CONTENTS
The Design and Analysis of a Double Transtibial Composite Prosthesis
and the Effect of Lateral Movement Loads
i
LIST OF TABLES
iii
LIST OF FIGURES
iv
TERMINOLOGY / LIST OF SYMBOLS / ACRONYMS
v
ACKNOWLEDGEMENTS
vii
ABSTRACT
viii
1. Introduction
1
1.1. Background
1
1.2. Challenges of this Study
3
2. Theory and Methodology
7
2.1. Reverse Engineering the Flex Foot Design
7
2.2. Lateral Forces, Friction, and Angle of Attack
11
2.3. Analytic Method Summary
13
3. Results and Discussion
17
3.1. Model Setup
17
3.2. Lateral Movement
21
4. Remarks and Conclusion
25
5. References
30
6. Appendices
32
6.1. Graphical Data
ii
LIST OF TABLES
Table 2-1: Properties of the Flex Foot
8
Table 2-2: Consistent Units for Analysis
8
Table 2-3: Coefficients of Friction Equations
10
Table 3-1: 0/90 Ply Orientation, Stress and Stiffness vs Load
18
Table 3-2: 0/-45/90/45 Stiffness at 1500 N
20
Table 3-3: Summary of Baseline Stresses and TSAIW
24
Table 4-1: Deflection and Modulus Response of Selected Materials
26
Table 4-2: Model Dimension Lengths
27
Table 4-3: Weight of Prosthetic Using Selected Materials
27
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LIST OF FIGURES
Figure 1-1: History of Leg Prostheses
1
Figure 1-2: Official Rendering of the Flex Foot Prosthetic
2
Figure 1-3: Ankle Power Response Curve
3
Figure 1-4: Diagram of Tennis Sole
4
Figure 1-5: Definitions of ankle eversion and inversion
5
Figure 1-6: Connection bolts of Flex Foot bolts
5
Figure 1-7: Ankle eversion in tennis lateral motion
6
Figure 2-1: Geometric Analysis of Flex Foot Prosthetic
7
Figure 2-2: Dimensions of Baseline Prosthetic
9
Figure 2-3: Comparison of Baseline Model to Original
9
Figure 2-4: Plot of Friction Equations
11
Figure 2-5: Maximum Force and Angle of Attack
12
Figure 2-6: Loads and Constraints
13
Figure 2-7: Assembly with Fixed Reference Point Shown
14
Figure 2-8: Assembly with Contact Interaction Method Shown
14
Figure 2-9: Tangential Behavior
15
Figure 2-10: Profile of Assembly
15
Figure 3-1: Mesh Experiment
17
Figure 3-2: Visualization of Linear Stiffness vs Load
19
Figure 3-3: Various Ply Stiffness at 1500 N
19
Figure 3-4: 0/-45/90/45 Stiffness at 1500 N, Various Plies
20
Figure 3-5: [0/90] Vertical Stress and TSAIW
21
Figure 3-6: [0/90] 45 Degree Stress and TSAIW
22
Figure 3-7: [0/45/90/-45] Vertical Stress and TSAIW
23
Figure 3-8: [0/45/90/-45] 45 Degree Stress and TSAIW
23
Figure 4-1: Modulus Response of Selected Materials
26
Figure 4-2: Dimensions of Baseline Prosthetic
27
Figure 4-3: Weight of Prosthetic Using Selected Materials
28
iv
TERMINOLOGY / LIST OF SYMBOLS / ACRONYMS
Transtibial – occurring across or involving the tibia
Abduction/Adduction – Ankle rotation around the shin axis
Plantar Flexion / Dorsiflexion – Ankle rotation about the ankle joint axis
Inversion / Eversion = Ankle rotation about the foot axis
FEA – Finite Element Analysis
FBD – Free Body Diagram
2D – 2 Dimensions
E – Modulus of Elasticity (Msi)
G – Modulus of Rigidity (Msi)
ν – Poisson’s Ratio
ρ – Density (lbf/in3)
tp – Ply Thickness (in)
YS – Yield Strength (ksi)
UTS – Ultimate Tensile Strength (ksi)
σ1t – Tensile strength in the 1 (longitudinal) direction (ksi)
σ1c – Compressive strength in the 1 (longitudinal) direction (ksi)
σ2t – Tensile strength in the 2 (transverse) direction (ksi)
σ2c – Tensile strength in the 2 (transverse) direction (ksi)
τ12f – Shear Strength (ksi)
[Orientation number of plies]S – Laminate Layup which is characterized by ply orientation,
number of plies and symmetry about the mid-plane (S, if applicable).
v
Abaqus – Computer Software used to perform modeling and FEA
Isotropic – Same properties in all directions
Orthotropic – Different properties in different directions
TSAIW – An abbreviation for Tsai-Wu Abaqus uses
vi
ACKNOWLEDGMENTS
I would first like to thank my Project Adviser, Professor Ernesto, for all of the help he
has given me and for his patience. I would like to thank Professor Hufner for his help
with composites analysis. I would also like to thank all those who are working in the
field of prosthetics. I would also like to thank the faculty of Rensselaer Polytechnic
Institute at Groton for their support throughout the Masters of Engineering program.
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ABSTRACT
The purpose of this project is to evaluate the performance of a prosthetic device similar
to the Flex Foot Cheetah design used by Olympian sprinters. This transtibial prosthetic
has been evaluated before to determine if it offers more mechanical advantage in a
forward sprint to a runner than does an anatomical leg, ankle and foot. This paper
determines the properties of such a prosthetic and then analyzes what changes, if any,
would benefit the prosthetic wearer in sports that require lateral movement in addition to
forward sprinting.
First a model was created by gathering all non-proprietary information about the Flex
Foot Cheetah model. Dimensions were ascertained by image analysis and from given
information by previous papers. The dimensioned model was then analyzed with two ply
orientation types to determine orientation, number, and thickness of composite plies to
have a similar baseline mechanical performance as the Flex Foot.
These models were then analyzed for stresses in the lateral direction at the maximum
amount of force seen by a tennis player changing direction. Modifications are proposed
to the Flex Foot design to accommodate these forces, such as resizing of the equivalent
ankle area and widening the contact foot for additional stability and traction.
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