SUMMARY OF RESPONSES to my e-mail:

JOINT ANGLE CALCULATION AND ERROR REDUCTION FROM FASTRAK DATA

> Dear Biomechanists

>=20

> I work at the National Institute of Working Life in Ume=E5, Sweden. We are

> using the FASTRAK (Polhemus Inc.) to collect orientation data from 1-4

> receivers fixed at different positions of the human body. Primarily we are

> studying arm and shoulder movements (receivers on Wrist, Upper arm and

> Acromion). We want to calculate the angles of different joints, using the

> standard recommended by the ISB Committee. The information, from the=

FASTRAK

> receivers, is over-determined (redundant) since we assume that the body

> segments are connected through ball/hinge joints. You can compare this

> redundance with the one you get when using multiple markers in a=

video-based

> positioning system. We want to use the redundant information for two=

purposes:

> 1. - Decide the length of the body segments

> - Decide the relation beween receiver and body segment orientation,=20

> (using sample series registrated during movement)

> This approach may give better estimations than measuring these=

entities

> manually.

> 2. Increase the precision of the calculated angles (in a least square

> sense), utilizing the fact that the data error has different variance in

> different angular and spatial directions.

>=20

> We would like to know if anyone has done something similar and if anyone

> knows any references to previous work concerning this matter.

>=20

> We would be very greatful if we could get some responses. Naturally we=

will

> send a summary of replies to the Biomech-server.

FIRST a clearification of my mail according to one of the responses:

I assume that you know that the FASTRAK receiver gives both angle and

position (totally 6 degree of freedom). If we assume that the receivers are

fixed on the segment and that the segment geometry is known then it is

sufficient with one receiver on the wrist and one on acromion to decide how

the upper arm segment is positioned and oriented. This is true because we

know that the elbow is a hinge joint. This means that the receiver fixed on

the upper arm just adds some redundant information. Since some of the values

are pretty bad due to soft tissue motion (especially the humerus rotation)

we hope that the redundant information may be used to decrease these errors.

Don't hesitate to ask us again if that wasn't totally clear.

THANK YOU all for the responses (n=3D8):

1. FROM Gideon Ariel =20

Recommending: http://www.arielnet.com

2. FROM "Jarrod Carter" (friend to

Randy below)

3. FROM "P. Ludewig" (asking a question,

answered above)

4. FROM Oyvind Stavdahl

He is about to use the MotionStar system for studies of kinematics on

artificial arms.

5. FROM "Nick Barnett" =20

Interested in a program that enables FASTRAK measuring in a Windows=

environment.

6. FROM "R. Ching"

Regarding your inquiry about the Polhemus 3Space Fastrak system, we have

been using this system in our lab for the past 3 years. We have been

investigating the kinematics of both normal and pathologic joints

including the spine, foot/ankle, knee, shoulder, etc. I have used the

system to obtain the humeral orientation relative to the scapula

(glenoid), but have not investigated the motions of the forearm or wrist

further up the "chain". I believe that you should be able to accomplish

your stated objectives based on your assumption of ball/hinge joints. I

assume you are willing to accept reduced accuracy in your data due to this

assumption and the likelihood that your "envelope" of motion will exceed

the specified 30" operating range of the receivers. I wish you success on

your project!

7. FROM Agnes.Roby-Brami@snv.jussieu.fr (Agnes ROBY-BRAMI)

We are involved in a similar approach with Polhemus Fastrack receivers

with EV Biryukova and AA Frolov from Moscow.

We calculate the angular configuration of the upperlimb by using the

position and orientation informations of 4 receivers (on the hand, forearm,

arm and acromion). Our work was presented by EV Biryukova (Acad Sci,

Moscow) at the 4th international Symposium on 3D analysis of human movement

in Grenoble (July 1996) "EV Biryukova, AA Frolov M Mokhtari and A.

Roby-Brami Reconstruction of joint centers and axes of rotation from

Spatial Tracking System recordings".

In brief we use the recordings of analytical movements performed in every

ddl to calculate the axis of rotation by reference to 2 receivers (upper

and lower) for each joint. Then it is possible to calculate the joint

angles of any movement. We shall test and adjust the algorithm by using a

direct kinematic reconstruction of the hand movement and by comparing the

calculated acceleration with a measure of 3D hand acceleration.

This work is now in progress, Lena Biryukova will be in France next month

to continue this work and perform some experiment in our lab. So, we shall

probably obtain more informations to send to you.

I am also very interested by your results and by all the answers that you

will get.

8. FROM Rebecca States

I recently submitted a paper to Clinical Biomechanics which does

not focus on, but does discuss the question of determining=20

segment lengths from surface markers. If one goes through a

process of adjusting the markers to insure that they are located

over the joint centers, then segment length variability decreases

considerably from initial estimates. I would guess that the

resulting values are more reliable than manual measures of

segment length, though I don't have data to back up that part. A

summary of the article follows. If you would like the complete text,

let me know, and I'll send it to you. I have also included the

bibliography for that paper which lists a number of sources you

may find useful in answering some of your other questions. =20

Summary

This study suggests a new approach to improving the

within-session reliability with which joint centers are estimated

from surface markers. Segment length standard deviations are

used to evaluate reliability, since they can be assessed under

ecologically valid conditions that allow for soft-tissue and

out-of-plane motion. Significant improvements in reliability were

achieved with either of two relatively simple methods for making

post-hoc adjustments, even when adjustments were applied to a

new data set. For the 3D optimization method introduced here,

reliability improved for both segments flanking the adjusted joint

center. In contrast, reliability only improved for one segment after

applying Spiegelman & Woo#s 2D method. Results suggest how

calibration trials conducted at the beginning of an experimental

session can be used along with post-hoc adjustment to improve

reliability, even when data collected during the experimental

procedures are unsuitable for deriving adjustment parameters.=20

Future research should verify the efficacy of this overall approach in

other experimental settings, and develop procedures to improve

between-session reliability.

Relevance

This study provides a practical means to assess

the reliability with which joint centers have been located in

experimental or clinical settings where the real-world problems of

out-of-plane and soft-tissue motion can not be avoided. The

approach suggested here demands less mathematical expertise

than do the six degree of freedom rigid body methods, and hence

may be useful for labs with limited technical support. =20

REFERENCE LIST:

Lower extremity angle measurement with accelerometers--error and

sensitivity analysis. Willemsen-AT; Frigo-C; Boom-HB IEEE-Trans-Biomed-Eng.

1991 Dec; 38(12): 1186-93=20

Advances in motion analysis. Clayton-HM

Vet-Clin-North-Am-Equine-Pract. 1991 Aug; 7(2): 365-82=20

New mathematical definition and calculation of axial rotation of

anatomical joints. Miyazaki-S; Ishida-A J-Biomech-Eng. 1991 Aug; 113(3):=

270-5=20

Calculation of the instantaneous centre of rotation for a rigid

body. Holzreiter-S J-Biomech. 1991; 24(7): 643-7=20

Measurement of joint kinematics using ExpertVision system. An-KN;

Growney-E; Chao-EY Biomed-Sci-Instrum. 1991; 27: 245-52=20

Three-dimensional kinematics of glenohumeral elevation. An-KN;

Browne-AO; Korinek-S; Tanaka-S; Morrey-BF J-Orthop-Res. 1991 Jan; 9(1):=

143-9=20

Measurement of finger joint angles and maximum finger forces during

cylinder grip activity. Lee-JW; Rim-K J-Biomed-Eng. 1991 Mar; 13(2): 152-62=

=20

Rigid body motion calculated from spatial co-ordinates of markers.

Spoor-CW; Veldpaus-FE J-Biomech. 1980; 13(4): 391-3=20

A least-squares algorithm for the equiform transformation from

spatial marker co-ordinates. Veldpaus-FE; Woltring-HJ; Dortmans-LJ

J-Biomech. 1988; 21(1): 45-54=20

Finite centroid and helical axis estimation from noisy landmark

measurements in the study of human joint kinematics. Woltring-HJ; Huiskes-R;

de-Lange-A; Veldpaus-FE J-Biomech. 1985; 18(5): 379-89=20

Determining the movements of the skeleton using well-configured

markers.=20

Soderkvist-I; Wedin-PA J-Biomech. 1993 Dec; 26(12): 1473-7=20

Finite centroid and helical axis estimation from noisy landmark

measurements in the study of human joint kinematics. Woltring-HJ; Huiskes-R;

de-Lange-A; Veldpaus-FE J-Biomech. 1985; 18(5): 379-89=20

Effects of data smoothing on the reconstruction of helical axis

parameters in human joint kinematics. de-Lange-A; Huiskes-R; Kauer-JM

J-Biomech-Eng. 1990 May; 112(2): 107-13=20

Measurement of the total motion between two body segments. I.

Analytical development. Kinzel-GL; Hall-AS Jr; Hillberry-BM J-Biomech. 1972

Jan; 5(1): 93-105=20

Reliable in vivo estimation of the instantaneous helical axis in

human segmental movements. Fioretti-S; Jetto-L; Leo-T IEEE-Trans-Biomed-Eng.

1990 Apr; 37(4): 398-409=20

Calculation of the instantaneous centre of rotation for a rigid

body. Holzreiter-S J-Biomech. 1991; 24(7): 643-7=20

A procedure for determining rigid body transformation parameters.

Challis-JH J-Biomech. 1995 Jun; 28(6): 733-7

An examination of procedures for determining body segment attitude

and position from noisy biomechanical data. Challis-JH Med-Eng-Phys. 1995

Mar; 17(2): 83-90=20

Errors in kinematic parameters of a planar joint: guidelines for

optimal experimental design. Panjabi-MM; Goel-VK; Walter-SD J-Biomech. 1982;

15(7): 537-44=20

Errors in the center and angle of rotation of a joint: an

experimental study. Panjabi-MM; Goel-VK; Walter-SD; Schick-S J-Biomech-Eng.

1982 Aug; 104(3): 232-7=20

Centers and angles of rotation of body joints: a study of errors=20

and optimization. Panjabi-MM J-Biomech. 1979; 12(12): 911-20=20

A rigid-body method for finding centers of rotation and angular

displacements of planar joint motion. Spiegelman-JJ; Woo-SL J-Biomech. 1987;

20(7): 715-21=20

Optimal marker placement for calculating the instantaneous center of

rotation. Crisco-JJ-3rd; Chen-X; Panjabi-MM; Wolfe-SW J-Biomech. 1994 Sep;

27(9): 1183-7=20

A procedure to validate three-dimensional motion assessment systems.

DeLuzio-KJ; Wyss-UP; Li-J; Costigan-PA J-Biomech. 1993 Jun; 26(6): 753-9=20

A comparison of the accuracy of several hip center location

prediction methods. Bell-AL; Pedersen-DR; Brand-RA J-Biomech. 1990; 23(6):

617-21=20

A finite helical axis as a landmark for kinematic reference of the

knee.=20

Hart-RA; Mote-CD Jr; Skinner-HB J-Biomech-Eng. 1991 May; 113(2): 215-22=20

On the estimation of joint kinematics during gait. Ramakrishnan-HK;

Kadaba-MP J-Biomech. 1991; 24(10): 969-77=20

Reproducibility and accuracy of angle measurements obtained under

static conditions with the Motion Analysis video system. Vander-Linden-DW;

Carlson-SJ; Hubbard-RL Phys-Ther. 1992 Apr; 72(4): 300-5 =20

Basic Biomechanics of the Musculoskeletal System. Frankel VH,

Forssen K, Nachamie H, Yelle L, Nordin M. Lea and Febiner, Philadelphia, PA,

1989.

Comparison of three methods for locating joint centers during planar arm

motion. States RA. Soc Neurosc Ab 1995; 21: #174.15.=20

Resolving indeterminacy associated with joint-level motor equivalence in

planar aimed arm movements. States RA. [PhD Dissertation] Columbia

University, New York, NY, 1995

Assessing and reporting the accuracy of position measurements made with

optical tracking systems. Haggard P, Wing AM. J Motor Beh 1990; 22: 315-321.=

=20

Experimental errors in the observation of body joint kinematics. Walter SD,

Panjabi MM. Technomet 1988; 30: 71-78.=20

The Kinematics of Machinery: Outline of a Theory of Machines (translated by

Kennedy, A.M.W.). Releaux F. Dover, New York, 1875; 56-70.=20

A method for the calculation of orthogonal rotation matrices and its

application in photogrammetry and other disciplines. Tienstra, M.

(1969)Ph.D.-thesis, Technical University of Delft, The Netherlands.

Waltman, Delft.

On definition and calculus of rigid-body kinematics using spatial

marker coordinates. Submitted for publication to the Journal of

Biomechanics. Woltring, H.J. (1981) [Ultimately published as Veldpaus et

al., Journal of Biomechanics, January 1988.]

One Hundred Years Photogrammetry in Bio In: V. Tosi & A. Cappozzo

(Eds) H.J. Woltring (1989), Proc. of the Symposium on Biolocomotion: a

Century of Research Using Moving Pictures (Formia, Italy, April 1989; in=

print).

A Fortran package for generalized, cross validatory spline smoothing

and differentiation. H.J. Woltring (1986) Advances in Engineering software

8(1986)2, pp. 104-113.

Prediction of Hip Joint Center location from External Landmarks, Bell A.,

Brand R., and Pedersen D. Human Movment Sciences 8(1989) 3-16.

Measurement error influence on helical axis accuracy in the description of

3-D, finite joint movement in biomechanics. Woltring, H.J., Huiskes, R., de

Lange, A. (1983) In: Biomechanics Symposium (Edited by Woo, S.L.-Y. and

Mates, R.E.), AMD 56 (FED 1), 19-22. ASME, New York.

Explanation, verification and application of helical-axis error propagation

formulas. Human Movement Science 3, 95-117. Spoor, C.W. (1984)

Measurement errors in roentgen-stereophotogrammetric joint-motion

analysis. A. de Lange, R. Huiskes, and J.M.G. Kauer (1990) J. Biomechanics

23(3):259-269.

Position and orientation in space of bones during movement: experimental

artefacts. Cappozzo A, Catani F, Leardini A, Benedetti MG, Della Croce U.

Clin Biomech 1996; 11: 90-100.

/Johan L=F6nn

JOINT ANGLE CALCULATION AND ERROR REDUCTION FROM FASTRAK DATA

> Dear Biomechanists

>=20

> I work at the National Institute of Working Life in Ume=E5, Sweden. We are

> using the FASTRAK (Polhemus Inc.) to collect orientation data from 1-4

> receivers fixed at different positions of the human body. Primarily we are

> studying arm and shoulder movements (receivers on Wrist, Upper arm and

> Acromion). We want to calculate the angles of different joints, using the

> standard recommended by the ISB Committee. The information, from the=

FASTRAK

> receivers, is over-determined (redundant) since we assume that the body

> segments are connected through ball/hinge joints. You can compare this

> redundance with the one you get when using multiple markers in a=

video-based

> positioning system. We want to use the redundant information for two=

purposes:

> 1. - Decide the length of the body segments

> - Decide the relation beween receiver and body segment orientation,=20

> (using sample series registrated during movement)

> This approach may give better estimations than measuring these=

entities

> manually.

> 2. Increase the precision of the calculated angles (in a least square

> sense), utilizing the fact that the data error has different variance in

> different angular and spatial directions.

>=20

> We would like to know if anyone has done something similar and if anyone

> knows any references to previous work concerning this matter.

>=20

> We would be very greatful if we could get some responses. Naturally we=

will

> send a summary of replies to the Biomech-server.

FIRST a clearification of my mail according to one of the responses:

I assume that you know that the FASTRAK receiver gives both angle and

position (totally 6 degree of freedom). If we assume that the receivers are

fixed on the segment and that the segment geometry is known then it is

sufficient with one receiver on the wrist and one on acromion to decide how

the upper arm segment is positioned and oriented. This is true because we

know that the elbow is a hinge joint. This means that the receiver fixed on

the upper arm just adds some redundant information. Since some of the values

are pretty bad due to soft tissue motion (especially the humerus rotation)

we hope that the redundant information may be used to decrease these errors.

Don't hesitate to ask us again if that wasn't totally clear.

THANK YOU all for the responses (n=3D8):

1. FROM Gideon Ariel =20

Recommending: http://www.arielnet.com

2. FROM "Jarrod Carter" (friend to

Randy below)

3. FROM "P. Ludewig" (asking a question,

answered above)

4. FROM Oyvind Stavdahl

He is about to use the MotionStar system for studies of kinematics on

artificial arms.

5. FROM "Nick Barnett" =20

Interested in a program that enables FASTRAK measuring in a Windows=

environment.

6. FROM "R. Ching"

Regarding your inquiry about the Polhemus 3Space Fastrak system, we have

been using this system in our lab for the past 3 years. We have been

investigating the kinematics of both normal and pathologic joints

including the spine, foot/ankle, knee, shoulder, etc. I have used the

system to obtain the humeral orientation relative to the scapula

(glenoid), but have not investigated the motions of the forearm or wrist

further up the "chain". I believe that you should be able to accomplish

your stated objectives based on your assumption of ball/hinge joints. I

assume you are willing to accept reduced accuracy in your data due to this

assumption and the likelihood that your "envelope" of motion will exceed

the specified 30" operating range of the receivers. I wish you success on

your project!

7. FROM Agnes.Roby-Brami@snv.jussieu.fr (Agnes ROBY-BRAMI)

We are involved in a similar approach with Polhemus Fastrack receivers

with EV Biryukova and AA Frolov from Moscow.

We calculate the angular configuration of the upperlimb by using the

position and orientation informations of 4 receivers (on the hand, forearm,

arm and acromion). Our work was presented by EV Biryukova (Acad Sci,

Moscow) at the 4th international Symposium on 3D analysis of human movement

in Grenoble (July 1996) "EV Biryukova, AA Frolov M Mokhtari and A.

Roby-Brami Reconstruction of joint centers and axes of rotation from

Spatial Tracking System recordings".

In brief we use the recordings of analytical movements performed in every

ddl to calculate the axis of rotation by reference to 2 receivers (upper

and lower) for each joint. Then it is possible to calculate the joint

angles of any movement. We shall test and adjust the algorithm by using a

direct kinematic reconstruction of the hand movement and by comparing the

calculated acceleration with a measure of 3D hand acceleration.

This work is now in progress, Lena Biryukova will be in France next month

to continue this work and perform some experiment in our lab. So, we shall

probably obtain more informations to send to you.

I am also very interested by your results and by all the answers that you

will get.

8. FROM Rebecca States

I recently submitted a paper to Clinical Biomechanics which does

not focus on, but does discuss the question of determining=20

segment lengths from surface markers. If one goes through a

process of adjusting the markers to insure that they are located

over the joint centers, then segment length variability decreases

considerably from initial estimates. I would guess that the

resulting values are more reliable than manual measures of

segment length, though I don't have data to back up that part. A

summary of the article follows. If you would like the complete text,

let me know, and I'll send it to you. I have also included the

bibliography for that paper which lists a number of sources you

may find useful in answering some of your other questions. =20

Summary

This study suggests a new approach to improving the

within-session reliability with which joint centers are estimated

from surface markers. Segment length standard deviations are

used to evaluate reliability, since they can be assessed under

ecologically valid conditions that allow for soft-tissue and

out-of-plane motion. Significant improvements in reliability were

achieved with either of two relatively simple methods for making

post-hoc adjustments, even when adjustments were applied to a

new data set. For the 3D optimization method introduced here,

reliability improved for both segments flanking the adjusted joint

center. In contrast, reliability only improved for one segment after

applying Spiegelman & Woo#s 2D method. Results suggest how

calibration trials conducted at the beginning of an experimental

session can be used along with post-hoc adjustment to improve

reliability, even when data collected during the experimental

procedures are unsuitable for deriving adjustment parameters.=20

Future research should verify the efficacy of this overall approach in

other experimental settings, and develop procedures to improve

between-session reliability.

Relevance

This study provides a practical means to assess

the reliability with which joint centers have been located in

experimental or clinical settings where the real-world problems of

out-of-plane and soft-tissue motion can not be avoided. The

approach suggested here demands less mathematical expertise

than do the six degree of freedom rigid body methods, and hence

may be useful for labs with limited technical support. =20

REFERENCE LIST:

Lower extremity angle measurement with accelerometers--error and

sensitivity analysis. Willemsen-AT; Frigo-C; Boom-HB IEEE-Trans-Biomed-Eng.

1991 Dec; 38(12): 1186-93=20

Advances in motion analysis. Clayton-HM

Vet-Clin-North-Am-Equine-Pract. 1991 Aug; 7(2): 365-82=20

New mathematical definition and calculation of axial rotation of

anatomical joints. Miyazaki-S; Ishida-A J-Biomech-Eng. 1991 Aug; 113(3):=

270-5=20

Calculation of the instantaneous centre of rotation for a rigid

body. Holzreiter-S J-Biomech. 1991; 24(7): 643-7=20

Measurement of joint kinematics using ExpertVision system. An-KN;

Growney-E; Chao-EY Biomed-Sci-Instrum. 1991; 27: 245-52=20

Three-dimensional kinematics of glenohumeral elevation. An-KN;

Browne-AO; Korinek-S; Tanaka-S; Morrey-BF J-Orthop-Res. 1991 Jan; 9(1):=

143-9=20

Measurement of finger joint angles and maximum finger forces during

cylinder grip activity. Lee-JW; Rim-K J-Biomed-Eng. 1991 Mar; 13(2): 152-62=

=20

Rigid body motion calculated from spatial co-ordinates of markers.

Spoor-CW; Veldpaus-FE J-Biomech. 1980; 13(4): 391-3=20

A least-squares algorithm for the equiform transformation from

spatial marker co-ordinates. Veldpaus-FE; Woltring-HJ; Dortmans-LJ

J-Biomech. 1988; 21(1): 45-54=20

Finite centroid and helical axis estimation from noisy landmark

measurements in the study of human joint kinematics. Woltring-HJ; Huiskes-R;

de-Lange-A; Veldpaus-FE J-Biomech. 1985; 18(5): 379-89=20

Determining the movements of the skeleton using well-configured

markers.=20

Soderkvist-I; Wedin-PA J-Biomech. 1993 Dec; 26(12): 1473-7=20

Finite centroid and helical axis estimation from noisy landmark

measurements in the study of human joint kinematics. Woltring-HJ; Huiskes-R;

de-Lange-A; Veldpaus-FE J-Biomech. 1985; 18(5): 379-89=20

Effects of data smoothing on the reconstruction of helical axis

parameters in human joint kinematics. de-Lange-A; Huiskes-R; Kauer-JM

J-Biomech-Eng. 1990 May; 112(2): 107-13=20

Measurement of the total motion between two body segments. I.

Analytical development. Kinzel-GL; Hall-AS Jr; Hillberry-BM J-Biomech. 1972

Jan; 5(1): 93-105=20

Reliable in vivo estimation of the instantaneous helical axis in

human segmental movements. Fioretti-S; Jetto-L; Leo-T IEEE-Trans-Biomed-Eng.

1990 Apr; 37(4): 398-409=20

Calculation of the instantaneous centre of rotation for a rigid

body. Holzreiter-S J-Biomech. 1991; 24(7): 643-7=20

A procedure for determining rigid body transformation parameters.

Challis-JH J-Biomech. 1995 Jun; 28(6): 733-7

An examination of procedures for determining body segment attitude

and position from noisy biomechanical data. Challis-JH Med-Eng-Phys. 1995

Mar; 17(2): 83-90=20

Errors in kinematic parameters of a planar joint: guidelines for

optimal experimental design. Panjabi-MM; Goel-VK; Walter-SD J-Biomech. 1982;

15(7): 537-44=20

Errors in the center and angle of rotation of a joint: an

experimental study. Panjabi-MM; Goel-VK; Walter-SD; Schick-S J-Biomech-Eng.

1982 Aug; 104(3): 232-7=20

Centers and angles of rotation of body joints: a study of errors=20

and optimization. Panjabi-MM J-Biomech. 1979; 12(12): 911-20=20

A rigid-body method for finding centers of rotation and angular

displacements of planar joint motion. Spiegelman-JJ; Woo-SL J-Biomech. 1987;

20(7): 715-21=20

Optimal marker placement for calculating the instantaneous center of

rotation. Crisco-JJ-3rd; Chen-X; Panjabi-MM; Wolfe-SW J-Biomech. 1994 Sep;

27(9): 1183-7=20

A procedure to validate three-dimensional motion assessment systems.

DeLuzio-KJ; Wyss-UP; Li-J; Costigan-PA J-Biomech. 1993 Jun; 26(6): 753-9=20

A comparison of the accuracy of several hip center location

prediction methods. Bell-AL; Pedersen-DR; Brand-RA J-Biomech. 1990; 23(6):

617-21=20

A finite helical axis as a landmark for kinematic reference of the

knee.=20

Hart-RA; Mote-CD Jr; Skinner-HB J-Biomech-Eng. 1991 May; 113(2): 215-22=20

On the estimation of joint kinematics during gait. Ramakrishnan-HK;

Kadaba-MP J-Biomech. 1991; 24(10): 969-77=20

Reproducibility and accuracy of angle measurements obtained under

static conditions with the Motion Analysis video system. Vander-Linden-DW;

Carlson-SJ; Hubbard-RL Phys-Ther. 1992 Apr; 72(4): 300-5 =20

Basic Biomechanics of the Musculoskeletal System. Frankel VH,

Forssen K, Nachamie H, Yelle L, Nordin M. Lea and Febiner, Philadelphia, PA,

1989.

Comparison of three methods for locating joint centers during planar arm

motion. States RA. Soc Neurosc Ab 1995; 21: #174.15.=20

Resolving indeterminacy associated with joint-level motor equivalence in

planar aimed arm movements. States RA. [PhD Dissertation] Columbia

University, New York, NY, 1995

Assessing and reporting the accuracy of position measurements made with

optical tracking systems. Haggard P, Wing AM. J Motor Beh 1990; 22: 315-321.=

=20

Experimental errors in the observation of body joint kinematics. Walter SD,

Panjabi MM. Technomet 1988; 30: 71-78.=20

The Kinematics of Machinery: Outline of a Theory of Machines (translated by

Kennedy, A.M.W.). Releaux F. Dover, New York, 1875; 56-70.=20

A method for the calculation of orthogonal rotation matrices and its

application in photogrammetry and other disciplines. Tienstra, M.

(1969)Ph.D.-thesis, Technical University of Delft, The Netherlands.

Waltman, Delft.

On definition and calculus of rigid-body kinematics using spatial

marker coordinates. Submitted for publication to the Journal of

Biomechanics. Woltring, H.J. (1981) [Ultimately published as Veldpaus et

al., Journal of Biomechanics, January 1988.]

One Hundred Years Photogrammetry in Bio In: V. Tosi & A. Cappozzo

(Eds) H.J. Woltring (1989), Proc. of the Symposium on Biolocomotion: a

Century of Research Using Moving Pictures (Formia, Italy, April 1989; in=

print).

A Fortran package for generalized, cross validatory spline smoothing

and differentiation. H.J. Woltring (1986) Advances in Engineering software

8(1986)2, pp. 104-113.

Prediction of Hip Joint Center location from External Landmarks, Bell A.,

Brand R., and Pedersen D. Human Movment Sciences 8(1989) 3-16.

Measurement error influence on helical axis accuracy in the description of

3-D, finite joint movement in biomechanics. Woltring, H.J., Huiskes, R., de

Lange, A. (1983) In: Biomechanics Symposium (Edited by Woo, S.L.-Y. and

Mates, R.E.), AMD 56 (FED 1), 19-22. ASME, New York.

Explanation, verification and application of helical-axis error propagation

formulas. Human Movement Science 3, 95-117. Spoor, C.W. (1984)

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/Johan L=F6nn