
Final Presentation
56
Testing and Manufacture Schedule
57
Constraint equation for four bar linkage knee’s design using the
free body diagram,
𝑃 + (𝐵 − 𝑃) = 𝐶 + (𝐵 − 𝐶)
𝑐𝑥
ℎ cos 𝜙
b cos 𝜓
𝑎 cos 𝜃
(
)+ (
)= (𝑐 )+ (
)
ℎ sin 𝜙
𝑦
𝑏 sin 𝜓
𝑎 sin 𝜃
Position Loop equation:
Velocity Loop equation: 𝑃̇ +
𝑑
𝑑𝑡
(𝐵 − 𝑃) =
𝑑
𝑑𝑡
(𝐵 − 𝐶)
−𝑎 cos 𝜃 ̇ ℎ cos 𝜙 ̇ −b cos 𝜓 ̇
(
) 𝜃+ (
) 𝜙= (
)𝜓
ℎ sin 𝜙
𝑏 sin 𝜓
𝑎 sin 𝜃
𝑑2
𝑑2
̈
Acceleration Loop equation: 𝑃 + 2 (𝐵 − 𝑃) = 2 (𝐵 − 𝐶)
𝑑𝑡
𝑑𝑡
−ℎ sin 𝜙 ̈
ℎ cos 𝜙 2̇
−𝑎 cos 𝜃 ̈ 𝑎 cos 𝜃 2̇
(
) 𝜃+ (
)𝜃 + (
)𝜙 − (
)𝜙
ℎ cos 𝜙
ℎ sin 𝜙
𝑎 sin 𝜃
𝑎 sin 𝜃
=(
−b cos 𝜓 ̈
−b cos 𝜓 2̇
)𝜓 − (
)𝜓
𝑏 sin 𝜓
𝑏 sin 𝜓
58
ABET Requirement
Professional Component – Capstone Design Report
Economic
The economic constraints were
addressed in this project on page 31.
Environmental
The environmental constraints were
addressed in this project on page 36 &
37.
Sustainability
The sustainability constraints were
considered but not addressed in the
report.
Manufacturability
The manufacturability constraints were
addressed in this project on page 18 &
37.
Ethical
The ethical constraints were considered
but not addressed in the report.
Health & Safety
The health and safety constraints were
addressed in this project on page 10.
Social
The social constraints were addressed
in this project on page 36.
Political
The political constraints were
considered but not addressed in the
report.
59