Abstract

This paper describes the design of a simple and low-cost compliant low-profile prosthetic foot based on a cantilevered beam of uniform strength. The prosthetic foot is developed such that the maximum stress experienced by the beam is distributed approximately evenly across the length of the beam. Due to this stress distribution, the prosthetic foot exhibits compliant behavior not achievable through standard design approaches (e.g., designs based on simple cantilevered beams). Additionally, due to its simplicity and use of flat structural members, the foot can be manufactured at low cost. An analytical model of the compliant behavior of the beam is developed that facilitates rapid design changes to vary foot size and stiffness. A characteristic prototype was designed and constructed to be used in both a benchtop quasi-static loading test as well as a dynamic walking test for validation. The model predicted the rotational stiffness of the prototype with 5% error. Furthermore, the prototype foot was tested alongside two commercially available prosthetic feet (a low profile foot and an energy storage and release foot) in level walking experiments with a single study participant. The prototype foot displayed the lowest stiffness of the three feet (6.0, 7.1, and 10.4 Nm/deg for the prototype foot, the commercial low profile foot, and the energy storage and release foot, respectively). This foot design approach and accompanying model may allow for compliant feet to be developed for individuals with long residual limbs.

References

1.
Ziegler-Graham
,
K.
,
MacKenzie
,
E. J.
,
Ephraim
,
P. L.
,
Travison
,
T. G.
, and
Brookmeyer
,
R.
,
2008
, “
Estimating the Prevalence of Limb Loss in the United States: 2005 to 2050
,”
Arch. Phys. Med. Rehabil.
,
89
(
3
), pp.
422
429
.10.1016/j.apmr.2007.11.005
2.
Rouse
,
E. J.
,
Gregg
,
R. D.
,
Hargrove
,
L. J.
, and
Sensinger
,
J. W.
,
2013
, “
The Difference Between Stiffness and Quasi-Stiffness in the Context of Biomechanical Modeling
,”
IEEE Trans. Biomed. Eng.
,
60
(
2
), pp.
562
568
.10.1109/TBME.2012.2230261
3.
Shamaei
,
K.
,
Sawicki
,
G. S.
, and
Dollar
,
A. M.
,
2013
, “
Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle in the Stance Phase of Walking
,”
PloS One
,
8
(
3
), p.
e59935
.10.1371/journal.pone.0059935
4.
Adamczyk
,
P. G.
,
Roland
,
M.
, and
Hahn
,
M. E.
,
2013
, “
Novel Method to Evaluate Angular Stiffness of Prosthetic Feet From Linear Compression Tests
,”
ASME J. Biomech. Eng.
,
135
(
10
), p. 104502. 10.1115/1.4025104
5.
Major
,
M. J.
,
Twiste
,
M.
,
Kenney
,
L. P.
, and
Howard
,
D.
,
2014
, “
The Effects of Prosthetic Ankle Stiffness on Ankle and Knee Kinematics, Prosthetic Limb Loading, and Net Metabolic Cost of Trans-Tibial Amputee Gait
,”
Clin. Biomech.
,
29
(
1
), pp.
98
104
.10.1016/j.clinbiomech.2013.10.012
6.
Singer
,
E.
,
Ishai
,
G.
, and
Kimmel
,
E.
,
1995
, “
Parameter Estimation for a Prosthetic Ankle
,”
Ann. Biomed. Eng.
,
23
(
5
), pp.
691
696
.10.1007/BF02584466
7.
Hansen
,
A.
,
Childress
,
D.
, and
Knox
,
E.
,
2000
, “
Prosthetic Foot Roll‐Over Shapes With Implications for Alignment of Trans‐Tibial Prostheses
,”
Prosth. Orthot. Int.
,
24
(
3
), pp.
205
215
.10.1080/03093640008726549
8.
Hafner
,
B. J.
,
Sanders
,
J. E.
,
Czerniecki
,
J.
, and
Fergason
,
J.
,
2002
, “
Energy Storage and Return Prostheses: Does Patient Perception Correlate With Biomechanical Analysis?
,”
Clin. Biomech.
,
17
(
5
), pp.
325
344
.10.1016/S0268-0033(02)00020-7
9.
Olesnavage
,
K. M.
,
Prost
,
V.
,
Johnson
,
W. B.
, and
Winter
,
A. G.
,
2018
, “
Passive Prosthetic Foot Shape and Size Optimization Using Lower Leg Trajectory Error
,”
ASME J. Mech. Des.
,
140
(
10
), p. 102302. 10.1115/1.4040779
10.
Morrison
,
S. G.
,
Thomson
,
P.
,
Lenze
,
U.
, and
Donnan
,
L. T.
,
2020
, “
Syme Amputation: Function, Satisfaction, and Prostheses
,”
J. Pediatric Orthopaedics
,
40
(
6
), pp.
e532
e536
.10.1097/BPO.0000000000001430
11.
Haberman
,
A.
, and
Bryant
,
J.
,
2008
,
Mechanical Properties of Dynamic Energy Return Prosthetic Feet
,
Queens University, Kingston, ON,
Canada
.
12.
Mason
,
Z. D.
,
Pearlman
,
J.
,
Cooper
,
R. A.
, and
Laferrier
,
J. Z.
,
2011
, “
Comparison of Prosthetic Feet Prescribed to Active Individuals Using ISO Standards
,”
Prosth. Orthot. Int.
,
35
(
4
), pp.
418
424
.10.1177/0309364611421692
13.
Elizabeth
,
A. T. T.
,
Halsne
,
G.
,
Curran
,
C.
,
Caputo
,
J.
,
Hansen
,
A. H.
,
Hafner
,
B. J.
, and
Morgenroth
,
D. C.
,
2020
, “
Measured Forefoot Stiffness Across Prosthetic Foot Stiffness Categories
,”
American Society of Biomechanics Conference
,
Atlanta, GA
, Aug. 4–7, p. 490.
14.
ISO,
2006
,
ISO 10328 Prosthetics: Testing of Ankle-Foot Devices and Foot Units: Requirements and Test Methods
, International Organization for Standardization (ISO), Geneva, Switzerland.
15.
Adamczyk
,
P. G.
,
Roland
,
M.
, and
Hahn
,
M. E.
,
2017
, “
Sensitivity of Biomechanical Outcomes to Independent Variations of Hindfoot and Forefoot Stiffness in Foot Prostheses
,”
Hum. Mov. Sci.
,
54
, pp.
154
171
(in English).10.1016/j.humov.2017.04.005
16.
Olesnavage
,
K. M.
,
2014
, “
Design and Evaluation of a Cantilever Beam-Type Prosthetic Foot for Indian Persons With Amputations
,”
Massachusetts Institute of Technology
, Cambridge, MA.
17.
Adamczyk
,
P. G.
,
Collins
,
S. H.
, and
Kuo
,
A. D.
,
2006
, “
The Advantages of a Rolling Foot in Human Walking
,”
J. Exp. Biol.
,
209
(
20
), pp.
3953
3963
.10.1242/jeb.02455
18.
Prost
,
V.
,
Olesnavage
,
K. M.
, and
Winter
,
A. G.
,
2017
, “
Design and Testing of a Prosthetic Foot Prototype With Interchangeable Custom Rotational Springs to Adjust Ankle Stiffness for Evaluating Lower Leg Trajectory Error, an Optimization Metric for Prosthetic Feet
,”
ASME
Paper No. DETC2017-67820.10.1115/DETC2017-67820
19.
Casillas
,
J.-M.
,
Dulieu
,
V.
,
Cohen
,
M.
,
Marcer
,
I.
, and
Didier
,
J.-P.
,
1995
, “
Bioenergetic Comparison of a New Energy-Storing Foot and SACH Foot in Traumatic Below-Knee Vascular Amputations
,”
Arch. Phys. Med. Rehab.
,
76
(
1
), pp.
39
44
.10.1016/S0003-9993(95)80040-9
20.
Postema
,
K.
,
Hermens
,
H. J.
,
De Vries
,
J.
,
Koopman
,
H. F.
, and
Eisma
,
W.
,
1997
, “
Energy Storage and Release of Prosthetic Feet Part 1: Biomechanical Analysis Related to User Benefits
,”
Prosth. Orthot. Int.
,
21
(
1
), pp.
17
27
.10.3109/03093649709164526
21.
Postema
,
K.
,
Hermens
,
H.
,
De Vries
,
J.
,
Koopman
,
H.
, and
Eisma
,
W.
,
1997
, “
Energy Storage and Release of Prosthetic Feet Part 2: Subjective Ratings of 2 Energy Storing and 2 Conventional Feet, User Choice of Foot and Deciding Factor
,”
Prosth. Orthot. Int.
,
21
(
1
), pp.
28
34
.10.3109/03093649709164527
22.
Zelik
,
K. E.
,
Collins
,
S. H.
,
Adamczyk
,
P. G.
,
Segal
,
A. D.
,
Klute
,
G. K.
,
Morgenroth
,
D. C.
,
Hahn
,
M. E.
,
Orendurff
,
M. S.
,
Czerniecki
,
J. M.
, and
Kuo
,
A. D.
,
2011
, “
Systematic Variation of Prosthetic Foot Spring Affects Center-of-Mass Mechanics and Metabolic Cost During Walking
,”
IEEE Trans. Neural Syst. Rehab. Eng.
,
19
(
4
), pp.
411
419
.10.1109/TNSRE.2011.2159018
23.
Fey
,
N. P.
,
Klute
,
G. K.
, and
Neptune
,
R. R.
,
2012
, “
Optimization of Prosthetic Foot Stiffness to Reduce Metabolic Cost and Intact Knee Loading During Below-Knee Amputee Walking: A Theoretical Study
,”
ASME J. Biomech. Eng.
,
134
(
11
), p. 111005.10.1115/1.4007824
24.
Baviskar
,
A.
,
Bhamre
,
V.
, and
Sarode
,
S.
,
2013
, “
Design and Analysis of a Leaf Spring for Automobile Suspension System: A Review
,”
Int. J. Emerging Technol. Adv. Eng.
,
3
(
6
), pp.
407
410
.https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.413.6597&rep=rep1&type=pdf
25.
Kumaravelan
,
R.
,
Ramesh
,
S.
,
Gandhi
,
V. S.
,
Agu
,
M. J.
, and
Thanmanaselvi
,
M.
,
2013
, “
Analysis of Multi Leaf Spring Based on Contact Mechanics–A Novel Approach
,”
Struct. Eng. Mech.
,
47
(
3
), pp.
443
454
.10.12989/sem.2013.47.3.443
26.
Chiu
,
M.-C.
,
Wu
,
H.-C.
, and
Chang
,
L.-Y.
,
2013
, “
Gait Speed and Gender Effects on Center of Pressure Progression During Normal Walking
,”
Gait Posture
,
37
(
1
), pp.
43
48
.10.1016/j.gaitpost.2012.05.030
27.
Lee
,
H.-J.
,
Lee
,
S.
,
Chang
,
W. H.
,
Seo
,
K.
,
Shim
,
Y.
,
Choi
,
B.-O.
,
Ryu
,
G.-H.
, and
Kim
,
Y.-H.
,
2017
, “
Design and Characterization of a Quasi-Passive Pneumatic Foot-Ankle Prosthesis
,”
IEEE Trans. Neural Syst. Rehabilitation Eng.
,
PP
(
99
), pp.
1
1
.10.1109/TNSRE.2017.2699867
28.
Winter
,
D. A.
,
1991
,
Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological
, University of Waterloo Press, Waterloo, ON, Canada.
29.
Shepherd
,
M. K.
,
Azocar
,
A. F.
,
Major
,
M. J.
, and
Rouse
,
E. J.
,
2018
, “
Amputee Perception of Prosthetic Ankle Stiffness During Locomotion
,”
J. Neuro Eng. Rehab.
,
15
(
1
), p.
99
.10.1186/s12984-018-0432-5
30.
Bartlett
,
H. L.
,
King
,
S. T.
,
Goldfarb
,
M.
, and
Lawson
,
B. E.
,
2021
, “
A Semi-Powered Ankle Prosthesis and Unified Controller for Level and Sloped Walking
,”
IEEE Trans. Neural Syst. Rehab. Eng.
,
29
, pp.
320
329
.10.1109/TNSRE.2021.3049194
31.
Lenzi
,
T.
,
Cempini
,
M.
,
Newkirk
,
J.
,
Hargrove
,
L. J.
, and
Kuiken
,
T. A.
,
2017
, “
A Lightweight Robotic Ankle Prosthesis With Non-Backdrivable Cam-Based Transmission
,” 2017 International Conference on Rehabilitation Robotics (ICORR), London, UK, July 17–20, pp.
1142
1147
.
32.
Shultz
,
A. H.
,
Mitchell
,
J. E.
,
Truex
,
D.
,
Lawson
,
B. E.
,
Ledoux
,
E.
, and
Goldfarb
,
M.
,
2014
, “
A Walking Controller for a Powered Ankle Prosthesis
,”
2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
,
Chicago, IL
, Aug. 26–30, pp.
6203
6206
.10.1109/EMBC.2014.6945046
33.
Cempini
,
M.
,
Hargrove
,
L. J.
, and
Lenzi
,
T.
,
2017
, “
Design, Development, and Bench-Top Testing of a Powered Polycentric Ankle Prosthesis
,” 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (
IROS
),
Vancouver, BC, Canada
, Sept. 24–28, pp.
1064
1069
.10.1109/IROS.2017.8202276
34.
Au
,
S. K.
, and
Herr
,
H. M.
,
2008
, “
Powered Ankle-Foot Prosthesis
,”
IEEE Rob. Autom. Mag.
,
15
(
3
), pp.
52
59
.10.1109/MRA.2008.927697
35.
CherelleMatthys
,
P.
,
Grosu
,
A.
,
Vanderborght
,
V. B.
, and
Lefeber
,
D.
,
2012
, “
The AMP-Foot 2.0: Mimicking Intact Ankle Behavior With a Powered Transtibial Prosthesis
,” 2012 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (
BioRob
),
Rome, Italy
, June 24–27, pp.
544
549
.10.1109/BioRob.2012.6290783
36.
Hitt
,
J. K.
,
Sugar
,
T. G.
,
Holgate
,
M.
, and
Bellman
,
R.
,
2010
, “
An Active Foot-Ankle Prosthesis With Biomechanical Energy Regeneration
,”
ASME J. Medical Devices
,
4
(
1
), p.
011003
.10.1115/1.4001139
37.
Carney
,
M. E.
,
Shu
,
T.
,
Stolyarov
,
R.
,
Duval
,
J.-F.
, and
Herr
,
H.
,
2021
, “
Design and Preliminary Results of a Reaction Force Series Elastic Actuator for Bionic Knee and Ankle Prostheses
,”
IEEE Trans. Medical Rob. Bionics
,
3
(
3
), pp.
542
553
.10.1109/TMRB.2021.3098921
38.
Lamers
,
E. P.
,
Eveld
,
M. E.
, and
Zelik
,
K. E.
,
2019
, “
Subject-Specific Responses to an Adaptive Ankle Prosthesis During Incline Walking
,”
J. Biomech.
,
95
, p.
109273
.10.1016/j.jbiomech.2019.07.017
You do not currently have access to this content.