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ISB Standardization and Terminology Committee

RECOMMENDATIONS FOR STANDARDIZATION IN THE
REPORTING OF KINEMATIC DATA

DRAFT Version 4.1
April 3, 1992

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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.

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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.

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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.

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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

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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)

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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.

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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.

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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."
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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.

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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.

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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)

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