joint attitude debate......

I was asked by a number of you to point
out better my opinion on the joint attitude and angles debate. I

I will send a personal answer to everybody but I'd also like to
summarize my ideas here.

I begin with SPACELIB. This is a software library I realized with
the help of a few colleagues in order to study spatial systems of
rigid bodies. We apply it in robotics as well as in biomechanics.
SPACELIB is based on a matrix approach involving 4*4 matrices. We
have six different kind of matrices to describe three kinematic
and three dynamic entities. They are POSITION, VELOCITY AND
ACCELERATION of bodies (or points) and ACTIONS (forces and
torques), MASS DISTRIBUTION (inertia moments) and MOMENTUM (both
angular and "linear"). Using this library we have written a
program for the whole body motion analysis we presented at the
last symposium on computer simulation in Biomechanics (DAVIS CA
1989). This matrix approach, that can be considered being the
extension of the homogeneous transformation approach to the whole
kinematics and dynamics, is documented in many papers. The library
written in C-language consists of about 40 modules which perform
all the elementary steps necessary in developing of the analysis
of any spatial system of rigid bodies.
We are planing to realize in the future an academic free sharable
version of SPACELIB.

We will be happy to send further documentation or papers to
anyone who is interested in.

**** Angles debate:

In a previous e-mail I summarized the most famous sets of angular
coordinates. I outlined also my opinion on the fact that I don't
believe that any of these sets are THE BEST in EVERY situation.
Before answering to whom asked me a deep discussion I want to
state a few points:
1) I am interested in (three dimensional) kinematic and dynamic
aspects of biomechanics.
2) I am NOT an expert in smoothing raw data.
3) I am not trying to give THE FINAL answer to the debate but I
am just trying to point out a few relevant aspects.
4) This mail isn't a well-organized paper but just a "hand-
written" note edited in order to give a general idea of my
opinion.

I believe that the central idea is "if we want to study something
(e.g. the elbow, the knee, ... the whole body ...), initially we
create a model of that thing (e.g. we decide if we will consider
or not the knee being a perfect revolute pair) and at last WE
CHOOSE A SET OF COORDINATES WHICH EMPHASIZE THE MAIN IMPORTANT
CHARACTERISTICS OF THE MOVEMENT"

I find that the relative angular position between two bodies A and
B generally falls in one of the following situations:

a) The two bodies are not linked by any angular constrains. In
this situation body B can assume any angular position with res-
pect to A (e.g. the trunk of a man during a jump can rotate
freely with respect to the Earth).

b) The two bodies are connected by a non-spherical joint. Many
situations can occur -- the most relevant are:
b.1) The two bodies are connected by a revolute pair or an
approximate rev.pair (i.e. arm and forearm are connected
by the elbow (an approximate revolute pair)).
b.2) The two bodies are connected by a "joint" which permits
two or more degrees of freedom (e.g. the head is connected
to the body by means of the neck (an approximately spheri-
cal joint)).

c) The two bodies are connected by a revolute pair or by a joint
which can be considered the sum of two or three revolute pairs.
(although this situation does not happen in Biomechanics, some
joints (e.g., the elbow) can be considered as approximately be-
longing to this category.)

In situation a) there is no preferred direction, axis or angle, so
it appears very obvious to choose a set of angular coordinates
which is "neutral" or "symmetric" with respect to the body and to
the reference frame (e.g. screw angle system (also called the
Euler angle and axis)).
On the contrary, in situation b.1) The movement is usually
composed of one large rotation (around the joint axis) and
possibly two smaller rotations. Anyway all these three rotation
angles are always contained in a well-known range. I think that in
this situation a system of coordinates which gives a different
importance to the first rotation (e.g. flexion-extension of the
elbow) with respect to the others (ab-adduction and endo-exorota-
tion) is more significant than other angular parameter sets.
At last in situation b.2) all the three angles can vary of about
the same maximum range but from a "physical" point of view we can
identify two different kinds of angular displacements. Let us
consider, for instance, the movement of the head with respect to
the trunk. It can be decomposed into two "flexions" and one
"twist" of the neck. Also in this case it looks to me that the
flexions and the twist can be considered having a different
"priority".
A further consideration is that, while in case a) the angles can
vary from 0 to +/- 180 degrees (or 0 -/+ 360),in the cases b)
their values are generally lower than 90 degrees.

Situations b.1 and b.2 can be possibly handled considering the
"joint" composed by two different joints connected in succession.
The first joint being a two degrees of freedom joint while the
second is a one degree of freedom joint. The first joint is a
"semi-spherical" joint which allows the orientation of an axis "a"
but do not permits a twist movement around the axis itself. The
second joint is a revolute pairs which allow a rotation about axis
"a" displaced by the previous joint. (I hope that anyone will
invent a easy way to send pictures on e-mail).
The three angles giving the body orientation can be: a sort of
Latitude and Longitude angles of axis "a" plus the twist angle
around the axis itself. These latitude and longitude angles can
be defined giving to both of them the same importance and making
these angles true measurable angles.

Situation c) "requires" the adoption of a "planar" convention (one
angle) or (sometimes) the adoption of an Euler/Cardanic convention
if the joint is considered being constituted of a series of
revolute pairs.

Any of these systems of angles can originate a rotation matrix
very useful in performing calculations.

Summarizing: I suggest to identify a (little) number of different
situations and to choose for each of them an appropriate
"standard" set of angular coordinates.

************** At last a one million dollars question ********

How can H. Woltring be so frequently present on e-mail, how can he
produce so fast new papers (by the way: thanks for the
acknowledgement) and how can he continue working at his lab at the
same time?

Do the days in The Nederland have more than 24 hours? Or are his
hours longer than everywhere else?

I'd like to have any suggestion from Herman in order to increase
my productivity.

have a good work.

Giovanni LEGNANI