Abstract

This paper presents a complete kinematic model of the tibiofemoral joint (TFJ) based on a RRPP + 4-SPS parallel mechanism, where R, P, and S stand for revolute, prismatic, and spherical joints, respectively. The model accounts for the contact between tibia and femur, and the four major ligaments: anterior cruciate, posterior cruciate, medial collateral, and lateral collateral, with anatomical significance in their length variations. An experimental flexion passive motion task is performed, and the kinematic model is tested to determine its capability to reproduce the workspace of the motion task. In addition, an optimization process is performed to simulate prescribed ligament length variations during the motion task. The proposed kinematic model is capable to reproduce with high accuracy an experimental three-dimensional workspace, and at the same time, to simulate prescribed ligament length variation during the spatial flexion task. Prescribed ligament length variations are achieved through an optimization process of the ligament insertion points. This model can be used to improve the multibody kinematic optimization (MKO) process during gait analysis, and also in the design of rehabilitation devices as well as trajectories to accelerate the recovery of injured ligaments. The model shows potential to predict ligament length variations during different motion tasks, and can serve as a basis to develop complex models for kinetostatic and dynamic analyses without dealing with computationally expensive models.

References

1.
An
,
V. V.
,
Mirza
,
Y.
,
Mazomenos
,
E.
,
Vasconcelos
,
F.
,
Stoyanov
,
D.
, and
Oussedik
,
S.
,
2018
, “
Arthroscopic Simulation Using a Knee Model Can Be Used to Train Speed and Gaze Strategies in Knee Arthroscopy
,”
Knee
,
25
(
6
), pp.
1214
1221
.10.1016/j.knee.2018.05.019
2.
Essinger
,
J.
,
Leyvraz
,
P.
,
Heegard
,
J.
, and
Robertson
,
D.
,
1989
, “
A Mathematical Model for the Evaluation of the Behaviour During Flexion of Condylar-Type Knee Prostheses
,”
J. Biomech.
,
22
(
11–12
), pp.
1229
1241
.10.1016/0021-9290(89)90225-X
3.
Goodfellow
,
J.
, and
O'Connor
,
J.
,
1978
, “
The Mechanics of the Knee and Prosthesis Design
,”
J. Bone Jt. Surg. Br. Vol.
,
60-B
(
3
), pp.
358
369
.10.1302/0301-620X.60B3.581081
4.
Stagni
,
R.
,
Fantozzi
,
S.
, and
Cappello
,
A.
,
2009
, “
Double Calibration vs. Global Optimisation: Performance and Effectiveness for Clinical Application
,”
Gait Posture
,
29
(
1
), pp.
119
122
.10.1016/j.gaitpost.2008.07.008
5.
O'Connor
,
J. J.
,
Shercliff
,
T. L.
,
Biden
,
E.
, and
Goodfellow
,
J. W.
,
1989
, “
The Geometry of the Knee in the Sagittal Plane
,”
Proc. Inst. Mech. Eng., Part H
,
203
(
4
), pp.
223
233
.10.1243/PIME_PROC_1989_203_043_01
6.
Moeinzadeh
,
M.
,
Engin
,
A.
, and
Akkas
,
N.
,
1982
, “
Two-Dimensional Dynamic Modeling of Human Knee Joint
,”
J. Biomech.
,
15
(
4
), p.
346
.10.1016/0021-9290(82)90225-1
7.
Van Eijden
,
T.
,
Kouwenhoven
,
E.
,
Verburg
,
J.
, and
Weijs
,
W.
,
1986
, “
A Mathematical Model of the Patellofemoral Joint
,”
J. Biomech.
,
19
(
3
), pp.
219
229
.10.1016/0021-9290(86)90154-5
8.
Abdel-Rahman
,
E.
, and
Hefzy
,
M.
,
1993
, “
A Two-Dimensional Dynamic Anatomical Model of the Human Knee Joint
,”
ASME J. Biomech. Eng.
,
115
(
4A
), pp.
357
365
.10.1115/1.2895498
9.
Gill
,
H. S.
, and
O'Connor
,
J. J.
,
1996
, “
Biarticulating Two-Dimensional Computer Model of the Human Patellofemoral Joint
,”
Clin. Biomech.
,
11
(
2
), pp.
81
89
.10.1016/0268-0033(95)00021-6
10.
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2011
, “
A Sequentially-Defined Stiffness Model of the Knee
,”
Mech. Mach. Theory
,
46
(
12
), pp.
1920
1928
.10.1016/j.mechmachtheory.2011.07.006
11.
Duprey
,
S.
,
Cheze
,
L.
, and
Dumas
,
R.
,
2010
, “
Influence of Joint Constraints on Lower Limb Kinematics Estimation From Skin Markers Using Global Optimization
,”
J. Biomech.
,
43
(
14
), pp.
2858
2862
.10.1016/j.jbiomech.2010.06.010
12.
Wilson
,
D. R.
, and
O'Connor
,
J. J.
,
1997
, “
A Three-Dimensional Geometric Model of the Knee for the Study of Joint Forces in Gait
,”
Gait Posture
,
5
(
2
), pp.
108
115
.10.1016/S0966-6362(96)01080-6
13.
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2011
, “
A New Kinematic Model of the Passive Motion of the Knee Inclusive of the Patella
,”
ASME J. Mech. Rob.
,
3
(
4
), p.
041003
.10.1115/1.4004890
14.
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2011
, “
A Novel 3D Parallel Mechanism for the Passive Motion Simulation of the Patella-Femur-Tibia Complex
,”
Meccanica
,
46
(
1
), pp.
207
220
.10.1007/s11012-010-9405-x
15.
Leardini
,
A.
,
Belvedere
,
C.
,
Nardini
,
F.
,
Sancisi
,
N.
,
Conconi
,
M.
, and
Parenti-Castelli
,
V.
,
2017
, “
Kinematic Models of Lower Limb Joints for Musculo-Skeletal Modelling and Optimization in Gait Analysis
,”
J. Biomech.
,
62
, pp.
77
86
.10.1016/j.jbiomech.2017.04.029
16.
Ottoboni
,
A.
,
Parenti-Castelli
,
V.
,
Sancisi
,
N.
,
Belvedere
,
C.
, and
Leardini
,
A.
,
2010
, “
Articular Surface Approximation in Equivalent Spatial Parallel Mechanism Models of the Human Knee Joint: An Experiment-Based Assessment
,”
Proc. Inst. Mech. Eng., Part H
,
224
(
9
), pp.
1121
1132
.10.1243/09544119JEIM684
17.
Bergamini
,
E.
,
Pillet
,
H.
,
Hausselle
,
J.
,
Thoreux
,
P.
,
Guerard
,
S.
,
Camomilla
,
V.
,
Cappozzo
,
A.
, and
Skalli
,
W.
,
2011
, “
Tibio-Femoral Joint Constraints for Bone Pose Estimation During Movement Using Multi-Body Optimization
,”
Gait Posture
,
33
(
4
), pp.
706
711
.10.1016/j.gaitpost.2011.03.006
18.
Gasparutto
,
X.
,
Dumas
,
R.
, and
Jacquelin
,
E.
,
2012
, “
Multi-Body Optimisation With Deformable Ligament Constraints: Influence of Ligament Geometry
,”
Comput. Methods Biomech. Biomed. Eng.
,
15
(
sup1
), pp.
191
193
.10.1080/10255842.2012.713666
19.
Parenti-Castelli
,
V.
, and
Di Gregorio
,
R.
,
2000
, “
Parallel Mechanisms Applied to the Human Knee Passive Motion Simulation
Advances in Robot Kinematics
,
Springer
, Dordrecht, pp.
333
344
.10.1007/978-94-011-4120-8_35
20.
Di Gregorio
,
R.
, and
Parenti-Castelli
,
V.
,
2003
, “
A Spatial Mechanism With Higher Pairs for Modelling the Human Knee Joint
,”
ASME J. Biomech. Eng.
,
125
(
2
), pp.
232
237
.10.1115/1.1559895
21.
Parenti-Castelli
,
V.
,
Leardini
,
A.
,
Di Gregorio
,
R.
, and
O'Connor
,
J. J.
,
2004
, “
On the Modeling of Passive Motion of the Human Knee Joint by Means of Equivalent Planar and Spatial Parallel Mechanisms
,”
Auton. Robots
,
16
(
2
), pp.
219
232
.10.1023/B:AURO.0000016867.17664.b1
22.
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2007
, “
A New 3D Kinematic Model of the Tibio-Femoral Joint During Knee Passive Motion
,”
Proceedings of AIMeTA
, Brescia, Italy, Sept. 11–14, pp.
11
14
.
23.
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2010
, “
A 1-Dof Parallel Spherical Wrist for the Modelling of the Knee Passive Motion
,”
Mech. Mach. Theory
,
45
(
4
), pp.
658
665
.10.1016/j.mechmachtheory.2009.11.009
24.
da Luz
,
S. B.
,
Modenese
,
L.
,
Sancisi
,
N.
,
Mills
,
P. M.
,
Kennedy
,
B.
,
Beck
,
B. R.
, and
Lloyd
,
D. G.
,
2017
, “
Feasibility of Using Mris to Create Subject-Specific Parallel-Mechanism Joint Models
,”
J. Biomech.
,
53
, pp.
45
55
.10.1016/j.jbiomech.2016.12.018
25.
Sintini
,
I.
,
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2018
, “
Comparison Between Anatomical and Approximate Surfaces in a 3D Kinetostatic Model of the Knee for the Study of the Unloaded and Loaded Joint Motion
,”
Meccanica
,
53
(
1–2
), pp.
7
20
.10.1007/s11012-017-0696-z
26.
Barzan
,
M.
,
Modenese
,
L.
,
Carty
,
C. P.
,
Maine
,
S.
,
Stockton
,
C. A.
,
Sancisi
,
N.
,
Lewis
,
A.
,
Grant
,
J.
,
Lloyd
,
D. G.
, and
da Luz
,
S. B.
,
2019
, “
Development and Validation of Subject-Specific Pediatric Multibody Knee Kinematic Models With Ligamentous Constraints
,”
J. Biomech.
,
93
, pp.
194
203
.10.1016/j.jbiomech.2019.07.001
27.
Hashemi
,
J.
,
Chandrashekar
,
N.
,
Gill
,
B.
,
Beynnon
,
B. D.
,
Slauterbeck
,
J. R.
,
Schutt
,
R. C.
, Jr.
,
Mansouri
,
H.
, and
Dabezies
,
E.
,
2008
, “
The Geometry of the Tibial Plateau and Its Influence on the Biomechanics of the Tibiofemoral Joint
,”
J. Bone Jt. Surg. Am. Vol.
,
90
(
12
), pp.
2724
2734
.10.2106/JBJS.G.01358
28.
Matsuda
,
S.
,
Miura
,
H.
,
Nagamine
,
R.
,
Urabe
,
K.
,
Ikenoue
,
T.
,
Okazaki
,
K.
, and
Iwamoto
,
Y.
,
1999
, “
Posterior Tibial Slope in the Normal and Varus Knee
,”
Am. J. Knee Surg.
,
12
(
3
), pp.
165
168
.http://europepmc.org/article/MED/10496466
29.
Griffin
,
F.
,
Math
,
K.
,
Scuderi
,
G.
,
Insall
,
J.
, and
Poilvache
,
P.
,
2000
, “
Anatomy of the Epicondyles of the Distal Femur: Mri Analysis of Normal Knees
,”
J. Arthroplasty
,
15
(
3
), pp.
354
359
.10.1016/S0883-5403(00)90739-3
30.
Netter
,
F.
,
2017
,
Atlas of Human Anatomy, E-Book
,
Elsevier Health Sciences
, Amsterdam, The Netherlands.
31.
Grood
,
E.
, and
Suntay
,
W.
,
1983
, “
A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee
,”
ASME J. Biomech. Eng.
,
105
(
2
), pp.
136
144
.10.1115/1.3138397
32.
Kapandji
,
I.
,
2010
, “
The Physiology of the Joint
,”
Churchill Livingstone
,
2
.
33.
Gollehon
,
D.
,
Torzilli
,
P.
, and
Warren
,
R.
,
1987
, “
The Role of the Posterolateral and Cruciate Ligaments in the Stability of the Human Knee. A Biomechanical Study
,”
J. Bone Jt. Surg. Am. Vol.
,
69
(
2
), pp.
233
242
.10.2106/00004623-198769020-00010
34.
Belvedere
,
C.
,
Ensini
,
A.
,
Feliciangeli
,
A.
,
Cenni
,
F.
,
D'Angeli
,
V.
,
Giannini
,
S.
, and
Leardini
,
A.
,
2012
, “
Geometrical Changes of Knee Ligaments and Patellar Tendon During Passive Flexion
,”
J. Biomech.
,
45
(
11
), pp.
1886
1892
.10.1016/j.jbiomech.2012.05.029
35.
LaPrade
,
R.
,
Ly
,
T.
,
Wentorf
,
F.
, and
Engebretsen
,
L.
,
2003
, “
The Posterolateral Attachments of the Knee
,”
Am. J. Sports Med.
,
31
(
6
), pp.
854
860
.10.1177/03635465030310062101
36.
Bradley
,
J.
,
FitzPatrick
,
D.
,
Daniel
,
D.
,
Shercliff
,
T.
, and
O'Connor
,
J.
,
1988
, “
Orientation of the Cruciate Ligament in the Sagittal Plane. A Method of Predicting Its Length-Change With Flexion
,”
J. Bone Jt. Surg. Br. Vol.
,
70-B
(
1
), pp.
94
99
.10.1302/0301-620X.70B1.3339068
37.
Friederich
,
N. F.
,
Müller
,
W.
, and
O'Brien
,
W. R.
,
1992
, “
Clinical Application of Biomechanic and Functional Anatomical Findings of the Knee Joint
,”
Der Orthopade
,
21
(
1
), pp.
41
50
.https://pubmed.ncbi.nlm.nih.gov/1549337/
38.
Lu
,
Y.
, and
Xu
,
J.-Y.
,
2008
, “
Simulation of Three-Dimensional Free-Form Surface Normal Machining by 3sps+Rrpu and 2sps+Rrprr Parallel Machine Tools
,”
Proc. Inst. Mech. Eng., Part B
,
222
(
4
), pp.
485
494
.10.1243/09544054JEM900
39.
Zhang
,
Z.
,
1999
, “
Flexible Camera Calibration by Viewing a Plane From Unknown Orientations
,”
ICCV
,
99
(
1
), pp.
666
673
.10.1109/ICCV.1999.791289
40.
Bouguet
,
J.-Y.
,
2004
, “
Camera Calibration Toolbox for Matlab
,” accessed Mar. 28, 2019, http://www.vision.caltech.edu/bouguetj/calib_doc/
41.
Leardini
,
A.
,
Chiari
,
L.
,
Della Croce
,
U.
, and
Cappozzo
,
A.
,
2005
, “
Human Movement Analysis Using Stereophotogrammetry—Part 3: Soft Tissue Artifact Assessment and Compensation
,”
Gait Posture
,
21
(
2
), pp.
212
225
.10.1016/j.gaitpost.2004.05.002
42.
Cappozzo
,
A.
,
Catani
,
F.
,
Della Croce
,
U.
, and
Leardini
,
A.
,
1995
, “
Position and Orientation in Space of Bones During Movement: Anatomical Frame Definition and Determination
,”
Clin. Biomech.
,
10
(
4
), pp.
171
178
.10.1016/0268-0033(95)91394-T
43.
Kainz
,
H.
,
Graham
,
D.
,
Edwards
,
J.
,
Walsh
,
H.
,
Maine
,
S.
,
Boyd
,
R. N.
,
Ll
,
D. G.
,
Modenese
,
L.
, and
Carty
,
C.
,
2017
, “
Reliability of Four Models for Clinical Gait Analysis
,”
Gait Posture
,
54
, pp.
325
331
.10.1016/j.gaitpost.2017.04.001
44.
Akbarshahi
,
M.
,
Schache
,
A.
,
Fernandez
,
J.
,
Baker
,
R.
,
Banks
,
S.
, and
Pandy
,
M.
,
2010
, “
Non-Invasive Assessment of Soft-Tissue Artifact and Its Effect on Knee Joint Kinematics During Functional Activity
,”
J. Biomech.
,
43
(
7
), pp.
1292
1301
.10.1016/j.jbiomech.2010.01.002
45.
Wang
,
C.
,
Walker
,
P.
, and
Wolf
,
B.
,
1973
, “
The Effects of Flexion and Rotation on the Length Patterns of the Ligaments of the Knee
,”
J. Biomech.
,
6
(
6
), pp.
587
596
.10.1016/0021-9290(73)90016-X
46.
Shakespeare
,
D.
, and
Fick
,
D.
,
2005
, “
Patellar Instability-Can the tt-tg Distance Be Measured Clinically?
,”
Knee
,
12
(
3
), pp.
201
204
.10.1016/j.knee.2003.08.007
47.
Iwaki
,
H.
,
Pinskerova
,
V.
, and
Freeman
,
M.
,
2000
, “
Tibiofemoral Movement 1: The Shapes and Relative Movements of the Femur and Tibia in the Unloaded Cadaver Knee
,”
J. Bone Jt. Surg. Br. Vol.
,
82-B
(
8
), pp.
1189
1195
.10.1302/0301-620X.82B8.0821189
48.
Angeles
,
J.
,
2002
,
Fundamentals of Robotic Mechanical Systems
, Ed. 2,
Springer
, New York.
You do not currently have access to this content.