Natural-Gait-FIU-FCRAR2015

2015 Florida Conference on Recent Advances in Robotics 1 Melbourne,Florida, May 14-15,2015
Natural Gait Inducing Transtibial Prosthetic
Alexis Garo, Lucia Melara, Robert Scott, Melissa Morris, Sabri Tosunoglu
Florida International University
Department of Mechanical and Materials Engineering
Miami, Florida 33174
(305) 348-1091
agaro001@fiu.edu, lmela001@fiu.edu, rscot007@fiu.edu, mmorr009@fiu.edu, tosun@fiu.edu
ABSTRACT
In this paper an actively powered ankle-foot prosthetic to reduce
the asymmetrical gait of a transtibial amputeeis discussed. Passive
prosthetics do not provide positive net work throughout the gait
cycle and as such patients face increased risk of secondary
disabilities. Powered active prosthetics seek to remedy this problem
through theuse of a powered actuator to providepositivenet torque
at the ankle joint. However current commercialized active
prosthesis are prohibitively expensive, and require nerve signal
input from the patient’s residual limb which increases cost and
system complexity. A modular and easily manufactured design of
a powered ankle-foot prosthetic which implements cost efficient
designs of the spring assemblies is presented. Overall it is
determined that thedesigns and concepts presented in this paper are
viable for reducing costs of a commercialized powered ankle-foot
prosthetic.
Keywords
Gait, Rehabilitation, Therapy, Robot, Prosthetic, Prosthesis,
Predictive Algorithms, Transtibial, Amputee
1. INTRODUCTION
1.1 Problem Statement
Presently the prostheticoptions for transtibial amputees consist of
passiveor ankle-foot prosthetics. Passiveprosthetics, providesome
level of energy absorption and recovery throughout the gait cycle
but cannot produce positive net work to assist in ambulation. In
contrast, active prosthetics use powered actuator systems to
producepositivenet torqueat theanklejoint similar to natural ankle
operation.
Both passiveand active prosthetics currently present complications
for transtibial amputee patients. Passive prosthetics do not provide
positivenetwork throughout thegait cycleand as such patients face
increased risk of secondary disabilities. This is due to the patients
post-amputation asymmetrical gait pattern caused by the natural
foot exerting greater force than that of the prosthetic. These
secondary disabilities include but are not limited to back and
posturerelated medical problems as well as an increased metabolic
cost of ambulation by 10%-60%. Powered active prosthetics seek
to remedy this problem through the use of a powered actuator to
provide positive net torque at the ankle joint. However current
commercialized active prosthesis are prohibitively expensive,
produce excessive operation noise for most social situations, and
require nerve signal input from the patient’s residual limb which
increases cost and system complexity.
1.2 Project Objectives
To design and commercialize a powered ankle-foot prostheticwith
increased range, reduced cost, reduced complexity, and increased
modularity than what is currently available for transtibialamputees.
The finalized product will be suitable for sale in economically
weaker regions than what is currently possible.
The desired outcome for the transtibial ankle-foot prosthetic is to
be able to give amputees as much mobility back as possible by
increasing the battery life; thus, reducing the time spent charging
and increasing the time for other activities. In addition, the aim is
for the prostheticto be modular meaning that the components may
be removed and replaced with similar parts without having to use
factory parts. By making it cost effective, the prosthetic can be
exported to countries in which transtibial amputees are common in
order to aid those in need all over the world.
1.3 Series Elastic Actuator
The Series elastic actuator (SEA) has some advantages compared
with theclassical direct drive system. An SEA incorporates aspring
in line with the force of the actuator. This will reduce the systems
total energy required for operation. This energy reduction will
allow for the device to be active longer or possibly even reduce the
battery size required for regular use.
Figure 1: SEA+UPS
An SEA+UPS (Series Elastic Actuator + Uni-Directional Spring)
utilizes an SEA systemin addition to a unidirectional spring. This
unidirectional spring activates at certain locations to prevent the
motor from losing power charging the parallel spring. This
configuration is favored in many cases due to its customization
properties which include; the activation location, spring constants,
and spring lengths.
To ensure the primary and secondary design goals of system cost
and operational range are optimized the SEA-UPS configuration
paired with an Ossur Vari-Flex LP prosthetic foot is proposed as
the primary design. This configuration-foot pair will provide a
balance between energy required, peak power, and operational
range while ensuring total systemcost is kept to a minimum when
compared to an SPEA configuration.

1.4 Gait Modeling Software
For a better understanding of the gait cycle, two programs,
OpenSim and C-motion, were used to accumulate sample data to
recreate torque curves. Amongst the recorded data were also the
forces, which act on the ankle and foot during thecycle of walking,
and information regarding thewalking speed, and stance and swing
time for the period of walking. The data obtained from OpenSim
includes the forces the specific tendons engaged in walking
experience with respect to the gait and ankle angle. Furthermore,
the data from C-motion includes the angular velocity, torque, and
force acting on the ankle and foot during walking. This data should
help in establishing the basis for the transtibial prosthetic.
1.5 Rehabilitation Lab
For a proper comparison of the theoretical and experimental torque
and force data for the ankle-foot prosthesis, Dr. Elbaum was
contacted to grant access to the gait lab in the Academic Health
Center 3 (AHC3) building on Florida International University’s
Modesto MadiqueCampus. A professor at the College of Nursing
and Health Sciences, Dr. Leonard Elbaum, was very helpful with
questions on locomotion and gait as he specializes in pediatric
physical therapy, gait disorders, and applications of new
technologies in physicalrehabilitation. Within the gait lab, a wide
array of infrared cameras are set up to capture the markers put on
the subject. Themarkers serve as a reference in space to which the
motion is captured. In addition to the markers and camera, a force
plate is integrated in the stage across, which the subject walks to
obtain the forces exerted on the joint and foot during walking.
Using the computerized model, the ankle torques, reaction forces,
and ankle angles can be found. In addition, the graphs of these can
be plotted to visualize the ankle torques, forces, and angles during
the gait cycle.
1.6 Hill Type Muscle Model
The Hill Type Muscle Model refers to a set of equations derived
from Archibald Vivian Hill which numerically describes muscle
mechanical response. The model views a muscle as spring like
structure and uses data obtained from experiments as well as a
lumped parameter approach to simulate a muscle and the passive
connective tissue such as tendons. Connective tissue contains
elastic properties parallel to that of the muscle, this property is
referred to as Parallel Element or (PE) in the model. Contractile
Element (CE) and Series Element (SE) refer to the muscle and
tendon respectively. In respect to a transtibial prosthesis the CE
models the calf muscle while theSE models theAchilles tendon. In
an elastic actuator themotor replaces thefunction of thecalf muscle
while the Achilles tendon is replaced with a series spring.
Utilizing the Hill TypeMuscleModel the torque around the ankle
joint can be calculated with respect to the angle of the ankle. By
substitutingthemechanical properties of themuscle and connective
tissue with that of the drive motor and spring(s) the torque-ankle
angle curve may be formed. Comparing this curve to that of a
natural ankle it is possible to analyze the prosthetic’s performance
in emulating natural ambulation. The goal of the prosthesis is to
produce this torque curve which matches that of a natural ankle as
closely as possible.
1.7 Biomechanics of Gait Cycle
In order to properly emulate the function of the natural ankle-foot
structure it is necessary to understand both the mechanical
properties of thebiological components that make up this structure
and the different phases of the gait cycle. The three biological
components of the system that will be studied will be the soleus
muscle, theAchilles tendon, and theanterior tibialis. In addition the
three different phases of the stance phase of the gait cycle will be
analyzed as well.
One complete cycle is defined as one foot leaving the ground (i.e
toe-off) to the same foot completing toe-off again. One gait cycle
is divided into two phases: swing phase and stance phase. Swing
phaseconsists of the time thefoot is not in contact with the ground
while in contrast thestancephase consists of the time between heel
strike with the ground of the foot and toe-off of the same foot.
Stance phase is divided into three sub-divisions: Controlled
Plantarflexion, Dorsiflexion, and Powered Plantarflexion.
Controlled Plantarflexion consists of the gait cycle between heel
strike to toe contact to the ground. The portion of the gait cycle
between toe contact and the heel leaving contact with the ground
(i.e. heel off) is defined as dorsiflexion. Powered plantarflexion is
defined from heel off to toe off.
Figure 2: Various phases of the gait cycle
The Hill typemuscle model takes several assumptions into
account for its equations. An example of this is the modeling of
the contractile element(s) connected to the moment arm. In a
natural biological systemthecontractile elements are the
gastrocnemius and soleus muscles with themoment arm
attachment point being the heel. TheHill typemuscle model
assumes only the soleus muscle is exerting force on the moment
arm. Using the software suite Opensimthe force of thesoleus
muscle at every point of the stance phasewas found. This data
was used as a baseline for the preliminary design calculations.
In a biological systemtheAchilles tendon acts as a compressive
spring, absorbing energy during controlled plantarflexion to be
released and assist in dorsiflexion. The kinetic energy released by
the Achilles tendon in dorsiflexion reduces the totalamount of
energy expended by theanterior tibialis to performdorsiflexion.
An assumption made in thehill typemuscle model is that the
Achilles tendon contributes to the overall ankle joint torque solely
from heel-strike to mid stance. From studies performed on human
subjects theAchilles tendon has been determined to function
similarly to a linear spring with an estimated stiffness of 150,000
N/m. The anterior tibialis serves two functions. Thefirst is to
bring the tibia toward thefoot during dorsiflexion. The second
being to act as a compressive spring from mid-stance to heel-off,
absorbing energy to be released during powered plantarflexion.
This second function is emulated mechanically with the use of a
unidirectional parallel spring.
2. ANALYSIS
2.1 Simulation Model
The process of obtaining a viable torque curve from a proposed
prostheticdesign required the computation of numerous equations.
These equations include those sourced from the Hill TypeMuscle
Model, mechanical design, circuit analysis, etc. As the manual
completion of the 30 plus different formulas required for design

analysis was time intensive Microsoft Excel is used to
automatically compute the necessary formulas. In addition the
torque-ankle angle curve is charted for visual comparison against
its natural counterpart.
This simulation model allowed the effects of design changes to be
seen an analyzed in real time. This allowed for a much greater
number of design choice combinations to be analyzed when
compared to manual computations. Additionally a system of
automated checks was written into the model. Thesedesign checks
automatically tested conditions that would render the design
unfeasible or inoperable. One such design check compares the
calculated necessary linear velocity of theactuator to the maximum
linear velocity possiblewith thedesigned motor/ballscrew/gearbox
combination. If the chosen design variables result in a linear
velocity below one necessary for proper operation the simulation
model will highlight a cell in red to alert the user that the design is
unfeasible.
Assumptions were made in the development of the simulation
model to both reduce the complexity of model and reduce the
amount of totalequations. Further assumptions were taken as well
to standardize certain variables to accurately compare different
studies against one another. The model notates plantar and
dorsiflexion as positive and negative torque respectively with the
force of the actuator following thesame convention. In addition all
springs are considered ideal with all damping properties not taken
into account.
The simulation model notates the tibia and foot as the positive Y
and X axes respectively when referencing the tibia-foot angle. The
average maximum angular displacement of an adult male tibia in
stance phase is -15◦ to +25◦ with the tibia and foot as the positive
Y and X axes respectively. All equations in the simulation model
are computed once at every degree of rotation of theankle in stance
phase. This results in an output of eighty data points of torque.
Natural torque data gathered from gait modeling software and
human subjects was formatted to comply with stance phase
subdivisions and 80 datapoint requirement. Swing phase(time foot
is in the air) is not analyzed.
2.2 Actuator Trigonometry
Just as thecalf muscle, tibia, and heel form a triangle in the human
body the proposed prosthetic design’s actuator system forms a
triangle as well. Side “a”as shown in Figure 3 is the linear actuator
emulating the soleus muscle function. This side increases and
decreases in length throughout the rotation of the tibia around the
ankle joint (angle “A”). Side “b”is the moment arm of the system.
The moment arm connects to the linear actuator converting its
linear motion into rotational motion around the ankle joint. The
human body accomplishes this using the connection of the soleus
muscle to the heel and the rigid link between the heel and ankle
joint. Similar to thedistance between theankle joint and attachment
point of the soleus muscle on the tibia, side “B” consists of the
distance between the ankle joint and the linear actuator mounting
revolute joint.
Figure 3: Actuator Trigonometry
Selection of the linear actuator internal components (motor,
gearbox, ballscrew, and ballnut) is dependent upon the necessary
linear velocity and force of the actuator to complete stance phase.
Utilizing a selected foot angle of maximum torque in stance phase
the actuator systemtriangle is formed by also choosing lengths for
sides “b” and “c”. Producing maximum torque utilizing a moment
arm requires the linear force to be perpendicular to the moment
arm, thus angle “C” is 90 degrees at point of maximum torque in
stance phase. The combined length of thelinear actuator and series
spring is found using Pythagorean’s theorem. Angle “A” at this
rotation point is also determined. Themaximum angle between the
tibia and moment arm (A) is found by calculating the necessary
displacement of the tibia to move to the+25 position fromthe point
of maximum torque. The minimum angle “A” is found by
subtracting the maximum by forty.
𝑎 = √𝑐2
− 𝑏2
(1)
𝐴 𝑚𝑖𝑛 = 𝐴 𝑚𝑎𝑥 − 40 (2)
With themaximum and minimum angle “A”found and the lengths
“b” and “c” held constant combined length of the linear actuator
and series spring (“a”) can be calculated for in any point in stance
phaseusing thelaw of cosines. Thelength of theside “a”was found
for every one degree in stance phaseresulting in eighty data points.
The absolute difference between each consecutive data point was
found. This difference was divided by (total time of stance
phase/80) to obtain the linear velocity. By analyzing these
velocities the maximum linear velocity of the actuator was
obtained.
𝑎 = √𝑏2
+ 𝑐2
− 2𝑏𝑐 cos 𝐴 (3)
2.3 Series Spring Analysis
Theseries compression springserves to absorb energy in controlled
plantarflexion and release it from the start of dorsiflexion to
midstance. The absorption serves to prevent the peak shock load
applied to the linear actuator from rising above the maximum load
rating. In addition this absorption and release has both a positive
and negative effect on the total resultant torque of the ankle joint
and it is assumed that theseries spring acts only in the 0--15◦ tibia-
foot angle range. In addition the series spring will be analyzed as a
pseudo leaf spring consisting of two plates connected via a torsion
spring. One plate is mounted to the foot while the other holds a
revolute joint to which the actuator mounts to. The force of the
actuator on this joint displaces the two plates angularly according
the rotary stiffness of the torsion spring between them. As the
moment arm is defined as the distance between the actuator
revolute joint and the ankle joint the moment arm length increases
throughout the angular displacement of the plates.
Figure 4: Series Spring Assembly

Analysis of the series spring is begun by calculating the initial
angle between the bottomand top plates. This is done by first
assuming the tibia to be in the upright position (90 degrees from
the horizontal) and subtracting angle A and the inclination of the
foot compared to level ground (24.22 degrees) from 90. This
difference is equal to angle “K”in Figure 24: Diagram of Series
Spring Assembly. The distance connecting theankle joint and end
of bottomplate(“𝐿 𝑏𝑜𝑡𝑡𝑜𝑚 𝑝𝑙𝑎𝑡𝑒")is chosen based on packaging
considerations. Additionally the moment arm (“a”) is selected
according to actuator trigonometry and maximum torque factors.
Utilizing thelength of the moment arm, bottomplate, and angle
(“K”) the law of sines is able to calculate the necessary length of
the top plate(“𝐿𝑡𝑜𝑝 𝑝𝑙𝑎𝑡𝑒") and angles (“M”) and (“N”).
𝑏 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 =
1
sin𝐾
𝐿 𝑡𝑜𝑝 𝑝𝑙 𝑎 𝑡𝑒∗sin𝑀
(4)
Angle (“K”) changes from theinitial value found when the Tibia
is upright to (“K-15”) as the foot travels through plantarflexion.
The moment arm length and angles (“M”) and (“N”) change in
accordance to the change in (“K”) and the law of sines. Through
the multiplication of angle (“N”) and thespring stiffness (“𝑘 𝑝”)
the torquebetween the plates is found for every data point in
controlled plantarflexion. Dividing this torque by thelinear
distance between the bottomof the top plateto theactuator
revolute joint produces thevalue of normal force exerted on the
actuator by theseries spring assembly.
𝐹𝑛𝑜𝑟𝑚𝑎𝑙 =
𝑇𝑠𝑒𝑟𝑖𝑒𝑠
𝑑 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑒
(5)
A line drawn perpendicular to the top platefrom theactuator
revolute joint is used to illustrate angles (“P”) and (“S”). Using
the trigonometric analysis and the law of sines the force along the
actuator due to the series spring (“𝐹𝑠𝑒𝑟𝑖𝑒𝑠”) is determined.
Multiplying(“𝐹𝑠𝑒𝑟𝑖𝑒𝑠”) by the moment arm length at the analyzed
controlled plantarflexion point produces the torqueabout the
ankle joint due to theseries spring (“𝑇𝑠𝑒𝑟𝑖𝑒𝑠”).
Torque due to the series spring is calculated by multiplying the
force on actuator due to the series spring by the horizontal
distance between the ankle joint and the actuator-moment arm
revolute attachment joints. Subtracting the angle between thefoot
and tibia at which maximum torque is reached (“∅max𝑡𝑜𝑟𝑞𝑢𝑒”)
from the foot-tibia angle of analysis (“𝜃 𝐹𝑜𝑜𝑡”) determines the
angle between the horizontaland actuator. Inputtingthis angle
into thecosine function and multiplying the result by themoment
arm length at the analyzed (“K”) calculates the projection of force
perpendicular to the moment arm. The product of this result to the
moment arm length at theanalyzed (“K”) produces thetorque
about theankle joint due to the series spring.
𝑄 = 𝑆 − ( 𝑄 + 𝑀) (6)
𝐹𝑠𝑒𝑟𝑖𝑒𝑠 = 𝐹𝑛𝑜𝑟𝑚𝑎𝑙 cos 𝑄
𝑇𝑠𝑒𝑟𝑖𝑒𝑠 = 𝐹𝑠𝑒𝑟𝑖𝑒𝑠 ∗ 𝑏 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 (7)
2.4 Uni-directional Parallel Spring Analysis
The unidirectional parallel spring (i.e UPS) is modeled as a rotary
spring with arotary springconstant “kp”. Energy is absorbed by the
UPS from midstance to the end of dorsiflexion and is released in
powered plantarflexion, increasing peak torqueoutput and reducing
the maximum load on thelinear actuator. Torquedue to theUPS is
calculated by multiplying the rotary springstiffness by the angular
displacement of the tibia.
𝑇 𝑈𝑃𝑆 = 𝑘 𝑝 𝜃 𝑇𝑖𝑏𝑖𝑎−𝐹𝑜𝑜𝑡 (8)
2.5 Linear Actuator Analysis
By combining an electric motor, gearbox reducer, ballscrew, and
ballnut an electric linear actuator may be formed. The
specifications of each component must be selected so the created
linear actuator is able to reach the linear velocity and thrust
requirements needed to emulate a natural ankle torque curve.
Ballscrews are used in placeof other linear motion alternatives such
as lead screws or worm gears as they are +90% efficient in the
conversion of rotational to linear motion. This allows for both
efficient energy usage of the systemand the ability to covert linear
motion into rotational motion. This ability is highly inefficient in
alternative linear motion systems. The capability to convert linear
into rotational motion is necessary for powered plantarflexion to
operate smoothly and naturally as the linear actuator would not
have to compress at exactly the correct velocity to avoid “locking
up” the ankle joint from heel strike to toe down.
The linear force of a ballnut when torqueis applied to its
ballscrew is function of the feed screw lead in mm (“Ph”), applied
torque in N*mm (“Tapplied”), and efficiency (“µ”). Feed screw lead
is defined as the distance between the peaks of one thread to the
next consecutive thread while efficiency is assumed to be .90 for
all tested cases. If a gearbox is implemented the applied torque is
multiplied by thetotal gearbox ratio (‘G”). The rotational speed of
the ballscrew (“RPMballscrew”) is equal to the RPM of the motor
divided by thegearbox ratio. Multiplyingtherotationalspeed of the
ballscrew by thefeed screw lead produces and dividing this product
by 60 seconds produces the linear velocity of the ballnut in mm/s
𝑇𝑎𝑝𝑝𝑙𝑖𝑒𝑑 = 𝑇 𝑚𝑜𝑡𝑜𝑟 𝐺 (9)
𝐹𝐵𝑎𝑙𝑙𝑛𝑢𝑡 =
2𝜋 ∗ 𝜇 ∗ 𝑇𝑎𝑝𝑝𝑙𝑖𝑒𝑑
𝑃ℎ
(10)
𝑉𝐵𝑎𝑙𝑙𝑛𝑢𝑡 =
𝑅𝑃𝑀 𝐵𝑎𝑙𝑙𝑠𝑐𝑟𝑒𝑤 𝑃ℎ
60
(11)
Torque due to the linear actuator is calculated by multiplying the
Force due to the ballnut by the horizontaldistance between the
ankle joint and the actuator-moment arm revolute attachment
joints. By subtracting the angle between thefoot and tibia at
which maximum torque is reached (“∅max 𝑡𝑜𝑟𝑞𝑢𝑒”) from the foot-
tibia angle of analysis (“𝜃 𝐹𝑜𝑜𝑡”) thehorizontal distance between
the ankle joint and moment arm revolute joint is determined.
𝑇𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟 = 𝐹𝐵𝑎𝑙𝑙𝑛𝑢𝑡cos(𝜃 𝐹𝑜𝑜𝑡 − ∅max 𝑡𝑜𝑟𝑞𝑢𝑒)𝑏 (12)
2.6 Resultant Torque and Error Analysis
In total three separate components generate torque in one or more
subdivisions of stance phase. These components are the series
spring, unidirectional parallel spring, and the linear actuator. The
torque at each of all the eighty data points is a sum of the torques
generated from every torque generating component. It is assumed
that in controlled plantarflexion torque due to the linear actuator
will be zero as the ground reaction force will compress the series
spring and rotate the foot about the ankle joint. Frictional and
moment of inertia resistance of the ballscrew and motor assembly
in controlled plantarflexion is not accounted for in this analysis.
𝑇0 𝑡𝑜−15 = −𝑇𝑆𝑒𝑟𝑖𝑒𝑠 𝑆𝑝𝑟𝑖𝑛𝑔 (13)
𝑇0 𝑡𝑜−15 = −𝑇𝑆𝑒𝑟𝑖𝑒𝑠 𝑆𝑝𝑟𝑖𝑛𝑔 + 𝑇𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟 (14)
𝑇0 𝑡𝑜 +25 = −𝑇𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟 + 𝑇 𝑈𝑃𝑆 (15)
𝑇+25 𝑡𝑜 0 = 𝑇𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟 + 𝑇 𝑈𝑃𝑆 (16)

Graphing the resultant torque values on they-axis of a Cartesian
chart with the x-axis listing the angles produces a torque curve.
Plotting the natural torque values on the same chart allows for
visual comparison between their respectivetorque performances
over the entire stance phase. It is the goal of the designed
prostheticto producethe same resultant torque values as the
inputted natural torquevalues and thus having both torque curves
overlap. The amount of error between the resultant and natural
torque curves is calculating using Equation 28: Mean Error Cost
between Resultant and Natural TorqueCurves. The squared mean
error cost places greater emphasis on data points thefarther they
lie from each other.
𝑀𝑒𝑎𝑛 𝐸𝑟𝑟𝑜𝑟 𝐶𝑜𝑠𝑡:
∑ | 𝑇𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 − 𝑇𝑛𝑎𝑡𝑢𝑟𝑎𝑙|80
𝑖=0
80
(17)
𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝑀𝑒𝑎𝑛 𝐸𝑟𝑟𝑜𝑟 𝐶𝑜𝑠𝑡:
∑ | 𝑇𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 − 𝑇 𝑛𝑎𝑡𝑢𝑟𝑎𝑙|280
𝑖=0
80
(18)
2.7 Energy Draw Analysis
For an active prostheticto be utilized effectively for everyday use
the energy storage system must be able to power the actuator
throughout a typicalday’s use. In the case of a transtibial prosthetic
the proposed design must be able to providepowered assistance in
ambulation for the average distance walked by the average healthy
patient. As a powered prosthetic is generally much heavier than its
passivecounterpart walking without powered assist would become
much more difficult than with just a passive prosthetic alone. To
calculate the distance the proposed design is able operate(“D”) the
amount of time in hours (“Toperation”) is converted to seconds and
then multiplied by the walking speed (“Vwalking”). One meter per
second is used to determine the operating distance.
𝐷 = (𝑇𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 ∗ 3600)∗ 𝑉 𝑤𝑎𝑙𝑘𝑖𝑛𝑔 (19)
The maximum operating time is found using two methods for the
sake of comparison. Battery life is affected by various factors
which are difficult or impossible to mathematically simulate such
as ambient temperatureand cell life. For this reason multiple
methods of estimation are critical in gaining an enhanced
understanding to the true capability of the proposed design. In the
first method 75% of the maximum current drawn by thelinear
actuator (“Amax”) is assumed to be constant over the entire gait
cycle. This value is then divided by the capacity of the battery
(“B”) measured in milliamps. Twenty percent of this result is
subtracted as safety factor against draining the battery 100%
possibly resulting in total battery failure.
𝑇𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
.75𝐴 𝑚𝑎𝑥
𝐵
. 8 (20)
In the second method the integral of the curve created by plotting
the time in stance phase over the current drawn is found.
Microsoft Excel does not include a function for calculating the
integral or a function. The method of Riemann sums is
incorporated as a substitute. Each rectangle area is found by
multiplying the current drawn at the respective data point by the
time between data point. Dividing thetotal time of stance phase
(“tstance phase”) by thenumber of data points results in thetime
between data points (“tdata point”). Thesummation of these areas
divided by the capacity of thebattery results in the totaltime of
operation. Any data point with current draw of zero will produce a
rectangle of area of zero. When computing theRiemann sum this
will result in a totaloperation time less than if a non-zero value of
current draw was inputted at this same data point. This is a logical
error of this computation method which requires compensation as
portions of the gait cycle may not require the motor to actively
run. Dividing thetotal time in which there is no current draw
(“𝑡 𝑛𝑜 𝑑𝑟𝑎𝑤”) by thetotal time of stance phaseresults in the
correction factor which is added to the 20% safety factor of the
battery.
𝑇𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜 𝑛 = ∑ ( 𝐴 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡 ∗
𝑡𝑠𝑡𝑎𝑛𝑐𝑒 𝑝ℎ𝑎𝑠𝑒
80
)(.8 +
𝑡 𝑛𝑜 𝑑𝑟𝑎𝑤
𝑡𝑠𝑡𝑎𝑛𝑐𝑒 𝑝ℎ𝑎𝑠𝑒
)
80
0
(21)
3. COMPONENTS AND DESIGN
3.1 Linear Actuator
Several components comprise the internals of a linear actuator.
These include all but are not limited to the motor, screw, nut,
gearbox, and screw mount. All components were chosen carefully
ensure compatibility with oneanother. TheMaxon EC 45 brushless
250 Watt electric motor (part #136211) was selected to drive the
linear actuator for its rare combination of high torque and RPM
specifications. TheEC 45’s maximum RPM of 10,400 allows for a
linear speed greater than the minimum required for a gait of one
meter per second. A Maxon GP 42 C Planetary Gearhead (part
#203115) containing a gear ratio of 1:12 provides sufficient driving
torque to the ballscrew to provide the necessary force on the
moment arm. The combination of the 1:12 transmission with the
maximum RPM rating of the EC 45 motor ensures theballscrew is
always driven at sufficient speed and torque.
Within the top casing of the linear actuator is a 1:1 gear train with
one gear connected to the planetary gearbox shaft and the second
connected to the ballscrew. It is important to note that a ballscrew
and ballnut are implemented within the linear actuator versus a
standard leadscrew and drive nut. Ballnut and screw combinations
offer a superior mechanical efficiency of +90% when compared to
leadscrew efficiency of (40%-70%). When implemented in a linear
actuator ballscrews allow for the conversion of linear to rotational
motion in scenarios where leadscrews would lock or highly resist
the linear travel of the actuator. The conversion of linear to
rotational energy is critical in controlled plantarflexion as slower
than normal linear velocity of the actuator or locking will in turn
affect theankle rotationalvelocity and disrupt naturalgait, possibly
causing injury to the user.
Thomson Linear Motion components were selected due the
compatibility of components and lower costs when compared to
various linear motion companies. The FK 16mm diameter, 5mm
lead ballscrew (Part #7832776-P5) is mounted by the FK metric
bearing support (Part #7833406). The bearing support is bolted to
the gear case and holds the ballscrew securely preventing axial
motion. The FK 16mm ballscrew (Part #78327777) provides the
linear motion and flange necessary to connect the linear actuator
rod. All components were selected with the minimum required
dimensions required to maintain structural integrity during
operation.
3.2 Elastic Components
Torsion springs are implemented for both the series spring
assembly and the unidirectional parallel spring. To ensure equal
force is distributed along the length across the foot and the series
plate, two torsion springs of opposite direction winding are used.
Each of the two series and UPS torsion springs has a rotational
spring stiffness of 8.79 N*m/deg and 50 N*m/deg respectively.

3.3 Microcontroller and Shields
Thenatural gait inducing prostheticneeds acontrol systemthat can
accurately adjust the performance of the device depending on the
input from various sensors. The sensors will communicate with a
micro controller which will give directions to a motor control
module. Themicro controller that will be used is an Arduino Mega
2560. The Arduino Mega has many features that make it a default
choice for a project of this scale. The Mega compared to other
micro controllers has a larger amount of digital input and output
pins which allows for many more sensors. In addition it has a faster
clock speed and memory which will be beneficial when operating
solely on the device and not connect to a computer.
3.4 Prosthetic Foot
In order for thenatural gait inducing prostheticto function properly,
it needs to have a flexible foot to absorb some of the shock of
walking. The most basic solution would be to fabricate a foot out
of a hard rubber or gel. Unfortunately, the previous solutions are
cheap and easy to manufacture but they are not the most efficient
at storing and releasing energy. In order to receive the most benefit
from a human’s potentialenergy a better solution was found, which
the LP Vari-Flex was. The LP Vari-Flex is a prostheticfoot made
out of carbon fiber. Due to its material and design, it is very useful
for absorbing a release energy during the gait cycle, which makes
it the best selection for the natural gait inducing prosthetic.
3.5 Battery and Electronics
In order for the natural gait inducing prostheticto work it needs to
have a source of energy a device to control it. In the case of this
project, a 5 cell battery will be used to provide the power and a
saber tooth motor controller will control the speed and direction of
the linear actuator. The power source that will be used will be a 5
cell 4000mAh Lithium Polymer battery, which has a maximum
discharge amperage of 64 amps. Thedischarge rateof 64 amps will
be plenty to providethepower needed for the Maxon motor, which
has a maximum amperage of 10.4 amps.
In order to properly controlthe motor, a motor controller will need
to be used in syncwith a rotary encoder. The rotary encoder that is
being used is the HEDS-9000, which will allow for the arduino to
accurately measure the displacement of the linear actuator.
Depending on the linear displacement of the actuator the motor
controller will speed up or slow down the motor. The motor
controller being used is theSaber tooth 2x25, this motor controller
uses pulsewith modulation in order to controlthemotor. Pulsewith
modulation limits the available power to motor which allows it to
control the speed of the motor.
3.6 Frame Design
Various frames were designed to increase the stability of the
structurethat will contain the motor, gear box, ball screw, ball nut,
and ankle mount. The frames were designed to fit tightly over the
ball screw and motor portion to minimize the use of material and
weight. Protruding fins were added to the structure to help
distribute the applied load it would have to withstand. This final
design was analyzed to then be manufactured.
Figure 5: Final Frame Design
4. TESTING
4.1 Testing Prototype
Theprototypeof theankle-foot prosthesis was not madeto sizeand
capability due to thelack of funding. Instead, a smaller scale model
was created to show theproof of concept. The prototypewas made
to support afraction of theamputee’s weight dueto theaccessibility
to weaker materials. In this case it would be 10 kg.
Figure 6: Testing Prototype
4.2 Overview
The validation of the simulation model and all the theoretical
calculations performed within it is the primary focus of the test
performed on the manufactured prototype. With the validation of
the simulation model ensured the financial investment into the
construction of a human testableprototypecan bemade. In addition
thevalidation of the simulation model allows for the reallocation of
increased resources towards the research of alternate designs and
design optimization, thus improving the performance of the final
product.
The primary performance variable of a transtibial prostheticis the
assistance it provides the patient throughout the gait cycle. This
equates to the prosthetic’s ability to match the natural ankle torque
curve in all phases of thegait cycle. The efficiency of theprosthetic
in which thenatural and designed torque curves are matched is also
a primary metric used in theevaluation of thedesign. Evaluation is
performed through the measurement of the maximum ankle torque
output of the prototype in powered plantarflexion. As the torque
contribution of the linear actuator is significantly greater than that
of either the series or uni-directional springs it is assumed that if
the simulated maximum torque is achieved then the simulated and
torque curves may match by controlling the motor torque output.
4.3 Designof Experiment
One of the most important aspects of any prototype is an accurate
experiment to proveits performance is up to par with its theoretical
counterpart. In the case of the natural gait inducing prosthetic the
proof of concept must be validated. The entire purpose of the
prostheticis to provide enough torque at a certain velocity at every
degree in the gait cycle. In order to provethat theconcept works, a
test would need to evaluate thetorqueat each point in thegait cycle.

There are several ways of calculating torquearound the ankle joint,
however some methods are more practical than others. In order to
achieve precise and accurate proof that the prosthetic ankle will
overcome the required torque a simple method will be used.
In order to provethetorque of the prostheticankle a simple testing
method will be used. The method consists of fixing a shaft to the
revolute joint which is also known as theankle. In order to measure
whether or not the ankle is strong enough a certain mass will be
added at the end of theshaft. If themotor over comes the mass and
rotates it proves that it can provide the torque required. The
following equations will illustrate the process to selecting the
proper mass for each degree in the gait cycle.
𝑇𝑟𝑒𝑞 = 𝑚 𝑟𝑒𝑞 𝑔𝑙 𝑠ℎ𝑎𝑓𝑡 (22)
𝑚 𝑟𝑒𝑞 =
𝑇 𝑟𝑒𝑞
𝑔𝑙 𝑠ℎ𝑎𝑓𝑡
(23)
4.4 Test Results
Thedata represented by Table1 shows theweight added to thefoot
during testing, its performance, and the output torqueeach weight
created. Moreover, it can be seen that with increasing load, the
linear actuator had more difficulty in raising the weights from their
starting position.
Table 1: Testing Results
Weight
(lbs - kg)
Torque(mNm) Results
7.5 - 3.40 5083.15
No effect on
motor
10.0 -
4.54
6787.50
No effect on
motor
12.5 -
5.67
8476.90
No effect on
motor
15.0 -
6.80
10166.30
Minor motor
struggle
17.5 -
7.94
11870.65 Hinge failure
4.5 Evaluation of Experimental Results
The minimum torquethat had to be produced about the ankle joint
was 13,006.88 N•mm at 8.70 kg. From Table 1, it can be noted that
the maximum torque achieved was 11,870.65 N•mm at 7.94 kg;
thus, meaning that the prosthesis failed during testing. This failure
lead to a percent error of 8.74% for the ankle-foot prosthesis. Such
a small value for error shows that the values obtained from testing
are precise in comparison to the natural gait data. However, it is
important to note that this failure can be attributed to a mishap
during testing that caused thesprings to hyperextend and break the
series spring assembly at 7.94 kg.
5. Conclusion
5.1 Contemporary Issues
With the age of retirement and the cost of healthcare rising rapidly
in modern day society theneed to return theamputee population to
the workforce or reduce secondary disabilities has never been
higher. Coupled with the reality of a rising amputee population, in
part due to an increase in diabetes and another due to an increase in
military conflicts around the world, powered prosthetics will
become increasingly common place in global society.
5.2 Impact in Global Context
Wide spread adoption of powered transtibial prosthetics in the
global market will reduce overall healthcare costs. This is
accomplished by the decrease of perpetualhealth care cost related
to thecomplications and secondary disabilities related to transtibial
amputations and asymmetrical gaits. Additionally the work force
population willincrease and stay constant as amputations no longer
end a person’s ability to work. With an increased global workforce
and reduced government and insurance spending on healthcare
economic productivity will improve. Additional funding may be
reallocated to other government institutions such as education or
preventative medicine, thus improving even further global
productivity and public health.
5.3 Discussion
The prototype of the active ankle-foot prosthetic discussed in this
paper represents the first iteration of analysis, design,
manufacturing, and testing towards thefuturecommercialization of
such a system. Successful preliminary testing of the prototype
maximum torque has proven several concepts presented in this
paper. Firstly that the alternative designs for the series and uni-
directional spring assemblies presented here are viable for real
world application. In addition thesealternative torsion spring based
designs provided the necessary shock load resistance and torque
assistance required to provide patients a natural torque curve
throughout ambulation. Secondly, that the use of “off the shelf”
components was proven to be a successful model for ensuring low
system cost while maintaining operability. Thirdly, partial
validation of the simulation model was achieved. This validation
will drive design innovations and shorten design to testing cycles
for future prototype iterations.
5.4 Commercialization Prospects
As the design and prototype of the low cost powered ankle-foot
prostheticpresented in this paper is a first iteration there are many
opportunities for improvements. These opportunities range across
all sub-systems of thedesign and may be made possibleeasily with
more time resources allocated to research and design.
For future designs the reduction in weight of the systemwould be
thehighest priority. Resources towards theresearch and analysis of
various materials and material types such as composites and
various metal alloys would be increased in an effort to reduce the
weight to the desired five pound specification. Alternative frame
designs would also be investigated for weight saving contribution.
The component selection process would be revised in order to
lengthen the time available to search for viable components.
Smaller, lighter, and more economical components may be
available commercially for implementation in future designs. This
includes research investigations towards the viability of custom
designing and manufacturing certain components versus
purchasing an equivalent product “off the shelf”. An area of
importance for such investigations of custom design is the
ballscrew mounting block and the purchase of an existing linear
actuator.

Computer engineers and scientists are required for the
implementation of onboard sensors and predictive algorithms in
order to achieve 100% automated functionality. In addition
electrical engineers would be consulted for the development of a
regenerative power system to operate throughout the controlled
plantar flexion phase. Biomedical engineers and or medical
professionals would be desired for collaboration of future designs
to ensure its compatibility with the human body and testing
patients.
5.5 Future Work
As the design and prototype of the low cost powered ankle-foot
prostheticpresented in this paper is a first iteration there are many
opportunities for improvements. These opportunities range across
all sub-systems of thedesign and may be made possibleeasily with
more time resources allocated to research and design.
For future designs the reduction in weight of the systemwould be
thehighest priority. Resources towards theresearch and analysis of
various materials and material types such as composites and
various metal alloys would be increased in an effort to reduce the
weight to the desired five pound specification. Alternative frame
designs would also be investigated for weight saving contribution.
The component selection process would be revised in order to
lengthen the time available to search for viable components.
Smaller, lighter, and more economical components may be
available commercially for implementation in future designs. This
includes research investigations towards the viability of custom
designing and manufacturing certain components versus
purchasing an equivalent product “off the shelf”. An area of
importance for such investigations of custom design is the
ballscrew mounting block and the purchase of an existing linear
actuator.
Computer engineers and scientists are required for the
implementation of onboard sensors and predictive algorithms in
order to achieve 100% automated functionality. In addition
electrical engineers would be consulted for the development of a
regenerative power system to operate throughout the controlled
plantar flexion phase. Biomedical engineers and or medical
professionals would be desired for collaboration of future designs
to ensure its compatibility with the human body and testing
patients.
6. ACKNOWLEDGMENTS
Our thanks to Doctoral Candidate Mellissa Morris and Dr.
Sabri Tosunoglu for their knowledge and assistance of this
project.
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