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

OutlineMuscle/Joint Mechanical work, power, & energy

DefinitionsExamples

Impulse-momentumDefinitionExamples

OutlineMuscle/Joint Mechanical work, power, & energy

DefinitionsExamples

Impulse-momentumDefinitionExamples

Net muscle mechanical work at a joint (Um)

Product of moment and angular displacementExample

Umus = Mmus * ∆Units: Joules

Mmus

∆Elbow

Positive net muscle work: Mmus & ∆ in same direction

• Umus = Mmus • ∆• Muscles do work on the

forearm

Mmus

∆Elbow

Fw

Example

• Umus = Mmus • ∆• Muscles absorb mechanical

energy

Mmus

∆Elbow

Fw

Negative net muscle work: Mmus & ∆ in opposite directions

Example

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

Pm = Mm *

Area under power vs. time is work.

Jump: no countermovementMechanical power & work

Always positive

Mechanical work Hip > Knee >Ankle

Compared to a jump without a countermovement, will the mechanical power in

a countermovment jump a) the same?b) different?

Time (s)

WALK1.25 m/s

0

700Fg,y (N)

0 0.4 0.8 1.2

350

1050

-210

0

0 0.4 0.8 1.2Time (s)

Fg,x (N)

WALK1.25 m/s

Backward

Forward

210

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

Walking & running: stance versus swing

Mmus = Iprox - Mw + MFg

Swing: MFg = 0

Stance: MFg large

Fg

Fw

Mmus

MFg + Mw Mw

MFg + Mw Mw

Ankle net muscle moment: walk versus run

Stance: extensor moments Run (250 Nm) >> Walk (120 Nm)

Swing: net muscle moments ~ 0

Knee net muscle moment: walk versus run

Stance: Run |Mmus| >> Walk |Mmus|

Swing: small Mmus in both

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

U = ∫Pmusdt

U = ∫Pmusdt

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

Leg

COM

Mechanical energy absorbed during first half of stance

stored as elastic energy in muscles and tendons recovered in second half of stance

Walk: Inverted pendulumPassive conservation of mechanical energy

reduction in muscle power requirements

COM

Leg

Walking net muscle powerNet muscle power

Walking <<< Running

Ankle has greatest net power production end of stance

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

Is it better to walk with a flat COM?

Joint Work

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)

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)

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)

Ankle

Knee

Hip

Does Oscar have an advantage?a) Yesb) Noc) Does it matter?

Ankle

Knee

Hip

OutlineMuscle/Joint Mechanical work, power, & energy

DefinitionsExamples

Impulse-momentumDefinitionExamples

Impulse-Momentum

• Angular Momentum• Principle of Impulse Momentum• Conservation of Angular Momentum

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

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

Iinitial winitial= Ifinal wfinal

• If I changes, w changes• I w

Aerial SomersaultAbout Transverse axis

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

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