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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To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------

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

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

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------