Movement Biomechanics
of Human Gait
SP2004N Biomechanics
http://homepages.unl.ac.uk/~woodwarc
1
Plan
1.
2.
3.
Basic terms and definitions
Overview
Forces: weight, GRF and
muscle
4. “Determinants” of gait
5. Energy considerations
6. Running vs walking
Self-directed learning supplement:
Joint movements and muscles
2
Gait
• movements that produces locomotion
• including, for humans:
–
–
–
–
walking,
running,
swimming,
cycling, etc
• characteristics:
– energy-economical, particularly walking
– flexibility to cope with different speeds, terrains etc.
– sophisticated control mechanisms (bipedal gait inherently
unstable)
3
Basic terms
• Stride: a complete gait cycle, measured from one
heelstrike to next heelstrike of the same foot
• Step (=pace): interval from heelstrike of one foot to
subsequent heelstrike of the other foot
• Therefore: 1 stride = 2 steps
• The terms “stride” and “step/pace” may refer to any of
the following properties of the relevant movement:
• time duration
• distance covered
• number
4
Note:
•Alternating periods of double and single support
•About 70:30 split between single and double support in normal
walking
5
• Cadence: = steps taken per minute
• Cycle time (= stride time): stride duration in seconds
• Therefore, cycle time = stride duration
= 2 x step duration
= 2 x 60/cadence = 120/cadence
• For young adult males:
Cadence
Cycle
Time (s)
Stride
length (m)
Speed
(m s-1)
90-135
0.9-1.3
1.2-1.8
1.1-1.8
• Natural walking speeds, and stride lengths, are close to the
optimum for energy efficiency
• Walking speeds higher in towns than in rural environments
6
Walking and running efficiency
(a) Metabolic power (W)
This diagram shows the metabolic
power (i.e. energy used per second)
to support walking (blue) and
running (red) at different speeds.
Note the disproportionate increase
in energy usage at fast walking
speeds. So slow walking is very
economical, because the blue line
stays close to the x-axis up to about
2 m/s. But faster walking and
running are not economical.
7
Walking and running efficiency
(b) Economy (J m-1)
This slide shows the
metabolic energy usage per
metre of movement (contrast
with energy usage per second
on the previous slide).
Blue=walking; red=running
Note the minimum energy
usage at intermediate walking
speeds, indicating optimum
efficiency for gait on a per
metre basis
8
Forces
• The principal forces are:
– body weight (BW)
– ground reaction force (GRF)
– muscle force (MF)
• BW and GRF are external forces; so the movement
of the centre of mass (CoM) can be predicted from
them alone.
• MF must be examined however if we wish to
consider either of the following:
– movements of individual limbs or body segments,
– why GRF changes in magnitude and direction during
the gait cycle.
9
Vitally important point:
Muscle forces can only influence
the movement of the body as a
whole indirectly, by their effects
on the GRF
10
The gait mechanism: an
overview
• Walking is a precise, co-ordinated set of movements
involving multiple joints and body segments
• It comprises a pattern of alternating action of the two
lower limbs
• Pendulum-like movements of the limbs give rise to
two distinct phases: swing and support (or stance)
• In walking, but not running, the support phases of the
two legs overlap
11
Walking as a “controlled fall”
• One way of beginning to understand the mechanics of
walking is to view the movements as a “controlled fall”
• When starting a walk, we lean forward, overbalancing
from the equilibrium position.
• This gives the upper part of the body forwards (and
downwards) motion
• As the body falls forwards, a leg is extended forwards and
halts the fall
• At the same time, the other leg “kicks off” in order to keep
the body moving forwards.
• This forward momentum carries the body forward into the
next forward fall, i.e. the start of the next step
12
Walking as a controlled fall:
forces involved
• When starting to move, we lean forward (MF)
• As the body starts to fall (BW), a leg is extended
forwards and halts the fall (MF; GRF)
• At the same time, the other leg “kicks off, upwards
and forwards” (MF; GRF) in order to keep the body
moving forwards.
• This forward momentum carries the body forward into
the next forward fall, i.e. the start of the next step
13
Body weight
• Always acts vertically downwards from the CoM
• If its line of action does not pass through a joint, it will
produce a torque about that joint
• The torque will cause rotation at the joint unless it is
opposed by another force (e.g. muscle, or ligament)
• BW contributes to GRF
14
Ground reaction force
“Action” force
• Push exerted on ground by foot
• Results from the sum of the following
Body weight
+ impact force of foot on ground (at footstrike only)
+ “pushing force” from contraction of extensor
muscles (towards end of stance phase)
“Reaction” force
• Push exerted by ground on foot, as a consequence of Newton’s
3rd Law.
• Equal magnitude, opposite direction, same point of application
as action force.
• If line of the reaction force does not pass through a joint, it will
produce a torque about that joint
15
Muscle force
In gait, as in all human movement, muscle
activation generates internal joint moments
(torques) that:
–
–
–
–
–
Contribute to ground reaction force
Ensure balance
Increase energy economy
Allow flexible gait patterns
Slow down and/or prevent limb movements
Much muscle activity during gait is eccentric
16
or isometric, rather than concentric
Combined effects of muscle force and BW on
GRF when standing
•
When standing still, the sum of the two GRF forces (one acting on each foot) is
equal and opposite to BW. So equilibrium prevails and there is no movement
•
When the individual squats down, GRF magnitude decreases below that of BW
during the phase of downwards movement.
•
This happens because flexion at the leg joints prevents the full force of body weight
from being transmitted down through the contact points between the feet and the
floor
•
So there is a net downwards force acting on the body: this is what causes the
downwards movement.
•
When the individual is at the low point of the squat, the sum of the two GRF forces
(one acting on each foot) is again equal and opposite to BW. So equilibrium prevails
and there is – momentarily - no movement
•
When the individual rises up from the squat position, GRF magnitude increases
above that of BW during the phases of upwards movement.
•
This happens because extension at the leg joints increases the action force pushing
on the floor above that of body weight
•
So there is a net upwards force acting on the body: this is what causes the upwards
movement.
17
Muscle activity influences the GRF
• The cause of the altered GRF is extensor muscle relaxation
(downwards/squat) phase and contraction (upwards/rise phase). The
altered muscle activity affects GRF by changing the extent to which
the foot presses against the support surface.
• So for example:
GRF = equal and opposite force to that exerted by foot on ground (by
definition)
= body weight + any extensor muscle activity
• When the extensors relax, on the other hand, body weight cannot be
effectively transmitted to the foot (because there is no longer a rigid
body structure to transmit it. Hence:
GRF = equal and opposite force to that exerted by foot on ground (by
definition)
< body weight
18
To summarise:
• Upwards GRF = BW
– The CoM of the body will remain at the same height (or
remain moving at the same rate)
• Upwards GRF > BW (e.g. jumping)
– The CoM of the body will move upwards (or downwards
movement of the CoM will be slowed or halted)
• Upwards GRF< BW (e.g. squatting)
– The CoM of the body will move downwards (or upwards
movement of the CoM will be slowed or halted)
19
Static posture: GRF
equal and opposite
to BW.
Downwards
squat:
GRF<BW
Upwards
movement:
GRF>BW
20
Butterfly diagram- showing GRF through
the stance (support) phase
The lines represent GRF
force vectors at intervals
off about 50 ms during the
stance phase
The line at the extreme left
hand end represents the
force vector at the
moment the foot touches
the ground. The next one
represent GRF 50 ms
later, and so on.
The line at the extreme
right-hand end represents
the GRF when the toe
leaves the ground.
Remember: vector lines incorporate three aspects of
the force they represent: magnitude (=length of line),
point of action, and direction of action
21
Butterfly diagram- showing GRF
through the stance (support) phase
• It’s obvious, from the previous slide, that GRF varies,
through the stance phase, in terms of all three
aspects namely:
– Magnitude
– Direction
– Point of action (= centre of pressure)
• We can understand GRF more readily if we resolve it
into components that act vertically and horizontally
22
Resolving the GRF into vertical and
horizontal components
•
“A” represents the GRF at the moment of
footstrike (see slide 20).
•
It is made up of a horizontal component (C)
and a vertical component (B).
•
In terms of force vectors, we can write:
A=B+C
(Note that this is not normal arithmetic
addition because it also takes account of the
relative directions of A, B and C)
•
Geometrically, the arrowhead ends of A, B,
and C, together with the common point of
origin of the four forces, form the corners of a
rectangle.
•
This fact enables us to calculate the
magnitude of B and C, provided we know A.
23
Resolving the GRF into vertical and
horizontal components
• Both the horizontal and vertical components of the
GRF vary during the stance phase
• The direction of the horizontal component (i.e.
forwards or backwards) tells us whether the body is
accelerating or decelerating in its forwards movement
at that moment of time
• The magnitude of the vertical component (and
specifically whether it is greater or less than body
weight) tells us what is happening to the vertical
movement of the body
24
GRF during the contact phase
•
Initially GRF acts diagonally backwards and upwards, from the heel.
The horizontal component acts backwards, and the vertical component
is greater than that of body weight. GRF at this moment therefore:
– stops the “controlled downwards fall” of the body
– exerts a braking, or slowing, effect on forward movement
•
During the middle of the stance phase the GRF:
– remains > body weight and therefore the CoM is lifted up slightly in
midstance.
– point of action moves forward from the heel.
– line of action becomes more nearly vertical and therefore the
braking/slowing effect disappears
•
After the midpoint of the stance phase the vertical component of GRF
falls (< body weight) as the leg passes the vertical position and the
CoM moves downwards.
•
At the end of the stance phase, the GRF increases in magnitude again,
acting forwards and upwards. This gives the necessary propulsive
force to stop downwards movement of the CoM, and to to keep the
body moving forwards.
25
Changes in the Centre of
Pressure (CoP)
• CoP is initially near the lateral edge of the heel
• As the stance (support) phase progresses, it moves forwards
and medially, ending up under the big toe.
26
CoP scans:
Red line shows passage of
CoP during a single stance
phase
Colours denote peak
pressures achieved at
different points on the foot.
27
Determinants of Gait
• 6 specific features that increase the efficiency
of walking and running gaits
• All reduce unnecessary movement of the
upper body, either vertically, or horizontally
in the lateral axis
28
DG1: Pelvic tilt
•
Reduces the vertical
movements of the upper body,
and thereby increases energy
efficiency.
•
The pelvis slopes downwards
laterally towards the leg which is
in swing phase. i.e. rotation
about an anterior-posterior axis
•
Only anatomically possible if the
swing leg can be shortened
sufficiently (principally by knee
flexion) to clear the ground.
•
Where this is not possible (e.g.
through injury), the absence of
pelvic tilt and pronounced
movements of the upper body
are obvious.
29
DG2: Pelvic rotation
•
Rotation about a
vertical axis enables a
given step length to be
achieved with less
vertical excursion of the
trunk.
•
Alternatively, longer
step lengths can be
achieved for the same
vertical movement.
30
DG3: Knee flexion in stance
phase
•
As the hip joint
passes over the foot
during the support
phase, there is some
flexion of the knee.
•
This reduces vertical
movements at the hip,
and therefore of the
trunk and head.
31
DG4: Ankle mechanism
•
At footstrike, the
effective length of the
leg is increased by the
projection of the
calcaneus behind the
ankle.
•
This is brought about
by dorsiflexion at the
ankle
32
DG5: Forefoot mechanism
•
During the final part of
the support phase, the
forefoot serves to
increase the effective
length of the leg lever.
•
This is brought about
by plantarflexion at
the ankle
33
DG6: Reduced lateral pelvic
displacement
•
Is minimised by having
a narrow walking base
i.e. feet closer together
than are hips.
•
Therefore less energy
is used moving hip from
side to side (less lateral
movement needed to
balance body over
stance foot.
•
Enabled by valgus
angulation at the knee
34
Efficiency, and energy considerations
Economy (J m-1)
• Walking is very energyefficient: little ATP is required.
• This is because of various
mechanisms that ensure the
mechanical energy the body has
is passed on from one step to
the next.
• The two forms of mechanical
energy involved are
•kinetic energy (energy due
to movement
•potential energy (energy
due to position)
35
Gait efficiency & pendulum action
• A pendulum is an object, swinging from a fulcrum,
under the influence of gravity.
• A pendulum has a natural frequency of swing that is
dependent on its mass, and the distance from the
fulcrum to its CoM.
• During the swing of a pendulum, potential and kinetic
energy are interconverted and therefore, overall,
energy is conserved.
• Both the upper and lower limbs of the human body can
move with pendulum motion, with or without muscle
assistance.
36
A conventional pendulum –
energy interconversion
P.E. – Potential energy
K.E. – Kinetic energy
Three points on a pendulum
swing are illustrated.
As the pendulum swings away
from the midpoint, in either
direction, KE is progressively
converted into PE
At the extreme points in the
swing, there is no KE at all and
all the energy is present as PE
37
Conventional pendulum action
during the swing phase
• The legs move as conventional pendulums during the swing
phase (with a little assistance from the hip flexors).
• This reduces the amount of muscle energy needed to move the
swinging leg forward
• It also accounts for the “natural” frequency of gait that has
optimal energy efficiency (see slide 7)
• Although the legs swing forwards much like pendulums, they are
prevented from swinging backwards by footstrike.
• During the stance phase, the leg can be viewed as an “inverted
pendulum”. This action also involves inter-conversion of
potential and kinetic energy
38
An “inverted” pendulum
The pendulum
“bounces”
backwards and
forwards, using
the springs.
39
“Inverted” pendulum action
during the stance phase
• During the stance phase, the leg can be viewed as an “inverted
pendulum”.
• The forward momentum of the body gives it the necessary initial
angular velocity of rotation (taking the place of the “spring” on the
previous slide).
• “Inverted” pendulum action also involves inter-conversion of
potential and kinetic energy, but in this case (unlike a conventional
pendulum) KE reaches a minimum at the midpoint of the motion,
and PE is highest at that point.
• When reaching the endpoint of its “inverted swing” the stance leg
does not swing back, as a real inverted pendulum would, because
the foot is taken off the floor, the fulcrum transfers from the foot to
the hip, and the leg swings again as a conventional pendulum.
40
Walking
modelled as a
rolling lemon
Slow
Pendulum considerations help
us understand energy
efficiency by concentrating on
the individual legs.
But ultimately we need to
consider the energy of the
whole body
A simple model that allows this
is that of a rolling ellipse, with
the midpoint of the ellipse
representing the CoM of the
body
Fast
41
Walking modelled
as a rolling lemon:
midstance
At the midstance point for
either leg, the CoM of the
whole body is relatively high
(despite the best efforts of the
Determinants of Gait).
Therefore PE for the whole
body is relatively high, and KE
(forwards movement velocity )
relatively low
42
Walking modelled as
a rolling lemon:
early/late stance
Towards the beginning or end
of the stance phase for either
leg, the CoM is lower.
Therefore the PE for the whole
body is reduced, and KE
(forwards movement velocity )
relatively high
43
Running
• The main qualitative difference between walking and
running is the flight phase (i.e. period of no support)
and the absence of a period of double support.
• An important quantitative difference is that, in running
gait, the foot hits the ground less far in front of the
body’s centre of gravity, compared with walking (i.e.
when we run, the forward swinging leg “sticks out”
less far in front of the trunk at footstrike).
• This characteristic is more pronounced the faster the
run.
44
The above two differences lead to the following
consequences:
• When running, the body’s momentum alone has to carry
it over the support foot, as the other foot is not in contact
with the ground.
• The position of heelstrike, relative to the CoM, helps with
this (see previous slide), because it means that the CoM
is not lowered as much at footstrike.
• The position of heelstrike relative to the CoM also
reduces the ‘braking effect’ of the GRF during the first
part of the stance phase
45
During transition from
walking to running,
•the period of double
support disappears
•a greater proportion of the
pace time is spent in the
swing phase:
Activity
Approx %time on:
stance
swing
Slow walk
60
40
Race walk
50
50
Run
30
70
Sprint
20
80
46
Stride rate and length
•
•
•
•
•
As running speed increases,
both stride rate and length
become higher.
Initially, at relatively low
speeds, the changes are
proportionally greater in
length than in rate
Near maximum speed,
however, rate increases more
than length.
The explanation for this is in
terms of energy efficiency
In energy terms, it is more
efficient to increase speed by
taking longer paces rather
than taking them more rapidly
47
GRF Butterfly during running
48
GRF during running
Compared with walking:
• Initial ‘contact’ peak is smaller and is not angled back
as far (less braking effect – see slide 45)
• Final ‘thrust’ peak is larger (need to project body into
flight phase, faster speeds etc)
• Duration of contact phase is shorter – of course!
49
Energy considerations during
running
• Energy usage differs fundamentally between running
and walking
• In running, both kinetic and potential energy are high
during the flight phase.
• Energy storage in elastic tissues at the start of the
support phase has a more prominent role in running.
• By contrast, elastic energy storage during walking is
smaller – in fact we ignored it altogether when
considering this topic earlier.
50
Energy during running: the
bouncing ball model
Contrast this with the
rolling lemon model for
walking.
Here, KE and PE are
both high at the top of
the “bounces”
(equivalent to the middle
of the flight phase)
During ground contact,
KE and PE are lower,
and energy is stored in
elastic tissues.
So, for running, we have to consider
interconversion between three different
forms of energy: PE, KE and elastic
51
Walking and running energy costs
(a) Metabolic power (W)
(b) Economy (J m-1)
52
Elastic energy storage during running
•
Total kinetic energy dissipation at footstrike= 100 J/pace (70 kg subject;
4.5. m s-1)
•
At start of support phase, elastic energy (from the foot impact) is stored
in:
– Achilles tendon
~35J
– Patellar tendon
~20J
– Arch of foot
~17J
TOTAL
~72J
• Thus, almost ¾ of the kinetic energy that would otherwise be lost
at footstrike, is instead stored as elastic energy, in ligaments and
tendons, and recovered in kinetic form during the latter parts of
the support phase
• Due to this elastic energy storage, muscles do not need to
contract as far or as fast, and metabolic energy use, in the form
of ATP, is reduced
53
Elastic properties of tendons
• Tendons can stretch up to 8% and recoil elastically
• >93% of stored energy is recovered
• Both patellar and Achilles tendons are relatively long
and thin. Hence they allow significant flexion while
storing energy
54
Experimental data on elastic
force and the Achilles tendon
• Marathon runner (2h 37 min)
• Peak force on ball of foot = 2.7×BW (=1900 N)
• Peak force in Achilles tendon = 4700 N
• Minimum cross sectional area of tendon = 90mm2
• Force per unit cross-section area = 50 N mm-2
• This will stretch tendon by 6%
• Margin of safety is about 100% i.e. tendon will rupture at
about 100 N mm-2
55
Running shoes and elastic
energy storage
• Heels of running shoes absorb a maximum of about
7J, and return less than 66% of this.
• Therefore, they make only a small contribution to
energy economy
• Lateral stability limits the degree of elasticity that can
be incorporated into shoes.
56
References
Coverage of gait in biomechanics textbooks is
variable.The following list is a selection that each
approach the topic from different angles:
Adrian MJ & Cooper, JM (1995) Biomechanics of
Human Movement. Brown & Benchmark
Enoka, RM (1994) Neuromechanical Basis of
Kinesiology. Human Kinetics
Luttgens, K & Hamilton, N (1997) Kinesiology. Brown &
Benchmark
McNeill Alexander, R. (1992) The Human Machine.
Natural History Museum Publications.
57
Movements at different joints
during the gait cycle, and
associated muscle activies
Supplementary slides for lecture,
showing involvement of the
Determinants of Gait (DG)
58
Swing phase: spine & pelvis
Movement:
• Rotation of pelvis towards support leg (i.e. non-support side goes
forward); DG2*
• Lateral tilt of pelvis towards unsupported leg DG1
• Movements at the vertebral joints of the spine aim to counteract
the consequences of the above pelvic movements:
– Upper spine rotates in opposite direction to pelvic rotation
– Lumbar spine flexes in opposite direction to pelvic tilt.
• These spinal movements ensure that the pelvic movements do
not result in rotation and flexion of the entire upper body.
*Determinants of gait, numbered as in main lecture slides
59
Swing phase: the hip
• Flexion is the main movement.
• Maximum hip flexion is reached about half way
through the swing phase.
• Hip rotation and adduction/abduction are needed to
ensure the swinging leg continues to point forwards,
despite pelvic rotation.
• Iliopsoas is prime mover, but active only early on
• Swing phase is therefore partly a ballistic movement
• At the start of the swing phase, gravity and energy
stored in the stretched hip ligaments also contribute
to movement.
60
Hip flexion reaches maximum about half
way through swing phase
61
Swing phase: the knee
• Flexion initially; this assists ground clearance and is
related to pelvic tilt (DG1)
• Then extension: preparation for heel-strike
• Little muscle activity during swing. Knee movements are
passive consequences of hip flexion. The leg acts as a
“double jointed pendulum”.
• Hamstring activity, at end, halts extension (eccentric
action). Quadriceps contraction prepares for heelstrike
(isometric, stabilising effect)
62
Knee movements during swing phase:
flexion initially, and then extension
63
Swing phase: ankle and foot
Movements:
• Dorsiflexion (for ground clearance and for ankle mechanism DG4).
Muscle actions:
• Tibialis anterior at start of swing (ground clearance, related to
pelvic tilt)
• activity tapers off in mid-swing
• contracts again for footstrike (prevention of footslap; stabilise
heelstrike).
64
Swing phase ankle movements:
dorsiflexion
65
Principal events during the stance
phase
1. Heelstrike
2. Foot-flat (followed by opposite toe-off)
3. Heel-rise (followed by opposite heelstrike)
4. Toe-off
66
Principal events during the stance phase:
heel-strike, foot-flat, heel-rise, toe-off
67
Stance phase: the hip
• Main movement is extension from flexed starting
point
• Hip rotation and adduction/abduction mediate the pelvic
movements required for DG1 and DG2
• Gluteals and hamstrings active during early phase,
tapering off during midstance as gravity takes over;
• During single support phase, gluteus medius and tensor
fascia lata (hip abductors) work isometrically/
eccentrically to maintain pelvic stability
68
The hip during stance phase:
Main movement is extension from flexed
starting point
69
Stance phase: the knee
• Slight flexion from heel-strike to midstance (DG3),
• Then extension after midstance to heel-lift.
• Quadriceps active during early phase (eccentric/
stabilising effect as GRF line of action passes behind
knee joint)
• This action stores energy which is recovered during
subsequent concentric activity
• Once leg has passed vertical position (midstance), the
knee locks (ie no need for extensors).
• Hamstrings active at start and end of the support phase
(initiating flexion during stance and swing respectively).
70
Stance phase - the knee:
slight flexion followed by extension
71
Stance phase: ankle movements
• Initially (at heelstrike) close to neutral position (DG4).
• Plantar flexion produces footflat
• Then slight dorsiflexion as upper leg and body swing
forward.
• Prevention of further dorsiflexion, which body weight
tends to cause.
• Plantar flexion at end of propulsive phase (DG5)
72
Stance phase – the ankle:
neutral at foot-strike; then plantarflexion as foot goes flat;
73
Stance phase – the ankle:
then dorsiflexion as upper body swings over
….………….and finally plantarflexion as heel lifts off
74
Stance phase: ankle muscle actions
• Tibialis anterior at heel strike (prevents ‘footslap’).
• Gastrocnemius and soleus from midstance to toe-off
• Along with the hip extensors, this activity by the
triceps surae group generates propulsive force
needed to maintain forward movement:
– Initial activity is eccentric: muscles become active while ankle
is still dorsiflexing.
– Subsequently action is concentric during ankle plantarflexion
– This “biphasic” action generates a stretch-shortening cycle,
giving rapid and powerful contraction
75
Running: movements and
muscle involvement
• Movements are in general similar to those for
walking, but
– range of joint movement usually greater
– co-ordination between the legs is different (e.g. no double
support phase).
– more muscle involvement, since emphasis is on speed
rather than energy economy
76
Running: swing phase
• Muscular rather than pendular motion at hip.
• Knee flexion, and ankle dorsiflexion, bring CoM of the
leg closer to the hip. This reduces moment of inertia
and increases angular velocity.
• Knee movements largely passive (i.e not due to
muscle activity), and result from transfer of
momentum from thigh.
• Depending on the speed of running, initial ground
contact may be with heel, whole foot, or ball of foot.
77
Running: support phase
• Hip: slight flexion followed by extension. Gluteus maximus
activity initially eccentric
• Knee: degree of flexion increases with speed; that of extension
decreases. Quadriceps active at knee, initially eccentrically
• Ankle : dorsiflexion followed by plantarflexion. Gastrocnemius
and soleus active during whole phase, particularly so at the end.
• Stretch shortening/energy storage activity occurs at all
three joints
78