Biomechanics of Walking and Stair Ascent and Descent

D. Gordon E. Robertson, Ph.D.

Biomechanics, Laboratory,

School of Human Kinetics,

University of Ottawa, Ottawa, CANADA

Quantitative Domains

• Temporal–Phases (stance/swing) and events

(foot-strike, toe-off), stride rate

• Kinematic (motion description)– stride length, velocity, ranges of

motion, acceleration

• Kinetic (causes of motion)– ground reaction forces, joint forces,

moments of force, work, energy and power

Temporal Analysis

• Stride time

• Stride rate = 1/rate

• Stride cadence = 120 x rate (b/min)

• Instrumentation–Photocells and timers

–Videography (1 frame = 1/30 second)

–Metronome

Motion Analysis Tools

EMG

Force platform

Cine or Video camera

Electromyography

Delsys system

Mega system

Noraxon system Bortec system

Kinematic Analysis

• Study of motion without consideration of its causes

• Motion description

• Based on Calculus developed by Newton and Leibnitz

Isaac Newton, 1642-1727

Kinematic Analysis

• Linear position– Ruler, tape measure, optical

• Angular position– Protractor, inclinometer,

goniometer

• Linear acceleration– Accelerometry, videography

• Angular acceleration– Videography

Miniature accelerometers

Manual goniometer

Motion Analysis

• Cinefilm, video or infrared video

• Subject is filmed and locations of joint centres are digitized

High-speed cinecamera

Videocamera

Infrared camera

Computerized Digitizing (APAS)

Computerized Digitizing (Simi)

Stick Figure Animation

Walking

Kinetic Analysis

Causes of motion

• Forces and moments of force

• Work, energy and power

• Impulse and momentum

• Inverse Dynamics derives forces and moments from kinematics and body segment parameters (mass, centre of gravity, and moment of inertia)

Force Platforms

2 Kistler force platforms

Ground reaction force

Steps for Inverse Dynamics

• Space diagram of the lower extremity

Divide Body into Segments and Make Free-Body Diagrams

• Make free-body diagrams of each segment

Add all Known Forces to FBD

• Weight (W)

• Ground reaction force (Fg)

Apply Newton’s Laws of Motion to Terminal Segment

• Start analysis with terminal segment(s), e.g., foot or hand

Apply Reactions of Terminal Segment to Distal End of Next Segment in Kinematic Chain

• Continue to next link in the kinematic chain, e.g., leg or forearm

Repeat with Next segment in Chain or Begin with Another Limb

• Repeat until all segments have been considered, e.g., thigh or arm

Joint 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

Normal Walking Example

• Female subject

• Laboratory walkway

• Speed was 1.77 m/s

• IFS = ipsilateral foot-strike

• ITO = ipsilateral toe-off

• CFS = contralateral foot-strike

• CTO = contralateral toe-off

Ankle angular velocity, moment of force and power

• Dorsiflexors produce dorsiflexion during swing

• Plantar flexors control dorsiflexion

• Large burst of power by plantar flexors for push-off 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Time (s)

-200

-100

0

100

-100

0

100

-10

0

10

P

ow

er

(W)

Mo

me

nt

(N.m

)

A

ng

. V

el.

(ra

d/s

)

Trial: 2SFN3Ang. velocityMomentPower

CFS ITO IFS CTO CFS ITO

Dorsiflexion

Plantar flexion

Dorsiflexors

Plantar flexors

Concentric

Eccentric

Knee angular velocity, moment of force and power

• Negative work by extensors to control flexion at push-off

• Burst of power to cushion landing

• Negative work by flexors to control extension prior to foot-strike

0.0 0.2 0.4 0.6 0.8 1.0 1.2Time (s)

-200

-100

0

100

-100

0

100

-10

0

10

P

ow

er

(W)

M

om

en

t (N

.m)

A

ng

. V

el.

(ra

d/s

)

Trial: 2SFN3Ang. velocityMomentPower

CFS ITO IFS CTO CFS ITO

Extension

Flexion

Extensors

Flexors

Concentric

Eccentric

Hip angular velocity, moment of force and power

0.0 0.2 0.4 0.6 0.8 1.0 1.2Time (s)

-200

-100

0

100

-100

0

100

-10

0

10

P

ow

er

(W)

Mo

me

nt

(N.m

)

A

ng

. V

el.

(ra

d/s

)

Trial: 2SFN3Ang. velocityMomentPower

CFS ITO IFS CTO CFS ITO

Flexion

Extension

Flexors

Extensors

Concentric

Eccentric

• Positive work by flexors to swing leg

• Positive work by extensors to extend thigh

• Negative work by flexors to control extension

Solid-Ankle, Cushioned Heel (SACH) Prostheses

Stick Figure Animation

Walking with SACH foot

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-200.

-100.

0.

100.

-100.

0.

100.

-10.

0.

10.

Po

we

r (W

)

Mo

me

nt

(N.m

)

An

gu

lar

ve

l. (

/s)

Ankle angular velocity, moment of force and power of SACH foot prosthesis

• No power produced during push-off

Trial: WB24MH-SAng. velocityNet momentPower

ITO IFS CTO CFS ITO

Dorsiflexing

Plantar flexing

Dorsiflexor

Plantar flexor

Concentric

Eccentric

• Power dissipation during weight acceptance and push-off

FlexFoot Prostheses(Energy Storing)

Recent models

Original model

Stick Figure Animation

Walking with FlexFoot prosthesis

Ankle angular velocity, moment of force and power of FlexFoot prosthesis

• Power returned during push-off

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Time (s)

-500.

-250.

0.

250.

-100.

0.

100.

-10.

0.

10.

Po

we

r (W

)

M

om

en

t (N

.m)

A

ng

ula

r v

el.

(/s

)

Trial: WB13MH-FAng. velocityNet momentPower

ITO IFS CTO CFS ITO

Dorsiflexing

Plantar flexing

Dorsiflexor

Plantar flexor

Concentric

Eccentric

Ankle angular velocity, moment of force and power of person with hemiplegia (stroke side)

• No power during push-off

0.0 0.2 0.4 0.6 0.8

Time (s)

-2000.

-1000.

0.

1000.

-200.

0.

200.

-15.

0.

15.

Po

we

r (W

)

M

om

en

t (N

.m)

A

ng

ula

r ve

l. (

/s)

Trial: WPP14EGAng. vel.Net momentPower

IFS CTO CFS ITO IFS

Dorsiflexing

Plantar flexing

Dorsiflexor

Plantar flexor

Concentric

Eccentric

Ankle angular velocity, moment of force and power of person with hemiplegia (normal side)

• Power at push-off is reduced due to slower gait

0.0 0.2 0.4 0.6 0.8

Time (s)

-2000.

-1000.

0.

1000.

-200.

0.

200.

-15.

0.

15.

P

ow

er

(W)

Mo

me

nt

(N.m

)

An

gu

lar

ve

l. (

/s)

Trial: WPN03EGAng. vel.Net momentPower

IFS CTO CFS ITO IFS

Dorsiflexing

Plantar flexing

Dorsiflexor

Plantar flexor

Concentric

Eccentric

• Negative power is also reduced

Other Gait Patterns

Above-knee Prostheses

Stick Figure Animation

Walking with Terry Fox prosthesis

Support Moment

• Used to quantify stability during stance of gait

• Sum of ankle, knee and hip moments

• Extensors moments are made positive

Msupport = Mankle + Mknee + Mhip

• Should remain positive throughout stance despite loss of function at one or more joints

• Studies have shown that even people with artificial joints produce a positive support moment throughout stance

(Winter, J. Biomech, 13, 923-927, 1980)

Support Moment during Walking

• Support moment is positive throughout stance

• Typically has two peaks one after IFS and one before ITO

0.0 0.2 0.4 0.6 0.8 1.0 1.2Time (seconds)

-200.

-100.

0.

100.

-100.

0.

100.

-100.

0.

100.

-100.

0.

100.

200.

Net

mo

men

ts o

f fo

rce

(N.m

)

Trial: CJWK

IFS CTO CFS ITO

Support moment

Hip extensor

Knee extensor

Ankle extensor• Ankle plantar

flexors are the most important from midstance to toe-off

Laboratory Stairs

• Step height = 24 cm

• Step tread = 30 cm

• Railings = 36 in.

• Height and tread are adjustable

Force platformsForce platforms

Stick Figure Animation

Up One Step from Landing

Up One Step from Landing

• Smaller ankle plantar flexor moment

• Larger than normal knee extensor moment

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3Time (seconds)

-200.

-100.

0.

100.

-100.

0.

100.

-100.

0.

100.

-100.

0.

100.

200.

Net

mo

men

ts o

f fo

rce

(N.m

)

Trial: STLUP7RH

ITO IFS ITO

Support moment

Hip extensor

Knee extensor

Ankle extensor

• Support moment similar to walking

Similarities to Walking

• Double support periods

• Ground reaction forces have double peak

• Cadence similar

• Support moment is similar (always positive with two peaks)

Differences with Walking

• Peak forces slightly higher• Centre of pressure is concentrated under

metatarsals, rarely near heel• Several types of steps

– ascent versus descent– single step up and down– double step up and down– start from or end at a landing

• Step height and tread vary from stairway to stairway

• Railings may be present

Ascent versus Descent

• Descent is more dangerous because if tripping occurs person will fall farther

• Descent is more likely to cause fall since centre of pressure and centre of gravity is closer to edge of stair

Factors Influencing Stability

• Weight

• Size of base of support (hand rails)

• Friction

• Distance from tipping edge

• Height of centre of gravity

• Visual field

• Vestibular system

• Inebriation/drugs

Stick Figure Animation

Down Two Stairs to Landing

Down Two Stairs Forwards

• Larger than normal negative power by ankle plantar flexors after foot-strike (IFS)

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1Time (seconds)

-500.

-250.

0.

250.

500.

-250.

0.

250.

-250.

0.

250.

500.

Po

wer

(w

atts

)

Trial: CJRFD

ITO IFS ITO

Hip powers

Knee powers

Ankle powers

• Positive work done after IFS by knee flexors

Possibly Safer Descent

• Descend backwards

• Centre of pressure and centre of gravity are farther from edge of stairs

• If tripping occurs person falls into stairs not down stairs

• Person will be “forced” to use railing

• Problem with seeing next step

• Some people may have problem with neck

Stick Figure Animation

Down Two Steps Backwards

Down Two Stairs Backwards

• No concentric knee power required after IFS

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1Time (seconds)

-500.

-250.

0.

250.

500.

-250.

0.

250.

-250.

0.

250.

500.

Po

wer

(w

atts

)

Trial: CJLBD

ITO IFS ITO

Hip powers

Knee powers

Ankle powers

• Larger than normal negative power by ankle plantar flexors after foot-strike (IFS)

• No push-off power needed from ankle

What’s Next

• Modify rise and tread• At-risk subjects

– Elderly– Infants– Disabled– Distracted– Prostheses– Robots

• Ramps versus stairs– Angle of ramp– Surface friction

• Cambered surfaces

Questions?

Answers?

Comments?