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Computational Biomechanics 2017
Lecture 04:
Forward vs. Inverse
Multi Body Dynamics
Ulli Simon, Martin Pietsch, Matthias Kost, Lucas Engelhardt
Scientific Computing Centre Ulm, UZWR Ulm University
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Mehrkörpersysteme (MKS):
Zum Merken:
MK-Modelle bestehen aus:
• Starrkörpern (mit Massen, Massenmomente)
• Gelenken (Bindungen)
Quelle: IFM, TU Chemnitz, alaska Quelle: UFB, Forster&Simon
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Beispiel: Kurbelantrieb
Raddampfer, New Orleans
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2D MK-Modell
Modellbildung:
• 2 starre Körper:
• 3 Gelenke:
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Freiheitsgrade und Bindungen
Zum Merken:
Gelenke sind Bindungen; sie reduzieren FG des Systems:
2D: FG Gesamtsystem = Anzahl Körper x 3 – Anzahl Bindungen
3D: FG Gesamtsystem = Anzahl Körper x 6 – Anzahl Bindungen
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Kinematik im 2D-Raum
Zusammenbau-Bedingungen:
• Gelenk A:
• Gelenk B:
• Gelenk C:
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0α t
Bindungsgleichungen (constraint equations)
0
cossin
sincos
4P
214P1P
214P1P
1P
1P
y
βlαlyy
βlαlxx
y
x
Antrieb: Rheonome Bindungen
(driver constraints)
Gelenke: kinematische-Bindungen
(kinematic constraints)
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(Vorwärts-)Dynamik / Inverse Dynamik
(Vorwärts-)Dynamik
Gegeben: MKS mit FG > 0, eingeprägte (äußere) Kräfte
Gesucht: Bewegung des MKS
Lösung: Numerische (Vorwärts-)Integration
Inverse Dynamik
Gegeben: MKS mit FG = 0, (Gemessene) Bewegung (z.B.: Ganganalyse)
Gesucht: Kräfte als Ursache der Bewegung (z.B.: Muskelkräfte)
Lösung: Numerisches Differenzieren, nichtlineare Gleichungssysteme, evtl.
Optimierungverfahren
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(Vorwärts-)Dynamik in der Unfallforschung:
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Beispiel: Eigener Versuchsstand zum Schleudertrauma
Schienen
Kopfdummy
Präparat
Schlitten
pneumatische Beschleunigungseinheit
F
Kipp-Plattform
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Beispiel: Simulation des Experiments mit „Madymo“
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Musculoskeletal Models —
Inverse Dynamics & Optimization
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Software
AnyBody
(http://www.anybodytech.com/)
Selfe-developed:
UFBSIM (http://www.biomechanics.de
www.uzwr.de)
Von Erik Forster
OpenSim
(http://opensim.stanford.edu/)
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Inverse Dynamics & Optimization
Anatomical Model
Inverse
Dynamics Movement
External Forces
Joint Reactions
Optimization
Muscle Forces Joint Contact
Forces
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Optimization Criterion:
Polynomial Criterion:
i
p
i
i
f
f
max,
GminG
Soft Saturation Criterion:
i
p
p
i
i
f
f
max,
1G
min/max Criterion:
i
i
f
f
max,
maxG
Optimization
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Two-Muscle Example, Synergy
b
af
b
cff
cfbfaf
MextM
extMM
12
21Moment equilibrium:
Static situation
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p = 1 p = 2
p = 3 (p = ∞)
“min/max”
Objective Function in the Activation Space
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Soft Saturation
p = 2 p = 3
i
p
p
i
i
f
f
max,
1G
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Problem: Predicting antagonistic muscle activity
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Objective function:
i
iifG
Optimization criterion:
minG
Extension:
)()( max sii x
xS – Shift parameter
Shift Factor (“Night and Fog Factor”) Forster et al.,
J Biomech 2004
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Two-Muscle Example, Co-Contraction
Moment equilibrium:
b
af
b
cff
cfbfaf
MextM
extMM
12
21
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Objective Function in the Activation Space
p = 2 p = 2
and shift
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Results: Muscle Activity
Conventional
Quadratic Criterion
xs=0.0
Quadratic Criterion with Extension
xs=0.2 xs=0.4
Flexor and extensor activity Flexor activity only
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Results: Muscle Activity
Conventional
Quadratic Criterion
xs=0.0
Quadratic Criterion with Extension
xs=0.2 xs=0.4
Preloading of joint
Flexor and extensor activity Flexor activity only
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Schaf: Anatomie
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Schaf: Gangzyklus
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Schaf: Interfragmentäre Bewegung
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Musculoskeletal Model: UFBSim Example
Human Lower Limb:
4 Segments
3 Joints
51 Muscles
5 DOF
Input data adapted from
Bergmann et al., 1998
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Human: Anatomie
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Human: Ganganalyse
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Human: Gangzyklus
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Results
Predicted hip contact forces during normal walking of one trial of normal walking for one subject over time
linear min/max
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DACHFx
Improvements:
18 segments (bones)
47 muscles
25 joints
32 DOF
22-May-17 41
Item 1: Bachelor thesis Dominik Vogelaar
Lucas Engelhardt, Dominik Vogelaar, Ulrich Simon