outline kinetics – linear & external forces in human motion mechanical work, power, &...
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Outline• Kinetics
– Linear & External• Forces in human motion• Mechanical work, power, & energy• Impulse-momentum
– Angular, External and Internal• Torques in human motion• Mechanical work, power, & energy• Impulse-momentum
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OutlineMuscle/Joint Mechanical work, power, & energy
DefinitionsExamples
Impulse-momentumDefinitionExamples
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OutlineMuscle/Joint Mechanical work, power, & energy
DefinitionsExamples
Impulse-momentumDefinitionExamples
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Net muscle mechanical work at a joint (Um)
Product of moment and angular displacementExample
Umus = Mmus * ∆Units: Joules
Mmus
∆Elbow
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Positive net muscle work: Mmus & ∆ in same direction
• Umus = Mmus • ∆• Muscles do work on the
forearm
Mmus
∆Elbow
Fw
Example
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• Umus = Mmus • ∆• Muscles absorb mechanical
energy
Mmus
∆Elbow
Fw
Negative net muscle work: Mmus & ∆ in opposite directions
Example
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Net muscle mechanical power (Pmus)
Product of moment and angular velocity Pmus = Umus / ∆t = Mmus *
Mmus & in same direction (same sign) Pmus > 0 (power output)
Mmus & in opposite directions (opposite signs)
Pmus < 0 (power absorption)
Mmus
Elbow
Fw
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Pm = Mm *
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Area under power vs. time is work.
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Jump: no countermovementMechanical power & work
Always positive
Mechanical work Hip > Knee >Ankle
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Compared to a jump without a countermovement, will the mechanical power in
a countermovment jump a) the same?b) different?
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Time (s)
WALK1.25 m/s
0
700Fg,y (N)
0 0.4 0.8 1.2
350
1050
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-210
0
0 0.4 0.8 1.2Time (s)
Fg,x (N)
WALK1.25 m/s
Backward
Forward
210
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Net muscle moment at the ankle during a stance phase in locomotion
Mankle = Iprox
Mmus + Mw - MFg = Iprox
Mmus = Iprox - Mw + MFg
Iprox & Mw---> segmental analysis & videoMFg ---> force platform & video
Fg
Fw
Mmus
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Walking & running: stance versus swing
Mmus = Iprox - Mw + MFg
Swing: MFg = 0
Stance: MFg large
Fg
Fw
Mmus
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MFg + Mw Mw
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MFg + Mw Mw
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Ankle net muscle moment: walk versus run
Stance: extensor moments Run (250 Nm) >> Walk (120 Nm)
Swing: net muscle moments ~ 0
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Knee net muscle moment: walk versus run
Stance: Run |Mmus| >> Walk |Mmus|
Swing: small Mmus in both
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Summary of walking & running net muscle moments
Run Mmus >> Walk Mmus
Both: Stance Mmus >> Swing Mmus
Both: Stance Ankle Mmus > Knee Mmus > Hip Mmus
Both: Swing Hip Mmus > Knee Mmus > Ankle Mmus
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U = ∫Pmusdt
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U = ∫Pmusdt
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RunningAnkle & Knee
1st half of stance: muscles absorb power 2nd half of stance: muscles produce power
Specific roles Ankle is primary power producer Knee is primary power absorber Hip has very low power output
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Leg
COM
Mechanical energy absorbed during first half of stance
stored as elastic energy in muscles and tendons recovered in second half of stance
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Walk: Inverted pendulumPassive conservation of mechanical energy
reduction in muscle power requirements
COM
Leg
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Walking net muscle powerNet muscle power
Walking <<< Running
Ankle has greatest net power production end of stance
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During walking, the knee joint generates 50Nm of extensor torque during the same interval of the stance phase when the knee joint moved from 0.14 rad of flexion to 0.2 rad of flexion in 0.02 s. Calculate the power of the knee joint muscles.
a)50Wb)-50Wc) 150 Wd)-150 W
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Is it better to walk with a flat COM?
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Joint Work
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Figure 3.34
Comparison of total joint torques during walking before and after ACL reconstruction
controls (solid lines)3 wks post (dotted lines)6 months post (dashed lines)
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Figure 3.33
Comparison of joint torques during walking before and after ACL reconstruction
controls (solid lines)3 wks post (dotted lines)6 months post (dashed lines)
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Figure 3.35
Comparison of joint powers during walking before and after ACL reconstruction
controls (solid lines)3 wks post (dotted lines)6 months post (dashed lines)
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Ankle
Knee
Hip
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Does Oscar have an advantage?a) Yesb) Noc) Does it matter?
Ankle
Knee
Hip
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OutlineMuscle/Joint Mechanical work, power, & energy
DefinitionsExamples
Impulse-momentumDefinitionExamples
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Impulse-Momentum
• Angular Momentum• Principle of Impulse Momentum• Conservation of Angular Momentum
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Angular MomentumLinear Momentum (L)
L=mvm:mass (kg)v:velocity (m/s)Units: kg-m/svector
Angular Momentum: quantity of angular motion of an object
H=IwI: moment of Inertiaw:angular velocity (rad/s)Units: kg-m2/svector
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Conservation of Angular Momentum
When gravity is the only force acting on an object, angular momentum is conserved
Angular momentum is conserved during flight
Hinitial = Hfinal
Iinitial winitial= Ifinal wfinal
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Iinitial winitial= Ifinal wfinal
• If I changes, w changes• I w
Aerial SomersaultAbout Transverse axis
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Principle of Impulse-momentum
Linear caseImpulse = DmvFavet=mvf-mvi
Angular caseImpulse = DIwTavet=Hf-Hi
When a torque is applied over a period of time, a change in angular momentum occurs
Impulse = Change in Momentum
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Tdt=d(H)Tavet=Hf-Hi
When a torque is applied over a period of time, a change in angular momentum occurs95.3 kgm2/s or 92.4 kgm2/sLoss of
– 33kgm2/s or 27.4 kgm2/s