Ground reaction forces and gait

[Gerrard Farrell]

In part , my interest in biomechanics comes from understanding the TMJ but also from my hobby ,throwing things in track and field ( not very far ) .

Recently, I developed the idea that ground reaction forces in the stance leg can help produce vertical acceleration of the pelvis during gait which will in turn will accelerate the swing leg provided it has started on a downward arc . I feel that this might be an important part of gait and also and important part generating leg speed when it comes to kicking things like a football .

My question is ,is this at all a novel idea and might it be correct ?

The following analogy might help explain the idea - It is taken from the early part of a thread on Podiatry Arena .


Quote -

"As we walk our pelvises move up and down in the vertical plane (among others ) .
So take a pencil to represent the pelvis , and our string with a weight on it to represent the swing leg . Tie the string to one end of the pencil and hold the other end of the pencil in your hand .

So now you have a pencil held out from your hand parallel to the ground and from this dangles the string . Now lift your hand vertically up and down to represent a straightening , lifting stance leg . The string and weight will simply mimic this up and down movement .
However , if you first start the weight and string moving to and fro , as in a pendulum , then when you lift and drop the held end of the pencil , energy will be imparted into the swinging weight . If you've got rhythm that is !

And so yes , " Vertical forces produce horizontal progression during gait . " Not "impossible" since accelerating the swing leg will cause it to advance , in part , horizontally ."

Gerrard Farrell

Glasgow
scotfoot, Tuesday at 7:11

[Zia Hasan]

Re: Ground reaction forces and gait

It has been clear since Newton that force in a particular direction does not necessarily produce progression in the same direction. For instance, the force (gravity) on a projectile is always vertically downward but the progression of the projectile is not. Similarly a vertical force on a swinging pendulum will affect the pendulum's motion in vertical as well as horizontal directions. But of course in gait the ground reaction force is not simply vertical.

In part , my interest in biomechanics comes from understanding the TMJ but also from my hobby ,throwing things in track and field ( not very far ) .

Recently, I developed the idea that ground reaction forces in the stance leg can help produce vertical acceleration of the pelvis during gait which will in turn will accelerate the swing leg provided it has started on a downward arc . I feel that this might be an important part of gait and also and important part generating leg speed when it comes to kicking things like a football .

My question is ,is this at all a novel idea and might it be correct ?

The following analogy might help explain the idea - It is taken from the early part of a thread on Podiatry Arena .


Quote -

"As we walk our pelvises move up and down in the vertical plane (among others ) .
So take a pencil to represent the pelvis , and our string with a weight on it to represent the swing leg . Tie the string to one end of the pencil and hold the other end of the pencil in your hand .

So now you have a pencil held out from your hand parallel to the ground and from this dangles the string . Now lift your hand vertically up and down to represent a straightening , lifting stance leg . The string and weight will simply mimic this up and down movement .
However , if you first start the weight and string moving to and fro , as in a pendulum , then when you lift and drop the held end of the pencil , energy will be imparted into the swinging weight . If you've got rhythm that is !

And so yes , " Vertical forces produce horizontal progression during gait . " Not "impossible" since accelerating the swing leg will cause it to advance , in part , horizontally ."

Gerrard Farrell

Glasgow
scotfoot, Tuesday at 7:11

[Gerrard Farrell]

Re: Ground reaction forces and gait

Hi Zia
Thank you for responding . So would I be correct in assuming that you agree that vertical acceleration of the pelvis , caused by forces acting through the stance leg ,can produce marked acceleration of the swing leg ,facilitating gait , if timed appropriately ?

What the pelvis allows us to do is advance the the body horizontally through a vertical force . Newton teaches that you cannot displace an object at ninety degrees to the applied force . True , but the pelvis can act to translate the vertical acceleration produced in the stance leg into the angular acceleration of the swing leg and hence horizontal displacement .

[Zia Hasan]

Re: Ground reaction forces and gait

You wrote: "Newton teaches that you cannot displace an object at ninety degrees to the applied force." Newton certainly does not teach us that. His genius was to see beyond this common assumption. The direction of motion of the moon is at 90 degrees to the force (earth's attraction) applied to it. One must not confuse direction of displacement with direction of acceleration. In the case of uniform circular motion, the two directions are 90 degrees apart..In general, they can be apart by any angle. Only in the case of straight line motion is the angle between them either 0 or 180.

[Gerrard Farrell]

Re: Ground reaction forces and gait

Hi Zia
I think I might have read up a bit more on Newton .

However , the main thrust of the thread is this question . Does vertical acceleration of the pelvis ,caused by forces acting through the stance leg , produce marked acceleration of the swing leg ,facilitating gait ,if timed appropriately ?

[Gerrard Farrell]

Re: Ground reaction forces and gait

I think it is likely that vertical movement of the pelvis , produced by forces generated through the stance leg , will help produce angular acceleration in the trailing swing leg during gait . For example in walking when moving from double support .

I also believe that the rapid , vertical , acceleration of the pelvis , through the explosive use of the standing leg, is and important contributory factor in the kicking action .

I should imagine all of the above is well documented and would appreciate a reference or two .

Cheers

Gerry

[Ton van den Bogert]

Re: Ground reaction forces and gait

I can add some numbers to the discussion.

If you write the equation of motion for a pendulum with a pivot that accelerates upward with acceleration a, you get exactly the same equation as for a fixed pivot pendulum, but the gravitational acceleration g is replaced by (g+a). So the pendulum behaves as if it is in a larger gravitational field and will accelerate faster on the downswing, exactly as Gerrard suggested. You can also accelerate the pivot downward on the upswing to get less deceleration during that phase. If you time the changes in vertical acceleration correctly, you can pump energy into the pendulum.

To see how large this effect is in real human motion, look at the vertical acceleration of the hip joint which is the pivot of the swing leg.

I quickly looked at one subject's data during walking at 1 m/s. The upward acceleration peak of the greater trochanter marker during push-off is 2 m/s^2 at about 50% of the gait cycle. There is a negative peak of -3 m/s^2 at about 70% of the gait cycle. The positive peak seems to have the capability to accelerate the leg on the downswing, and the effect would be about 20% increase compared to gravity alone. The negative peak happens in mid-swing and may not contribute much. These accelerations will be larger for faster walking and for running, and the timing will be different also.

My numbers are anecdotal and you can probably find references on vertical motion of the pelvis, but keep in mind you want the vertical acceleration of the hip, not the center of the pelvis or the center of mass of the whole body.

As a mechanism for producing forward swing, it is not very efficient so I don't think you should teach people to increase their vertical motion for that reason. You have to accelerate the whole body upward. Using a hip flexor muscle will only accelerate the leg and require much less force and energy for the same effect. Or you can flex the knee more and reduce the moment of inertia.

Finally, don't forget about horizontal acceleration of the pelvis which also happens during gait. For control of swing leg rotation, a horizontal acceleration (a) is equivalent to an extra horizontal force m*a acting on each mass (m) in the swing leg.

Ton van den Bogert

[Gerrard Farrell]

Re: Ground reaction forces and gait

Hi Ton ,
Many thanks for joining the discussion and for adding a bit of mathematical elegance to proceedings .

However , things may be bit more complex than just the vertical acceleration of the pelvis (as discussed above ) causing angular acceleration of the swing leg .

Through the spinal column , such accelerations of the pelvis will , as you say , accelerate the whole body upwards and this in turn may produce an angular acceleration of the swinging arms , even though they are swinging in different directions at any given time .

Thus the vertical forces produced by the standing leg will feed energy into 3 pendulums and not just one .

Gerry

[Allan Carman]

Re: Ground reaction forces and gait

Gerrard,

There are some major errors in the physics presented in discussion. To understand the forces and motion a good place to start is with a free body diagram which includes all external forces in both the vertical and horizontal directions. Newton’s law states that the acceleration of an object is in direction of the applied force and not at 90 degrees or any other angle.

The pendulum mass has two forces acting in it; gravity acting down through the CoM and the tension in the string that has a horizontal and vertical component. The later components vary in magnitude depending on the angle of the string and velocity of the mass. There is also an equal and opposite reaction force at the distal end of the string (horizontal and vertical components) that are required to elicit the pendulum motion.

Initially, with the mass stationary (v=0) and string horizontal, gravitational force (Fg = m.g) accelerates (g) the mass (m) downwards. This generates tension in the string (Ft = m.g.cosθ + m.v2.r). The string tensile force is initially zero but increases during the downward swing as the component of gravitational force (Fg) in the direction of the string increases and velocity (v) and centripetal force (Fc = m.v2/r) increase. At the bottom of the swing, with the string vertical and aligned with g and with maximum velocity, the tensile force is at is greatest (Ft = Fg + Fc). The vertical (up) component of string tensile force acts to de-accelerate the mass (opposing gravity) to reach zero vertical velocity at the bottom of the swing while the horizontal component of the string tensile force accelerates the mass horizontally. The magnitude of these components change during the swing. The upwards swing is essentially the opposite, the horizontal component of string tensile force acts to slow the mass horizontally and the diminishing vertical component acts to accelerate the mass upwards but is opposed by gravity, until the mass is again at rest.

In holding the end of the string you will be aware of the equal but opposite vertical reaction force at the distal end of the string to keep the distal end of the sting (pivot point) from falling. There is however an equal but opposite horizontal reaction force you supply while holding the distal end of the string. The horizontal reaction force alternates in direction as the pendulum swings from side to side, pulling one way then the other. Without the horizontal reaction force at the distal end of the string there would be no horizontal motion and the pendulum mass would simply drop.

If you were to lift (accelerate) the distal end of the string pivot point upwards while the pendulum was dropping then you would increase vertical reaction force and tension in the string. This also increases the horizontal force component of the string tension and horizontal acceleration and velocity of the pendulum mass. But only if there is an equal and opposite increase in the horizontal reaction force you apply to the string to keep the distal end of the string from moving horizontally.

To the question. Theoretically there may be a tiny effect on accelerating the pendulum motion of the thigh when the pelvis accelerates upwards. However given the size of the vertical acceleration in gait and concurrent horizontal accelerations of the pelvis, the later will produce its own pendulum accelerating effect but in a horizontal sense and oppose those seen by the vertical acceleration. So I doubt that the vertical acceleration of the pelvis in gait will have a 'meaningful' effect on thigh motion.

Cheers
Allan

[Gerrard Farrell]

Re: Ground reaction forces and gait

Hi Allan
Leaving aside the "arm component " the thread is about accelerating the swing leg and not advancing the COM forwards.

The arm swing introduced in my previous post is primarily about body segment co-ordination .



Gerry

[Gerrard Farrell]

Re: Ground reaction forces and gait

To put it in a nutshell , gait is not just about using your limbs etc to propel you forwards . You must first be able to get your limbs into the correct positions to perform their various roles . This is particularly true in sprinting . If the COM of a top class printer is moving at 28 mph , the trail leg/foot must be accelerated very quickly to get it out in front of the COM for the next stride in the cycle .

Interestingly , I was once stood on the inside of the track when a world class 400 m runner ran past during a training session . She must have had a peak vertical displacement of at least a foot and a half . I have wondered about that ever since .

[Gerrard Farrell]

Re: Ground reaction forces and gait

Away from gait but still talking about angular acceleration of swinging appendages through the linear , vertical acceleration of the pelvis , this slow motion video (1 below ) is fascinating . The video is 1 min long but the bits of interest happen 30 secs in . In slow motion you can see McIlroy first sitting a little , and then ,as his arms swing past horizontal to the ground , he drives up hard on his left leg . This is were the club head speed comes from .

So watch his belt from seconds number 30 to 45 .

Rory McIlroy - Driver Extreme Slow Motion (2014) - YouTube

https://www.youtube.com/watch?v=kk67dfDnpKQ

▶ 1:04

4 Nov 2014 - Uploaded by RollYourRock
Rory McIlroy - Driver Extreme Slow Motion (2014). RollYourRock. Loading... Unsubscribe from RollYourR

[Gerrard Farrell]

Re: Ground reaction forces and gait

Adding to the present thread it should be noted that although vertical acceleration of the pelvis produces angular acceleration of swinging limbs so does vertical deceleration .

To understand this imagine a person standing on a raised platform with a rucksack on their back and where the shoulder straps of said rucksack are made of elastic . If our imaginary person now jumps from the platform they will accelerate towards the floor . When they land the body will rapidly decelerate but the rucksack will keep going till stopped by the stretching straps . The straps have been put under tension by the rapid deceleration of the pelvis and spine .

Now imagine a runner , mid stride ,with both feet of the ground and with the pelvis at peak vertical displacement . When the runner comes back down , he/she will meet the ground with a pretensioned (stiff ) subject leg causing deceleration of the pelvis and tension in the swinging leg and arms . This will result in their angular acceleration .

With regard to kicking a football /rugby ball after a run up , at least some of angular momentum generated in the kicking leg seems likely to be generated by the vertical deceleration of the pelvis cause by the standing /support foot meeting the ground after the final approach stride .

Gerry

[Gerrard Farrell]

Re: Ground reaction forces and gait

Any thoughts on the above Ton ?

Gerry

[Allan Carman]

Re: Ground reaction forces and gait

Gerrard,

The pendulum analogy is a good way to describe the passive or inertial forces acting on the leg. However you have to look beyond the vertical reaction force at the pendulum pivot point (hip) to describe and understand the horizontal and vertical accelerations and resulting motion of the pendulum mass. The forces acting on mass (thigh COM) are the vertical gravitational force and string tension (centripetal). The string tension has vertical and horizontal components that change depending on the angle of the pendulum. The vertical component opposes gravity while the horizontal component gives rise to the horizontal accelerations and changes in horizontal velocity of the mass. So yes it is all about the vertical and horizontal acceleration of the COM of the leg or mass of the pendulum. Even though the pivot point or hip is stationary there are vertical and horizontal reaction forces acting at the pivot point or hip (equal and opposite to the horizontal and vertical components of string tension) to produce pendulum motion. Without the pivot horizontal reaction force there would be no pendulum motion. I agree that introducing a vertical acceleration of the hip or pivot point of the pendulum during the downward swing will increase swing velocity. This however comes about through an increase in string tension and both vertical and horizontal reaction forces at the hip or pivot point. The increase in horizontal reaction force will keep the pivot point stationary in the horizontal direction and produce the increase in a horizontal velocity of the pendulum or thigh COM and increase in angular velocity.

When applied to gait or running there are both vertical and horizontal accelerations at the hip (the pivot point). During the forward and upward acceleration of the hip, these two acceleration produce opposing inertial angular accelerations of the trailing thigh mass. In gait these acceleration and induced angular velocities of the thigh are likely to be negligible. While in sprinting I would guess that they are measurable but likely of no meaningful magnitude compared to the active forces driving the leg forward.

In the Moon example the difference is the moon has an initial velocity and the only force acting is the centripetal (gravity) force towards the Earth. The acceleration and change in velocity are both in the same direction as the force (towards the Earth), not at any other angle. The current tangential velocity pus the change in velocity (towards the Earth) gives the new Moon velocity. Such that the Moons velocity progresses around the Earth. Remove the centripetal force, acceleration and change in velocity (all directed towards the Earth) and the Moon continues in a straight line.

The velocity of the golf swing comes from trunk and shoulder rotation. Not vertical acceleration of the mid-shoulder center of rotation. The head remains almost stationary and the hands trace out a near perfect circle (see picture attached). As a non-golfer I would suggest that a skill would be keep the head stationary right through contact and not to lift the head (and center of rotation) too early.

cheers
Allan