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Moment Power Analysis andAbsolute Power Method
D. Gordon E. Robertson, PhD, FCSB
Biomechanics Laboratory,
School of Human Kinetics,
University of Ottawa, Ottawa, Canada1Biomechanics Lab., University of Ottawa
Biomechanics Lab., University of Ottawa 2
Inverse Dynamics Review
• divide body into kinematic chains• divide chains into segments• from free-body diagrams
combine forces at each joint into a single “net force and moment of force”
• measure external forces and their points of application
• compute net forces and moments starting at distal segment then proceeding up the chain
Fground
FankleMankle k
Biomechanics Lab., University of Ottawa 3
External Work
• Inverse Dynamics Method– compute net moments of
force at each joint
• Integrate (sum) over time and sum over the powers produced by the net moments of force at each joint (j)
• External work =
jjt) = Pjt)
Biomechanics Lab., University of Ottawa 4
Internal Work by theAbsolute Power Method
• take absolute values of moment powers
• sum over all joint moments and over duration of movement
• Total mechanical work =
jjt) = Pjt)• Internal work = Total mechanical work – External work
Biomechanics Lab., University of Ottawa 5
Moment Power Analysis
0.0 0.1 0.2 0.3 0.4Time (s)
-4000.
-2000.
0.
2000.
-300.
0.
300.
-20.
0.
20.
Pow
er
(W)
Mom
en
t (N
.m)
A
ng
ula
r vel.
(/s
)
SR11BJ
ITO CFS CTO IFS
Extending
Flexing
Extensor
Flexor
Concentric
Eccentric
• compute the net moment of force at the joint
• multiply angular velocity and moment of force to obtain the “moment power”
• this is the power produced by the net moment of force acting across the joint
• it is mainly caused by muscle forces
• compute the angular velocity of the joint
Biomechanics Lab., University of Ottawa 6
Moment Power Analysis
0.0 0.1 0.2 0.3 0.4Time (s)
-4000.
-2000.
0.
2000.
-300.
0.
300.
-20.
0.
20.
Pow
er
(W)
Mom
en
t (N
.m)
A
ng
ula
r vel.
(/s
)
SR11BJ
ITO CFS CTO IFS
Extending
Flexing
Extensor
Flexor
Concentric
Eccentric
• net moment of force indicates which “muscle group” or “single equivalent muscle” is acting
• moment power tells what the moment of force is doing
• positive power shows “concentric work” while negative power shows “eccentric work”
• angular velocity determines whether joint is flexing or extending
Biomechanics Lab., University of Ottawa 7
Limitations & Errors• can only be used on “free-ended”
extremities or extremities where external forces can be measured (by force platforms or force transducers)
• cannot be used with closed kinematic chains (slap shot, golf, batting, etc.)
• assumes elastic storage and release of energy is due to muscle eccentric and concentric work, respectively
• assumes no multijoint transfers of energy• therefore overestimates internal work
External, Total and Internal Work
Absolute work method
Wexternal = nEtotal body )
= Efinal − Einitial
Wtotal = n|Etotal body |
Winternal = Wtotal − Wexternal
Absolute power method
W*external = njjt)
= nPjt)
W*total = njjjt )
= njPj t )
W*internal = W*total − W*external
Biomechanics Lab., University of Ottawa 8
