View Full Version : Re: symbolic expression for angular velocitie

03-25-2004, 05:12 AM
Dear all,

The following is what I got from a former student of mine, Jaekun Shim.


Hi Dr. Kwon,

Just a small comment;

As you may know, one of the most important questions which researchers
in motor control and neuroscience have been trying to answer is what
variable the CNS controls to produce a voluntary movement and how it is

There are two dominant competing hypotheses about this issue:
equilibrium hypothesis (equilibrium control, Mark Latash) and internal
model hypothesis (force/moment control, Kawato) although the second one
is not likely.

To study how the CNS controls movements, it is also important to
identify in what space the CNS controls the control variables because
the brain and muscular activities can covary/correlate with the control
variables differently in one space and another. The notions of intrinsic
space (e.g. joint space) and extrinsic space (externally fixed
coordinate system; e.g. Cartesian coordinates) have been discussed in
this sense and there have been many studies about this matter. A general
agreement among researchers is that the CNS controls the control
variables mostly in intrinsic coordinate systems rather than extrinsic.

If we are just interested in computations of mechanical variables during
movements, we do not even need to use JCS or should not use it. And,
mechanically speaking, changing coordinate systems means simply changing
notations. However, it may not be that simple in terms of human body
which produces voluntary movements associated with the CNS. I think that
JCS needs be treated with more careful attention.


Shim, Jae Kun

The Pennsylvania State University

Biomechanics Laboratory, 39 Recreation Building/

Motor Control Laboratory, 20 Recreation Building

Department of Kinesiology, College of Health and Human Development

University Park, PA 16802

Email shimjaekun@psu.edu

Phone 814) 865-3445 (Biomechanics), 863-4424 (Motor Control)

Fax 814) 865-2440

Web Home www.personal.psu.edu/jus149


This was in response to my earlier posting:

|Tomislav brought up an interesting issue: JCS. To me, a coordinate

|system just means how to describe a vector into components:

|polar, cylindrical, hyperbolic, etc. What's more important in

|motions of the body parts is the reference frame or the perspective

|description. The only entities that can carry perspectives to me are

|segments, not the joints. As the orientation of a segment changes,

|reference frame fixed to it also moves with the segment. However, the

|relative relationship between the segment and the local frame does

|change. On the other hand, joint motion is simply the relative motion

|the distal segment to its linked proximal segment. The relative

|orientation of the Cardanic axes (JCS) changes as the joint motion

|progresses. The JCS may be used to decompose the angular velocity

|into meaningful sub vectors, but JCS shouldn't be treated as a

|frame (or perspective). The confusion shown in Eq. 1 originates from

|concept of JCS. In Eq. 2, the vectors can be described in any

|frame (global or segmental). However, the perspective used in the

|computation does not affect the three power terms to be obtained from

|Eq. 2.

I think Jae's point is valid. However, what I tried to say was that the
non-orthogonal JCS is not a reasonable perspective to use. Investigators
generally use the term joint coordinate system for the systems actually
fixed to the segments. For example in the lower extremity studies, the
knee joint system is often defined at the knee, fixed to the thigh. The
origin is at the mid point of the two epicondyles. One axis is aligned
with the thigh segment line (knee to hip). The second axis is defined as
perpendicular to the plane formed by the thigh line and the
inter-epicondyle line. The third axis is perpendicular to the previously
defined axes. My point is: although it is called as the knee joint
coordinate system, it is actually fixed to the thigh and it is what I
call "thigh reference frame" with the origin being at the knee joint. It
is just a matter of terminology.

The local reference frames fixed to the segments (regardless of the
location of the origin) can be Jae's intrinsic coordinate systems. But
the non-orthogonal JCS which has been the centerfold of our discussion
cannot be a physical perspective, in my opinion.


- Young-Hoo Kwon, Ph.D.
- Biomechanics Lab, Texas Woman's University
- kwon3d@kwon3d.com
- http://kwon3d.com

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