Biomechanics and Stair and
Ramp Ascent and Descent
D. Gordon E. Robertson, Ph.D.
Edward Lemaire, Ph.D.
François D. Beaulieu, B.Sc.
Leslie-Ann Stewart, B.Sc.
Jon Singer, B.Sc.
Biomechanics, Laboratory,
School of Human Kinetics,
University of Ottawa, Ottawa, CANADA
Motion Analysis Tools
EMG
Force platform
Cine
or
Video
camera
Kinetic Analysis
Causes of motion
• Inverse Dynamics derives forces and
moments from kinematics and body
segment parameters
• Support Moment shows effects of all
moments of lower extremity
• Joint Power Analysis determines
contributions of each joint’s moment
of force
Divide Body into Segments and
Make Free-Body Diagrams
• Make freebody diagrams
of each
segment
Apply Newton’s Laws of
Motion to Terminal Segment
• Start analysis
with terminal
segment(s),
e.g., foot
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
Repeat with Next segment in
Chain or Begin with Another Limb
• Repeat until
all segments
have been
considered,
e.g., thigh
Joint Power Analysis
An Example from Sprinting
• compute the angular velocity
of the joint
• compute the net moment
of force at the joint
20.
Extending
0.
-20.
Flexing
SR11BJ
300. Extensor
• multiply angular velocity
and moment of force to
obtain the “moment power”
0.
-300.
Flexor
2000. Concentric
• this is the power produced by
the net moment of force acting
across the joint
• it is mainly caused by muscle
forces
0.
-2000.
Eccentric
ITO
CFS
CTO
-4000.
0.0
0.1
0.2
Time (s)
IFS
0.3
0.4
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
10
Dorsiflexion
0
-10
• Dorsiflexors
produce dorsiflexion
during swing
100
Trial: 2SFN3
Ang. velocity
Moment
Power
Dorsiflexors
0
-100
• Plantar flexors
control dorsiflexion
Plantar flexion
100
Plantar flexors
Concentric
0
• Large burst of
power by plantar
flexors for push-off
-100
Eccentric
-200CFS ITO
0.0
0.2
IFS CTO
0.4
0.6
Time (s)
CFS ITO
0.8
1.0
1.2
Knee angular
velocity, moment
of force and
power
10
Extension
0
-10 Flexion
• Negative work by
flexors to control
extension prior to
foot-strike
• Burst of power to
cushion landing
• Negative work by
extensors to control
flexion at push-off
100
Trial: 2SFN3
Ang. velocity
Moment
Power
Extensors
0
-100
100
Flexors
Concentric
0
-100
Eccentric
-200CFS ITO
0.0
0.2
IFS CTO
0.4
0.6
Time (s)
CFS ITO
0.8
1.0
1.2
Hip angular
velocity, moment
of force and
power
10
Flexion
0
-10
• Positive work by
flexors to swing leg
• Positive work by
extensors to extend
thigh
• Negative work by
flexors to control
extension
100
Extension
Trial: 2SFN3
Ang. velocity
Moment
Power
Flexors
0
-100
Extensors
Concentric
100
0
-100
Eccentric
-200CFS ITO
0.0
0.2
IFS CTO
0.4
0.6
Time (s)
CFS ITO
0.8
1.0
1.2
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
(D.A. 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
200.
Support moment
100.
Trial: CJWK
0.
-100.
Hip extensor
100.
0.
-100.
100. Knee extensor
0.
• Ankle plantar flexors
are the most
important from
midstance to toe-off
-100.
100.
Ankle extensor
0.
-100.
IFS
-200.
0.0
0.2
CTO
CFS ITO
0.4
0.6
0.8
Time (seconds)
1.0
1.2
Stick Figure Animation
Up One Stair Step from Landing
Up One Step from Landing
• Support moment
similar to walking
200.
Support moment
Trial: STLUP7RH
100.
0.
-100.
• Larger than normal
knee extensor
moment in early
stance
100.
0.
-100.
100. Knee extensor
0.
-100.
100.
• Smaller ankle
plantar flexor
moment
Hip extensor
Ankle extensor
0.
-100.
IFS
ITO
-200. ITO
0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3
Time (seconds)
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
• Step height and tread vary from
stairway to stairway
• Railings may be present
Stick Figure Animation
A/K Amputee Walking Up One Stair
Introduction
• Investigate mechanics of descending stairs in
forwards and backwards directions compared
with level walking.
• Why? Descending stairs is more difficult and
dangerous than ascending stairs.
• Falls from stair descent especially in the elderly
can be fatal (Simoneau, et al., 1991; Winter,
1995)
• Macleans: 236 Canadians died in 2000 from stair
falls vs. 404 pedestrian deaths.
Research Questions
• How does stair descent differ
from level walking?
• Will peak moment and forces
about the ankle, knee and hip be
reduced in the backward stair
descent versus forward
descent?
Laboratory Stairs
•
•
•
•
Step height = 20 cm
Step tread = 30 cm
Railings = 91 cm
Height and tread are
adjustable
Force platforms
Study Design
Forces & moments of force
Ankle, Knee & Hip
10 healthy
subjects
(4 F + 6 M)
•Warm up period
•Descent Forward
•Descent Backward
•Descent Forward
No previous
at same speed as
lower
extremities backward
injuries
5 trials each
type of descent
Support moment computed
by adding 3 moments
Msupport= -Mankle+ Mknee- Mhip
(Winter, 1980)
Work done by moments
Leg closest to camera
Moment powers
Moment of force times
joint angular velocity
Stick Figure Animation
Down Two Stairs to Landing
Results
• Stance phase was 65-70% of cycle
(versus 60% for walking)
• Differences in average cycle duration:
forward (1.13 s) vs. backward (1.35 s) or
20% longer
• Ground reaction forces were larger than
walking
• Forces were farther from stair edge with
backwards
Moments of Force (Support)
Support moments larger with similar double peaks as walking
6
6
Support moment
3
3
0
0
-3
-3
Hip extensor
3
3
0
0
-3
-3
Knee extensor
3
3
0
0
-3 Ankle extensor
3
0
0
20
40
60
80
Percentage of Cycle
Forwards
Hip extensor
Knee extensor
-3 Ankle extensor
3
-3
0
Support moment
100
-3
0
20
40
60
Percentage of Cycle
80
Backwards
100
Show Animation Here
Down Two Stairs Backwards to Landing
Moments of Force (Ankle)
Ankle plantar flexor reduced (means +/- 95th% CI)
6
6
Support moment
3
3
0
0
-3
-3
Hip extensor
3
3
0
0
-3
-3
Knee extensor
3
3
0
0
-3 Ankle extensor
3
0
0
20
40
60
80
Percentage of Cycle
Forwards
Hip extensor
Knee extensor
-3 Ankle extensor
3
-3
0
Support moment
100
-3
0
20
40
60
Percentage of Cycle
80
Backwards
100
Moments of Force (Knee)
Knee extensor moment increased
6
6
Support moment
3
3
0
0
-3
-3
Hip extensor
3
3
0
0
-3
-3
Knee extensor
3
3
0
0
-3 Ankle extensor
3
0
0
20
40
60
80
Percentage of Cycle
Forwards
Hip extensor
Knee extensor
-3 Ankle extensor
3
-3
0
Support moment
100
-3
0
20
40
60
Percentage of Cycle
80
Backwards
100
Moments of Force (Hip)
Hip moments small and highly variable with little power
6
6
Support moment
3
3
0
0
-3
-3
Hip extensor
3
3
0
0
-3
-3
Knee extensor
3
3
0
0
-3 Ankle extensor
3
0
0
20
40
60
Percentage of Cycle
Forwards
Hip extensor
Knee extensor
-3 Ankle extensor
3
-3
0
Support moment
80
100
-3
0
20
40
60
Percentage of Cycle
80
Backwards
100
Comparison with Walking
Ankle Power:
No initial dorsiflexor
phase
5.0
Plantar Flexor
2.5
0.0
Plantar flexor eccentric
phase was earlier and
larger
Plantar flexor concentric
phase much smaller
(just to clear step)
Large variability during
swing phase possibly
due to uncertainty of
landing
-2.5
-5.0
Dorsiflexor
5.0
Concentric
2.5
0.0
-2.5
Eccentric
-5.0
0
10 20 30 40 50 60 70 80 90 100
Percent cycle
Forwards
Comparison with Walking
Knee Power:
5.0
Extensor
2.5
Little or no concentric
extensor phase
0.0
-2.5
-5.0
Larger eccentric
extensor phase at
midstance
Flexor
5.0
Concentric
2.5
0.0
Eccentric flexor power
throughout swing
same as walking
-2.5
Eccentric
-5.0
0
10 20 30 40 50 60 70 80 90 100
Percent cycle
Forwards
Ankle Moment and Power
Larger peak eccentric power (5%) during weight acceptance
Smaller peak plantar flexor push-off power
5.0
5.0
Plantar Flexor
Plantar Flexor
2.5
2.5
0.0
0.0
-2.5
-2.5
-5.0 Dorsiflexor
-5.0 Dorsiflexor
5.0 Concentric
5.0 Concentric
2.5
2.5
0.0
0.0
-2.5
-5.0
0
Eccentric
10 20 30 40 50 60 70 80 90 100
Percent cycle
Forwards
-2.5
-5.0
0
Eccentric
10 20 30 40 50 60 70 80 90 100
Percent cycle
Backwards
Knee Moment and Power
Slightly more extensor concentric work
Significantly reduced peak extensor eccentric power
5.0
5.0
Extensor
Extensor
2.5
2.5
0.0
0.0
-2.5
-2.5
-5.0 Flexor
-5.0 Flexor
5.0 Concentric
5.0 Concentric
2.5
2.5
0.0
0.0
-2.5
-5.0
0
Eccentric
10 20 30 40 50 60 70 80 90 100
Percent cycle
Forwards
-2.5
-5.0
0
Eccentric
10 20 30 40 50 60 70 80 90 100
Percent cycle
Backwards
Discussion
Benefits of Backwards Stair Descent
• 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 more inclined to use handrails
• Moments and powers were smaller than
forwards but larger than walking
• No concentric ankle power needed (e.g.,
B-K amputees)
Discussion
Concerns with Backwards Stair Descent
• Problems with seeing next step and
landing
• Unconventional therefore may affect
compliance
• Does require railings for most
people
• Irregular stairs may be problematic
Stick Figure Animation
A-K C-Leg Down Two Stairs to Landing
A-K amputee Down Stairs
Moment Powers:
4
Little or ankle power
2
Trial: C-Leg
Hip
0
Large eccentric knee
extensor phase at
end of stance
-2
-4
2
Knee
0
-2
Concentric hip flexor
power at end of
stance and into swing
same as walking
-4
2
0
-2
-4
0
Ankle
10
20
30
40
50
60
Percentage of Stride
70
80
90
100
Laboratory Ramp
•
•
•
•
10-degree incline
one step before ramp
opposite leg on ramp
2nd step on ramp
Force platforms
Stick Figure Animation
Walking Up 10-degree Ramp
Up a 10-Degree Ramp
Moments:
3
Larger knee extensor
moment at beginning
of stance
Ankle plantarflexor
moment similar to
walking
Trial: RUAP03
1
0
Net moments of force (N.m/kg)
Support moment
similar to walking but
smaller 2nd peak
before ramp
Support
moment
2
Hip
extensor
-1
1
0
-1
Knee
extensor
1
0
-1
Ankle
extensor
1
0
-1
TO
FS
-2
0.0
0.2
0.4
0.6
0.8
FS
1.0
1.2
Time (seconds)
TO
1.4
1.6
1.8
2.0
Up a 10-Degree Ramp
Moment Powers:
Larger concentric knee
extensor phase at
midstance
Trial: RUAP03
250.
H1
Hip
powers
H3
H1
H3
0.
H2
H2
- 250.
Knee
powers
250.
Power (watts)
Concentric hip flexor
power at end of
stance and into swing
same as walking
500.
K2
0.
K4
K3
- 250.
K1
K3
500.
A2
A2
Ankle
powers
250.
0.
Ankle power similar to
walking
A1
A1
- 250.
FS
- 500.
0.0
TO
0.2
0.4
0.6
0 .8
FS
1.0
1.2
Time (seconds)
TO
1.4
1.6
1.8
2.0
Questions?
Answers?
Comments?