MECHANICAL PROPERTIES OF DYNAMIC ENERGY RETURN PROSTHETIC FEET
by
Andrea Haberman
A thesis submitted to the Department of Mechanical and Materials Engineering
in conformity with the requirements for
the degree of Master of Science (Engineering)
Queen’s University
Kingston, Ontario, Canada
April, 2008
Copyright ©Andrea Haberman, 2008
ii
Abstract
The long-term goal of this study is to improve the ability of designers and prosthetists to match
the mechanical characteristics of prosthetic feet to patient specific parameters, including, needs,
abilities and biomechanical characteristics. While patient measures of performance are well
developed, there is a need to develop a practical method by which non-linear and time-dependent
mechanical properties of the prosthetic component can be measured. In this study, testing
methodologies were developed that separately evaluated the elastic and time-dependent
properties. Three styles of feet were tested to span the range of designs of interest: a standard
solid ankle cushioned heel (SACH) foot, two energy return feet for active users and a new
prosthetic foot designed to provide partial energy return.
The first testing regime involved mechanically characterizing prostheses under conditions similar
to gait. The heels and toes of four sample feet were loaded to peak forces based on their design
mass at a series of angles and forces that the prosthetic system would go through during the gait
cycle, based on the waveform in ISO 22675. Tangential stiffnesses of the samples were
determined using numerical differentiation. The force-displacement responses of prosthetic feet
reflect increasing stiffnesses with increasing loads and a decreasing pylon angle. Key features
reflecting foot design are: the relative stiffness of the heel and toe and the displacement gap at
midstance. Stable feet tend to exhibit lower heel stiffnesses and higher toe stiffnesses, whereas
dynamics energy return (DER) feet tend to exhibit higher heel stiffnesses and lower toe
stiffnesses. The differences in heel and toe loading at midstance suggest that DER feet can aid in
the transition from heel to toe, providing a smooth rollover whereas SACH feet provide greater
stability.
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A second testing regime examined the time-dependent properties of the heel and toe. A three-
parameter reduced relaxation response of the form BttAAtL −−−+= )exp()1()( τ was able to
capture the force-relaxation characteristics with RMS differences ranging from 0.0006 to 0.0119.
In this model, A is the initial decay, B is the decay coefficient, a linear decay term, and τ is a time
constant. While the model is practical for comparing various prostheses at a single load level, a
fully non-linear model is required to model the time-dependent response at all loading levels.
iv
Co-Authorship
This thesis is written in manuscript format. Two manuscripts are included that were written as a
collaborative effort. The first manuscript entitled “Mechanical Characterization of Dynamic
Energy Return Prosthetic Feet,” was co-authored with Tim Bryant, PEng., PhD., Mary Beshai,
PEng., MSc. and Robert Gabourie C.P.O. The second manuscript entiled “Force-Relaxation
Properties of Dynamic Energy Return Feet,” was co-authored with Tim Bryant, PEng., PhD.
v
Acknowledgements
Otto Bock®, Dupont™ and Niagara Prosthetics and Orthotics International Ltd. donated samples
used in this study, for which I am grateful.
Rob Gabourie: your vision, passion and desire to change the world resulted in the development of
the Niagara Foot™. Thank you for providing me with the opportunity to work on this project,
taking me under your wing and sharing your expertise in all things foot related.
Tim: your quest for knowledge is surpassed only by your passion for sharing it. I feel privileged
to have had the opportunity to study with you. Thank you for your guidance, encouragement,
patience and for the opportunity to work on this project. This was an experience I will never
forget.
Mary: thank you for teaching me the meaning of insanity rather than allowing me to discover it on
my own. I can not express how much I appreciate your help and support throughout my studies.
Leone: thank you for answering my endless string of technical questions and helping to fix all of
my equipment-related blunders.
To all of my friends and family, who now know more about prosthetic feet than they ever thought
they would: your support, encouragement and patience were invaluable, especially Amanda, Iris,
Carol and my parents.
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Table of Contents Abstract ............................................................................................................................................ ii Co-Authorship................................................................................................................................. iv Acknowledgements.......................................................................................................................... v Table of Contents ............................................................................................................................ vi List of Figures ............................................................................................................................... viii List of Tables .................................................................................................................................. xi Chapter 1 Introduction ..................................................................................................................... 1
1.1 Causes of Amputation............................................................................................................ 1 1.2 Anatomical Planes, Directions and Movement ...................................................................... 3 1.3 Transtibial Prosthetic System Design Principles ................................................................... 5 1.4 Objective ................................................................................................................................ 8 1.5 Thesis Format......................................................................................................................... 8
Chapter 2 Review of the Literature.................................................................................................. 9 2.1 Normal Gait ........................................................................................................................... 9 2.2 Gait in Transtibial Amputee Patients ................................................................................... 12 2.3 Prosthetic Systems ............................................................................................................... 14
2.3.1 Sockets .......................................................................................................................... 15 2.3.2 Suspension .................................................................................................................... 16 2.3.3 Prosthetic Feet............................................................................................................... 18 2.3.4 Prosthetic Feet: Principles of Design ............................................................................ 20
2.4 Alignment ............................................................................................................................ 24 2.5 Assessing Patient Performance ............................................................................................ 26
2.5.1 Physical Measurements................................................................................................. 27 2.5.2 Self-reported Measures ................................................................................................. 28
2.6 Relationship of Mechanical Characteristics to Performance ............................................... 28 2.7 Summary .............................................................................................................................. 30
Chapter 3 Mechanical Characterization of Dynamic Energy Return Prosthetic Feet .................... 31 3.1 Introduction.......................................................................................................................... 31 3.2 Critical Points....................................................................................................................... 36 3.3 Methods................................................................................................................................ 38 3.4 Data Analysis ....................................................................................................................... 42 3.5 Results and Discussion......................................................................................................... 46
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3.6 Conclusions.......................................................................................................................... 57 Chapter 4 Force Relaxation Properties of Dynamic Energy Return Feet ...................................... 58
4.1 Introduction.......................................................................................................................... 58 4.2 Theory .................................................................................................................................. 60 4.3 Methods................................................................................................................................ 64 4.4 Results and Discussion......................................................................................................... 67 4.5 Conclusions.......................................................................................................................... 73
Chapter 5 General Discussion........................................................................................................ 74 5.1 Patient-related Variables ...................................................................................................... 78 5.2 Prosthetist-related Variables ................................................................................................ 80 5.3 Component Design Variables .............................................................................................. 80
Chapter 6 Conclusions and Future Work....................................................................................... 82 6.1 Conclusions.......................................................................................................................... 82 6.2 Future Work ......................................................................................................................... 84
Appendix A Determination of Displacement Rate ....................................................................... 89 Appendix B Linear Extrapolation and Interpolation..................................................................... 94 Appendix C Mechanical Characterization of Dynamic Energy Return Prosthetic Feet: Complete
Data Set .......................................................................................................................................... 97 Appendix D Force-Relaxation Properties of Dynamic Energy Return Feet: Complete
Data Set ........................................................................................................................................ 110
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List of Figures Figure 1: Common amputation levels. ............................................................................................. 2 Figure 2: Planes used to describe the human body. ......................................................................... 3 Figure 3: Terms used to describe joint motion................................................................................. 4 Figure 4: Right lower limb progressing through the stance phase of gait...................................... 10 Figure 5: Typical ground reaction forces occurring during normal gait ........................................ 12 Figure 6: Endoskeletal and exoskeletal transtibial prosthetic systems .......................................... 15 Figure 7: Suspension systems ........................................................................................................ 17 Figure 8: Cross section schematic of a SACH foot, a single-axis foot, a Greissinger multi-axis
foot, a Multiflex multi-axis foot, and a Flex Foot™...................................................................... 19 Figure 9: Feet having features from more than one class of foot................................................... 20 Figure 10: The Ohio Willow Wood Impulse® ............................................................................. 24 Figure 11: Loading the residual limb............................................................................................. 25 Figure 12: Testing waveforms from ISO 22675 ............................................................................ 35 Figure 13: Fifteen critical points extracted from ISO 22675 ......................................................... 37 Figure 14: Photographs of the SACH foot, Axtion™ keel and the Niagara Foot™...................... 40 Figure 15: Test configuration......................................................................................................... 41 Figure 16: Typical force displacement curve................................................................................. 43 Figure 17: Overview of the data analysis process.......................................................................... 44 Figure 18: Peak displacements that occurred as a function of time. .............................................. 45 Figure 19: First difference between peak displacements as a function of time. ............................ 45 Figure 20: The contact point between the heel and the platen at displacements of 0mm, 4mm and
8mm ............................................................................................................................................... 47 Figure 21: Force-displacement curves for the heel and the toe of the Niagara Foot™.................. 48 Figure 22: Stiffness-displacement curves for the heel and toe of the Niagara Foot™................... 49 Figure 23: Predicting displacement and stiffness profiles of prostheses during gait ..................... 51 Figure 24: Predicted displacements of the Niagara Foot ™ during gait ........................................ 52 Figure 25: Predicted tangential stiffness values of the Niagara Foot™......................................... 53 Figure 26: Normalized displacements occurring at the critical forces identified........................... 55 Figure 27: Normalized tangential stiffness values occurring at the critical forces ........................ 56 Figure 28: Typical force response of the toe of a prosthetic foot .................................................. 61 Figure 29: The reduced relaxation response, L(t) .......................................................................... 62 Figure 30: Photographs of the SACH foot, Axtion™ keel and the Niagara Foot™...................... 65
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Figure 31: Test configuration......................................................................................................... 66 Figure 32: Force-relaxation response for the toe of the Model 2 Version 18 Niagara Foot™. ..... 69 Figure 33: Description of a typical force deflection curve of a heel using three
parametersarameters ...................................................................................................................... 90 Figure 34: Determination of the x-intercept using linear extrapolation......................................... 94 Figure 35: Adjustment of the force-displacement data to compensate for the offset origin .......... 95 Figure 36: Determination of displacement at the design load using linear interpolation............... 96 Figure 37: Force-displacement curves for the heel and toe of the Niagara Foot™. ...................... 98 Figure 38: Stiffness-displacement curves for the heel and toe of the Niagara Foot™................... 99 Figure 39: Displacements and tangential stiffness values of the Niagara Foot ™ occurring at the
critical forces identified. .............................................................................................................. 100 Figure 40: Force-displacement curves for the heel and toe of the Axtion™ foot with a maximum
recommended user weight of 106kg ............................................................................................ 101 Figure 41: Stiffness-displacement curves for the heel and toe of the Axtion™ foot with a
maximum recommended user weight of 106kg ........................................................................... 102 Figure 42: Displacements and tangential stiffness values of the Axtion™ foot with a maximum
recommended user weight of 106kg occurring at the critical forces identified. .......................... 103 Figure 43: Force-displacement curves for the heel and toe of the Axtion™ foot with a maximum
recommended user weight of 124kg ............................................................................................ 104 Figure 44: Stiffness-displacement curves for the heel and toe of the Axtion™ foot with a
maximum recommended user weight of 124kg ........................................................................... 105 Figure 45: Displacements and tangential stiffness values of the Axtion™ foot with a maximum
recommended user weight of 124kg occurring at the critical forces identified. .......................... 106 Figure 46: Force-displacement curves for the heel and toe of the SACH foot. ........................... 107 Figure 47: Stiffness-displacement curves for the heel and toe of the SACH foot ....................... 108 Figure 48: Displacements and tangential stiffness values of the SACH foot occurring at the
critical forces identified ............................................................................................................... 109 Figure 49: Reduced relaxation data for the heel of the sample feet. ............................................ 110 Figure 50: Reduced relaxation data for the toe of the sample feet............................................... 111 Figure 51: Reduced relaxation response for the heel of the Model 2 Version 18
Niagara Foot™............................................................................................................................. 112 Figure 52: Reduced relaxation response for the toe of the Model 2 Version 18
Niagara Foot™............................................................................................................................. 113
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Figure 53: Reduced relaxation response for the heel of the Axtion® foot with a maximum
recommended user weight of 106kg. ........................................................................................... 114 Figure 54: Reduced relaxation response for the toe region of the Axtion® foot with a maximum
recommended user weight of 106kg. ........................................................................................... 115 Figure 55: Reduced relaxation response for the heel region of the Axtion™ foot with a maximum
recommended user weight of 124kg. ........................................................................................... 116 Figure 56: Reduced relaxation response for the toe region of the Axtion® foot with a maximum
recommended user weight of 124kg. ........................................................................................... 117 Figure 57: Reduced relaxation response for the heel region of the SACH foot........................... 118 Figure 58: Reduced relaxation response for the toe region of the SACH foot. ........................... 119
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List of Tables Table 1: The effect of patient-, prosthetist- and device-controlled factors on the needs of an
amputee during gait.......................................................................................................................... 6 Table 2: Data extracted from the P4 test loading level curve ........................................................ 38 Table 3: Specifications of the sample feet tested in the mechanical characterization study.......... 39 Table 4. Specifications of the sample feet tested in the force-relaxation study. ............................ 64 Table 5: Parameters and degree of fit of a two-parameter model. ................................................. 69 Table 6: Parameters and degree of fit of a three-parameter model. ............................................... 70 Table 7: Results study examining linearity using a three-parameter model. ................................. 72 Table 8: Three stiffness values from mechanical testing of a Model 2 Version 18 Niagara Foot™
conducted at varying time intervals. .............................................................................................. 91 Table 9: Stiffness values for the heel and toe regions of a Model 2 Version 18 Niagara Foot™
tested at various displacement rates. .............................................................................................. 92 Table 10: Relaxation parameters of the four sample feet. ............................................................. 93
1
Chapter 1
Introduction
1.1 Causes of Amputation
Every year, hundreds of thousands of people lose a limb due to diseases such as diabetes and
cancer, as well as to the trauma associated with automobile collisions and violence. In the United
States over 130,000 people had a lower limb amputated in 1997 [1]. Of those amputations, 67%
were as a result of complications due to diabetes. In 2001, the International Committee of the Red
Cross (ICRC) fitted a total 7,418 people with their first prostheses and distributed 9,779
prostheses to land mine survivors in fourteen post-conflict countries [2].
The level of amputation is determined by which tissues need to be removed, how well the incision
will heal and the ability to create a functional residual limb [3]. Common lower limb amputation
levels are shown in Figure 1. Lower limb amputations above the knee are referred to as
transfemoral; the most common occur at the mid thigh. Lower limb amputations that leave the
knee intact are referred to as transtibial; they can occur anywhere below the knee including the
ankle and foot. [4]. For the patient, amputation requires a period of rehabilitation to address issues
associated with pain and loss of function and may involve a number of professionals, including
psychologists, physiatrists, physiotherapists and prosthetists. The provision of mobility is a
particular focus of medical treatment.
2
Figure 1: Common (a) above knee or transfemoral and (b) below knee or transtibial amputation levels [5].
(a) (b)
3
1.2 Anatomical Planes, Directions and Movement
Anatomical Planes and Directions. The body, like any other three-dimensional object, can be
described in terms of three planes: the sagittal, transverse and frontal planes, as shown in Figure
2. The sagittal plane divides the body into left and right sections, the transverse plane divides it
into upper and lower sections and the frontal plane divides it into anterior (front) and posterior
(back) sections. Motion forward in the sagittal plane is referred to as anterior, while motion
backward is posterior. Motion toward the mid-line of the body in the frontal plane is termed
medial, while motion away from the mid-line is lateral [6].
Figure 2: Planes used to describe the human body [6].
4
Anatomical Movement. When describing joint motion, commonly used terms are: flexion,
extension, plantar flexion, dorsiflexion, inversion and eversion, as shown in Figure 3. Generally,
flexion is a movement that decreases a joint angle while extension increases it. There are specific
terms used to describe motion of the toes and ankle. Dorsiflexion and plantar flexion refer to
decreasing and increasing these joint angles and take place in the sagittal plane. When the sole of
the foot is turned inward it is referred to as inversion, turned outward is eversion [6].
(a) (b)
(c)
Figure 3: Terms used to describe joint motion: (a) flexion and extension, (b) dorsiflexion and plantar flexion, (c) inversion and eversion [6].
5
1.3 Transtibial Prosthetic System Design Principles
Transfemoral prosthetic systems are more complex than transtibial ones, as they require a
mechanism to function in place of a knee joint. These range from single hinges to computerized
active controls. Other prosthetic components are common to both transfemoral and transtibial
prosthetic systems, including feet. However, typically 80% of lower limb amputations are
transtibial [4]. As such, there is a great deal more effort in the design of components used by
transtibial amputees, and these systems are the focus of the current study.
As with other products, prosthetic components must meet the general design goals of user
acceptance, ease of use, reliability and durability [7, 8]. Additional, specific, user-based
requirements include the provision of comfort and efficient locomotion. For comfort to be
achieved, the socket must fit the residual limb well; pistoning between the residual limb and the
socket or excessive loading of tissues can lead to discomfort. To achieve efficient locomotion
three criteria must be met: (1) the foot should be stable while in contact with the ground1; (2)
rollover from when the heel strikes the ground until the toe leaves it should be smooth; and (3)
when the toe leaves the ground it should be able to efficiently propel the limb forward. These user
requirements are outlined in Table 1.
A number of complex interactions take place during gait, all of which can affect comfort and
locomotion. Each of these is influenced by one of three factors: the patient, the prosthetist and the
1 This contact is referred to as stance.
6
prosthetic components. The influence of these factors on the user requirements is shown in Table
1, in which symbols are used to indicate the relative strengths of the relationships.
Influencing Factors
Patient- controlled
Prosthetist -controlled Device-controlled
User Needs Gait Adaptations
Socket Fit Alignment Socket
Interface Foot
Design Comfort ○ ● ○ ● ○
Smooth action during stance
● ○ ● ○ ●
Stability while in stance
○ ○ ○ ● Locomotion
Efficient propulsion ● ○ ● ●
Table 1: The effect of patient-, prosthetist- and device-controlled factors on the needs of an amputee during gait; ○ indicates a relationship and ● indicates a strong influence.
Patient-controlled Factors. Patients can influence the adaptations they make during gait to a
certain degree, for instance in knee flexion and loading of the prosthetic limb [3]. The manner in
which amputees walk impacts all of the user needs, but it has the greatest influence over their
ability to have a smooth rollover in stance and efficiently propel themselves.
7
Prosthetist-controlled Factors. In North America, the socket is custom made for each patient by
a prosthetist. The socket is the part that contacts the residual limb; as such, it impacts all of the
user needs. It is the most important factor associated with comfort of the user: a poor fit can result
in blistering, skin breakdown and inappropriate pressures being applied to sensitive tissues [3].
The prosthetist also aligns or sets the position of the prosthetic foot relative to the socket.
Ensuring that the alignment of the system meets the abilities of the users also affects all of their
needs. Alignment controls the location of the contact point between the foot and the floor.
Changes in alignment can change the length of the lever arms of the heel and toe thus changing
the effective stiffness of the foot [9]. The moments experienced by the limb and joints are also
influenced by the alignment [3]. Prosthetists face an added challenge when fitting their patients
with a prosthetic system, since different sockets, socket interfaces and foot designs can result in
different gait adaptations.
Device-controlled Factors. Device-controlled factors refer to the interface between the socket
and the residual limb and the prosthetic foot. The interface usually comprises a liner and
suspension system. The devices used in a prosthetic system influence all of the user needs. A
correct interface between the socket and the limb is integral: if it restricts movement it can affect a
patient’s comfort and impede their ability to have a smooth rollover during gait [3].
The design of the foot affects all of the user needs, having the strongest influence on efficient
locomotion. The design must meet the needs and abilities of the users; otherwise it can affect the
ability to have a smooth rollover, stability and efficient propulsion [3].
8
1.4 Objective
Recently there has been an increase in the number of foot designs on the market. Scientific
understanding of these components continues to develop; however, the relationship between the
mechanical characteristics of prosthetic feet and their performance is not well defined. The long-
term goal of this study is to improve the ability of designers and prosthetists to match the
mechanical characteristics of prosthetic feet to the patient-specific locomotion needs, including
stability, smooth rollover and efficient propulsion. The specific objective of this study is to
develop a practical method by which non-linear and time-dependent mechanical properties of the
prosthetic components can be measured.
1.5 Thesis Format
This document is presented in the form of two manuscripts isolating the elastic and time-
dependent properties of prosthetic feet. The first manuscript, “Mechanical Characterization of
Dynamic Energy Return Prosthetic Feet,” examines the elastic properties of prostheses,
specifically stiffness and displacement as they relate to the performance and function of these
devices. The second manuscript, “Force Relaxation Properties of Dynamic Energy Return
Prosthetic Feet,” examines the time-dependent properties of prostheses.
Although there are some redundancies in the Introduction and Discussion of the two manuscripts,
the Literature Review (Chapter 2) is intended to be comprehensive. A General Discussion
(Chapter 5) is included to address issues common to both manuscripts. Literature Citations and
Appendices are common for all sections of the document.
9
Chapter 2
Review of the Literature
2.1 Normal Gait
Gait refers to how people propel themselves using their lower limbs. One gait cycle occurs over
the time it takes for two successive events to occur involving the same limb, usually when the foot
first impacts the ground or supporting surface [10]. This process can be broken down into two
phases, stance and swing, as shown in Figure 4.2
During the stance phase, the foot is in contact with the supporting surface. This typically makes
up 60% of the cycle. Swing makes up the remaining 40% of gait; it occurs when the foot is not in
contact with the supporting surface [11]. Twice during each gait cycle, both feet are in contact
with the ground; this is referred to as double support. At a normal walking speed, each period of
double support takes up about 10% of the gait cycle; thus 80% of the time a person’s body weight
is supported by one limb [12]. Stance can be further broken down into three parts: heel strike,
midstance and push off.
At heel strike, the heel first makes contact with the ground. In a typical subject, the horizontal
velocity reduces to 0.4 m/sec and the vertical velocity reduces to 0.05 m/sec [13]. In abnormal
gait, the heel may not be the first part of the foot that contacts the ground; it could be the toes or
the whole foot [10].
2 Different sets of terminology exist to describe the various aspects of gait, the two most common being the
traditional and the Rancho Los Amigos terminologies. The traditional terminology is used here.
10
Both the midstance and push off phases can be further broken down into subsections. During the
midstance phase, foot flat and the midstance point occur. Foot flat refers to the first time that the
foot is flat on the supporting surface. It occurs after heel strike at approximately 7% of the gait
cycle. The midstance point when a person’s body weight is directly over the supporting limb,
about 30% of the way through the gait cycle.
The push off phase consists of heel off and toe off. During heel off, the heel leaves the supporting
surface, at about 40% of the gait cycle. Next, the toe leaves the supporting surface (toe off) at
about 60% of the cycle.
Figure 4: Right lower limb progressing through the stance phase of gait [10].
11
Swing can also be broken down into three phases: acceleration, midswing and deceleration. Once
the toe leaves the ground, the leg begins to increase its angular speed; this acceleration continues
until midswing. Midswing begins when the leg is directly beneath the body and continues until
deceleration. During deceleration at late swing, the leg beings to reduce its angular speed in
preparation for heel strike [10].
During stance, there are three forces acting on the foot, the vertical ground reaction force and the
anterior-posterior and medial-lateral forces, as shown in Figure 5 as functions of time [14]. In the
vertical ground reaction force curve, there is an initial spike and two peaks that are greater than
body weight. The spike is due to the impact of the foot with the supporting surface during heel
strike. The first peak occurs during weight acceptance and the second at push off [15].
12
Figure 5: Typical ground reaction forces occurring during normal gait: V vertical ground reaction force, A anterior-posterior force, M medial-lateral force. Adapted from Trew et al. [14].
2.2 Gait in Transtibial Amputee Patients
During amputee gait, compensations for the loss of bone, joints and musculature are required on
both the affected (prosthetic) and unaffected (intact) limbs. Amputees typically unload their
affected limb faster during the latter half of midstance and the push off phase compared to the
unaffected limb. In turn, less time is spent loading their affected limb and more time loading the
unaffected one. This results in stride asymmetry with a shortened stance phase and a longer swing
phase on the affected side [16]. This asymmetry results in a discrepancy between the loading of
the two limbs. Amputees experience a greater weight acceptance peak on their unaffected limb
relative to their affected limb depending on the walking velocity. Furthermore, the peak forces are
V
A
M
13
greater than in normal gait. As walking speed increases, so does the peak force due to the increase
in acceleration; however, the increase on the unaffected side is greater than on the affected side
[15]. Amputees often have a slower than average walking speed, and knee flexion during the
stance phase on the affected side is often lower [17].
The assessment of gait characteristics is used by prosthetists and therapists in order to provide
good long-term function in patients. Treatment goals include specific features at each phase of the
gait cycle. They are:
Heel Strike
− Stride lengths on the affected and unaffected sides should be equal
− Knee on the affected side should be flexed from 5° to 10°
− The prosthetic foot should contact the ground in a linear forward progression
Foot Flat
− Flexion of the knee on the affected side should have increased to between 15° to 20°
− Heel region of the prosthesis should have compressed so plantar flexion can occur
− Position of the residual limb in the prosthetic socket should remain constant
Midstance
− Should have a smooth progression forward while maintaining knee stability
− Top of the prosthesis should be level
− Upright trunk position should occur with minimal lateral bending
Push Off
− Heel off should occur smoothly
− Knee should begin to flex as soon as the heel rises to prepare for toe off
Swing Phase
− There must be enough toe clearance to allow for swing phase
− Limb should swing forward in the line of progression
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Failure to achieve these actions can lead to pain or discomfort and increased energy exertion [3].
This is particularly challenging because prosthetic systems must do more than replace lost
musculature and bone structure; they must be customized to the individual needs and abilities of
each patient [18].
2.3 Prosthetic Systems
Prosthetic systems require integration of a number of components. Many parts are available off
the shelf, while others need to be custom made for each individual. There are two general
classifications of transtibial prosthetic systems, endoskeletal and exoskeletal, as shown in Figure
6. Both systems have three main components: a socket, suspension and foot. In addition to fitting
the patient, the components must be aligned to ensure optimal performance of the overall system
[3].
In an endoskeletal system a hollow cylindrical shaft, called a pylon, connects the socket to the
foot. This configuration, shown in Figure 6a, is lightweight, adjustable and modular in design
(meaning it is possible to replace individual components). The system can be covered with a
cosmetic skin if desired [5]. Exoskeletal designs, such as the one shown in Figure 6b, have a rigid
laminate cover that connects the socket to the foot. One advantage of this system is its durability;
however, it is the heavier of the two. The socket is fixed into position making it difficult to adjust
it or the alignment of the prosthesis [3].
15
(a) (b)
Figure 6: (a) Endoskeletal and (b) Exoskeletal transtibial prosthetic systems. Three of the four components are shown: a socket, pylon and prosthetic foot. A suspension system is not depicted here [5].
2.3.1 Sockets
The socket is the component that contacts the residual limb. A sock is often worn over the
residual limb to provide some cushioning and accommodation for fluctuation in its volume [3].
There are two types of sockets, the patellar tendon bearing (PTB) and the total surface bearing
(TSB). The principle of the PTB socket is to control pressure distribution between the socket and
underlying anatomy. It is designed to load areas such as the patellar tendon, the medial flare, and
the anterior side of the tibia, which can tolerate the pressure. Other parts of the limb remain
unloaded or minimally loaded [4]. A TSB socket loads the entire surface of the residual limb
varying the force distribution according to the different types of tissue rather than the underlying
16
anatomy. In addition, a liner is usually worn over the residual limb. Liners provide an
intermediate layer between the limb and socket to improve the pressure distribution and to reduce
the tendency of the socket to move with respect to the underlying tissue [3].
2.3.2 Suspension
Suspension systems are designed to keep the socket and, in turn, the system securely attached to
the residual limb. They are one aspect of the socket-limb interface that can affect an amputee’s
ability to have a smooth rollover during stance. There is also a strong correlation between the
suspension and the overall comfort of the system. If the suspension system is not fitted correctly,
it can place the knee in a position of too much flexion or it can lead to the knee being fully
extended during heel strike. The latter can lead to skin break down [3]. A number of suspension
systems are available, as shown in Figure 7.
17
(a) (b) (c)
(d) (e) (f)
Figure 7: Suspension systems: (a) thigh corset with knee joints [4], (b) sleeve suspension [3], (c) supracondylar suspension [5] , (d) supracondylar cuff [4], (e) waist belt and anterior strap [3], (f) shuttle lock mechanism [5].
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2.3.3 Prosthetic Feet
The stiff, structural part of a prosthetic foot is termed the keel. In single unit designs, the keel is
incorporated into the rest of the foot. In other designs, the cover is a separate component into
which the keel is inserted; this allows for the cover to be replaced when needed, while continuing
to use the same keel [5]. Prosthetic feet can generally be placed into one of four categories:
conventional, single-axis, multi-axis and dynamic energy return [19].
Conventional. Conventional feet are basic designs that have no moving components. The widely
used solid ankle cushioned heel (SACH) foot, shown in Figure 8a, is one example. SACH feet
have a wooden or rigid plastic keel that extends until the toe section. Dense foam makes up the
heel and the remainder of the foot is rubberized foam. Belting is attached to the end of the keel
and extends into the toe region.
Single-Axis. As the name suggests, a single-axis foot has a hinge or other mechanism that allows
the foot to plantar flex and dorsiflex, as shown in Figure 8b. Single-axis feet were the first
prostheses to provide ankle articulations. They typically consist of a keel, with an ankle joint and
a molded foot shell. The keel has a plantar flexion bumper located in the heel behind the ankle
joint. Some feet have a second dorsiflexion bumper anterior to the ankle. Feet that do not have
this second bumper have a dorsiflexion stop. Similar to the SACH foot, belting is attached to the
end of the keel and extends into the toes.
Multi-Axis. A typical multi-axis design, the Otto Bock® Greissinger, shown in Figure 8c, has a
multi-directional hinge that allows for eversion and inversion as well as plantar and dorsiflexion.
The Endolite Multiflex, a newer style of multi-axis foot shown in Figure 8d, has a rubber ball
19
inside the stem of the ankle assembly with an O-ring sitting just below it. This system allows for
some rotation of the foot, in addition to eversion, inversion, plantar flexion and dorsiflexion.
Dynamic Energy Return. Dynamic energy return (DER) feet are able to store and return energy
during the gait cycle [19]. As such, these are not classified in terms of the structure, but rather by
their performance characteristics. One example of a DER foot is a Flex Foot™, shown in Figure
8e. It is a leaf spring design made of a carbon fibre composite that deflects extensively to provide
motion.
(a) (b) (c)
(d) (e)
Figure 8: Cross section schematic of (a) a SACH foot [4], (b) a single-axis foot [4], (c) a Greissinger multi-axis foot [3], (d) a Multiflex multi-axis foot [3], and a photograph of (e) a Flex Foot™, one type of dynamic energy return foot [4].
belting
20
The use of elastic properties in this way is also evident in prostheses with features from more than
one class of foot, including the Niagara Foot™, a single-axis DER foot, shown in Figure 9a, and
the College Park Industries TruStep™, a multi-axis DER foot, shown in Figure 9b.
(a) (b)
Figure 9: Feet having features from more than one class of foot, (a) The Niagara Foot™ is a single-axis DER foot and (b) The College Park Industries TruStep™, is a multi-axis DER foot [20].
2.3.4 Prosthetic Feet: Principles of Design
A prosthetic foot is designed to compensate for the musculature and bone structure lost due to
amputation and to facilitate the various actions that would occur during normal gait [3]. During
gait, the human foot and ankle are able to adapt to uneven terrain and to adjust the length of the
lower limb while providing shock absorption and stabilization of the knee. Ideally, a prosthetic
foot should be able to mimic these functions; however, this remains a challenge [4].
horns
top plate
C-section
21
During heel strike, a prosthetic foot is designed to absorb the impact of the heel hitting the ground
to reduce the forces transferred to the residual limb. The point of contact of the foot with the
ground is posterior to the ankle during heel strike, causing the foot to plantar flex. Prosthetic feet
control the rate of plantar flexion, which in turn controls the time it takes to reach foot flat, a
stable position. In transtibial amputees, this helps to control the rate at which the tibia advances.
The tibia next progresses from posterior to anterior of the ankle during midstance, causing the
foot to dorsiflex. In an unaffected limb, musculature controls the speed at which this occurs,
helping to maintain stability. The keel of a prosthetic foot provides this stability.
The tibia continues to advance during the heel off phase of push off. In normal gait, the point of
contact transfers to the forefoot as the foot rolls over the metatarsophalangeal joints. In a
prosthetic foot, this joint is sometimes replaced with a mechanical element, a toe break that
simulates dorsiflexion of the toes. At this point, toe off begins and the body weight is transferred
to the other leg. Ideally, a prosthesis should provide support to aid in balance, allowing for a
smooth transition. At the end of push off, rapid knee flexion occurs, allowing the foot to clear the
ground and the swing phase to begin. A spring action in the toes of a prosthesis can facilitate this
rapid knee flexion [3].
SACH Foot Design. During heel strike, the cushioned heel of a SACH foot, shown in Figure 8a,
helps to absorb the impact of the heel hitting the ground and controls the rate of plantar flexion.
SACH feet are available in a variety of heel stiffnesses that depend on the weight of the user and
the need for stability. The softer the heel, the faster the user is able to reach the stable foot flat
position. The rigid keel of the foot controls the transition of the tibia (the pylon) from posterior to
22
anterior of the ankle. The keel continues to offer resistance until the toe break is reached. In a
SACH foot, the toe break is located at the end of the keel. Belting helps to control the dorsiflexion
of the toes, allowing the tibia to progress smoothly. At this phase of loading, the toes offer very
little support. At the end of toe off, the belting provides a small spring action of the toes to aid in
knee flexion.
Single-Axis Foot Design. The rubber heel of the foot shell and the plantar flexion bumper of a
typical single-axis foot, shown in Figure 8b, absorb the initial impact occurring at heel strike and
control the rate of plantar flexion. Similar to the heel of the SACH foot, the bumper(s) are
available in a variety of stiffnesses. The stiffness of the bumper(s) depends on the user’s weight
and the need for stability. The softer the bumper, the faster foot flat is reached. If present, the
dorsiflexion bumper controls tibia advancement. Once the dorsiflexion bumper is fully
compressed, heel off begins. For feet without a second bumper, the dorsiflexion stop transfers the
forces to the foot. Once the stop is engaged, heel rise begins. At this point, the front of the keel
acts as a rocker, and toe dorsiflexion begins. The toe break is located at the end of the keel and
behaves in a manner similar to the SACH foot. Dorsiflexion of the toes is controlled by belting.
At the end of toe off this provides a small spring action of the toes to aid in knee flexion.
Multi-Axis Foot Design. Multi-axis feet, with multi-directional hinges, shown in Figure 8c,
function in a manner similar to single-axis feet. The ball and stem style of multi-axis feet, such as
the Multiflex, shown in Figure 8d are more complex. Shock absorption is provided by the
compression of the rubber ball against the walls of the ankle stem and the O-ring compressed by
the ankle stem and the foot. These components continue to compress, controlling the rate of
plantar flexion. The O-ring is available in a variety of stiffnesses so this rate of plantar flexion can
23
be customized to the needs of the patient. During midstance, the ball and O-ring compress either
medially or laterally in addition to anteriorly to allow for eversion or inversion. The foot is
capable of limited rotation; thus reducing the rotational torque transmitted to the residual limb.
The advancement of the tibia continues until the ball is fully compressed. At this point, heel off
begins. The toe break is located at the end of the keel. As the heel rises, the edge of the keel acts
as a pivot and the toes begin to dorsiflex. The toes provide a small spring action that encourages
the knee to flex as the limb enters swing phase.
Dynamic Energy Return Foot Design. There are dozens of different designs of DER feet. Some,
like the Impulse®, shown in Figure 10, are composed of one unit. In the Impulse® design the keel
is incorporated in the rest of the foot, and it has a cushioned heel that behaves very similarly to a
SACH foot on heel strike. Other feet like the Flex Foot™, shown in Figure 8e, have a keel and a
separate cover. The keel has a distinct heel region that deflects under the weight of the user,
absorbing the impact of the heel striking the ground [3, 21]. Both plantar flexion and the
progression of the tibia are controlled by the keel; as the tibia progresses the keel deflects. The toe
section of the foot begins to dorsiflex as the point of contact moves to the forefoot. Unlike a
SACH foot, the keel extends into the toes; this longer keel provides greater stability. As the body
weight is transferred to the other limb, the keel begins to unload and return to its original shape.
Note that this action is controlled by the elasticity of the elements.
The Niagara Foot™, shown in Figure 9a, is a single-axis DER foot. It does not have a hinge or the
bumpers normally associated with single-axis feet. Instead, movement of the C-section allows for
ankle articulation and aids in propulsion of the limb. During heel loading, the gap between the
horns and the top plate increases. Upon toe loading, the horns slide across the underside of the
24
plate, causing the C-section to wind. The College Park Industries TruStep™, shown in Figure
9b, is a multi-axis DER foot. The split toe allows for eversion and inversion. Bumpers on the heel
and midsection of the foot help to control dorsiflexion and plantar flexion [20]. As the keel of a
DER foot unloads, it provides a push off and helps to start the swing phase.
Figure 10: The Ohio Willow Wood Impulse® has a composite heel plate attached to a Kevlar® and nylon keel [22].
2.4 Alignment
Alignment refers to the position of the socket relative to the foot and is set by the prosthetist. It
has a strong influence on a patients’ comfort and their ability to have a smooth rollover during
stance. Patients’ natural gait, the characteristics of their prosthetic foot and the ability of the
residual limb to tolerate pressure all influence the prosthetist’s choice in three steps: bench
alignment, static alignment and dynamic alignment.
25
Bench alignment is undertaken in the prosthetist’s lab, before the patient has worn the prosthesis.
This alignment is based on the patient’s range of motion, strength, stability, and established
practice guidelines. The socket is flexed by 3°-5°, as shown in Figure 11. This helps to distribute
the load across the length of the tibia instead of the end of the limb, which is one of the more
pressure-sensitive areas.
Figure 11: Placing the socket in a vertical position, as shown on the left, loads the distal end of the residual limb. Flexing the socket slightly, as shown on the right, spreads the load over the length of the tibia [3].
26
During static alignment, the patient stands wearing the prosthesis for the first time. Fit of the
prosthesis and the patient’s ability to evenly distribute his/her weight across both limbs is
assessed. Limb length is evaluated to ensure that both limbs are equal length. A slight variation
can lead to lower back pain over time. The forces being applied to the knee are evaluated because
incorrect socket alignment can result in the patient feeling as if his/her knee is being forced into
flexion or extension. Any problems are addressed before the patient is allowed to walk for the
next phase of alignment.
The final step is dynamic alignment. The alignment of the foot relative to the socket has a
noticeable impact on the biomechanics of amputee gait. Shifting the foot in the sagittal plane
alters the point of contact of the foot with the floor. This changes the effective lever arm of the
heel and toe, altering both of their stiffnesses. The stability of the knee is also affected. Shifting
the foot anteriorly increases the time spent with the knee extended, while shifting the foot
posteriorly increases the time spent with the knee flexed. Changing the angle of the foot affects
the maximum knee extension moment occurring during the latter half of stance. Plantar flexing
the foot increases the knee extension moments, whereas dorsiflexing the foot decreases it.
Changes in the angle of the foot also increase the mean oxygen consumption rate during gait,
especially at higher walking speeds [9].
2.5 Assessing Patient Performance
The design of the components as well as the manner in which they are aligned affects patient
performance. This can be reflected in a number of measurable parameters, including oxygen
consumption, joint motion, forces and moments, as well as patient satisfaction.
27
2.5.1 Physical Measurements
An important functional outcome of an amputee being fit with a prosthesis is the degree of
mobility attained. This level of mobility is heavily dependant on the biomechanical characteristics
of the prosthetic foot [18]. Biomechanical data are often collected and studied to determine what
if any impact different types of prosthetic feet have on various characteristics of gait. The most
commonly studied areas are stride characteristics, kinematics, kinetics, and energy expenditure.
Stride characteristics, such as self-selected walking velocity (SSWV), stride length and cadence,
have been studied at length in regards to amputee gait. An increase in any of these values is
viewed as a positive outcome [23]. Gait symmetry, the variations in the time that the sound limb
and the affected limb spend at each phase of gait, is also of interest [16].
Joint angles, specifically range of motion are also of interest when comparing the effect of various
prosthetic treatment strategies [23]. Knee flexion, in particular, is of interest. It is essential during
normal gait and found to decrease significantly during amputee gait [18].
Energy expended during gait is also frequently studied. Oxygen consumption or cost, heart rate
and respiration rate are all indicators of energy expenditure. These are all measures of efficient
propulsion, which is influenced strongly by foot design. An amputee will expend more energy
during gait than an able bodied individual; therefore prostheses that allow an amputee to expend
less energy during walking would indicate an improvement [23].
28
2.5.2 Self-reported Measures
User feedback obtained using self-reported measures can identify aspects of prosthetic function
and performance that might be overlooked in biomechanical analysis. Several methods can be
used to determine an amputee’s perceived performance and preference, ranging from descriptive
dialogue to self-reported questionnaires [23].
The most detailed analyses include numerical rating scales, such as the 20-point Borg rating of
perceived exertion, and can be adapted to reflect a variety of activities [24]. Amputees are asked
to rate specific activities and parameters, such as ascending and descending stairs, comfort and
ease of use. These data can be analyzed to determine statistical significance [23].
2.6 Relationship of Mechanical Characteristics to Performance
Studies have found that amputees prefer prosthetic feet that provide energy return over those that
do not [23-25]. However, findings of the biomechanical studies have been mixed.
Lehmann et al. [27, 28] found that there were no significant differences in the SSWV or energy
efficiency between amputees who used a SACH foot, a Seattle Foot™ and a Flex Foot™. Hafner
et al. [19] observed that trends in the published literature do indicate differences in gait and
improved performance when using a DER foot; however these trends are discounted because of a
lack of statistical significance due in part to small sample sizes and variations in the subject
populations. However these trends do appear in other studies. For example, Hsu et al. [25] found
that energy expenditure was lower when walking on a Flex Foot™ compared to a SACH foot. At
certain speeds, oxygen consumption was lower when using the C-Walk foot compared to a Flex
Foot™. The study also found that the SSWV improved when subjects used a Flex Foot™ or a C-
29
Walk™ foot. Macfarlane et al. [16] found that subjects were able to spend more time in single
support during the stance phase of the gait cycle when they used a Flex Foot™ compared to a
conventional SACH foot. The keel of the Flex Foot™ provided greater support while under
dorsiflexion allowing for a longer stride length. This allowed users wearing the Flex Foot™, to
take fewer steps while maintaining their walking speed; in addition, their trunk motion was
smoother and more uniform while walking with a Flex Foot™, indicating that there were some
biomechanical advantages to walking with a Flex Foot™ [16].
Structural properties, particularly structural stiffness, strongly influence the function of prostheses
because this affects deflection during loading [29]. In addition, when subjected to equivalent
loads, a softer system stores more energy than a stiffer one [30]. However, the concept of
structural stiffness of a prosthesis is complicated by the nature of loading and motion during gait
and such factors as the angle of force application and the displacement rate must be considered.
Geil [29] tested eleven different prosthetic feet to determine material and structural properties
including stiffness, as well as energy expended and returned upon loading and unloading. The feet
were plantar flexed at 12° and loaded at a displacement rate of 1mm/sec to a load of 800N.
Stiffness was approximated from the slope of the force deformation curve. The samples
consistently fell into one of four categories: most stiff, more stiff, less stiff, least stiff. However,
only the toe regions of the samples were tested, multiple pylon angles were not considered and the
forces applied did not reflect peak loading during gait.
Van Jaarsveld et al. [30] conducted a comprehensive study of nine different prosthetic feet with
and without shoes. The feet were loaded from -30° (dorsiflexion) to 35° (plantar flexion) in
increments of 1°. At each angle, a plate representing the floor was lowered onto the foot in 1mm
30
increments until a vertical force of 1000N or 35mm of deflection was reached. A relationship
between the pylon angles (angle of the pylon relative to the vertical) and the stiffness of the
prosthesis, as well as its energy return, was determined. While this provided a comprehensive
description of mechanical behaviour, the results did not relate to specific activities of daily living.
2.7 Summary
A variety of performance measures can be used to determine the effects of alignment and
prosthetic components on amputee gait. These measures include biomechanical data, user
preference and perceived difficulties while ambulating. Even with these measures, the
relationship between mechanical characteristics of prosthetic feet and performance is not well
understood. This is, in part, due to an inability to define these mechanical characteristics.
31
Chapter 3
Mechanical Characterization of Dynamic Energy Return Prosthetic Feet
3.1 Introduction
In recent years, there have been advances in the field of prosthetic foot design and materials, most
notably with the emergence of DER feet. These feet are designed to store energy at the beginning
of the gait cycle and return it later, helping to propel the limb forward [31]. SACH feet were one
of the first commercially available prosthetic feet, and they continue to be used to this day [3]. For
this reason, SACH feet are often used as a benchmark to compare new designs.
During heel strike, the cushioned heel of a SACH foot helps to absorb the impact of the heel
hitting the ground and controls the rate of plantar flexion. SACH feet are prescribed in a variety of
heel stiffnesses, depending on the weight of the user and the need for stability. The softer the heel,
the faster the user is able to reach the stable foot-flat position. The rigid keel of the foot controls
the transition of the tibia going from posterior to anterior of the ankle. The keel continues to offer
resistance until the toe break is reached. In a SACH foot, the toe break is located at the end of the
keel. Belting that connects the keel and toe regions helps to control dorsiflexion of the toes,
allowing the tibia to progress smoothly. At this point, the toes offer little support. At the end of
toe off, the belting provides a limited spring action of the toes to aid in knee flexion.
Many single-axis and multi-axis foot designs use a variety of similar features to control motion
[3].
Dynamic energy return feet have features specifically designed to store and release energy, in
addition to controlling motion [3]. The Ohio Willow Wood Impulse® Foot is a single-unit design
32
in which the keel is incorporated into the rest of the foot. Although this design has a cushioned
heel that is similar to a SACH foot on heel strike, the keels are made of an elastic polymer. On
other feet such as the Flex Foot™, the Otto Bock® C-Walk™, and the Niagara Foot™, the keel
and cover are separate pieces. The keel has a distinct heel region that deflects under the weight of
the user, absorbing the impact of striking the ground [3, 21]. Plantar flexion and the progression
of the tibia are also controlled by the keel. As the tibia progresses, the keel deflects and the toe
begins to dorsiflex as the point of contact moves to the forefoot. As the body weight is transferred
to the other limb, the keel begins to unload and return to its original shape, providing a push off to
start the swing phase.
Studies have found that amputees prefer prosthetic feet that provide energy return over those that
do not [24-26]. However, the biomechanical studies investigating these findings have been mixed.
Lehmann et al. [26, 27] found that there were no significant differences in the self-selected
walking velocity or energy efficiency between amputees who used a SACH foot, a Seattle Foot™
or a Flex Foot™. Hafner et al. [19] observed that trends in the published literature do indicate
differences in gait and improved performance when using a DER foot; however, these trends are
discounted because of a lack of statistical significance in part due to small sample sizes and
variations in the subject populations. These trends do, however, appear in other studies. For
example, Hsu et al. [25] found that energy expenditure was lower when walking on a Flex Foot™
compared to a SACH foot. At certain speeds, oxygen consumption was lower when using a C-
Walk foot compared to a Flex Foot™. The study also found that self-selected walking velocity
improved when a subject used a Flex Foot™ or a C-Walk foot. Macfarlane et al. [16] found that
subjects were able to spend more time in single support during the stance phase of the gait cycle
when they used a Flex Foot™ compared to a conventional SACH foot. The keel of the Flex
33
Foot™ provided greater support while under dorsiflexion, allowing for a longer stride length. This
allowed users to take fewer steps while maintaining their walking speed. In addition, their trunk
motion was smoother and more uniform while walking with a Flex Foot™, indicating that there
were some biomechanical advantages to walking with a Flex Foot™ [16].
Structural properties, particularly structural stiffness, strongly influence the function of
prostheses since this affects deflection during loading [29]. In addition, when subjected to
equivalent loads, a softer system stores more energy than a stiffer one [30]. However, the concept
of structural stiffness of a prosthesis is complicated by the nature of loading and motion during
gait. Factors such as the angle of force application and the displacement rate must be considered.
Geil [29] tested eleven different prosthetic feet to determine material and structural properties
including stiffness as well as energy expended and returned upon loading and unloading. The feet
were plantar flexed at 12° and loaded at a displacement rate of 1mm/sec to a load of 800N.
Stiffness was defined as the slope of the force deformation curve. The samples consistently fell
into one of four categories: most stiff, more stiff, less stiff, least stiff. However, only the toe
regions of the samples were tested, multiple pylon angles were not considered, and the forces
applied did not reflect peak loading during gait.
Van Jaarsveld et al. [30] conducted a comprehensive study of nine different prosthetic feet with
and without shoes. The feet were loaded from -30° (dorsiflexion) to 35° (plantar flexion) in
increments of 1°. At each angle, a plate representing the floor was lowered onto the foot in 1mm
increments until a vertical force of 1000N or 35mm of deflection of was reached. A relationship
between the pylon angles (angle of the pylon relative to the vertical) and the stiffness of the
34
prosthesis as well as their energy return was determined. While this provided a comprehensive
description of mechanical behaviour, the results did not relate to specific activities of daily living.
A standardized waveform for prosthetic gait has recently been published by the International
Organization for Standardization (ISO) in their updated standards for the testing of ankle-foot
devices and prosthetic feet (ISO 22675). The document outlines a cyclic durability testing
procedure for lower limb prosthetic devices [32]. Although the waveform was not proposed as a
general description of prosthetic loading conditions, it is a practical testing regime designed to
simulate conditions during the stance phase of prosthetic gait.
The waveform is shown in Figure 12, in which test forces and tilting angle of the loading platform
are plotted as functions of time. (ISO 22675, Figure 6). Time can be related to the percentage of
gait cycle by assuming that each cycle takes one second and the stance phase of gait accounts for
600 msec or 60% of the overall cycle. The three different loading levels, P3, P4 and P5, represent
the vertical ground reaction forces during stance. The P3 and P4 loading curves are based on gait
data of amputees whose masses were less than 60 kg and 80 kg respectively; the P5 loading curve
is based on all the data including some subjects whose masses were over 100kg. Note that the
initial impact peak, evident in Figure 5, is not reflected in the waveform. This feature is generally
omitted in testing unless the high-frequency response of the device is of interest. The tilt angle is
comparable to the pylon angle relative to the vertical during gait.
The objective of this study was to use the ISO standardized waveform as a basis for determining
mechanical properties of the heel and toe regions of prosthetic feet. It is proposed that force-
displacement testing be conducted on the heel and toe at pylon angles corresponding to the tilt
angles in the ISO 22675 testing protocol. The samples were loaded to peak loads based on their
35
design masses (the maximum recommended user mass) at a series of different angles and forces
that would occur during the gait cycle.
Time (sec)
Forc
e (N
)A
ngle ((Degrees)
tilt angle
P5
P4
P3
TiltAngle
Time (msec)
Angle (D
egrees)Fo
rce
(N)
Time (sec)
Forc
e (N
)A
ngle ((Degrees)
tilt angle
P5
P4
P3
TiltAngle
Time (msec)
Angle (D
egrees)Fo
rce
(N)
Figure 12: Testing waveforms from ISO 22675 outlining the tilting angle and test profiles for the P3, P4 and P5 loading levels for cyclic fatigue testing. Adapted from ISO 22675 [32].
36
3.2 Critical Points
To approximate the loading conditions represented in Figure 12, fifteen critical data points were
extracted from the P4 loading curve. Based on the tilting angle, force and corresponding time
values were extracted in 5° increments for angles of -20° to 0° for the heel and 0° to 35° for the
toe. These data, shown in Figure 13 and Table 2, also included whether the component was being
loaded or unloaded at the identified point. If the extracted force was higher than the force value at
the previous time, loading was occurring. This distinction is important due to the energy lost
when unloading a component; at the same displacement, a lower force exists when unloading the
structure compared to loading it. To scale the data, a multiplier at each critical point was
determined by dividing the force at that point by the design mass, in this case 80kg.
One adjustment was required to facilitate a practical testing protocol. Initial contact of the heel
occurs at -20°; at this point, both time and force are equal to zero. A rapid increase in loading of
the heel occurs from this initial contact until a pylon angle of -15° is reached, as a result there are
few data points during heel loading. In order to have data for two angles during heel loading, data
were extracted from the graph at -19.5°.
37
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600
Time (msec)
Forc
e (N
)
-30
-20
-10
0
10
20
30
40
50
Ang
le (D
egre
es)
LoadAngle
1
2
3
4
5 6
7
8 9
1011
12
13
14
15
Figure 13: Fifteen critical points extracted from ISO 22675 as functions of time. Negative angles indicate dorsiflexion and positive ones plantar flexion.
38
Table 2: Data extracted from the P4 test loading level curve, show in Figure 12. Negative angles indicate dorsiflexion and positive ones plantar flexion.
Section Point Number
Time (msec)
Angle (°)
Loading Direction
Force (N)
Multiplier(m/s2)
1 0 -20 Loading 0 0 2 36 -19.5 Loading 354 4.4 3 150 -15 Loading 1173 14.7 4 212 -10 Unloading 983 12.3 5 260 -5 Unloading 821 10.3
Heel
6 300 0 Unloading 785 9.8 7 300 0 Loading 785 9.8 8 337 5 Loading 831 10.4 9 372 10 Loading 885 11.1
10 408 15 Loading 1100 13.8 11 450 20 Loading 1173 14.7 12 487 25 Unloading 1062 13.3 13 522 30 Unloading 769 9.6 14 560 35 Unloading 392 4.9
Toe
15 600 40 Unloading 0 0
3.3 Methods
Force-deflection testing was conducted using an Instron™ 5500 series material testing machine
with a 5kN load cell and Merlin Version 4.3 Software at a sampling rate of 4Hz. Initial testing
showed that the sample feet had minimum time constants in the order of three seconds and as
such a sampling rate of 4Hz was sufficient to capture the behaviour of the prostheses while
providing manageable quantities of data.
Three designs of feet were tested to span the range of designs of interest: a standard SACH foot,
two energy return feet for active users and a new prosthetic foot designed to provide partial
energy return. Four different components were evaluated: an Otto Bock® SACH foot, two Otto
39
Bock® Axtion™ feet and a Model 2 Version 18 Niagara Foot™ made of Hytrel®, as described in
Table 3. All tests were conducted without footwear or covers.
Table 3: Specifications of the sample feet tested
Sample Manufacturer Length (cm)
Maximum Recommended User Mass (kg)
Notes Heel
Height (mm)
Model 2 Version18 Niagara Foot™
Niagara Prosthetics and Orthotics
25 80 kg Adapter Connection 13
Axtion™ Otto Bock® 26 106 kg Standard Pylon 13
Axtion™ Otto Bock® 26 124 kg Standard Pylon 13
SACH 01763 Otto Bock® 25 100 kg Standard Pylon 20
The SACH foot, such as the one shown in Figure 14a, is composed of a wooden or rigid plastic
keel, a cushioned heel and it has a rubber shell that is integrated into the foot. This style of foot is
targeted to less active amputees who require greater stability [3]. The Axtion™ keel, as shown in
Figure 14b, is composed of two layers of a carbon fiber composite joined by an elastomeric layer;
it has distinct heel and toe regions and is designed for active amputees [33]. Two feet of different
stiffnesses were examined. The Niagara Foot™ keel, shown in Figure 14c, is a single component
3 An older SACH foot was tested. It was the same length and had the same weight limit as the Otto Bock®
1S37 SACH Foot.
40
made of Hytrel® with distinct heel and toe regions; a C-shaped region at the top of the foot
mimics ankle articulation [34].
(a) (b) (c)
Figure 14: (a) SACH foot, (b) Axtion™ keel [33] and (c) the Niagara Foot™
A pylon or comparable adapter was attached to the sample feet and aligned according to the
manufacturers’ specifications. For the feet that required the use of a pylon, the heel of the foot
was raised by the specified heel height. A pylon was then attached to the foot and a laser level
was used to ensure that the pylon was vertical. For feet that had a smooth, flat interface, an
adapter was used, consisting of a rectangular section of steel with the threaded hole in the centre
welded to a piece of square steel tubing.
Once the foot was attached to the pylon or adapter, it was placed in a machine vice and a clamp
was used to secure the pylons in the vice. A series of gauge blocks were used to set the machine
vice to the desired angle within 0.1°. The assembly was placed in the testing machine and fixed to
the base plate using step clamps as shown in Figure 15. A flat platen, 14.6 cm in diameter, was
used to load the heel and toe. To reduce the effects of contact friction, a thin layer of silicone-
top plate
horns
C-sectionelastomeric layer
41
based spray was applied to the sample feet whose soles were smooth. In those with textured soles,
a 0.8mm thick layer of Teflon® sheet provided an interposing layer between the specimen and the
platen.
Figure 15: Test configuration, (a) testing rig in the Instron™ testing machine, (b) clamps and gauge blocks.
The samples were loaded to a peak force equal to the product of their design mass and their peak
multiplier, shown in Table 2, to within 4%. A displacement rate of 2.0mm/sec was used.4
4 The displacement rate was selected based on the results of a pilot of three Model 2 Version 18 Niagara
Feet™ loaded at different displacement rates, as described in Appendix A.
(a) (b)
42
The samples were preconditioned by loading them cyclically 10 times at each critical angle. The
order of tests was randomized between pylon angles and at least five minutes elapsed between
each successive test. To determine test precision, the Model 2 Version 18 Niagara Foot™
underwent the testing protocol on three separate occasions; a maximum of one testing protocol
was conducted per day.
It should be noted that the testing on the Otto Bock® Axtion™ with a maximum recommended
user weight of 106kg at a pylon angle of 35° could not be completed due to slippage within the
system. The adhesive was not able to resist the shear forces that occurred at this angle. As a result
the Teflon® film began to peel of during loading.
3.4 Data Analysis
A typical force displacement curve is shown in Figure 16, showing ten cycles of the Model 2
Version 18 Niagara Foot™ toe loaded to 1173N at an angle of 20°. Note the peak displacement
increasing with each successive cycle.
Data were collected and analyzed according to the steps outlined in Figure 17 for each pylon
angle. The RAW data files from the force-displacement tests were first imported into Microsoft
Excel. To determine the cycle at which the preconditioning was complete, the peak displacements
reached during loading were plotted against time. A typical plot is shown in Figure 18. The
differences between the peak loads for each subsequent cycle were also plotted against time, as
shown in Figure 19. The cycle at which this difference reached a steady state determined when
the specimen was preconditioned. One preconditioned cycle was selected for each of the samples;
data collected during this cycle was parsed and analyzed.
43
Data collected during the transition from loading to unloading were removed and force values
below 0.15N were also disregarded. The origin of the force displacement curve was defined by
linear extrapolation of the first two data points to determine the x-intercept, as outlined in
Appendix B. Similarly, small overshoots in the peak force were adjusted.5
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35 40 45
Displacement (mm)
Forc
e (N
)
Figure 16: Typical force displacement curve of a toe region loaded to 1173N at a pylon angle of 20°.
5 This target force value was generally overshot by 0.04% to 0.43%. As such, the displacement that
occurred was estimated using linear interpolation, as outlined in Appendix B; all data collected after that
point were disregarded.
44
Store as a .RAW file
Import to Excel
Plot Force vs. Disp.
Data Collection
Determine Tangential Stiffness
Adjust Force Data
Determine Steady State Response
1. Peak Displacement vs. Time
2. First Difference vs. Time
Select Pre-Conditioned
Cycle
Parse Data
Offset Compensation
1. Determine Origin Offset
2. Adjust
Loading Unloading
Determine Displacement and
Tangential Stiffness at Critical Force
Plot
Figure 17: Overview of the data analysis process.
Shown in Figure 19
Shown in Figure 18
Shown in Figure 16
Shown in Figure 24
45
37.4
37.6
37.8
38
38.2
38.4
38.6
38.8
39
0 50 100 150 200 250 300 350 400
Time (sec)
Pea
k D
ispl
acem
ent (
mm
)
Figure 18: Peak displacements that occurred as a function of time.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 50 100 150 200 250 300 350 400
Time (sec)
Firs
t Diff
eren
ce
Figure 19: First difference between peak displacements as a function of time.
46
The Instron™ material testing machine was programmed to load the feet to a force equal to the
product of their design massess times the multiplier shown in Table 2. For each point of interest,
the tangential stiffness was calculated from the force-displacement data using the first central
difference method. For the first and last data points in a given set, the first forward and first
backward difference method were used respectively.
3.5 Results and Discussion
Test Precision. For the Model 2 Version 18 Niagara Foot™, the average displacement and
stiffness values for the three test runs at each of the critical points were calculated. The coefficient
of variation (COV) and the standard deviation (SD) were also determined. High precision was
found with average SD and COV of 0.72mm and 4.34% for the displacement and 13.36 kN/m and
6.39% for the stiffness. Measurement errors compounded when calculating stiffness values likely
resulted in the larger SD and COV values observed. Based on these results, it was concluded that
one testing run would be sufficient to characterize the other samples.
Typical Results. Typical force-displacement and stiffness-displacement curves for the heel and
toe are shown in Figure 21 and Figure 22, respectively. There is a non-linear relationship between
the force and displacement values in which the stiffness of the heel and toe increases as the
applied load increases. A sudden drop in displacement values occurs as the toe begins to unload at
angles of 25°, 30° and 35°. This is likely due to friction internal to the system and is consistent
with the design of the Niagara Foot™ in which sliding occurs between the horns and the top plate
noted in Figure 20. This drop in displacement results in uncharacteristically high stiffness values
during the unloading of the toe. The pylon angle at which the feet were loaded also affected their
stiffness. As the pylon angle increases, the stiffness values decrease. These observations are
consistent with the location of the point of contact between the foot and the platen. The point
47
moves anteriorly as testing progresses, as shown in Figure 20. This causes the length of the
moment arm to decrease and the measured stiffness to increase. This effect is also noted with
pylon angle: as the pylon moves away from the vertical, the contact point moves posterior on the
heel or toe, increasing the lever arm. This results in a softer response. A complete data set is
shown in Appendix C.
(a) (b) (c)
Figure 20: The contact point between the heel and the platen at displacements of (a) 0mm, (b) 4mm and (c) 8mm. Note the sliding contact between the horns and top plate.
48
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12 14 16
Displacement (mm)
Forc
e (N
)
0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50
Displacement (mm)
Forc
e (N
)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 21: Force-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
49
0
100
200
300
400
500
600
700
800
0 5 10 15
Displacement (mm)
Stif
fnes
s (k
N/m
) 0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
50
100
150
200
250
300
0 10 20 30 40 50 60 70 80
Displacement (mm)
Stiff
ness
(kN/
m)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 22: Stiffness-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
50
Stiffness is derived by differentiating the displacement data, therefore small discrepancies in the
displacement can lead to anomalies in the stiffness values. The noise in the toe stiffness data at the
angle of 30° is likely due to the two slips evident in the corresponding displacement curve at 900
N and 1100 N. The sudden drop in force values during unloading of the toe corresponds to the
high stiffness values at this point. Future consideration could be given to numerical smoothing
methods for stiffness data when this mechanical behaviour is well understood.
Behaviour of the prostheses can be predicted by extracting data from the force-displacement and
stiffness-displacement curves corresponding to the critical points. For example, to determine the
predicted displacement of the heel of the Niagara Foot™ at -15°, as shown in Figure 23c, the
force the heel was expected to experience was first extracted from the load waveform in Figure
23b (1173N). Note that Figure 23b is reproduced from Figure 13. Next, the displacement
occurring at this force was extracted from the -15° force displacement curve, as shown in Figure
23a. Note that this is for heel loading in this case, because it occurs in this portion of the gait
cycle. Finally, this displacement and the corresponding time (from Figure 23b) are plotted on a
single graph, Figure 23c. The process is repeated for all fifteen critical points.
51
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Time (msec)
Dis
plac
emen
t (m
m)
HeelToe
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12 14 16
Displacement (mm)
Forc
e (N
)
0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600
Time (msec)
Forc
e (N
)
-30
-20
-10
0
10
20
30
40
50
Ang
le (D
egre
es)
LoadAngle
1
2
3
4
5 6
7
8 9
1011
12
13
14
15
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Time (msec)
Dis
plac
emen
t (m
m)
HeelToe
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12 14 16
Displacement (mm)
Forc
e (N
)
0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600
Time (msec)
Forc
e (N
)
-30
-20
-10
0
10
20
30
40
50
Ang
le (D
egre
es)
LoadAngle
1
2
3
4
5 6
7
8 9
1011
12
13
14
15
Figure 23: Predicting displacement and stiffness profiles of prostheses during gait, (a) force-displacement curves for the heel of the Model 2 Version 18 Niagara Foot™, displacement occurring at 1173 N is highlighted, (b) critical points extracted from ISO 22675 as functions of time, predicted force occurring at a pylon angle of -15° is highlighted, (c) predicted displacement profiles of the prosthesis during gait.
.
The predicted displacement and stiffness values of the Niagara Foot™ are plotted as functions of
time in Figure 24 and Figure 25 respectively. When the heel is first loaded in this sample, a
displacement of 8.5 mm occurs at 36 msec, which corresponds to an angle of -19.5° and a force of
354 N. The displacement remains approximately constant until the heel begins to unload at 150
msec, which corresponds to an angle of -15° and a force of 1173 N. At this point, the
displacement at the critical forces continues to decrease. As shown in Figure 25, the heel stiffness
at the critical forces increases steadily as the pylon angle approaches the vertical at a time of 300
(a) (b)
(c)
52
msec. This is expected due to the decrease in lever arm as the contact point between the heel and
the platen moves anteriorly.
At 300 msec, the pylon angle is 0° and the foot is supported by both the heel and toe. Assuming
that the force is instantaneously transferred to the toe, a displacement of 15.4 mm is predicted in
Figure 24. This displacement continues to increase even after the toe begins to unload at 500
msec, which corresponds to an angle of 25° and a force of 1062 N. As shown in Figure 25, the
stiffness of the toe increases sharply at this point and then steadily decreases as the pylon angle
continues to decrease.
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Time (msec)
Disp
lace
men
t (m
m)
HeelToe
Figure 24: Predicted displacements of the Niagara Foot ™ during gait based on the waveform in Figure 12.
53
0
100
200
300
400
500
600
700
0 100 200 300 400 500 600 700
Time (msec)
Stiff
ness
(kN/
m)
HeelToe
Figure 25: Predicted tangential stiffness values of the Niagara Foot™ during gait based on the waveform in Figure 12.
Comparison of Designs. In order to compare designs, displacement and stiffness values were
normalized against the maximum recommended user mass. These normalized values are plotted
as functions of time for all four designs in Figure 26 and Figure 27.
The heel region of the SACH foot experienced the highest displacements and had the lowest
stiffness values. The heel compressed quickly during loading and the level of compression was
constant. This indicated foot flat was reached early on in the gait cycle. The SACH toe was stiffer
than the three other samples. This is consistent with the SACH design in which the toe acts as a
rocker. In contrast, the DER designs flex upon toe loading.
The heel and toe of the two Axtion™ feet had very similar displacement profiles, which is
consistent with two feet having the same design. It is likely that the absolute values of
54
displacement and stiffness are simply scaled by mass in this product. Compared to the SACH, the
heels were two-and-a-half times stiffer, while the toes were 63% softer. There were notable
differences in the heel stiffness. These can likely be attributed to small differences in the heel
displacements because the errors in stiffness are compounded in differentiation.
The toe of the Niagara Foot™ had the highest peak stiffness values despite having the highest
peak displacement values. From 350 msec-450 msec the stiffness values are constant. During this
period, the horns of the foot are sliding across the top plate. If at 450 msec the sliding stops, this
would effectively stiffen the toe. The sudden drop in displacement during unloading shown in
Figure 21 could have also contributed to the high stiffness values. The high displacement values
indicate that overall the toe region of the Niagara Foot™ is soft compared to other designs, which
has been confirmed by patients in field trials [35]. The toe region of the Niagara Foot™ also
reached its peak displacement later in the gait cycle than the Axtion™. The difference in the
timing of the peak displacements is likely due to geometric differences in the feet. The Axtion™
has heel and toe levers as does the Niagara Foot™; however, the Niagara Foot™ has a C-section
that allows for ankle articulation.
The toe region of all the feet had greater displacements than the heel at a pylon angle of 0°. The
Axtion™ feet had the smallest displacement gap between the heel and toe at this angle, whereas
the SACH foot had the largest gap. During gait at a pylon angle of 0°, the foot would be in
midstance. During testing at this angle, the heel of the Niagara™ and Axtion™ Feet were found
to be much stiffer than the toe. This difference could aid in a smoother transition from heel to toe
loading. In contrast, the heel and toe stiffness values of the SACH foot were found to be similar,
suggesting greater stability for the user.
55
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400 500 600 700
Time (msec)
Norm
aliz
ed D
ispl
acem
ent (
mm
/kg)
Niagara FootAxtion 106kgAxtion 124 kgSACH
Figure 26: Normalized displacements occurring at the critical forces identified for all the sample feet.
56
0
1
2
3
4
5
6
7
8
9
0 100 200 300 400 500 600 700
Time (msec)
Norm
aliz
ed S
tiffn
ess
(kN/
m-k
g)Niagara FootAxtion 106kgAxtion 124kgSACH
Figure 27: Normalized tangential stiffness values occurring at the critical forces identified for all the sample feet.
These trends indicate feet designed for stability, such as the SACH, have soft heels and stiffer
toes. The softer heel allows the user to reach foot flat quickly, a position of stability. Furthermore
the toe is stiffer than the DER feet; this is consistent with it acting as a rocker late in stance.
The stiffness profile of the DER Axtion™ design was the opposite of the SACH foot. The trends
indicate that DER feet have stiff heels and soft toes. It is likely that the stiffer heel allows for a
smooth rollover from heel to toe. When subjected to equivalent loads, a softer system stores more
energy than a stiffer one [30], thus the lower toe stiffness values may provide a greater spring
action than a SACH foot at the end of stance. As the keel unloads, it provides a push off and helps
to start the swing phase.
57
The performance of the Niagara Foot™ indicates that it is an intermediate foot, having traits of
both the SACH and DER feet. The heel is quite stiff, experiencing displacements lower than the
Axtion™. Initially the toe has approximately the same stiffness as the Axtion™ feet, but it
becomes increasingly stiff as gait continues.
3.6 Conclusions
A method had been presented by which the mechanical properties of prosthetic feet can be
evaluated based on the standard loading waveform of ISO 22675. The stiffness characteristics and
displacement profile of the SACH, Axtion™ and Niagara Foot™ were consistent with their
design features, indicating that the testing protocol is able to capture the mechanical
characteristics of these designs and to detect differences in function.
This methodology could be used to classify new designs of feet based on prostheses whose
mechanical properties are well understood, such as the SACH and the Flex Foot™.
58
Chapter 4
Force Relaxation Properties of Dynamic Energy Return Feet
4.1 Introduction
Many prosthetic foot designs are intended to match the mechanical characteristics of the device to
the needs and physical demands of the user [18]. Interestingly, user preference is not always
reflected in biomechanical performance or physiological measures, such as gait characteristics or
energy expenditure [23]. This suggests that the relationship between mechanical properties of
prosthetic feet and user preference is not well defined. This may be due, in part, to a need to
improve methods of characterizing the mechanical properties of these devices. It is particularly
necessary to address factors associated with the non-linear structural response and time
dependency of the materials used in fabrication.
There are a number of approaches to determining the mechanical properties of prosthetic feet
including finite element analysis (FEA) and structural testing. FEA can be used when material
properties, loading, and boundary conditions are well defined. These methods can provide a
complete prediction of the force, deformation, stress and strain responses of the system, and have
distinct advantages in design optimization [36]. However, this approach also requires the
establishment of design objectives for the structural response of the system under varying loading
conditions. In order to provide these data, structural testing is required.
The structural response of a prosthetic foot can be defined in terms of displacements resulting
from the application of loads corresponding to vertical ground reaction forces. If loading
conditions are consistent with activities of daily living, this response can provide a robust method
for describing mechanical characteristics of a prosthesis.
59
Geil [29] tested eleven different prosthetic feet to determine material and structural properties,
including stiffness and energy expended and returned upon loading and unloading. The feet were
plantar flexed at 12°, loaded at a displacement rate of 1mm/sec to a load of 800N. Stiffness was
estimated based on the slope of the force deformation curve. The samples consistently fell into
one of four categories: most stiff, more stiff, less stiff, least stiff. However, only the toe region
was tested, multiple pylon angles were not considered and the forces applied did not reflect peak
loading values during gait.
Van Jaarsveld et al. [30] conducted a comprehensive study of nine different prosthetic feet with
and without shoes. The feet were loaded from -30° (dorsiflexion) to 35° (plantar flexion) in
increments of 1°. At each angle, a plate representing the floor was lowered onto the foot in 1mm
increments until a vertical force of 1000N or 35mm of deflection was reached. A relationship
between the pylon angles (angle of the pylon relative to the vertical) and the stiffness of the
prosthesis, as well as their energy return, was determined. While this provided a comprehensive
description of mechanical behaviour, the results did not relate to specific activities of daily living.
Time dependencies of the mechanical response have been investigated in terms of impact
response and viscoelastic modeling. Klute et al. [37] studied the initial impact of the heel region
of seven prosthetic feet. Feet were modeled as non-linear springs in parallel with position-
dependent dampers and experimental data were collected using a pendulum striking the heel at a
velocity of 0.4m/s. Although the model was able to predict the energy dissipation to within 6%, it
was less applicable as a generalized model under other loading conditions. As such, it is necessary
to develop models for the structural response of prostheses in situations other than at impact.
60
Based on a previous study, Geil [38] used a three-parameter model to examine the stiffness and
dampening properties of the toe region of eleven prosthetic feet. The approach was successful
when predicting linear mechanical responses; however, it had limited success when non-
linearities were dominant.
A recognized strategy to address the presence of structural non-linearities is to separate the time
dependency from the elastic properties. Haberman et al. [39] approached this by identifying
loading regimes for prosthetic feet that isolated the elastic characteristics from the time-dependent
response. This quasi-linear method allowed for non-linearities in the force-displacement response
to be quantified and facilitated the comparison of different foot designs.
The purpose of this study was to develop an appropriate model of the time-dependant properties
for these devices. Two viscoelastic models were examined: a standard three-parameter solid
model and one with a linear decay term included.
4.2 Theory
Fung introduced the concept of a time-dependent, quasi-linear, stress-relaxation function, K(λ,t),
for biological materials,
),()(),( )( λλ eTtGtK = where ,1)0( =G (1)
where λ is the elongation and t is time. G(t) is a normalized function of time called the reduced
relaxation function, and )()( λeT is the elastic response of the material [40].
61
The structural analogy of a stress-relaxation function can be determined using force-relaxation
testing, in which a step displacement is applied and the force response measured. In practice, a
step displacement is rarely achieved, so a high displacement rate is used until a predetermined
force or displacement is measured. A typical force response is shown in Figure 28, in which the
toe region of a sample component was displaced at a rate of 3.25mm/sec until a peak load of
1173N was attained. The displacement was then held constant and the force recorded for an
additional 90 seconds.
0
250
500
750
1000
1250
0 20 40 60 80 100 120
Time (sec)
Forc
e (N
)
Figure 28: Typical force response of the toe of a prosthetic foot. A displacement rate of 3.25mm/sec was applied until a peak load of 1173N was attained and the displacement was held constant for an additional 90 seconds. Specific data are for a Model 2 Version 18 Niagara Foot™.
62
The relaxation response can be isolated and then normalized against the peak force (F0=1173N) to
produce the reduced relaxation response, L(t), as shown in Figure 29. Thus,
,)()(0FtFtL = where .1)0( =L (2)
0.7
0.75
0.8
0.85
0.9
0.95
1
0 10 20 30 40 50 60 70 80 90 100
Time (sec)
L(t)
Figure 29: The solid line is the reduced relaxation response, L(t). The dashed line is the steady state response predicted by Equation 4.
Two functions were considered for L(t). Geil [38] used a three-parameter solid viscoelastic model
for prosthetic foot components consisting of a spring in series with a damper parallel to a second
63
spring. This leads to a reduced relaxation response which is a two-parameter equation of the form:
),exp()1()( τtAAtL −−+= (3)
where τ is a time constant, A is a constant and t is time in seconds.6 The constant, A, represents
the steady state value of the function when the exponential decay no longer dominates.
A second model was proposed for L(t), based on observations in pilot studies in which the force-
relaxation response did not achieve a constant steady state value. A linear decay term, Bt, was
added to L(t), such that
,)exp()1()( BttAAtL −−−+= τ (4)
where B is a constant, termed the decay coefficient. The term A in Equation 4 can be interpreted
by examining the response when the exponential decay no longer dominates. When the
exponential decay is removed the reduced relaxation response becomes L(t)=A-Bt, and is shown
as the dashed line in Figure 29. Note that A is the y-intercept and is defined as the initial decay. In
this case, A=0.83. To determine the effect of the linear decay term, the degree of fit between the
two models and experimental results was assessed on four test specimens.
6 Note that the number of parameters is reduced due to the normalization of the data.
64
4.3 Methods
Three styles of feet were tested to span the range of designs of interest: a standard SACH foot,
two energy return feet for active users and a new prosthetic foot designed to provide partial
energy return. They are detailed in Table 4.
Table 4. Specifications of the sample feet tested.
Sample Manufacturer Length (cm)
Maximum Recommended
User Weight (kg) Notes
Heel Height (mm)
Model 2 Version18 Niagara Foot™
Niagara Prosthetics and Orthotics
25 80 kg Adapter Connection 13
Axtion™ Otto Bock® 26 106 kg Standard Pylon 13
Axtion™ Otto Bock® 26 124 kg Standard Pylon 13
SACH 01767 Otto Bock® 25 100 kg Standard Pylon 20
SACH feet, such as the one shown in Figure 30a, are composed of a wooden keel, a cushioned
heel and they have a rubber shell that is integrated into the foot. This style of foot is targeted to
less active amputees who require greater stability. The Axtion™ keel, as shown in Figure 30b, is
composed of two layers of a carbon fiber composite joined by an elastomeric layer. It has distinct
7 An older SACH foot was tested. It was the same length and had the same weight limit as the Otto Bock®
1S37 SACH Foot.
65
heel and toe regions and is designed for active amputees. The Axtion™ keel can be placed in a
separate foot shell. Two feet of different stiffnesses were chosen to examine the sensitivity of the
reduced relaxation response to this parameter.
The Niagara Foot™ keel, shown in Figure 30c, is a single component made of a polymer and has
distinct heel and toe regions. A C-shaped region at the top of the foot mimics ankle articulation. It
can be worn with a separate cosmetic foot cover.
(a) (b) (c)
Figure 30: (a) SACH foot, (b) Axtion™ keel [33] and (c) the Niagara Foot™.
Testing parameters were selected based on peak loading conditions occurring during the gait
cycle as described by Haberman et al. [39]. The heel and toe were tested at angles of 15° and 20°
respectively. The product design mass (maximum recommended user mass) was multiplied by
14.7 to determine the maximum test forces, which correspond to the peak forces expected during
gait. Force relaxation testing was conducted using an Instron™ 5500 series material-testing
machine with a 5kN load cell and Merlin Version 4.3 Software with a sampling rate of 4 Hz.
top plate horns
C-sectionelastomeric layer
66
For the feet that required the use of a pylon, the heel of the foot was raised by the specified heel
height. A pylon was then attached to the foot and a laser level was used to ensure that the pylon
was vertical. For the Niagara Foot™, an adapter was used that consisted of a rectangular section
of steel with a threaded hole in the centre welded to a piece of square steel tubing.
Once the foot was attached, it was placed in a machine vice, and gauge blocks were used to set it
to the desired angle within 0.1°. The assembly was placed in the testing machine and was fixed to
the base plate using step clamps, as shown in Figure 31. A flat platen 5.75” in diameter was used
to load the feet.
Figure 31: Test configuration of (a) testing rig in the Instron™ and (b) clamps and gauge blocks used.
(a) (b)
67
To reduce friction between the sample and platen, a thin layer of silicone-based spray was applied
to the sample feet whose soles were smooth. A 0.8 mm thick piece of Teflon® film was attached
to the soles of the sample feet whose soles were textured or to the loading platen using a double-
sided adhesive tape.
The samples were loaded to their expected peak loads at a rate of 3.25 mm/sec. Once the peak
load was reached the platen position remained constant for 90 seconds and the resulting forces
recorded.
The data were first adjusted to obtain the reduced relaxation response as shown in Figure 29. The
parameters for Equations 3 and 4 were then determined by minimizing the squared residuals
between the models and the experimental data, using the Solver function in Microsoft Excel. The
RMS differences between the models and the experimental data were also determined.
For a quasi-linear model to be applicable, it is necessary for the reduced relaxation function to be
independent of force. A test for linearity was conducted using three Model 2 Version 14 Niagara
Feet™ made of Delrin™ ST. The heel regions of the samples were each loaded at a rate of
100mm/min on three separate occasions. They were each displaced until peak loads of 300N,
700N and 1200N were reached.
4.4 Results and Discussion
In the two-parameter model (Equation 3), τ is the time constant and A represents the steady state
value. As shown in Table 5, the time constant varied from 6-13 seconds; however, these values
did not capture the rapid decay in the early phase of the response. This is evident in the interval of
0 < t < 20s in Figure 32. In the latter phase of the response, the model fails to capture the decay
68
and instead approaches the steady state value, A. This is shown in the interval 50 < t < 90 in
Figure 32. In contrast, the three-parameter model of Equation 4 was able to capture the initial and
long-term features of the response. A complete data set is shown in Appendix D.
These differences are reflected in the RMS values found in Table 5. The average RMS values for
the Niagara Foot™ using the two-parameter model values were 0.0504 and 0.0080 for the heel
and toe respectively. For the three-parameter model, the average RMS values were 0.0067 and
0.0033 for the heel and toe respectively, providing improvements of 87% and 59% in the quality
of fit when the linear decay term was included in the model.
Similar results were observed for all feet tested as summarized in Table 5 and Table 6. Overall the
three-parameter model had RMS values 57% to 93% lower than the two-parameter one. The toe
regions of the Otto Bock® Axtion™ feet were modeled with the best fit, with the 106kg and
124kg Axtion™ toes having RMS values of 0.0007 and 0.0006 respectively. The heel and toe
regions of the SACH and the Model 2 Version 18 Niagara Foot™ were modeled with comparable
degrees of fit and had the highest RMS values.
69
0.7
0.75
0.8
0.85
0.9
0.95
1
0 20 40 60 80 100
Time (sec)
Forc
e (N
) Experimental2 Parameter3 Parameter
Figure 32: Force-relaxation response for the toe of the Model 2 Version 18 Niagara Foot™. Experimental data and curve fits are shown for a two-parameter model (Equation 3) and a three-parameter model (Equation 4).
Table 5: Parameters and degree of fit of a two-parameter model.
Heel Toe Sample A τ RMS A τ RMS Niagara Foot™ 0.752 10.417 0.0880 0.791 12.658 0.0139Axtion™ 106 kg 0.907 10.417 0.0330 0.967 13.333 0.0019Axtion™ 124 kg 0.884 8.621 0.0080 0.974 13.158 0.0016SACH 0.802 11.242 0.0726 0.775 6.046 0.0147
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Table 6: Parameters and degree of fit of a three-parameter model.
Heel Toe Sample A B τ RMS A B τ RMS
Niagara Foot™ 0.815 0.0010 4.717 0.0061 0.855 0.0098 4.926 0.0060Axtion™ 106 kg 0.931 0.0004 4.505 0.0119 0.977 0.0001 5.747 0.0007Axtion™ 124 kg 0.911 0.0004 3.891 0.0030 0.982 0.0001 5.435 0.0006SACH 0.86 0.0009 4.098 0.0059 0.817 0.0007 3.030 0.0061
In the three-parameter model (Equation 4), A is the initial decay term, τ is the time constant, and
B is the decay coefficient. The decay coefficient, B, is very small. Initially, the exponential decay
dominates the equation, and as time increases B begins to dominate. It is possible that the decay
coefficient, B, could be modeled as two time constants, a rapid one that acts early in the response
and a slow one that acts later. It is recognized that fitting multiple time constants is susceptible to
inaccuracies due to noise in the data. The use of a linear approximation of the decay is sufficient
for the time scale that is being examined and likely represents the behaviour of polymers over
long-term loading. Interestingly, the absence of B in the two-parameter model resulted in an
artificially high time constant.
Prosthetic feet experience two types of friction during use, external and internal. External friction
is due to the contact between the foot and the ground, or during loading, the platen. External
friction was minimized during testing through the use of a silicone based spray and Teflon® film.
Internal friction is due to motion within the prosthesis, such has one section sliding against
another. Hysteresis or energy loss of a material during unloading is associated with internal
friction [30]. A, the initial decay, is indicative of friction internal to the system. The higher the A
value, the less friction exists. The highest initial decay, A, values are those for the two Axtion™
71
feet compared to the other two designs, and the lowest are for the Niagara Foot™ and the SACH.
The Axtion™ designs have stiff elastic elements with low friction. In contrast, the design of the
Niagara Foot™ is such that when the heel is subjected to higher loads, the horns on the foot meet
the top of the foot. The resulting friction at this contact point could result in a greater initial decay
and a lower A value. The values for the SACH likely reflect the energy lost in compression of the
soft foam heel.
The toe of the Axtion™ had the highest time constant (τ = 5.7 sec), whereas the SACH toe had
the lowest time constant (τ = 3.0sec). This is likely due to the longer time response of the
elastomer in the Axtion™ design compared to the more rigid keel in the SACH design. The
Hytrel™ used in the Niagara Foot™ design is a semi-crystalline form of polyester with a modulus
of approximately 1.2 GPa. Its intermediate time constant is consistent with its bulk properties.
The results of the test for linearity study using the three-parameter model are shown in Table 7.
As the loading levels increased, the initial decay values, A, continued to decrease. Overall, this
difference in the A values decreased as the loading levels increased. Most notably, the time
constants tended to decrease as forces increased. Because this force dependency exists, a true non-
linear approach is required to completely model the force relaxation response of the samples
tested. However, providing the load levels are standardized, the method is useful for comparing
different designs of feet.
72
Table 7: Results study examining linearity using a three-parameter model.
300N 700N 1200N Sample A B τ RMS A B τ RMS A B τ RMS
006 0.953 0.00048 8.547 0.00111 0.918 0.0006 3.731 0.004 0.897 0.00067 1.135 0.00548 012 0.947 0.00045 3.891 0.00058 0.922 0.00061 3.891 0.00345 0.898 0.00069 2.146 0.00547 015 0.962 0.00039 8.772 0.00082 0.928 0.00059 3.953 0.00325 0.912 0.00066 3.115 0.00441
73
4.5 Conclusions
A reduced relaxation function of the form BttAAtL −−−+= )exp()1()( τ is able to capture
the time-dependent characteristics of the heel and toe regions of prosthetic feet. In this model, A
is the initial decay, B is the decay coefficient, and τ is a time constant. Lower A values indicate
that prosthetic feet have higher friction internal to the system. Low time constants indicate that the
initial decay occurs over a brief period of time, whereas high time constants indicate that the
initial decay occurs over a longer period of time. This reflects bulk material properties of the
component. The three-parameter model is practical for comparing various prostheses at single
load level. To model the reduced relaxation response at all loading levels a fully non-linear model
is required.
74
Chapter 5
General Discussion
The long-term goal of this study is to improve the ability of designers and prosthetists to match
the mechanical characteristics of prosthetic feet to the patient-specific parameters, including their
needs, abilities and biomechanical characteristics. While patient measures of performance are
well developed, there is a need to develop a practical method by which non-linear and time-
dependent mechanical properties of the prosthetic component can be measured. Testing
methodologies were developed that separately evaluated the elastic and time-dependent
properties.
The first testing regime involved mechanically characterizing prostheses under conditions similar
to gait. The heel and toe of four sample feet were loaded to peak forces based on their design
mass at a series of angles that the prosthetic system would go through during the gait cycle. Using
the force-displacement data, tangential stiffnesses of the samples were determined.
The amputee gait waveform in ISO 22675 was used to identify critical vertical forces that the foot
would be expected to experience at each pylon angle. The displacements and stiffness values
occurring at each of the critical forces were identified in four sample feet and normalized against
their design mass. This allowed for the designs to be compared against one another.
75
Differences in function, style and geometric shape were noted between the different styles of feet.
The heel of the SACH foot compressed quickly and the level of compression was constant,
indicating foot flat was reached early on in the gait cycle. These observations are consistent with
the design features of the foot. The heel and toe regions of the two Axtion™ feet had very similar
displacement profiles, which is consistent with two feet having the same design. The toe region of
the Niagara Foot™ reached its peak displacement after the Axtion™. The difference in the timing
of the peak displacements is likely due to geometric differences in the feet.
Although this method was based on a gait waveform, some simplifications were required. The
combined loading of the heel and toe regions during the midstance phase of gait was not
duplicated during testing. The midstance phase begins when foot flat occurs at approximately 7%
of the gait cycle; this is the first time that the foot is flat with the ground. The loads experienced
by the heel begin to decrease while those on the toe begin to increase. At 30% of the gait cycle
midstance occurs; at this point, a person’s body weight is directly over the supporting limb. The
heel continues to unload until heel off occurs and the heel is no longer in contact with the ground
[10]. If both regions of the foot had been loading during this complex phase of gait, it would have
been difficult to separate out the individual heel and toe responses from the data. Testing the
regions separately allowed for an understanding of the properties of these sections and how they
contributed to the performance of the foot at each point in the gait cycle.
When prosthetists prescribe a device they rely primarily on their experience and input from their
patients. Observations include the rate of ambulation, activity level and weight of the patient [41].
Predicting the behaviour of prosthetic feet during gait may make it possible for a prosthetist to
76
prescribe components that better suit the needs of their patients. In addition, this information gives
designers more control over the performance of new prosthetic feet and the ability to modify
current designs to meet the needs of users. Patients requiring greater stability are often prescribed
a foot that reaches the foot flat phase of stance quickly. This type of foot tends to have a softer
heel and stiffer toe, such as the SACH foot. More active patients are often prescribed feet that
provide greater energy return allowing for easier propulsion of the limb such as a DER foot.
These feet typically have stiffer heels and softer toes.
A recognized strategy when modeling non-linear systems is to separate the time dependency from
the elastic properties. A second testing regime examined the time-dependent properties of the heel
and toe region of prostheses. Force relaxation testing was conducted on the heel and toe regions
of four sample feet. This response was predicted using two models for the reduced relaxation
response, and the RMS errors were calculated. The first was a standard model of the form of:
).exp()1()( τtAAtL −−+=
This model was unable to capture the initial rapid decay or the quasi-linear decay occurring later
on in the response.
The second model was a reduced relaxation response in the form of:
.)exp()1()( BttAAtL −−−+= τ
This model was able to capture the initial rapid decay and the longer-term linear decay that was
noted in the relaxation behaviour. Improvements of 87% and 59% in the quality of fit for the heel
and toe respectively were achieved. Based on a previous study, Geil used a three-parameter model
77
to examine the stiffness and dampening properties of the toe region of eleven prosthetic feet. The
approach was successful when predicting linear mechanical responses; however, it had limited
success when non-linearities were dominant [38]. The addition of the decay coefficient to the
three-parameter model may increase the robustness of the model in future studies.
In this model, A is the initial decay. Friction internal to the system occurs when the Niagara
Foot™ is loaded due to its design. The Niagara Foot™ exhibited initial decay values that were
consistently lower than the other samples. Lower initial decay values likely indicate that
prosthetic feet have higher friction values internal to the system; systems with higher initial decay
values have lower internal friction levels.
B is the decay coefficient. It is possible that this parameter could also be modeled as two time
constants, a rapid one that acts early on in the response and a slow one that acts later on.
However, it is recognized that fitting multiple time constants is susceptible to inaccuracies due to
noise in the data. The use of a linear approximation of the decay was sufficient for the time period
of interest. The decay coefficient is necessary to derive parameters consistent with the relaxation
response.
τ is a time constant. Low time constants indicate that the initial decay occurred over a brief period
of time, while high time constants indicate that it occurred over a longer period of time.
Comparing these constants across feet can provide insight into how different feet function and
how different features, especially bulk properties, affect performance.
78
Using the two testing regimes, mechanical properties of the sample feet tested were determined.
Linking the testing to the gait cycles provides insight into how these properties relate to their
performance. There are, however, a number of basic assumptions that must be considered in order
to interpret the measured data. This study tested all of the prosthetic feet according to the same
standard, making it possible to compare the different designs and styles against one another and
draw conclusions about their performance. However, changes in gait due to alignment of the
prosthetic system or adaptations made by an amputee are not taken into account.
This characterization method does not consider long-term behaviour of the component. In
particular, hysteresis occurring during cyclic loading of the feet associated with normal use will
lead to an increase in the temperature of the component. Long term cycling of feet may provide
different results such as greater displacements and lower stiffness values. This should be
considered when extending this work to other activities of daily living.
5.1 Patient-related Variables
The loading levels used in the mechanical characterization and force-relaxation testing were based
on a standardized waveform found in ISO 22675. The testing regime was designed to simulate the
conditions that these components will perform under during the stance phase of prosthetic gait.
However it was designed to test the durability of prostheses, not further the understanding of how
they function.
79
The majority of the subjects who participated in the study were male, and almost half were
between the ages of 41-65 years old [42]. The types of prostheses available at the time are still
worn by amputees today; however, many prosthetic devices have been introduced since the time
of the study. The type of foot worn can influence the gait patterns of the user. For example,
Macfarlane et al. [16] found that subjects were able to spend more time in single support during
the stance when they used a Flex Foot™ compared to a conventional SACH foot. This allowed
them to take fewer steps while maintaining their walking speed. In addition, their trunk motion
was smoother and more uniform while walking with a Flex Foot™ [16]. It is expected that the
gait waveform would vary if the study were reproduced with subjects using different types of
prostheses.
Gait waveforms provide an indication of how the average person walks. The speed at which
someone walks, as well as the cause of amputation, can cause variations in gait from the normal
pattern. The speed at which someone walks affects the peak vertical ground reaction forces
occurring during gait. As walking speed increases, the peak forces on both the affected and
unaffected sides do as well. Walking speed also affects the amount of time a limb spends in
stance. As walking speed increases, the time spent in stance decreases [15]. Self-selected walking
speed varies from person to person; therefore the peak forces the prosthesis is subjected to will
vary as well. Amputees who had a limb amputated due to vascular disease tend to walk at a
slower speed with a lower cadence and a shorter stride length compared to traumatic amputees
[43]. This variation is not necessarily reflected in the test protocol.
80
5.2 Prosthetist-related Variables
Proper alignment of a prosthetic system is essential for patient comfort and their ability to
efficiently transition from heel strike to toe off during the stance phase of gait. This alignment is
carried out by a prosthetist, it varies from patient to patient, and has a noticeable impact on the
biomechanics of amputee gait. Shifting the foot in the sagittal plane alters the point of contact of
the foot with the floor. This changes the effective lever arm length of the heel and toe, altering
both of their stiffnesses. The stability of the knee is also affected. Shifting the foot anteriorly
increases the amount of time someone spends with the knee extended, whereas shifting the foot
posteriorly increases the time spent with the knee flexed. Changing the angle of the foot affects
the maximum knee extension moment occurring during the later half of stance. Plantar flexing the
foot increases the knee extension moment, while dorsiflexing the foot decreases them. Changes in
the angle also increase the mean oxygen consumption during gait especially at higher walking
speeds [9]. While the results of this study do not reflect the impact that changes in alignment
would have on the performance of the system, they do provide baseline data. Adaptations in gait
and the effects of changing the alignment can be extended in future work using methods similar to
the current study.
5.3 Component Design Variables
This study examined the mechanical properties of various prosthetic feet without covers or
footwear except for the SACH foot whose cover is integrated into the keel. This allowed for the
characteristics of the keel alone to be studied. However, feet are generally worn with cosmetic
covers and various styles of shoes.
81
Van Jaasrsveld et al. [30] studied the stiffness and hysteresis properties of nine different
prosthetic feet with and without shoes. The effects of a leather shoe and a running shoe were
examined. In all but two of the samples, the leather shoe resulted in an increase in the maximum
stiffness during loading. Six of the feet experienced a 50kN/m increase in the maximum stiffness,
while the Otto Bock® uni-axial feet experienced an 180kN/m increase. The Hanger Quantum and
Otto Bock® dynamic foot experienced a decrease in stiffness of 30kN/m. The running shoe
influenced the maximum stiffness values to a lesser extent.
Klute et al. [37] examined the deformation and energy dissipation properties of the heel region of
prosthetic feet during the initial contact at heel strike. Of the seven feet tested, one, a Seattle
Lightfoot 2 was tested with three different shoes: a walking, a running and an orthopedic shoe.
The use of all three shoes resulted in greater energy dissipation at all velocities compared to the
foot alone. The running and orthopaedic shoes resulted in an increased peak at all velocities
compared to the foot alone.
Much in the same way footwear can affect the characteristics of prostheses, covers would be
expected to do so as well. Given that different covers are made of different materials, it is likely
that they would affect the characteristics of prosthetic feet in different manners. The effect of
different shoe styles and foot covers should be examined in future studies, especially with regard
to time-dependent properties.
82
Chapter 6
Conclusions and Future Work
6.1 Conclusions
1. A method has been proposed by which the mechanical properties of prosthetic feet can be
evaluated based on the standard loading waveform in ISO 22675. The mechanical properties
of prosthetic feet can be described using a quasi-linear approach.
2. The force-displacement responses of prosthetic feet reflect increasing stiffnesses with
increasing loads and a decreasing pylon angle. These changes are consistent with the position
of the contact point during loading.
3. Key features reflecting foot design are: the relative stiffness of the heel and toe and the
displacement gap at midstance.
A) Feet designed to provide greater stability tend to exhibit lower heel stiffnesses and higher
toe stiffnesses, while the DER feet tested exhibited higher heel stiffnesses and lower toe
stiffnesses.
B) The displacement gap, the differences in heel and toe displacement at a pylon angle of 0°,
suggests that DER feet can aid in the transition from heel to toe, providing a smooth
rollover, whereas SACH feet provide greater stability.
C) Based on the characteristics of well-understood prostheses, benchmark values can be
established. New designs of prosthetic feet could be compared against these values and
classified.
83
4. The reduced relaxation response of the form BttAAtL −−−+= )exp()1()( τ is able to
capture the relaxation characteristics of the heel and toe regions of prosthetic feet. In this
model, A, is the initial decay, B is the decay coefficient, and τ, is a time constant.
5. Lower A values indicate that prosthetic feet have higher friction internal to the system.
Systems with higher A values have lower internal friction levels.
6. Low time constants indicate that the initial decay occurs over a brief period of time, while
high time constants indicate that the initial decay occurs over a longer period of time. This
reflects bulk material properties of the component.
7. The decay coefficient is not well understood; it is, however, necessary to capture the initial
rapid decay and latter phase of the relaxation response.
8. The model used to predict time-dependent properties of the feet was able to capture the
relaxation properties with a better degree of fit than in previous studies using a linear model.
The three-parameter model is practical for comparing various prostheses at single load level.
To model the reduced relaxation response at all loading levels, a fully non-linear model is
required.
84
6.2 Future Work
Future work is required to improve the methods outlined in this study. Conducting the mechanical
characterization protocol twice, once loading the heel and toe separately and a second time
allowing for combined loading, would yield a more complete data set. The results of testing the
heel and toe separately could be used to help interpret the combined loading data, which would
more accurately mimic gait. This could be achieved using a larger platen during loading that is
able to capture both the heel and toe regions of the samples.
To ensure correct alignment of the samples, a prosthetist or other trained professional should
oversee this procedure. Examining the effect of alignment on the mechanical properties of
prosthetic feet could provide insight into how different patients will perceive different prostheses.
Testing should be conducted using different alignments.
It is known that shoes can influence the mechanical properties of prosthetic feet. Conducting the
protocols with foot covers and different types of footwear would examine their effect on the
elastic and viscoelastic properties of prosthetic feet. This could also provide insight into how
patients perceive their prostheses during gait.
Understanding the effects of DER prostheses on the amputee gait waveform used would be
beneficial. Comprehensive studies should be conducted to examine the effect different prostheses
have on amputee gait. The vertical ground reaction forces relative to pylon angle are of particular
interest. Testing protocols could be customized to different styles of feet, which would produce
more realistic prediction of performance.
85
Long term cycling of feet may provide different results due to an increase in the temperature of
the component. Studies should be conducted to examine the effect that increased temperatures
will have on the displacement and stiffness values of prosthetic feet.
A fully non-linear model of the reduced relaxation response should be developed so the response
can be modelled at all loading levels.
To have a more complete understanding of the effects of design on the performance of prosthetic
feet, other activities of daily living that are well understood should be examined and modelled.
86
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[42] McKenzie, D. S., and Muilenburg, A., 1978, "Standards for Lower-Limb Prostheses – Report of a Conference 1977," International Society for Prosthetics and Orthotics.
[43] Barth, D. G., and Sienko Thomas, S., 1992, "Gait Analysis and Energy Cost of Below-Knee Amputees Wearing Six Different Prosthetic Feet," Journal of Prosthetics and Orthotics, 4(2) p. 63.
[44] Haberman, A., Bryant, J. T., Beshai, L. M., 2007, "Mechanical Characterization of Prosthetic Feet," Proceedings of the 12th World Congress of the International Society of Prosthetics and Orthotics, Vancouver, BC, p.374.
89
Appendix A
Determination of Displacement Rate
During heel strike, the vertical velocity of the foot approaches 50 mm/sec. This rate of
displacement is difficult to achieve in a laboratory setting [13]. To determine if a slower more
reasonable rate of displacement could achieve similar displacement and stiffness values, a pilot
study was conducted.
The heel region of one of three Model 2 Version 18 Niagara Feet™ was loaded ten times with
varying wait times between tests. These wait time were randomized, and are shown in Table 8.
The foot was loaded at a rate of 2.0mm/sec to a peak load of 1173N. A pylon angle of 15° was
used.
A typical force-deflection curve of a heel can be described using three parameters, as shown in
Figure 33. The k1, k2 and kh values were determined for each test and the results are shown in
Table 8. The stiffness values appeared to be independent of the wait times tested. A wait time of
five minutes between tests was determined to be sufficient.
90
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12
Displacement (mm)
Forc
e (N
)
Region 2Region 1
k1
k2kh
Figure 33: Typical force deflection curve of a heel can be described using three parameters: k1, the slope of the curve in the first region, is defined as the initial stiffness of the foot; k2 is defined as the slope at the design load in the second region; kh is the average stiffness between 0N and the design load. For the toe region the same protocol is followed and the analogous parameters k3, k4 and kt are used [44].
91
Table 8: Three stiffness values from mechanical testing of a Model 2 Version 18 Niagara Foot™ conducted at varying time intervals.
Time Between Tests (min)
Test Number
Testing Order
k1 (kN/m)
k2 (kN/m)
kh (kN/m)
x @ 1000 (mm)
0 32.7 260.4 113.6 8.8
5 1 2 30.8 259.6 113.6 8.8
10 2 5 32.2 261.3 117.6 8.5
15 3 7 32.2 260.7 114.9 8.7
20 4 4 32.4 260.9 114.9 8.7
25 5 6 31.5 262.2 116.3 8.6
30 6 3 32.1 260.6 113.6 8.8
40 7 8 32.4 261.9 114.9 8.7
50 8 9 32.2 259.9 114.9 8.7
60 9 1 30.8 259.3 113.6 8.8
The heel and toe regions of one of three Model 2 Version 18 Niagara Feet™ were loaded at rates
of 0.25, 0.5, 1.0, 2.0 and 5.0mm/sec to a peak force of 1173N. Pylon angles of 15° and 20° were
used for the heel and toe regions respectively, and five minutes were allowed between each test.
The initial, average and tangential stiffness at 1000N was determined, as shown in Table 9. The
breakpoint for each of the three-parameters for both regions of the foot occurred at the
displacement rate of 1.0mm/sec. A displacement rate of 2.0mm/sec was selected because it was
above the breakpoint and allowed for the testing to be done in an efficient manner.
92
Table 9: Stiffness values for the heel and toe regions of a Model 2 Version 18 Niagara Foot™ tested at various displacement rates.
Heel Toe
Displacement Rate
(mm/sec)
Test Number
k1 (kN/m)
k2 (kN/m)
kh (kN/m)
Test Number
k3 (kN/m)
k4 (kN/m)
kt (kN/m)
0.25 9 26.5 229.2 105.3 10 4.7 52.2 26.4
0.5 2 28.5 230.8 109.9 5 4.9 52.8 26.9
1.0 7 28.9 235.9 107.5 6 5.1 54.9 27.9
2.0 4 29.9 239.1 112.4 8 5.2 55.3 28
5.0 3 30.5 238.5 114.9 1 5.4 55.8 28.2
To ascertain if the same displacement rate could be used to characterize the other three sample
feet, relaxation testing was conducted using the Instron™. The heel and toe of the four samples
were loaded to 1.495 times their design mass at a rate of 3.25mm/sec. Once again, pylon angles of
15° and 20° were used for the heel and toe regions respectively. Once the peak load was reached,
the platen’s position remained constant for 90 seconds and the resulting force values were
recorded. Using these data, the relaxation time and three constants were determined for the heel
and toe region of each of the feet as shown in Table 10. The values for the Model 2 Version 18
Niagara Foot™ were used as a benchmark; values for the other three feet were compared to those
of the Niagara Foot™. The relaxation times, initial decay values and decay coefficients for the
two Axtion™ Feet and the SACH foot were of the same order of magnitude as the benchmark
93
values. As a result, the heel and toe regions of these feet were also characterized at a displacement
rate of 2.0mm/sec.
Table 10: Relaxation parameters of the four sample feet.
Heel Toe Sample
A B tau A B tau
Niagara Foot 0.815 0.001 4.717 0.855 0.00982 4.9261
Axtion™ 106 kg 0.931 0.000388 4.505 0.977 0.000148 5.7471
Axtion™ 124 kg 0.911 0.000441 3.891 0.982 0.000122 5.4348
SACH 0.86 0.000919 4.098 0.817 0.000737 3.0303
94
Appendix B
Linear Extrapolation and Interpolation
The x-intercept of the force-displacement curves were determined by extrapolating back from the
first two data points, as shown in Figure 34.
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7
Displacement (mm)
Forc
e (N
)
x0
Figure 34: Determination of the x-intercept using linear extrapolation.
x0
95
The x-intercept was subtracted from the displacement data to compensate for the offset origin, as
shown in Figure 35.
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35 40
1st Cycle8th Cycle
offset
Figure 35: Adjustment of the force-displacement data to compensate for the offset origin.
96
Linear interpolation of the data points above and below the design load was conducted to
determine the displacement at the design load, as shown in Figure 36.
1172.2
1172.3
1172.4
1172.5
1172.6
1172.7
1172.8
1172.9
1173
1173.1
30.542 30.544 30.546 30.548 30.55 30.552 30.554 30.556
Displacement (mm)
Forc
e (N
)
Experimental Data
Design Load
Figure 36: Determination of displacement at the design load using linear interpolation.
X1173
97
Appendix C
Mechanical Characterization of Dynamic Energy Return Prosthetic Feet: Complete Data Set
This Appendix contains the complete data set from the mechanical characterization study. Force-
displacement and stiffness-displacement curves, as well as the forces and tangential stiffnesses
occurring at the critical forces for the sample feet are shown in the following figures.
98
The data for the Niagara Foot™ are shown in Figure 37, Figure 38 and Figure 39
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12 14 16
Displacement (mm)
Forc
e (N
)
0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50
Displacement (mm)
Forc
e (N
)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 37: Force-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
99
0
100
200
300
400
500
600
700
800
0 5 10 15
Displacement (mm)
Stiff
ness
(kN
/m) 0 Degrees
-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
50
100
150
200
250
300
0 10 20 30 40 50 60 70 80
Displacement (mm)
Stif
fnes
s (k
N/m
)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 38: Stiffness-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
100
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Time (msec)
Dis
plac
emen
t (m
m)
HeelToe
(a)
0
100
200
300
400
500
600
700
0 100 200 300 400 500 600 700
Time (msec)
Stiff
ness
(kN/
m)
HeelToe
(b)
Figure 39: (a) Displacements and (b) tangential stiffness values of the Niagara Foot ™ occurring at the critical forces identified.
101
The data for the Axtion™ with a maximum recommended user weight of 106kg are shown in
Figure 40, Figure 41 and Figure 42.
0
200
400
600
800
1000
1200
1400
1600
1800
0 5 10 15 20 25
Displacement (mm)
Forc
e (N
)
0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
200
400
600
800
1000
1200
1400
1600
1800
0 5 10 15 20 25 30
Displacement (mm)
Forc
e (N
)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees
(b) toe
Figure 40: Force-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 106kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12. .
102
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25
Displacement (mm)
Stif
fnes
s (k
N/m
) 0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
50
100
150
200
250
0 5 10 15 20 25 30
Displacement (mm)
Stiff
ness
(kN
/m)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees
(b) toe
Figure 41: Stiffness-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 106kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
103
0
5
10
15
20
25
30
0 100 200 300 400 500 600
Time (msec)
Disp
lace
men
t (m
m)
HeelToe
(a)
0
100
200
300
400
500
600
700
800
0 100 200 300 400 500 600
Time (msec)
Stif
fnes
s (k
N/m
)
HeelToe
(b)
Figure 42: (a) Displacements and (b) tangential stiffness values of the Axtion™ foot with a maximum recommended user weight of 106kg occurring at the critical forces identified.
104
The data for the Axtion™ with a maximum recommended user weight of 124kg are shown in
Figure 43, Figure 44 and Figure 45.
0200400600800
100012001400160018002000
0 5 10 15 20 25 30
Displacement (mm)
Forc
e (N
)
0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0200400600800
100012001400160018002000
0 5 10 15 20 25 30 35 40
Displacement (mm)
Forc
e (N
)
0 Degrees5 Degrees10 Degress15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 43: Force-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 124kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12
105
0100200300400500600700800900
1000
0 5 10 15 20 25 30
Displacement (mm)
Stiff
ness
(kN/
m) 0 Degrees
-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
50
100
150
200
250
0 5 10 15 20 25 30 35 40
Displacement (mm)
Stiff
ness
(kN/
m)
0 Degrees5 Degrees10 Degree15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 44: Stiffness-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 124kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
106
0
5
10
15
20
25
30
35
40
0 100 200 300 400 500 600
Time (msec)
Disp
lace
men
t (m
m)
HeelToe
(a)
0
100
200
300
400
500
600
700
800
900
0 100 200 300 400 500 600 700
Time (msec)
Stiff
ness
(kN
/m)
HeelToe
(b)
Figure 45: (a) Displacements and (b) tangential stiffness values of the Axtion™ foot with a maximum recommended user weight of 124kg occurring at the critical forces identified.
107
The data for the SACH foot are shown in Figure 46, Figure 47 and Figure 48.
0
200
400
600
800
1000
1200
1400
1600
1800
0 5 10 15 20 25 30 35 40
Displacement (mm)
Forc
e (N
)
0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
200
400
600
800
1000
1200
1400
1600
1800
0 10 20 30 40 50 60
Displacement (mm)
Forc
e (N
)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 46: Force-displacement curves for (a) the heel and (b) the toe of the SACH foot. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
108
0
200
400
600
800
1000
1200
1400
1600
1800
0 50 100 150 200 250 300 350 400
Displacement (mm)
Stiff
ness
(kN/
m) 0 Degrees
-5 Degrees-10 Degrees-15 Degrees-20 Degrees
(a) heel
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60
Displacement (mm)
Stiff
ness
(kN
/m)
0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees
(b) toe
Figure 47: Stiffness-displacement curves for (a) the heel and (b) the toe of the SACH foot. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.
109
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Time (msec)
Dis
plac
emen
t (m
m)
HeelToe
(a)
0
50
100
150
200
250
300
350
0 100 200 300 400 500 600
Time (msec)
Stif
fnes
s (k
N/m
)
HeelToe
(b)
Figure 48: (a) Displacements and (b) tangential stiffness values of the SACH foot occurring at the critical forces identified.
110
Appendix D
Force-Relaxation Properties of Dynamic Energy Return Feet: Complete Data Set
This appendix contains the complete data set from the mechanical characterization study.
Reduced relaxation curves for the heel and toe sections of the sample feet are show in Figure 49
and Figure 50 respectively.
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
0 20 40 60 80 100
Time (sec)
F(t)/
F0
Niagara FootAxtion 106kgAxtion 124kgSACH
Figure 49: Reduced relaxation data for the heel of the sample feet.
111
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
0 20 40 60 80 100
Time (sec)
F(t)/
F0
Niagara FootAxtion 106kgAxtion 124kgSACH
Figure 50: Reduced relaxation data for the toe of the sample feet.
112
Experimental data, as well as the results of the two models, are shown in Figure 51 and Figure 52,
for the heel and toe of the Niagara Foot™ respectively.
0.7
0.75
0.8
0.85
0.9
0.95
1
0 20 40 60 80 100
Time (sec)
L(t)
Experimental2 Parameter3 Parameter
Figure 51: Reduced relaxation response for the heel of the Model 2 Version 18 Niagara Foot™.
113
0.7
0.75
0.8
0.85
0.9
0.95
1
0 20 40 60 80 100
Time (sec)
Forc
e (N
) Experimental2 Parameter3 Parameter
Figure 52: Reduced relaxation response for the toe of the Model 2 Version 18 Niagara Foot™.
114
Experimental data, as well as the results of the two models, are shown in Figure 53 and Figure 54,
for the heel and toe of the Axtion™ foot with a maximum recommended user weight of 106kg.
0.88
0.9
0.92
0.94
0.96
0.98
1
0 20 40 60 80 100Time (sec)
L(t) Experimental
2 Parameter3 Parameter
Figure 53: Reduced relaxation response for the heel of the Axtion® foot with a maximum recommended user weight of 106kg.
115
0.88
0.9
0.92
0.94
0.96
0.98
1
0 20 40 60 80 100Time (sec)
L(t) Experimental
2 Parameter3 Parameter
Figure 54: Reduced relaxation response for the toe region of the Axtion® foot with a maximum recommended user weight of 106kg.
116
Experimental data, as well as the results of the two models, are shown in Figure 55 and Figure 56,
for the heel and toe of the Axtion® foot rated for 124kg.
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
0 20 40 60 80 100
Time (sec)
L(t) Experimental
2 Parameter3 Parameter
Figure 55: Reduced relaxation response for the heel region of the Axtion™ foot with a maximum recommended user weight of 124kg.
117
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
0 20 40 60 80 100
Time (sec)
L(t)
Experimental2 Parameter3 Parameter
Figure 56: Reduced relaxation response for the toe region of the Axtion® foot with a maximum recommended user weight of 124kg.
118
The experimental data, as well as the results of the two models, are shown in Figure 57 and Figure
58, for the heel and toe of the SACH foot.
0.75
0.8
0.85
0.9
0.95
1
0 20 40 60 80 100
Time (sec)
L(t)
Experimental2 Parameter3 Parameter
Figure 57: Reduced relaxation response for the heel region of the SACH foot.
119
0.7
0.75
0.8
0.85
0.9
0.95
1
0 20 40 60 80 100
Time (sec)
L(t)
Experimental2 Parameter3 Parameter
Figure 58: Reduced relaxation response for the toe region of the SACH foot.
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