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Movement Biomechanicsof Human Gait

SP2004N Biomechanics

http://homepages.unl.ac.uk/~woodwarc

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Plan

1. Basic terms and definitions2. Overview 3. Forces: weight, GRF and

muscle4. “Determinants” of gait5. Energy considerations6. Running vs walking

Self-directed learning supplement: Joint movements and muscles

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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)

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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

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Note:

•Alternating periods of double and single support

•About 70:30 split between single and double support in normal walking

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• 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 Stride SpeedTime (s) length (m) (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

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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.

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Walking and running efficiency

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

(b) Economy (J m-1)

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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.

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Vitally important point:

Muscle forces can only influence the movement of the body as a whole indirectly, by their effects on the GRF

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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

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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

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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

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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

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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

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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 or isometric, rather than concentric

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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.

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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

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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)

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Static posture: GRF equal and opposite

to BW.

Downwards squat: GRF<BW

Upwards movement: GRF>BW

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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

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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

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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.

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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

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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.

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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.

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CoP scans:

Red line shows passage of CoP during a single stance phase

Colours denote peak pressures achieved at different points on the foot.

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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

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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.

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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.

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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.

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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

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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

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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

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Efficiency, and energy considerations

•Walking is very energy-efficient: 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)

Economy (J m-1)

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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.

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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

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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

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An “inverted” pendulum

The pendulum “bounces” backwards and forwards, using the springs.

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“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.

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Walking modelled as a rolling lemon

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

Slow

Fast

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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

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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

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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.

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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

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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

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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

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GRF Butterfly during running

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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!

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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.

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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

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Walking and running energy costs

(a) Metabolic power (W) (b) Economy (J m-1)

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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

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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

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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

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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.

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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.

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Movements at different joints during the gait cycle, and

associated muscle activies

Supplementary slides for lecture, showing involvement of the Determinants of Gait (DG)

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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

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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.

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Hip flexion reaches maximum about half way through swing phase

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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)

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Knee movements during swing phase: flexion initially, and then extension

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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).

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Swing phase ankle movements:dorsiflexion

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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

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Principal events during the stance phase: heel-strike, foot-flat, heel-rise, toe-off

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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

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The hip during stance phase:Main movement is extension from flexed

starting point

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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).

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Stance phase - the knee:slight flexion followed by extension

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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)

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Stance phase – the ankle:neutral at foot-strike; then plantarflexion as foot goes flat;

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Stance phase – the ankle:then dorsiflexion as upper body swings over ….

………….and finally plantarflexion as heel lifts off

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• 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

Stance phase: ankle muscle actions

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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

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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.

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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