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takhounts31
03-19-2001, 06:36 AM
Dear list member:

About a week ago I posted a question for ME students (see below the original q
uestion).
The question was based on a "real life" experience when a brief confusion was
caused due to an inaccurate (interchangeable) use of such fundamental terms as
reference frames (rigid bodies) and coordinate systems attached to the refere
nce frames. Specifically, in the second sentence of the question I've used "M
HD...measures angular velocities wrt the body-fixed local coordinate system".
This statement is inaccurate (erroneous is a better word) because we don't "m
easure" vector quantities wrt the coordinate systems, we measure vector quanti
ties wrt the reference frames. We "resolve" vectors in the coordinate systems
Consequently there are two possibilities to rephrase the second sentence:
1) replace the "body-fixed local coordinate system" with the "local reference
frame", or 2) replace the word "measures" with "resolves".
In the first case, an MHD sensor indeed will measure zero angular velocity at
all times, thus defeating the purpose of its own creation. The second case is
the only possibility for an MHD (or any other sensor) to be of any use, i.e.
"measure" the angular velocity vector wrt some other reference frame (in this
case it is a laboratory/global reference frame), and "resolve" the measured ve
ctor in its own local coordinate system (after all this is the only coordinate
system the sensor is aware of).

I wish to thank all the participants whose responses are included below.

Erik G. Takhounts

Original question:

MHD is a sensor designed to measure angular velocities of rigid bodies. Suppo
se an MHD is attached to a moving (translating and rotating) rigid body, so th
at it measures angular velocities wrt the body-fixed local coordinate system.
If the MHD measures angular velocities in a body-fixed local coordinate system
, then these angular velocities should always be equal to zero since the body
does not rotate wrt to the body-fixed coordinate system. The question is: wha
t does MHD measure? Why?

Responses:

?----------------------------------------------------

1.
The answer depends on how the MHD actually measures the angular velocity.
Assuming that it uses an optical goniometer and differentiates the angle to
provide angular velocity, the reading will correctly indicate zero angular
velocity. If, on the other hand, it uses accelerometers to determine the
angle, then the angular velocities it reads will be incorrect since it is
mounted in a non-inertial reference frame and corriolis and centrifugal
forces will fool the accelerometers.


/************************************************** **
Christopher J. Poletto, Ph.D.
Biomedical Engineer
Laryngeal and Speech Section
Medical Neurology Branch, NINDS
National Institutes of Health
Building 10, Room 5D38
10 Center Drive, MSC 1416
Bethesda, MD 20892-1416

Phone: (301) 402-1496
FAX: (301) 480-0803
?----------------------------------------------------

2.
Erik,

If the MHD is rigidly fixed to the body, then it measures the rotation of the
body-fixed local coordinate system with respect to the inertial frame. The MH
D
works by measuring the motion of an annulus of mercury, which has mass and
therefore inertia. When the body moves with respect to the inertial frame, th
e
mercury moves with respect to the body and produces a signal.

Jim Funk
Auto Safety Lab
1011 Linden Ave.
Charlottesville, VA 22902
Phone: (804) 296-7288
Fax: (804) 296-3453
?----------------------------------------------

3.
Hello Erik.

I am not a student, but I feel compelled to reply to your ill-posed
question.

I don't know what an MHD is, but I can make some assumptions based on the
way you posed the question. You said that the MHD measures angular
velocities wrt the body-fixed local coordinate system. If that is true,
then, in fact, yes, it will just give zero. However, if the MHD measures
angular velocities of the rigid body wrt an inertial frame, EXPRESSED in the
local coordinate system (as would be the case if the MHD is any sort of
useful device), then you have your answer. The paradox (or apparent
paradox) in your question comes from your innacurate word choice.

Ian Wright
?--------------------------------------

4.
Most sensors are based on measuring a shange in voltage across a resistor. My

guess is that the senor in question contains a mass that experiences
centripital force during the angular movement of the rigid body. This mass
would strech a resistor and give a change in voltage which could be calibrated

wrt angular velocity.

Ian Aldous
Mechanical Engineering
Dalhousie University
?---------------------------------------------

5.
Erik,

This is somewhat related to the centrifugal force discussion
last December.

The angular velocity is probably derived from centrifugal
forces measured in the sensor and represents an angular
velocity relative to the global reference frame. However,
its XYZ components are given relative to a local XYZ
reference frame. This is inevitable, because the sensor
has no way of knowing its own orientation relative to
global.

I am not familiar with this MHD sensor. Who makes it?

Ton van den Bogert
Department of Biomedical Engineering
Cleveland Clinic Foundation
?---------------------------------------------

6.
Could you provide a bit more information about the MHD sensor? Perhaps a
product description, wed page, photo, or something to that effect.

There are several ways to measure angular velocity, but without more
information, I could not tell you any more about this specific product.

Rob

"I never did anything worth doing by accident, nor did any of my inventions
come by accident; they came by work." - Thomas A. Edison
?-------------------------------

7.
I hope I understand the question completely? I believe this instrument
measures voltage. The instrument must contain a variable resistor and having

a known current, the voltage output would change linearly with respect to
position according to the relationship (V=IR). What's more, the velocity
(dv/dt) and acceleration (dv2/d2v) can then be calculated by the numerical
derivatives of the position data.

*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~

Adam B Ryals
Research Assistant/M.S. Student
Department Bioengineering
University of Illinois at Chicago
Ph: 312.942.5814
e-mail: aryals1@uic.edu
?----------------------------------------

8.
Erik,

Here's a shot...

I'm not sure I understand your question exactly, but I think the answer is
that the fluid in the MHD has inertia, so it is really measuring angular
rates relative to an earth-fixed reference frame. The problem is with your
given (by your reasoning, an accelerometer on, for example, a crash sled,
shouldn't measure any acceleration because it's fixed to the body). The
fluid in an MHD is analogous to the sprung mass in an accelerometer.

The fluid's inertia is the reason that an MHD is only accurate for a
relatively short time while the rotational acceleration is positive (i.e.,
the angular velocity is increasing). As soon as the angular acceleration
becomes negative (i.e., the rotational velocity decreases), the angular
velocity measurement from the MHD is dubious because the fluid continues to
rotate inside the sensor under its own intertia.

Rich
?----------------------------------

9.
> If the MHD measures angular velocities in a body-fixed local coordinate
syste
> m, then these angular velocities should always be equal to zero since the
body
> does not rotate wrt to the body-fixed coordinate system.

MHD measures the angular velocity of the point where it is placed. In fact I
suppose that its measure is based on the
evaluation of an accleration (or a force, presumably centrifugal force):
while traslation and constant velocity can be 'hidden' moving from an
inertial system to another one, this does not hold for force and
acceleration: they do not depend on reference system. For example: I see a
car moving at constant velocity, if I am in the car I do not realise it is
moving if it has constant velocity (and I don't watch out of the window!!),
but if it accelerates I do realise it even if I am in the car!

Elisabetta Zanetti, Ph.D.

Post-Doctoral Student
Dipartimento di Meccanica
Politecnico di Torino
Cso Duca degli Abruzzi 24
TORINO 10129
?----------------------------------

10.
Erik,

I don't think it measures angular velocities wrt a body-fixed
local coordinate system, otherwise it would always be zero as
you stated. It measures angular velocities wrt
the local inertial frame (i.e. MHD motion within a circular
channel). However, I don't think the problem as posed below is
going to help you since what the MHD measures is not related to
a dynamics question, but a question of exactly how the sensor
responds physically. I'd ask ATA exactly how the sensing element
works. That will likely be more fruitful since I only know
in broad brush. Greg Hall may know more.

Dale
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