__________________________________________________ __

ISB Standardization and Terminology Committee

RECOMMENDATIONS FOR STANDARDIZATION IN THE

REPORTING OF KINEMATIC DATA

DRAFT Version 4.1

April 3, 1992

__________________________________________________ __

The Standardization and Terminology Committee of the

International Society of Biomechanics has been charged

by the Society with the development of standards for use

in the field of kinematic and kinetic analyses of human

and animal movement.

Many other efforts of this nature are in progress and

the committee has received input in its deliberations

from a number of groups and individuals. At the First

International Symposium on Three Dimensional Motion

Analysis in Montreal Canada in July 1991, a round table

was held to discuss the topic of standardization. An

apparent consensus of panel members and meeting

participants was that each investigator should be free

to collect and process their data according to the

conventions and methods of their choice, but that a

standard set of conventions for the presentation of data

in the refereed literature would be welcomed by most

workers. A major effort towards standardization of

protocols for gait analysis is also underway by a

European Community group (CAMARC). Clearly

standardization is a topic for the 1990's and the ISB

intends to take a leadership position in this area.

The committee has decided to make its first task the

definition of a series of reference frames and

conventions for the description of the absolute and

relative orientations of body segments. In the future,

we intend to address the issue of terminology extending

the work of Winter (1987) and Vaughan, Davis and

O'Connor (1992).

This first step, described below, leans heavily on the

work of biomechanists such as Chao, Grood, Suntay,

Sommer and Buczek and employs the 4 x 4 matrix notation

for the description of segment position and orientation.

An ad hoc committee of ISB members has already provided

input on early drafts of this document and suggestions

have been incorporated from a number of other

individuals. We would stress that this is still a

consultative document and represents a first foundation

on which an eventual standard can be built.

Each section is organized in the form of the need for

the standard, a recommendation, a suggested notation,

and notes concerning implementation.

__________________________________________________ __

PART 1. DEFINITION OF A GLOBAL REFERENCE FRAME

Need: A global inertial reference frame with the

direction of the global axes being consistent, no matter

which activities or subjects are being studied, or which

investigator is conducting the experiment.

Notation: Xg, Yg, Zg

Recommendation: A right handed orthogonal triad

fixed in the ground (assuming performer is on level

ground) with the +Xg axis forward and horizontal, +Yg

axis upward, the +Zg axis to the right and horizontal

(see figure 1). All directions are given for the

subject facing in the direction of work or travel

that is of most interest to the particular activity. If

forces are being measured, it is recommended that the

origin of the XgYgZg reference frame be located at the

center of the top surface of one of the force platforms

being used. A ground reaction force convention (i.e. forces

applied to the body not forces applied to the platform)

should be used such that ground reaction force components

acting along the respective axes should be designated with

the same conventions i.e. positive Fx is acting in the

forward horizontal direction, positive Fy in the upward

vertical, and positive Fz in the right lateral

direction.

Notes: a. The directions have been chosen so that

for those conducting two dimensional studies, Xg,Yg will

lie in a sagittal plane. This will be consistent with the

three dimensional convention.

b. In tasks such as exercise in zero gravity, the

Xg axis should be defined according to some arbitrary

but visible surface in the environment and in a

direction that is meaningful to the task.

c. Where there is no clear direction of travel or

work for the definition of positive Xg (as is the

case for insect flight) one should be defined by the

investigator.

In cases of locomotion on inclined planes, the Yg

axis will remain vertical and the Xg and Zg axes will be

in the same horizontal plane.

d. We acknowledge that there may be situations

where non-Cartesian axes are more appropriate to the

task being studied (for example cylindrical coordinates

are useful for the study of asymmetric manual exertion).

Since the majority of studies use a Cartesian approach,

it will be left to individual investigators to devise

systems for the reporting of more unique situations.

__________________________________________________ __

PART 2: DEFINITION OF SEGMENTAL LOCAL CENTER OF MASS

REFERENCE FRAMES

Need: A coherent system to describe segment pose

(position and attitude) with respect to global.

Recommendation: A series of right handed orthogonal

triads fixed at the segmental centers of mass with two of the

axes defined relative to anatomically identifiable reference

points. The third is automatically defined as being mutually

perpendicular to the other two (as defined by a right hand

rule.) The positive Yi should be in a proximal direction, and

the positive Zi should be to the right of the subject (see figure 1).

Notation: Xi, Yi, Zi

Notes: Sub groups of specialists in each region of

the body will be recruited by the ISB Standardization

Committee to formulate the appropriate anatomical

landmarks to be used in the orientation of the axes for

each segment of the body.

The convention that the positive Zi direction is to

the right implies that positive movements and moments

about the Xi and Yi axes of a segment on the left side

of the body will have the opposite effects of movements

and moments of similar sign on the right side of the

body (figure 2). This difference will be accounted for

by describing the movements and moments in their

anatomical terms in any presentation of the data (see

below). This convention has been chosen to avoid the

use of both left and right handed coordinate systems.

__________________________________________________ __

Part 3: Global displacements

Need: Specification of displacements relative to the

Global Reference Frame

Recommendation: Report the coordinates of local

center of mass reference frame origins with respect to

the global origin in meters. The position of the local

origin will represent the first column of the 4 x 4

matrix in the local to global transformation matrix

(see below).

Notation: xi,yi,zi

__________________________________________________ __

Part 4: Global Attitudes.

Need: To express the orientation of a segment with

respect to the global reference frame.

Recommendation: A standard ZYX decomposition of the

lower right 3x3 rotation submatrix of the 4 x 4 matrix

defining the local to global transformation.

{X}g = [Tlg] {x}l

where {X}g = [1 Xi Yi Zi] T

{x}l = [1 xl yl zl] T

where [Tlg] is the local to global coordinate

transformation describing the pose of the local

coordinate frame with respect to the global frame.

and [Tlg] = 1 0 0 0

Xi c11i c12i c13i

Yi c21i c22i c23i

Zi c31i c32i c33i

Xi,Yi,Zi is the location of the origin of the ith

local center of mass reference frame with respect to the

global frame, xl,yl,zl are the coordinates of a point

with respect to the local origin and cij are the

direction cosines expressing the orientation of the

local axes with respect to global. c11i, c21i, c31i are

the direction cosines of the local xi axes with respect

to Xg,Yg, and Zg respectively.

Notation: If A, B, G are ordered series of rotations

about z, y and x axes respectively then:

1 0 0 0

X cAcB cAsBsG-sAcG cAsBcG+sAsG

Y sAcB sAsBsG+cAcG sAsBcG-cAsG

Z -sB cBsG cBcG

Where sA = sine A and cA = cosine A etc.

The individual Euler angles can be found as follows:

Bi = arcsin (-c31i)

Ai = arcsin(c21i/cosBi)

Ai = arccos(c11i/cosBi)

Gi = arcsin(c32i/cosBi)

Gi = arccos(c33i/cosBi)

__________________________________________________ __

Part 5: Relative attitudes.

Need: A system to express the relative orientation

of the body segments with respect to each other.

Recommendation: Joint coordinate systems (which

might better be called Joint Rotation Conventions)

defined for each joint individually. This system allows

sequence independent rotations about axes which can be

anatomically meaningful at the sacrifice of establishing

a reference frame with non-orthogonal axes. As long as

force and moments are not resolved along these non-

orthogonal axes, this does not present a problem. This

approach allows the preservation of an important linkage

with clinical medicine where the use of independent

paired rotations (ad/ab, internal/external etc.) is

common usage.

We further propose that no particular system of

symbolic nomenclature be adopted for the description of

joint motion but that accepted anatomical nomenclature

be used in presentations.

The most well known example of such systems are

those developed for the knee by Grood and Suntay (1983)

and Chao (1986) (figure 3). Two body fixed axes are

established relative to anatomical landmarks, one in

each body on opposing sides of the joint. The third

axes, called the floating axis, is defined as being

perpendicular to each of the two body fixed axes.

Notation:

A=rotation about the proximal body fixed axis

G=rotation about the distal body fixed axis

B=rotation about floating axis

Notes:

We propose that sub-groups of specialists in each

region of the body will be recruited by the ISB

Standardization Committee to formulate the appropriate

joint rotation conventions for each joint of the body.

These groups might also address the issue of accuracy

(which no doubt varies between joints) and the question

of the relationship between the (usually) surface

markers and the actual anatomical arrangement.

In order to determine these angles from

conventional segment pose data, the following points

are important:

a. The orientation of the proximal and distal axes

must be carefully specified.

b. The choice of the location of the origins

drastically affects the distraction displacement terms.

c. The Euler angle set in part 4 (Global attitudes)

should match the angle decomposition for joints as

closely as possible.

Woltring (1990, 1991) and others have supported the use

of helical axes for the description of joint motion since it

avoids some problems - such as gimbal lock - inherent in Euler

angle representations. More recently, Woltring suggests the

use of :"an attitude vector standard". At present, we are not

proposing a standard for this approach as debate continues on

its clinical application. Should there be widespread support

for such a representation we would certainly consider a recom-

mendation for standardization of helical axis representation.

__________________________________________________ __

Part 6 Joint Moments

Need: A system to report net joint moments that will

avoid confusion concerning the anatomical actions being

represented. Such a system needs to be consistent

across joints and across sides of the body.

Recommendation: Net joint moments should be reported

according to the conventions described by Winter (1987)

such that net moments tending to cause extension,

internal rotation, and abduction are positive.

Notation: Mfe, Mie, Mbd for moments tending to cause

flexion/extension, internal/external rotation, and

abduction/adduction respectively.

Notes: Any definition of joint moments assumes a

definition of joint axis system. See Part 5 relative

Attitudes above for the recommended approach.

__________________________________________________ __

Part 7 Minority report

Professor John Paul, a member of the ISB Standardization

and Terminology Committee made two recommendations that

have not been incorporated into the present version due

to divided opinion from those who have reviewed these

initial standards. They are reproduced here so that

members will have a chance to comment on these views.

With reference to Part 1:

"Many equipment manufacturers already format data

according to their own XYZ system. I feel that we

should avoid the awkward transposition exemplified by

Yisb = Z kister etc. I suggest that ISB could avoid

these problems by using hitherto not generally used

symbols which do not suggest an anatomical part (e.g.

avoid A H K). What about RST?"

With reference to Part 2:

"All humans and animals have left and right sides. Why

standardize on a right handed system of axes? The only

difference between the two is a minor matter of signs

before some terms in mathematics which can easily be

incorporated into the software! International Standards

Organization Technical Committee 168 Working Group 3 -

Prosthetics and Orthotics Testing specifies the

"Forward, Outward, Upwards" system which is right handed

or left handed as appropriate. It has the advantage

exemplified by having the same sign for the moment

produced at the left hip by the left gluteus medius as

the moment produced by the right hip by right gluteus

medius."

__________________________________________________ __

REFERENCES

Beggs, J. S. (1966) Advanced Mechanism, New York,

Macmillan

Buczek, F. L. (1990) Three-Dimensional Kinematics and

Kinetics of the Ankle and Knee Joints During Uphill,

Level, and Downhill Walking, Ph.D.. thesis, The

Pennsylvania State University.

Chao E.Y.S. Biomechanics of Human Gait. In Frontiers in

Biomechanics, Schmid-Schonbein G.W., Woo S.L-Y., and

Zweifach, B.W. (Eds). New York, Springer Verlag.

Grood, E. S. and W. J. Suntay (1983) A Joint Co-ordinate

System for the Clinical Description of Three-Dimensional

Motions: Application to the Knee, J. Biomechanical

Engr. 105:136-144

Kinzel, G. L., A. S. Hall, and B. M. Hillberry (1972)

Measurement of the Total Motion between Two Body

Segments-1.Analytical Development, J. Biomechanics,

5:93-105.

Sommer, H. J., and F. L. Buczek (1990) Least Squares

Estimation of the Instant Screw Axis and Angular

Acceleration Axis 1990 Advances in Bioengineering, ASME.

Vaughan C. L., Davis, B.L. and O'Connor J. (1992) The

Gait Lab. Champaign, IL Human Kinetics Publishers

Winter D.A. (1987) The Biomechanics and Motor Control of

Gait. Waterloo, ONT. University of Waterloo Press.

Woltring, H.J. (1990) 3-D attitude representation: a new

standardization proposal. In Hogfors, C. (Ed).

Proceedings of the Fourth Biomechanics Seminar. Centre

for Biomechanics, Chalmers University of Technology and

Gothenburg University, Sweden. Biomechanics Seminar 4. p

58-61. (ISBN 1100-2247).

Woltring, H.J. (1991) Representation and calculation of

3D joint movement. Human Movement Science, 10: 603-616.

__________________________________________________ __

Figure 1. Conventions for global reference frame

Figure 2. The same rotations about segmental local center of mass

reference frames produce anatomically different motions on the left and

right sides of the body.

Figure 3. A joint coordinate system for the knee joint.

__________________________________________________ __

A Project of the ISB Standardization and Terminology

Committee

Prof D.W. Grieve

Prof J.P. Paul

Prof D.A.Winter

Prof P.R. Cavanagh, Chair

Input on these draft recommendations should to sent to:

Peter.R. Cavanagh,

The Center for Locomotion Studies

Penn State University

University Park

PA 16802

USA

Tel: +814-865-1972

FAX: +814-863-4755

EMail PRC@ECL.PSU.EDU (Internet)

Note: Formatted copies of this document with embedded figures

are available on the BIOMCH-L list on the listserver @ HEARN.

Microsoft WORD 4.0/5.0 files for the Macintosh

and WordPerfect 5.1 for MS-DOS compatible platforms are

available. The BIOMCH-L moderators will post details of

the relevant file names in the near future.

PRC

ISB Standardization and Terminology Committee

RECOMMENDATIONS FOR STANDARDIZATION IN THE

REPORTING OF KINEMATIC DATA

DRAFT Version 4.1

April 3, 1992

__________________________________________________ __

The Standardization and Terminology Committee of the

International Society of Biomechanics has been charged

by the Society with the development of standards for use

in the field of kinematic and kinetic analyses of human

and animal movement.

Many other efforts of this nature are in progress and

the committee has received input in its deliberations

from a number of groups and individuals. At the First

International Symposium on Three Dimensional Motion

Analysis in Montreal Canada in July 1991, a round table

was held to discuss the topic of standardization. An

apparent consensus of panel members and meeting

participants was that each investigator should be free

to collect and process their data according to the

conventions and methods of their choice, but that a

standard set of conventions for the presentation of data

in the refereed literature would be welcomed by most

workers. A major effort towards standardization of

protocols for gait analysis is also underway by a

European Community group (CAMARC). Clearly

standardization is a topic for the 1990's and the ISB

intends to take a leadership position in this area.

The committee has decided to make its first task the

definition of a series of reference frames and

conventions for the description of the absolute and

relative orientations of body segments. In the future,

we intend to address the issue of terminology extending

the work of Winter (1987) and Vaughan, Davis and

O'Connor (1992).

This first step, described below, leans heavily on the

work of biomechanists such as Chao, Grood, Suntay,

Sommer and Buczek and employs the 4 x 4 matrix notation

for the description of segment position and orientation.

An ad hoc committee of ISB members has already provided

input on early drafts of this document and suggestions

have been incorporated from a number of other

individuals. We would stress that this is still a

consultative document and represents a first foundation

on which an eventual standard can be built.

Each section is organized in the form of the need for

the standard, a recommendation, a suggested notation,

and notes concerning implementation.

__________________________________________________ __

PART 1. DEFINITION OF A GLOBAL REFERENCE FRAME

Need: A global inertial reference frame with the

direction of the global axes being consistent, no matter

which activities or subjects are being studied, or which

investigator is conducting the experiment.

Notation: Xg, Yg, Zg

Recommendation: A right handed orthogonal triad

fixed in the ground (assuming performer is on level

ground) with the +Xg axis forward and horizontal, +Yg

axis upward, the +Zg axis to the right and horizontal

(see figure 1). All directions are given for the

subject facing in the direction of work or travel

that is of most interest to the particular activity. If

forces are being measured, it is recommended that the

origin of the XgYgZg reference frame be located at the

center of the top surface of one of the force platforms

being used. A ground reaction force convention (i.e. forces

applied to the body not forces applied to the platform)

should be used such that ground reaction force components

acting along the respective axes should be designated with

the same conventions i.e. positive Fx is acting in the

forward horizontal direction, positive Fy in the upward

vertical, and positive Fz in the right lateral

direction.

Notes: a. The directions have been chosen so that

for those conducting two dimensional studies, Xg,Yg will

lie in a sagittal plane. This will be consistent with the

three dimensional convention.

b. In tasks such as exercise in zero gravity, the

Xg axis should be defined according to some arbitrary

but visible surface in the environment and in a

direction that is meaningful to the task.

c. Where there is no clear direction of travel or

work for the definition of positive Xg (as is the

case for insect flight) one should be defined by the

investigator.

In cases of locomotion on inclined planes, the Yg

axis will remain vertical and the Xg and Zg axes will be

in the same horizontal plane.

d. We acknowledge that there may be situations

where non-Cartesian axes are more appropriate to the

task being studied (for example cylindrical coordinates

are useful for the study of asymmetric manual exertion).

Since the majority of studies use a Cartesian approach,

it will be left to individual investigators to devise

systems for the reporting of more unique situations.

__________________________________________________ __

PART 2: DEFINITION OF SEGMENTAL LOCAL CENTER OF MASS

REFERENCE FRAMES

Need: A coherent system to describe segment pose

(position and attitude) with respect to global.

Recommendation: A series of right handed orthogonal

triads fixed at the segmental centers of mass with two of the

axes defined relative to anatomically identifiable reference

points. The third is automatically defined as being mutually

perpendicular to the other two (as defined by a right hand

rule.) The positive Yi should be in a proximal direction, and

the positive Zi should be to the right of the subject (see figure 1).

Notation: Xi, Yi, Zi

Notes: Sub groups of specialists in each region of

the body will be recruited by the ISB Standardization

Committee to formulate the appropriate anatomical

landmarks to be used in the orientation of the axes for

each segment of the body.

The convention that the positive Zi direction is to

the right implies that positive movements and moments

about the Xi and Yi axes of a segment on the left side

of the body will have the opposite effects of movements

and moments of similar sign on the right side of the

body (figure 2). This difference will be accounted for

by describing the movements and moments in their

anatomical terms in any presentation of the data (see

below). This convention has been chosen to avoid the

use of both left and right handed coordinate systems.

__________________________________________________ __

Part 3: Global displacements

Need: Specification of displacements relative to the

Global Reference Frame

Recommendation: Report the coordinates of local

center of mass reference frame origins with respect to

the global origin in meters. The position of the local

origin will represent the first column of the 4 x 4

matrix in the local to global transformation matrix

(see below).

Notation: xi,yi,zi

__________________________________________________ __

Part 4: Global Attitudes.

Need: To express the orientation of a segment with

respect to the global reference frame.

Recommendation: A standard ZYX decomposition of the

lower right 3x3 rotation submatrix of the 4 x 4 matrix

defining the local to global transformation.

{X}g = [Tlg] {x}l

where {X}g = [1 Xi Yi Zi] T

{x}l = [1 xl yl zl] T

where [Tlg] is the local to global coordinate

transformation describing the pose of the local

coordinate frame with respect to the global frame.

and [Tlg] = 1 0 0 0

Xi c11i c12i c13i

Yi c21i c22i c23i

Zi c31i c32i c33i

Xi,Yi,Zi is the location of the origin of the ith

local center of mass reference frame with respect to the

global frame, xl,yl,zl are the coordinates of a point

with respect to the local origin and cij are the

direction cosines expressing the orientation of the

local axes with respect to global. c11i, c21i, c31i are

the direction cosines of the local xi axes with respect

to Xg,Yg, and Zg respectively.

Notation: If A, B, G are ordered series of rotations

about z, y and x axes respectively then:

1 0 0 0

X cAcB cAsBsG-sAcG cAsBcG+sAsG

Y sAcB sAsBsG+cAcG sAsBcG-cAsG

Z -sB cBsG cBcG

Where sA = sine A and cA = cosine A etc.

The individual Euler angles can be found as follows:

Bi = arcsin (-c31i)

Ai = arcsin(c21i/cosBi)

Ai = arccos(c11i/cosBi)

Gi = arcsin(c32i/cosBi)

Gi = arccos(c33i/cosBi)

__________________________________________________ __

Part 5: Relative attitudes.

Need: A system to express the relative orientation

of the body segments with respect to each other.

Recommendation: Joint coordinate systems (which

might better be called Joint Rotation Conventions)

defined for each joint individually. This system allows

sequence independent rotations about axes which can be

anatomically meaningful at the sacrifice of establishing

a reference frame with non-orthogonal axes. As long as

force and moments are not resolved along these non-

orthogonal axes, this does not present a problem. This

approach allows the preservation of an important linkage

with clinical medicine where the use of independent

paired rotations (ad/ab, internal/external etc.) is

common usage.

We further propose that no particular system of

symbolic nomenclature be adopted for the description of

joint motion but that accepted anatomical nomenclature

be used in presentations.

The most well known example of such systems are

those developed for the knee by Grood and Suntay (1983)

and Chao (1986) (figure 3). Two body fixed axes are

established relative to anatomical landmarks, one in

each body on opposing sides of the joint. The third

axes, called the floating axis, is defined as being

perpendicular to each of the two body fixed axes.

Notation:

A=rotation about the proximal body fixed axis

G=rotation about the distal body fixed axis

B=rotation about floating axis

Notes:

We propose that sub-groups of specialists in each

region of the body will be recruited by the ISB

Standardization Committee to formulate the appropriate

joint rotation conventions for each joint of the body.

These groups might also address the issue of accuracy

(which no doubt varies between joints) and the question

of the relationship between the (usually) surface

markers and the actual anatomical arrangement.

In order to determine these angles from

conventional segment pose data, the following points

are important:

a. The orientation of the proximal and distal axes

must be carefully specified.

b. The choice of the location of the origins

drastically affects the distraction displacement terms.

c. The Euler angle set in part 4 (Global attitudes)

should match the angle decomposition for joints as

closely as possible.

Woltring (1990, 1991) and others have supported the use

of helical axes for the description of joint motion since it

avoids some problems - such as gimbal lock - inherent in Euler

angle representations. More recently, Woltring suggests the

use of :"an attitude vector standard". At present, we are not

proposing a standard for this approach as debate continues on

its clinical application. Should there be widespread support

for such a representation we would certainly consider a recom-

mendation for standardization of helical axis representation.

__________________________________________________ __

Part 6 Joint Moments

Need: A system to report net joint moments that will

avoid confusion concerning the anatomical actions being

represented. Such a system needs to be consistent

across joints and across sides of the body.

Recommendation: Net joint moments should be reported

according to the conventions described by Winter (1987)

such that net moments tending to cause extension,

internal rotation, and abduction are positive.

Notation: Mfe, Mie, Mbd for moments tending to cause

flexion/extension, internal/external rotation, and

abduction/adduction respectively.

Notes: Any definition of joint moments assumes a

definition of joint axis system. See Part 5 relative

Attitudes above for the recommended approach.

__________________________________________________ __

Part 7 Minority report

Professor John Paul, a member of the ISB Standardization

and Terminology Committee made two recommendations that

have not been incorporated into the present version due

to divided opinion from those who have reviewed these

initial standards. They are reproduced here so that

members will have a chance to comment on these views.

With reference to Part 1:

"Many equipment manufacturers already format data

according to their own XYZ system. I feel that we

should avoid the awkward transposition exemplified by

Yisb = Z kister etc. I suggest that ISB could avoid

these problems by using hitherto not generally used

symbols which do not suggest an anatomical part (e.g.

avoid A H K). What about RST?"

With reference to Part 2:

"All humans and animals have left and right sides. Why

standardize on a right handed system of axes? The only

difference between the two is a minor matter of signs

before some terms in mathematics which can easily be

incorporated into the software! International Standards

Organization Technical Committee 168 Working Group 3 -

Prosthetics and Orthotics Testing specifies the

"Forward, Outward, Upwards" system which is right handed

or left handed as appropriate. It has the advantage

exemplified by having the same sign for the moment

produced at the left hip by the left gluteus medius as

the moment produced by the right hip by right gluteus

medius."

__________________________________________________ __

REFERENCES

Beggs, J. S. (1966) Advanced Mechanism, New York,

Macmillan

Buczek, F. L. (1990) Three-Dimensional Kinematics and

Kinetics of the Ankle and Knee Joints During Uphill,

Level, and Downhill Walking, Ph.D.. thesis, The

Pennsylvania State University.

Chao E.Y.S. Biomechanics of Human Gait. In Frontiers in

Biomechanics, Schmid-Schonbein G.W., Woo S.L-Y., and

Zweifach, B.W. (Eds). New York, Springer Verlag.

Grood, E. S. and W. J. Suntay (1983) A Joint Co-ordinate

System for the Clinical Description of Three-Dimensional

Motions: Application to the Knee, J. Biomechanical

Engr. 105:136-144

Kinzel, G. L., A. S. Hall, and B. M. Hillberry (1972)

Measurement of the Total Motion between Two Body

Segments-1.Analytical Development, J. Biomechanics,

5:93-105.

Sommer, H. J., and F. L. Buczek (1990) Least Squares

Estimation of the Instant Screw Axis and Angular

Acceleration Axis 1990 Advances in Bioengineering, ASME.

Vaughan C. L., Davis, B.L. and O'Connor J. (1992) The

Gait Lab. Champaign, IL Human Kinetics Publishers

Winter D.A. (1987) The Biomechanics and Motor Control of

Gait. Waterloo, ONT. University of Waterloo Press.

Woltring, H.J. (1990) 3-D attitude representation: a new

standardization proposal. In Hogfors, C. (Ed).

Proceedings of the Fourth Biomechanics Seminar. Centre

for Biomechanics, Chalmers University of Technology and

Gothenburg University, Sweden. Biomechanics Seminar 4. p

58-61. (ISBN 1100-2247).

Woltring, H.J. (1991) Representation and calculation of

3D joint movement. Human Movement Science, 10: 603-616.

__________________________________________________ __

Figure 1. Conventions for global reference frame

Figure 2. The same rotations about segmental local center of mass

reference frames produce anatomically different motions on the left and

right sides of the body.

Figure 3. A joint coordinate system for the knee joint.

__________________________________________________ __

A Project of the ISB Standardization and Terminology

Committee

Prof D.W. Grieve

Prof J.P. Paul

Prof D.A.Winter

Prof P.R. Cavanagh, Chair

Input on these draft recommendations should to sent to:

Peter.R. Cavanagh,

The Center for Locomotion Studies

Penn State University

University Park

PA 16802

USA

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