Giovanni Legnani. University Of Brescia - Italy - Europeaneconomic Community

03-28-1990, 09:41 PM

Dear biomch-l readers,

I was asked by a number of you to point

out better my opinion on the joint attitude and angles debate. I

was also asked to give information about SPACELIB.

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

P.S. Please generally excuse me for my bad English.

I was asked by a number of you to point

out better my opinion on the joint attitude and angles debate. I

was also asked to give information about SPACELIB.

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

P.S. Please generally excuse me for my bad English.