Dear all,

Last month, I requested your help about the measurement accuracy in

anthropometic data, kinematic measurement, and ground reactions. Here

is the collective replies. I really thank those you answered my request.

Your valuable suggestions are sincerely appreciated. Since the replies

are very clear and there are few numbers given, there is no summary or

number table in this post.

However, I still need your help to give me the actual error numbers of

measurement in practice (e.g. +/- 2 N for vertical ground reaction by X

force plate, +/- 0.005kg for the shank mass by Y method, etc.). I hope

I can gather enough numbers, table them, and post them. I think this

table would be very helpful for knowing the availability and limition of

current measurement techniques.

Thanks for you help again.

---------------- Original Post ------------------------------------

Dear All,

As you already know, "inverse dynamics" is a widely used method to

estimate the (net) leg-joint moments (and forces) for human gait. The

inverse dynamic calculation is an indirct method, i.e. instead of

measuring the joint moment directly,(1) ground reaction forces,

(2)kinematic variable (postions, velocities, accelerations of segments

or leg joints), and (3) anthropometric data of individuals are measured.

>From these three differnet kinds of independent variable, the net

legjoint moments can be calculated.

Theoretically, this approach seems fine to me. But, there is a question

bothers me when we want to use the joint moments for paraplegic FES

(functional electrical stimulation) feedback control : whether or not

the estimated joint moments are accurate enough as feedback signals.

Unfortunately, after searching literature, I found little discussion

about the accuracy of estimated net joint moment by inverse dynamic

calculation.

Surely, the accuracy of estimated net joint moments by inverse dynamic

calculation is influenced by many factors. They include the measuring

device/approach for independent variables, the drift of markers (or

misaliament of goniometer, etc), soft tissues, moving axes of joints,

unaccuracy of anthropometric data, motion mode (quick or slow, etc),

quantization of sampling, properties of signal filter, etc, etc.

----- (Ignore this paragraph, if you hate equations as I do :-) ----

I managed to derive the error equations to relate the resultant errors

to independent variable, for example :

dM_k = dM_a - (dCP_s x F_k) - (dCP_s x dF_k) - (CP_s x dF_k)

+ (dCD_s x F_a) + (dCD_s x dF_a) + (CD_s x df_a)

+ (dw_s x I_s . w_s) + (w_s x dI_s . w_s) + (w_s x I_s . dw_s)

+ (dw_s x I_s . dw_s) + (dw_s x dI_s . dw_s) + (dI_s . a_s)

+ (I_s . da_s) + (dI_s . da_s)

where d= delta (error of); M= moment; F=force; CD= distance from center

of mass (CM) to Distal joint; CP= distance from CM to Proxmal joint;

_a=ankle joint; _k=knee joint; _s=shank, a=angular acceleration;

w=angular veloccity; I=momnet and product of inertia matrix;

x=cross product; . = dot product.

----- end of equation example ---

To understand the accuary of estimated joint moments, among others, it

seems necessary to find the accuracy of the systems for measruing

indepent variables. However, I have no idea in practice what the

possible accuracy of independent variables are. Please, would any one

help to give me the numbers from your experience or your measurement

systems in ...

(1) the accuracy / resolution of force plate (ground fixed or shoe

insole type) in Fx, Fy, Fz, COP (centre of pressure) / Mx, My, Mz

(2) accuracy of kinematic variables, i.e. accuracy of linear and/or

angular position, velocity, acceleration of segments and/or joints

from camara system, goniometers, accelerometer, etc.

(3) the accuracy of anthropometric data from look up table, regression

equations, volumetric measurement, etc.

(4) the moving range of "joint centre" (if it can be defined)

Furthermore, it seems to me that there is no practical way to calibrate

the calculated joint moments. Hope I am wrong and tell me please.

Sorry for long post and poor English but thanks very much for your

attention and help in advance.

P.S. I will post the collected replies and their summary in due course.

----------------- Collective Replies ------------------

--

From: Ton van den Bogert

Dear Chung-huang,

You wrote to Biomch-L regarding error propagation in inverse

dynamics, and proposed the following equation:

>dM_k = dM_a - (dCP_s x F_k) - (dCP_s x dF_k) - (CP_s x dF_k)

> + (dCD_s x F_a) + (dCD_s x dF_a) + (CD_s x df_a)

> + (dw_s x I_s . w_s) + (w_s x dI_s . w_s) + (w_s x I_s . dw_s)

> + (dw_s x I_s . dw_s) + (dw_s x dI_s . dw_s) + (dI_s . a_s)

> + (I_s . da_s) + (dI_s . da_s)

This is not entirely correct if errors are stochastic variables

(random noise), i.e. they can be positive or negative. Every

input variable will then increase the output error, so you

should never get minus-signs in front of any terms. The correct

error propagation for random errors is calculated as follows.

If X1,X2,..Xn are n input variables, with errors E1,E2,...En, and

you have a function f which describes how the output variable Y

(in your case: M_k) depends on the input:

Y = f(X1,X2,...Xn)

The error Ey in Y can be estimated by:

2 2 df 2 2 df 2 2 df 2

Ey = E1 (---) + E2 (---) + ... + En (---)

dX1 dX2 dXn

So, you need the partial derivatives of f with respect to the

input variables, which should be easy for the inverse dynamics

equations.

These calculations can become quite involved. Personally, I

prefer to use Monte-Carlo simulations to evaluate error

propagation. You use random numbers with a certain Gaussian

distribution to perturb the input data, and see what effect this

has on the output. This has to be repeated many times, and the

results analyzed statistically.

I just finished such a study on 2-D inverse dynamics, and you can

find the information on the ISB website:

http://www.kin.ucalgary.ca/isb/data/invdyn

You asked for some error estimates:

>(1) the accuracy / resolution of force plate (ground fixed or shoe

> insole type) in Fx, Fy, Fz, COP (centre of pressure) / Mx, My, Mz

Force plate: error in forces are neglegible. There is an error

in COP of several cm, but this is *not* a stochastic error! It

depends on landing position. Since the error is has opposite

sign on opposite sides of the center of the plate, the error

becomes almost stochastic (zero-mean, random error) if you

collect a large number of trials. See Bobbert & Schamhardt,

J. Biomech. 23,705-710.

>(2) accuracy of kinematic variables, i.e. accuracy of linear and/or

>angular

> position, velocity, acceleration of segments and/or joints from

> camara system, goniometers, accelerometer, etc.

Position error: is random and depends highly on field of view and

measuring technique. Try 1 mm for a standard video gait analysis

system. There's also a non-random error due to lens distortion.

>(3) the accuracy of anthropometric data from look up table, regression

> equations, volumetric measurement, etc.

No idea, but you can probably find some estimate in papers where

regression models were developed from cadaver data. The 'fit

error': E = SQRT(SUM(model-measurement)/(N-M)), where N is the number of

data points and M is the number of parameters in the regression

model, will be a good error estimate. Be aware that these are

not random errors, so use your version of the error propagation

rather than mine.

>(4) the moving range of "joint centre" (if it can be defined)

Joint centre moves with respect to external markers, due to

movement between skin and bone. Typical: 2 cm at knee and hip,

probably less at ankle.

>Furthermore, it seems to me that there is no practical way to calibrate

>the calculated joint moments. Hope I am wrong and tell me please.

You are correct, and a big problem if you want to assess accuracy

of inverse dynamics analysis methods. That's why I applied my

own error analysis to data generated by computer simulation,

where the actual joint moments are exactly known. See the web

page I mentioned before.

>P.S. I will post the collected replies and their summary in due course.

Please do that.

-- Ton van den Bogert

Human Performance Laboratory

The University of Calgary

-----------------------------------------------------------------------

From: D Tabakin

Date: Thu, 13 Jun 1996 11:27:00 GMT+2

Subject: Re: Accuracy of calculated joint moment by invese dynamics

On the question of anthropometric data from a look up table.

I used data from a published article by Zatsiorsky (excuse the

spelling). Unfortunately I do not have the reference with me. But if

you are interested I can send it to you.

The article describes a method of using gamma rays to calculate the

segment masses , centres of gravity and moments of inertia of the

body. As you move further away from the centre of gravity, errors

increase. Therefore if we are dealing with the whole body, when

calculating the moment of inertia of the feet, the error can be large.

However as the feet weigh much less than the trunk or other segments,

the error can be ignored. (This was relevant for my research last

year, as I was viewing the complete body. in motion.). I do not know

if it is relevant to your research but if you are interested I can

send the reference.

Good Luck

Dudley Tabakin

Wits University South Africa

-----------------------------------------------------------------------

Date: Thu, 13 Jun 1996 07:51:19 -0400 (EDT)

From: cheng cao

To: Chung-huang YU

Subject: Re: Accuracy of calculated joint moment by invese dynamics

Hi, Chung-huang:

I think it is a good point for discussion. The accuracy seems to be

influenced mostly by the approximations of anthropometry and soft tissue

as well as intermediate joint movements. For example many publications

calculated the ankle joint moments by assuming foot as a rigid body and

assuming an anthropometry table. Maybe it's fine for their purposes.

Furthermore, an assumption of a spherical joint may ignore the

translations within the joint for example.

I did a kinematic study in finding the center of of rotation of thorax

relative to pelvis. It locates approximate 10 cm above and 8 cm

anterior the first sacrum during voluntary flexion and extension.

Good luck to you.

Cheng Cao. - Department of Mechanical Engineering and Applied Mechanics

The University of Michigan, Ann Arbor. -*-

-----------------------------------------------------------------------

Date: Fri, 14 Jun 1996 10:42:56 +0100 (MET)

From: "A.L.HOF"

Subject: Re: Accuracy of calculated joint moment by invese dynamics

To: Chung-huang YU , c.yu@ucl.ac.UK

Dear Chung-Huang,

The question you posted is very relevant indeed. I suspect many

biomechanists are sleeping badly when they think of it.

If I see it well, your error formula can be simplified. Some time

ago I wrote a short Technical Note in the J. Biomechanics 25: 1209-

1211, in which the joint moment is directly expressed in the measured

variables. The (error in the) moment depends on:

1) distance between joint centre (JC) and ground reaction vector

(GRF) x GRF

2) sum(distances between JC and CoM of segments between ground and

JC x weight of segment)

3) sum(distances between JC and CoM of segments between ground and

JC x mass.acceleration)

4) sum (I.angular acceleration).

My opinions, not strongly founded on evidence but more on

prejudice, are the following:

In stance, thus when a big GRF is present, term 1 is by far the

biggest, and so is the associated error. Mind that 1 cm error in JC x

1000 N GRF = 10 Nm! Errors of several cm in knee or hip JC are hard

to avoid, I think.(Work of Cappozzo, several sources.) Errors in the

GRF vector seem also to be present (paper of vd Bogert and Schamhart

in J.Biomech, 2-3 yr ago).

Term 2) can be relatively accurate, as long as the trunk

is not among the segments.

Term 3) is rather inaccurate, because the acceleration is so

noisy, but it is much smaller than 1) as long as a ground reaction

is present. Term 4), the rotational moment, needs a lot of high

mathematics to be calculated, but as far as I can see, it is in all

practical cases relatively small.

I suppose you have the book "3-D analysis of human movement" by

Allard, Stokes and Bianchi (Human Kinetics, 1995). Woltring also has

discussed the problem in Ch 11 of "Biolocomotion: A century of

research using moving pictures" ISB series no 1 (1992).

I am very interested in your results! Good luck,

At Hof

Department of Medical Physiology

University of Groningen

Bloemsingel 10

NL-9712 KZ GRONINGEN

The Netherlands

Phone: (31) 50 3632645

Fax: (31) 50 3632751

-----------------------------------------------------------------------

Date: Thu, 13 Jun 1996 17:14:27 -0400 (EDT)

From: Louise A Gilchrist

To: c.yu@ucl.ac.uk

Subject: errors posting

In response to your BIOMCH-L post, here are some papers that you may want

to check (if you haven't already!):

Angulo and Dapena (1992). "comparison of film and video techniques for

estimating three-dimensional coordinates within a large field" Int J

Sport Biomech 8: 145-151.

Cappozzo et al. (1975). "A general computing method for the analysis of

human locomotion" J Biomechanics 23: 617-621.

Cappozzo and Gazzani (1990). "Joint kinematic assessment during physical

exercise" in Biomechanics of Human Movement. N.Berme and A. Cappozzo

(eds), Worthington, Ohio, Bertec Corporation, 263-274.

Cappozzo, A. (1991). "Three-dimensional analysis of human walking:

Experimental methods and associated artifacts." Hum Mov Sci 10: 589-602.

Chen et al. (1994). "An investigation on the accuracy of three-dimensional

space reconstruction using the direct linear transformation technique". J

Biomechanics 27(4): 493-500.

Dapena et al (1982). "Three-dimensional cinematography with control object

of unknown shape." J Biomechanics 15(1): 11-19.

DeLuzio et al (1993). "A procedure to validate three-dimensional motion

assessment systems." J Biomechanics 26(6): 753-759.

Kennedy et al (1989). "Comparison of film and video techniques for

three-dimensional DLT repredictions". Int J Sport Biomech 5: 457-460.

These don't address all the issues that you've raised but they do cover

some of them. Good luck!

Louise Gilchrist

Department of Physical Therapy and Exercise Science

SUNY at Buffalo

405 Kimball Tower

Buffalo, NY 14214

ph: 716-829-2941 ext 102

lag@acsu.buffalo.edu

----------- End of Collective Replies ----------------------------

Chung-huang YU

Medical Physics & Bioengineering,

1st floor Shropshire House,

11-20 Capper Street,

University College London,

London WC1E 6JA

tel: (44) 0171-3807777 ext 5715

fax: (44) 0171-209-6269

Last month, I requested your help about the measurement accuracy in

anthropometic data, kinematic measurement, and ground reactions. Here

is the collective replies. I really thank those you answered my request.

Your valuable suggestions are sincerely appreciated. Since the replies

are very clear and there are few numbers given, there is no summary or

number table in this post.

However, I still need your help to give me the actual error numbers of

measurement in practice (e.g. +/- 2 N for vertical ground reaction by X

force plate, +/- 0.005kg for the shank mass by Y method, etc.). I hope

I can gather enough numbers, table them, and post them. I think this

table would be very helpful for knowing the availability and limition of

current measurement techniques.

Thanks for you help again.

---------------- Original Post ------------------------------------

Dear All,

As you already know, "inverse dynamics" is a widely used method to

estimate the (net) leg-joint moments (and forces) for human gait. The

inverse dynamic calculation is an indirct method, i.e. instead of

measuring the joint moment directly,(1) ground reaction forces,

(2)kinematic variable (postions, velocities, accelerations of segments

or leg joints), and (3) anthropometric data of individuals are measured.

>From these three differnet kinds of independent variable, the net

legjoint moments can be calculated.

Theoretically, this approach seems fine to me. But, there is a question

bothers me when we want to use the joint moments for paraplegic FES

(functional electrical stimulation) feedback control : whether or not

the estimated joint moments are accurate enough as feedback signals.

Unfortunately, after searching literature, I found little discussion

about the accuracy of estimated net joint moment by inverse dynamic

calculation.

Surely, the accuracy of estimated net joint moments by inverse dynamic

calculation is influenced by many factors. They include the measuring

device/approach for independent variables, the drift of markers (or

misaliament of goniometer, etc), soft tissues, moving axes of joints,

unaccuracy of anthropometric data, motion mode (quick or slow, etc),

quantization of sampling, properties of signal filter, etc, etc.

----- (Ignore this paragraph, if you hate equations as I do :-) ----

I managed to derive the error equations to relate the resultant errors

to independent variable, for example :

dM_k = dM_a - (dCP_s x F_k) - (dCP_s x dF_k) - (CP_s x dF_k)

+ (dCD_s x F_a) + (dCD_s x dF_a) + (CD_s x df_a)

+ (dw_s x I_s . w_s) + (w_s x dI_s . w_s) + (w_s x I_s . dw_s)

+ (dw_s x I_s . dw_s) + (dw_s x dI_s . dw_s) + (dI_s . a_s)

+ (I_s . da_s) + (dI_s . da_s)

where d= delta (error of); M= moment; F=force; CD= distance from center

of mass (CM) to Distal joint; CP= distance from CM to Proxmal joint;

_a=ankle joint; _k=knee joint; _s=shank, a=angular acceleration;

w=angular veloccity; I=momnet and product of inertia matrix;

x=cross product; . = dot product.

----- end of equation example ---

To understand the accuary of estimated joint moments, among others, it

seems necessary to find the accuracy of the systems for measruing

indepent variables. However, I have no idea in practice what the

possible accuracy of independent variables are. Please, would any one

help to give me the numbers from your experience or your measurement

systems in ...

(1) the accuracy / resolution of force plate (ground fixed or shoe

insole type) in Fx, Fy, Fz, COP (centre of pressure) / Mx, My, Mz

(2) accuracy of kinematic variables, i.e. accuracy of linear and/or

angular position, velocity, acceleration of segments and/or joints

from camara system, goniometers, accelerometer, etc.

(3) the accuracy of anthropometric data from look up table, regression

equations, volumetric measurement, etc.

(4) the moving range of "joint centre" (if it can be defined)

Furthermore, it seems to me that there is no practical way to calibrate

the calculated joint moments. Hope I am wrong and tell me please.

Sorry for long post and poor English but thanks very much for your

attention and help in advance.

P.S. I will post the collected replies and their summary in due course.

----------------- Collective Replies ------------------

--

From: Ton van den Bogert

Dear Chung-huang,

You wrote to Biomch-L regarding error propagation in inverse

dynamics, and proposed the following equation:

>dM_k = dM_a - (dCP_s x F_k) - (dCP_s x dF_k) - (CP_s x dF_k)

> + (dCD_s x F_a) + (dCD_s x dF_a) + (CD_s x df_a)

> + (dw_s x I_s . w_s) + (w_s x dI_s . w_s) + (w_s x I_s . dw_s)

> + (dw_s x I_s . dw_s) + (dw_s x dI_s . dw_s) + (dI_s . a_s)

> + (I_s . da_s) + (dI_s . da_s)

This is not entirely correct if errors are stochastic variables

(random noise), i.e. they can be positive or negative. Every

input variable will then increase the output error, so you

should never get minus-signs in front of any terms. The correct

error propagation for random errors is calculated as follows.

If X1,X2,..Xn are n input variables, with errors E1,E2,...En, and

you have a function f which describes how the output variable Y

(in your case: M_k) depends on the input:

Y = f(X1,X2,...Xn)

The error Ey in Y can be estimated by:

2 2 df 2 2 df 2 2 df 2

Ey = E1 (---) + E2 (---) + ... + En (---)

dX1 dX2 dXn

So, you need the partial derivatives of f with respect to the

input variables, which should be easy for the inverse dynamics

equations.

These calculations can become quite involved. Personally, I

prefer to use Monte-Carlo simulations to evaluate error

propagation. You use random numbers with a certain Gaussian

distribution to perturb the input data, and see what effect this

has on the output. This has to be repeated many times, and the

results analyzed statistically.

I just finished such a study on 2-D inverse dynamics, and you can

find the information on the ISB website:

http://www.kin.ucalgary.ca/isb/data/invdyn

You asked for some error estimates:

>(1) the accuracy / resolution of force plate (ground fixed or shoe

> insole type) in Fx, Fy, Fz, COP (centre of pressure) / Mx, My, Mz

Force plate: error in forces are neglegible. There is an error

in COP of several cm, but this is *not* a stochastic error! It

depends on landing position. Since the error is has opposite

sign on opposite sides of the center of the plate, the error

becomes almost stochastic (zero-mean, random error) if you

collect a large number of trials. See Bobbert & Schamhardt,

J. Biomech. 23,705-710.

>(2) accuracy of kinematic variables, i.e. accuracy of linear and/or

>angular

> position, velocity, acceleration of segments and/or joints from

> camara system, goniometers, accelerometer, etc.

Position error: is random and depends highly on field of view and

measuring technique. Try 1 mm for a standard video gait analysis

system. There's also a non-random error due to lens distortion.

>(3) the accuracy of anthropometric data from look up table, regression

> equations, volumetric measurement, etc.

No idea, but you can probably find some estimate in papers where

regression models were developed from cadaver data. The 'fit

error': E = SQRT(SUM(model-measurement)/(N-M)), where N is the number of

data points and M is the number of parameters in the regression

model, will be a good error estimate. Be aware that these are

not random errors, so use your version of the error propagation

rather than mine.

>(4) the moving range of "joint centre" (if it can be defined)

Joint centre moves with respect to external markers, due to

movement between skin and bone. Typical: 2 cm at knee and hip,

probably less at ankle.

>Furthermore, it seems to me that there is no practical way to calibrate

>the calculated joint moments. Hope I am wrong and tell me please.

You are correct, and a big problem if you want to assess accuracy

of inverse dynamics analysis methods. That's why I applied my

own error analysis to data generated by computer simulation,

where the actual joint moments are exactly known. See the web

page I mentioned before.

>P.S. I will post the collected replies and their summary in due course.

Please do that.

-- Ton van den Bogert

Human Performance Laboratory

The University of Calgary

-----------------------------------------------------------------------

From: D Tabakin

Date: Thu, 13 Jun 1996 11:27:00 GMT+2

Subject: Re: Accuracy of calculated joint moment by invese dynamics

On the question of anthropometric data from a look up table.

I used data from a published article by Zatsiorsky (excuse the

spelling). Unfortunately I do not have the reference with me. But if

you are interested I can send it to you.

The article describes a method of using gamma rays to calculate the

segment masses , centres of gravity and moments of inertia of the

body. As you move further away from the centre of gravity, errors

increase. Therefore if we are dealing with the whole body, when

calculating the moment of inertia of the feet, the error can be large.

However as the feet weigh much less than the trunk or other segments,

the error can be ignored. (This was relevant for my research last

year, as I was viewing the complete body. in motion.). I do not know

if it is relevant to your research but if you are interested I can

send the reference.

Good Luck

Dudley Tabakin

Wits University South Africa

-----------------------------------------------------------------------

Date: Thu, 13 Jun 1996 07:51:19 -0400 (EDT)

From: cheng cao

To: Chung-huang YU

Subject: Re: Accuracy of calculated joint moment by invese dynamics

Hi, Chung-huang:

I think it is a good point for discussion. The accuracy seems to be

influenced mostly by the approximations of anthropometry and soft tissue

as well as intermediate joint movements. For example many publications

calculated the ankle joint moments by assuming foot as a rigid body and

assuming an anthropometry table. Maybe it's fine for their purposes.

Furthermore, an assumption of a spherical joint may ignore the

translations within the joint for example.

I did a kinematic study in finding the center of of rotation of thorax

relative to pelvis. It locates approximate 10 cm above and 8 cm

anterior the first sacrum during voluntary flexion and extension.

Good luck to you.

Cheng Cao. - Department of Mechanical Engineering and Applied Mechanics

The University of Michigan, Ann Arbor. -*-

-----------------------------------------------------------------------

Date: Fri, 14 Jun 1996 10:42:56 +0100 (MET)

From: "A.L.HOF"

Subject: Re: Accuracy of calculated joint moment by invese dynamics

To: Chung-huang YU , c.yu@ucl.ac.UK

Dear Chung-Huang,

The question you posted is very relevant indeed. I suspect many

biomechanists are sleeping badly when they think of it.

If I see it well, your error formula can be simplified. Some time

ago I wrote a short Technical Note in the J. Biomechanics 25: 1209-

1211, in which the joint moment is directly expressed in the measured

variables. The (error in the) moment depends on:

1) distance between joint centre (JC) and ground reaction vector

(GRF) x GRF

2) sum(distances between JC and CoM of segments between ground and

JC x weight of segment)

3) sum(distances between JC and CoM of segments between ground and

JC x mass.acceleration)

4) sum (I.angular acceleration).

My opinions, not strongly founded on evidence but more on

prejudice, are the following:

In stance, thus when a big GRF is present, term 1 is by far the

biggest, and so is the associated error. Mind that 1 cm error in JC x

1000 N GRF = 10 Nm! Errors of several cm in knee or hip JC are hard

to avoid, I think.(Work of Cappozzo, several sources.) Errors in the

GRF vector seem also to be present (paper of vd Bogert and Schamhart

in J.Biomech, 2-3 yr ago).

Term 2) can be relatively accurate, as long as the trunk

is not among the segments.

Term 3) is rather inaccurate, because the acceleration is so

noisy, but it is much smaller than 1) as long as a ground reaction

is present. Term 4), the rotational moment, needs a lot of high

mathematics to be calculated, but as far as I can see, it is in all

practical cases relatively small.

I suppose you have the book "3-D analysis of human movement" by

Allard, Stokes and Bianchi (Human Kinetics, 1995). Woltring also has

discussed the problem in Ch 11 of "Biolocomotion: A century of

research using moving pictures" ISB series no 1 (1992).

I am very interested in your results! Good luck,

At Hof

Department of Medical Physiology

University of Groningen

Bloemsingel 10

NL-9712 KZ GRONINGEN

The Netherlands

Phone: (31) 50 3632645

Fax: (31) 50 3632751

-----------------------------------------------------------------------

Date: Thu, 13 Jun 1996 17:14:27 -0400 (EDT)

From: Louise A Gilchrist

To: c.yu@ucl.ac.uk

Subject: errors posting

In response to your BIOMCH-L post, here are some papers that you may want

to check (if you haven't already!):

Angulo and Dapena (1992). "comparison of film and video techniques for

estimating three-dimensional coordinates within a large field" Int J

Sport Biomech 8: 145-151.

Cappozzo et al. (1975). "A general computing method for the analysis of

human locomotion" J Biomechanics 23: 617-621.

Cappozzo and Gazzani (1990). "Joint kinematic assessment during physical

exercise" in Biomechanics of Human Movement. N.Berme and A. Cappozzo

(eds), Worthington, Ohio, Bertec Corporation, 263-274.

Cappozzo, A. (1991). "Three-dimensional analysis of human walking:

Experimental methods and associated artifacts." Hum Mov Sci 10: 589-602.

Chen et al. (1994). "An investigation on the accuracy of three-dimensional

space reconstruction using the direct linear transformation technique". J

Biomechanics 27(4): 493-500.

Dapena et al (1982). "Three-dimensional cinematography with control object

of unknown shape." J Biomechanics 15(1): 11-19.

DeLuzio et al (1993). "A procedure to validate three-dimensional motion

assessment systems." J Biomechanics 26(6): 753-759.

Kennedy et al (1989). "Comparison of film and video techniques for

three-dimensional DLT repredictions". Int J Sport Biomech 5: 457-460.

These don't address all the issues that you've raised but they do cover

some of them. Good luck!

Louise Gilchrist

Department of Physical Therapy and Exercise Science

SUNY at Buffalo

405 Kimball Tower

Buffalo, NY 14214

ph: 716-829-2941 ext 102

lag@acsu.buffalo.edu

----------- End of Collective Replies ----------------------------

Chung-huang YU

Medical Physics & Bioengineering,

1st floor Shropshire House,

11-20 Capper Street,

University College London,

London WC1E 6JA

tel: (44) 0171-3807777 ext 5715

fax: (44) 0171-209-6269