A biomechanical model of the squat

[Guest guest]

Interesting article.

It would be interesting to take into account the angle of the ankle

joint. That would complicate matters of course.

Regards,

Johan Bastiaansen

Deurne, Belgium

>

> I'm probably treading on dangerous ground here given the apparent

> enthusiasm of many members here for the squat exercise, but I

would be

> grateful for any comments on or criticisms of a basic 2-dimensional

> model of the squat that I have developed.

>

> An article describing it is titled, " A biomechanical model for

> estimating moments of force at hip and knee joints in the barbell

> squat " , and can be accessed at:

> http://www.myoquip.com.au/Biomechanical_model_squat_article.htm

> <http://www.myoquip.com.au/Biomechanical_model_squat_article.htm> .

>

> Extracts can be seen below.

>

> Regards

>

> Bruce Ross

> Sydney, Australia

[Guest guest]

>

> Interesting article.

>

> It would be interesting to take into account the angle of the ankle

> joint. That would complicate matters of course.

****

Thanks for the comment, Johan.

As I see it, factoring in the ankle joint wouldn't make much difference.

In my model the weight bar FWT and the center of gravity of the upper

body cgUB lie directly above the ankle joint which is itself directly

above the ground reaction force FGR. As a result none of them would

contribute to the moment about the ankle joint. Therefore we are left

with the contributions from the thighs and shanks. These would appear to

almost totally offset one another - a positive effect from the shanks

being almost matched by a negative effect from the thighs.

Even if I had shifted the centre of gravity from being in line with the

ankle joint to the mid point of the foot, the moment about the ankle

joint would have been very small through the full range of the squat.

Regards

Bruce Ross

Sydney, Australia

[Guest guest]

I do not post here much anymore, but I feel compelled to respond to this and the

original posting by Mr. Ross. This model, quite simply is incorrect. It's

presence (on the internet), however, is dangerous as it provides fuel for the

many individuals and groups who attack various exercises without a proper

understanding of biomechanics.

The moment at the ankle can be considerably large during the squat exercise. In

fact, this is a basic premise in calculating the net joint moments of force

(herein abbrievated NJM), where a small change in the moment arm can result in a

considerably large change in the NJM. In biomechanical analyses of the squat

exercise, the NJM at the ankle ranges from 2-3.5N.m/kg bodymass. Contrast this

to 2.5-4N.m/kg bodymass for the NJM at the hip and knee.

There are two general methods of determining NJM. The first is to determine the

force vector of the ground reaction force (GRF) and the distance of this vector

from any given axis of rotation (i.e. the knee joint center). The second method

is to determine the NJM about a given segment in a kinematic/kinetic chain based

on the forces acting on that segment. Mr. Ross has utilized a combination of

both methods, resulting in a very large overestimation of the NJM. In addition,

Mr. Ross reports NJM for the combined limbs (left + right), although NJM are

typically reported for a single limb (this in and of itself is not incorrect,

but should be stated outright as it influences the interpretation of results).

The former method is not truly accurate, as it does not take into account

segmental linear and joint angular accelerations, which influence determination

of the NJM. Although the squat is generally a slow exercise, these

accelerations can have a large impact, particularly above parallel, where the

movement is more efficient, thus allowing greater accelerations. The latter

method is the most accurate, however, requires determination of GRF, center of

pressure, and kinematics of the segments. The GRF is applied to determine

proximal joint reaction forces. The cross-product of the GRF and proximal joint

reaction force with their respective moment arms is determined and added to the

moment calculated from the moment of inertia and the angular acceleration of the

foot. This gives the NJM about the ankle joint. The ankle NJM and proximal

joint reaction force are transferred up to the shank, and the procedure is

applied to yield knee NJM, and than up to the femur to get hip NJM.

Depending on the style of squatting, the hypothetical 100kg individual squatting

100kg, would most likely have NJM at the hip and knee ~200N.m, and at the ankle

~100-150N.m (remember, this is for one limb only). So Mr. Ross has

overestimated by 100% the NJM, which makes sense since he used the force vectors

for both the GRF and the combined lifter-barbell system, where it should be one

or the other.

The question than becomes, what does this data mean. Is a NJM of 200N.m

dangerous? What about 400N.m, 600N.m, etc. It is impossible to say, without

considering other factors, such as bodymass, training age and experience,

strength and so on. This is, unfortunately common, to suggest that increases in

force or torque are dangerous, when the threshold of the tissues has not been

established. From a materials safety standpoint, an increase in force is not

dangerous unless that increase exceeds the tolerance of the tissue(s). The fact

that middleweight weightlifters may generate in excess of 400N.m at the hip

during the weightlifting pull suggests that a heavier individual generating only

200N.m is well within the safe range.

Of course, anyone who has visited Mr. Ross' site is aware that he sells a

machine that is supposedly superior and safer compared to squatting, which is

why such a post by him is appalling. This " article " has not been peer reviewed,

such as in a scientific journal, nor has Mr. Ross searched for comparative data

(and there is plenty) to determine if his NJM are even in the ballpark (which

they are not). However, the typical viewer of this article likely does not have

the biomechanics background to understand the errors and will buy into the

philosophy that squats are dangerous and machine training is superior.

--

Loren Chiu

Los Angeles, CA

-------------- Original message --------------

<<Thanks for the comment, Johan.

As I see it, factoring in the ankle joint wouldn't make much difference.

In my model the weight bar FWT and the center of gravity of the upper

body cgUB lie directly above the ankle joint which is itself directly

above the ground reaction force FGR. As a result none of them would

contribute to the moment about the ankle joint. Therefore we are left

with the contributions from the thighs and shanks. These would appear to

almost totally offset one another - a positive effect from the shanks

being almost matched by a negative effect from the thighs.

Even if I had shifted the centre of gravity from being in line with the

ankle joint to the mid point of the foot, the moment about the ankle

joint would have been very small through the full range of the squat.>>>

[Guest guest]

<<I do not post here much anymore, but I feel compelled to respond to

this and the original posting by Mr. Ross. This model, quite simply is

incorrect. It's presence (on the internet), however, is dangerous as it

provides fuel for the many individuals and groups who attack various

exercises without a proper understanding of biomechanics.>>>

***

Loren, thank you for your comments.

In relation to my reply to Johan Bastiaansen you state: " The moment at

the ankle can be considerably large during the squat exercise. " However,

the relevant question is not how large it " can be " but how large it

would be in terms of the model I used.

Among the simplying assumptions that I made were the following:

" ... the force vector of the weight bar (FWB) was assumed to be located

directly above that of the upper body (cgUB). ... it was assumed that

the centre of gravity of the system remains directly above the ankle

joint rather than at the midpoint of the foot as is usually assumed.

" At each observation point throughout the exercise the body is evaluated

in a static or constant velocity state and therefore can be treated as

rigid. "

It was in the context of these assumptions that I stated in my reply to

Johan that " the moment about the ankle joint would have been very small

through the full range of the squat. " In terms of the model, do you

disagree?

In relation to my original post you state: " This 'article' has not been

peer reviewed, such as in a scientific journal. " I would have thought

that my asking members of the Supertraining group for comments and

criticisms was a genuine attempt to obtain peer review such as that

which you have provided. Further, your mention of scientific journals

raises the obvious point that, irrespective of its quality, there is no

way that any relevant scientific journal would have considered it for

publication, simply because I have no academic credentials in this

field.

I had a long academic career in a totally unrelated discipline and thus

have some experience of the realities of academic publishing. Not only

is journal publication restricted to the cognoscente but also articles

which are critical of the dominant paradigm of a discipline are rarely

published in mainstream journals. Further, the fact that ownership of

scholarly journals has been almost entirely appropriated by

profit-seeking publishing companies means that access to them is

basically restricted to those with direct affiliation to universities.

The recent series of posts here on the topic, " Does Sports-Science

Research Influence Practice? " is testimony to the gap between science

and practice. My contribution, however flawed, is an attempt to raise

and discuss important issues within the public domain and written to be

understood even by those " without a proper understanding of

biomechanics. " When the academic community begins to publish studies

that can be comprehended by outsiders then there will be no need for

people like me to try to fill the void.

You state that I have not " searched for comparative data (and there is

plenty) to determine if his NJM are even in the ballpark (which they are

not). " I can assure you that I have searched over a long period for data

relevant to the issue with which I am concerned, namely the extent to

which the perceived " excessive loading in the bottom part of the

movement " and inadequate loading through the top range " may be

attributable to changing values of resistive torque in moving from deep

flexion to full extension of the hip and knee joints. " If there is

indeed " plenty " of data on this please direct me to it.

The only study that I could find that was broadly relevant to this issue

was that by Abelbeck (2002) which evaluated " a linear motion squat

performed on a machine. " I attempted to base my model of the free

squat on his methodology. As for my NJM not being " in the ballpark " of

comparative data, Abelbeck's study, which was published in The Journal

of Strength and Conditioning Research, shows for the most comparable

body position to that of the free squat, knee moment values ranging from

greater than 1000N.m at 80 degrees of flexion to negative values above

165.6 degrees. My own results show 692.0N.m at 80 degrees and zero at

180 degrees, differences which could be attributable to the studies

being of different types of squat.

You further state that:

" Mr. Ross reports NJM for the combined limbs (left + right), although

NJM are typically reported for a single limb (this in and of itself is

not incorrect, but should be stated outright as it influences the

interpretation of results). "

Surely this is carping criticism. On all four occasions when I mention

" thighs " and " shanks " it is in the plural. What more should I have done

to make clear what I was measuring?

Your really substantive criticism would appear to be that " Mr. Ross has

overestimated by 100% the NJM, which makes sense since he used the force

vectors for both the GRF and the combined lifter-barbell system, where

it should be one or the other. " I have no reason to doubt your

competence to make this judgement and therefore will have to look again

at my methodology. This was what I was looking for when I asked members

of this group for comments. I would just make the point that even if my

reported numbers overestimate by 100%, that does not affect the

relativity between moments of force at deep flexion and full extension.

Thank you again, Loren, for taking the trouble to look at my model and

comment on it.

Regards

Bruce Ross

Sydney, Australia

[Guest guest]

Nick,

To determine NJM, the body is segmented. In determining the NJM from the GRF

vector and the distance from the hip joint center, only the lower extremity is

considered. The body above the hip is modelled only as a point load acting on

the hip joint center. Because the point load goes through the hip joint center,

it cannot exert a moment about this point. The same is true for the knee. For

a full description of this method, see Plagoenhoff's text.

--

Loren Chiu

Los Angeles, CA

-------------- Original message --------------

Loren

<<On reflection of your email I better understand your response and have better

understood your comments. Either the force is calculated from the ground up

or the weight down and not both. I will re look at Bruce's model with this

thought in mind.>>>

[Guest guest]

Bruce,

See my comments below preceded by ###

***

Loren, thank you for your comments.

In relation to my reply to Johan Bastiaansen you state: " The moment at

the ankle can be considerably large during the squat exercise. " However,

the relevant question is not how large it " can be " but how large it

would be in terms of the model I used.

Among the simplying assumptions that I made were the following:

" ... the force vector of the weight bar (FWB) was assumed to be located

directly above that of the upper body (cgUB). ... it was assumed that

the centre of gravity of the system remains directly above the ankle

joint rather than at the midpoint of the foot as is usually assumed.

" At each observation point throughout the exercise the body is evaluated

in a static or constant velocity state and therefore can be treated as

rigid. "

It was in the context of these assumptions that I stated in my reply to

Johan that " the moment about the ankle joint would have been very small

through the full range of the squat. " In terms of the model, do you

disagree?

### First, your assumption is not correct. The COG does not stay over the ankle

joint throughout the squatting motion, and in fact shifts anterior while

descending into the squat. This is an important consideration of squatting

technique (note this is for a typical high-bar squat), as it increases the

plantarflexor NJM which in turn reduces the NJM at the knee. You are attempting

to provide biomechanical data by simplifying the basic characteristics of

movement, which nullifies any possibility for accuracy.

In relation to my original post you state: " This 'article' has not been

peer reviewed, such as in a scientific journal. " I would have thought

that my asking members of the Supertraining group for comments and

criticisms was a genuine attempt to obtain peer review such as that

which you have provided. Further, your mention of scientific journals

raises the obvious point that, irrespective of its quality, there is no

way that any relevant scientific journal would have considered it for

publication, simply because I have no academic credentials in this

field.

### By your own admission, you do not have credentials in biomechanics, yet you

are still posting an (mis)informative article utilizing biomechanical techniques

on your website (where you sell equipment that benefits from the conclusion of

your article). Is this not a conflict of interest? As a researcher, I have to

disclose all possible conflicts of interest, both to my institutional review

board and the journal I seek to publish research in. This is on top of

accurately processing and analyzing data.

I had a long academic career in a totally unrelated discipline and thus

have some experience of the realities of academic publishing. Not only

is journal publication restricted to the cognoscente but also articles

which are critical of the dominant paradigm of a discipline are rarely

published in mainstream journals. Further, the fact that ownership of

scholarly journals has been almost entirely appropriated by

profit-seeking publishing companies means that access to them is

basically restricted to those with direct affiliation to universities.

The recent series of posts here on the topic, " Does Sports-Science

Research Influence Practice? " is testimony to the gap between science

and practice. My contribution, however flawed, is an attempt to raise

and discuss important issues within the public domain and written to be

understood even by those " without a proper understanding of

biomechanics. " When the academic community begins to publish studies

that can be comprehended by outsiders then there will be no need for

people like me to try to fill the void.

### There are better ways to raise issues than to generate “scientific dataâ€

utilizing methods you do not understand. For example, you could perform a

literature review of existing research. Or you could ask the question on

Supertraining and ask for the opinions of researchers. Rather you have posted

false data on your website that anyone can read and be misinformed by.

You state that I have not " searched for comparative data (and there is

plenty) to determine if his NJM are even in the ballpark (which they are

not). " I can assure you that I have searched over a long period for data

relevant to the issue with which I am concerned, namely the extent to

which the perceived " excessive loading in the bottom part of the

movement " and inadequate loading through the top range " may be

attributable to changing values of resistive torque in moving from deep

flexion to full extension of the hip and knee joints. " If there is

indeed " plenty " of data on this please direct me to it.

### See my recent article (Chiu & Salem, JSCR 2006) that has a NJM-time curve

for a front squat. Wretenberg et al. (Med. Sci. Sports Exerc. 1993) also has

NJM-time curves for high- and low-bar squats. Escamilla also has a number of

articles investigating the biomechanics of squatting exercise. There are more,

if you search through the biomechanics journals. BTW, you have a preconceived

notion that more (i.e. in a full squat) is excessive, and less (i.e. standing

up) is inadequate. You clearly did not read my post carefully. At what point

does more become excessive? You never define excessive.

The only study that I could find that was broadly relevant to this issue

was that by Abelbeck (2002) which evaluated " a linear motion squat

performed on a machine. " I attempted to base my model of the free

squat on his methodology. As for my NJM not being " in the ballpark " of

comparative data, Abelbeck's study, which was published in The Journal

of Strength and Conditioning Research, shows for the most comparable

body position to that of the free squat, knee moment values ranging from

greater than 1000N.m at 80 degrees of flexion to negative values above

165.6 degrees. My own results show 692.0N.m at 80 degrees and zero at

180 degrees, differences which could be attributable to the studies

being of different types of squat.

You further state that:

" Mr. Ross reports NJM for the combined limbs (left + right), although

NJM are typically reported for a single limb (this in and of itself is

not incorrect, but should be stated outright as it influences the

interpretation of results). "

Surely this is carping criticism. On all four occasions when I mention

" thighs " and " shanks " it is in the plural. What more should I have done

to make clear what I was measuring?

### It should be stated outright that the NJM is that for both knees or both

hips. The traditional convention for reporting NJM is for a single limb,

therefore, unless it is otherwise stated, the reader of a biomechanics article

interprets the data as being for a single limb.

Your really substantive criticism would appear to be that " Mr. Ross has

overestimated by 100% the NJM, which makes sense since he used the force

vectors for both the GRF and the combined lifter-barbell system, where

it should be one or the other. " I have no reason to doubt your

competence to make this judgement and therefore will have to look again

at my methodology. This was what I was looking for when I asked members

of this group for comments. I would just make the point that even if my

reported numbers overestimate by 100%, that does not affect the

relativity between moments of force at deep flexion and full extension.

### Again, you did not read my post carefully. The method you use does not take

into account segmental and angular accelerations, which are greater during the

above parallel portion of the squat. Incidentally, what you are discussing is

simply a strength curve, which is not novel, and is well known and discussed

frequently in the strength and conditioning world. Most readers are aware of

Arthur and his Nautilus machines which attempted to modify strength curves

compared to free weights. The problem with discussing strength curves in

isolation, is that it is simply a characteristic of an exercise, and provides

only an insight into the adaptations that can be elicited via the exercise.

However, to truly understand the adaptations, one has to consider the actual

adaptations, i.e. a longitudinal training study.

Loren Chiu

Los Angeles, CA

[Guest guest]

Loren Chiu wrote:

### Again, you did not read my post carefully. The method you use does not

take into account segmental and angular accelerations, which are greater

during the above parallel portion of the squat. Incidentally, what you are

discussing is simply a strength curve, which is not novel, and is well known

and discussed frequently in the strength and conditioning world. Most

readers are aware of Arthur and his Nautilus machines which attempted

to modify strength curves compared to free weights. The problem with

discussing strength curves in isolation, is that it is simply a

characteristic of an exercise, and provides only an insight into the

adaptations that can be elicited via the exercise. However, to truly

understand the adaptations, one has to consider the actual adaptations, i.e.

a longitudinal training study.

Casler writes:

Hi Loren, this post is not in direct response to yours, and I am only

offering additional information to consider and don't feel qualified to

" enter the fray " based on equational physics/mathematics/biomechanics.

First I generally find the OP's explorations " interesting but lacking " at

all levels since the body is much like the " Liquid Metal Terminator "

character played in Terminator II, and has the ability to go from plastic to

solid via instant physiological change.

This many times " skews " the " matchstick physics models " involved to perform

the computations.

And I might add two other elements for the OP to consider:

1) Lombard's Paradox

2) Muscular and Tissue Rebound Effect

1) Lombard's Paradox info can be found with a simple Google search. Here is

the first one that came up for me

http://anybody.auc.dk/pdf/antag.pdf

2) Mel Siff and I used to speculate as to the effect of " elastic and

muscular rebound " from the compression of tissues, and the expansion of

tissues due to muscular expansion, on the " inside " of the joint.

For example, in the full squat, the upper thigh and lower abdominal tissues

compress against one another. Additionally the activation of the upper

thigh musculature, and lower abdominal activation, in conjunction with the

IAP (intra-abdominal Pressure) pressing into the upper thigh, present a very

formidable " resistive " and " active " force on the inside of the hip joint,

that sums with the SSC of the hip extenders, to create a moment around the

hip joint adding to the extension action of the hip.

The same is, and can be observed on the inside of the knee joint, but to a

slightly lesser degree.

The complex interaction of these forces, play key assisting roles, that are

many times (in fact most all times) not accounted for in the " force

accounting " physics and math used.

Due to the complex interactive nature of these forces, I would be the last

to offer detailed information as to how to include them in your observations

and computations, but without inclusion, the computations are incomplete and

inaccurate to the real world.

Sorry if that adds difficulty to the OP's project, and projections, but the

complexity to the task is not my doing.

I am but a messenger, and observer.

Regards,

Casler

TRI-VECTOR 3-D Force Systems

Century City, CA

[Guest guest]

As a consequence of criticisms by Loren Chiu of the model which appears

on my company's website at

http://www.myoquip.com.au/Biomechanical_model_squat_article.htm

<http://www.myoquip.com.au/Biomechanical_model_squat_article.htm> , I

have spent considerable time reviewing it and have recalculated the

torque curves using a link segment model of the form described in Winter

(1990).

[Mod: Please note that Bruce initially tried to post his article as an

attachment to the list making no reference to his website or products. However,

as members may be aware the list automatically deletes attachments.]

I have not taken account of quite a few of Loren's criticisms because

his suggestions were at odds with what I was trying to measure and focus

on. Having said that, I would like to again thank him for taking the

trouble to critique my article even though I feel that his comments were

couched in unnecessarily aggressive language.

I welcome any further comments or criticisms.

Regards

Bruce Ross

Sydney, Australia