Searching \ for '[OT] Calculating torque' in subject line. ()
Help us get a faster server
FAQ page: www.piclist.com/techref/index.htm?key=calculating+torque
Search entire site for: 'Calculating torque'.

Exact match. Not showing close matches.
'[OT] Calculating torque'
2006\01\18@152712 by

I was a bit unsure if this should be [OT] or [EE]. I guess it will change to EE later when I start talking about motors, but let's go to the question.

I have to choose a motor (DC, servo, stepper, whatever) to automate the steering column of my robot. The platform I'm using is a gas powered all-terrain vehicle (aka ATV). I believe that measuring the torque necessary to spin the handlebar is the first and foremost step right? As my physics skills are a bit rusty, please someone stick with me and tell me if I've done something wrong.

So here's what I did: I've attached a fish scale (the spring type) to the end of the handlebar, and then measured the spring deflection under different circunstances (lock to lock on asphalt, dirt, moving, stopped, etc). The maximum reading I got was 13Kg, which is the same as holding a 13Kg weight with that scale. Assuming that is correct, then the force needed to pull the spring to that position is 13kg x g. I took the measurements at sea level, so g should be 9.81m/s2, hence the force is 127.5N.

The distance from the steering column axis to the point in the handlebar where I took the measurements (I tried to apply force to the tangent of that point) is 0.34m, so I take that the torque necessary to steer my robot is 43.35Nm. Is that correct?

There is also the issue of how fast I want to turn it from lock to lock, and I believe 250ms would be appropriate (60rpm). From that I've calculated that the motor needs to have a power rating of no less than 273.4W (roughly 1/3HP). Here's how I got this number:

Is that correct? I don't know why but I was expecting less power.

Additionally, I'll have to automate the gear shifting and the brake levers, which demands even more applied force to be actuated.

Can you suggest what type of motor should I use for each case keeping in mind that I don't have a large budget to do it (about \$1500). That will certainly help me narrow my search.

Cheers

I think your calculations are correct. The power rating you came up with
though is a continuous power rating. You won't need that much power all the
time. E.g., servo motors are specified for much larger impulse than
continuous torque. Generally, I would expect your steering mechanism to be

Also, your 250 ms lock to lock seems somewhat ambitious. Do you really need
it to be that fast? If not, you can further downrate the motor.

Perhaps you can add gearing to get greater torque.

As for motors, in this application, I would be using a high torque stepper
motor. For the gear shift, I don't know.

Neil

{Quote hidden}

> -
Padu wrote regarding '[OT] Calculating torque' on Wed, Jan 18 at 14:32:
> I have to choose a motor (DC, servo, stepper, whatever) to automate
> the steering column of my robot. The platform I'm using is a gas
> powered all-terrain vehicle (aka ATV). I believe that measuring the
> torque necessary to spin the handlebar is the first and foremost
> step right? As my physics skills are a bit rusty, please someone
> stick with me and tell me if I've done something wrong.

This may be sidestepping the question (your calculations are correct
in spirit, but I didn't check the math), but is there any particular
reason to not use a linear actuator rather than a stepper-type motor?
It'd make your calculations easier (just caluclate force and distance
required) and probably be easier to mechanically implement - given
that you obviously already have a bar which can be yanked on to
provide steering.  Having operated an ATV manually for years, a linear
actuator for steering, a solonoid or two for shifting, and a servo for
throttle would be my first instinct...

--Danny
From: "Danny Sauer" <piclistdannysauer.com>
{Quote hidden}

Well, one of the requirements is to get rid of the handlebar, so I can't use
it as a yoke, but the idea of a linear motion on the form of a leadscrew or
something like that is starting to spark. All the handlebar does is to spin
the steering column that is connected directly to two articulated rods that
turn the wheels. Instead of rotating the axis, I could attach the rods to a
table and move it linearly with some kind of leadscrew mechanism, I don't
know if that could help me though.

Cheers

Yes, if you can attach to the steering rods directly, you can drive them
with leadscrews. A leadscrew driven by a stepper motor will be simplest to
control. Otherwise, a leadscrew driven by a servomotor will be faster, but
more complex to design. Do the rods move in the same direction? If so, you
can drive them with a stepper motor that has a leadscrew passing through the
center of the motor (double ended). This will cut down on friction, allowing
for a smaller motor.

Neil

{Quote hidden}

--
http://www.pixpopuli.com
> The distance from the steering column axis to the point in the
> handlebar where I took the measurements (I tried to apply force to
> the tangent of that point) is 0.34m, so I take that the torque
> necessary to steer my robot is 43.35Nm. Is that correct?
>
> There is also the issue of how fast I want to turn it from lock to
> lock, and I believe 250ms would be appropriate (60rpm). From that
> I've calculated that the motor needs to have a power rating of no
> less than 273.4W (roughly 1/3HP).

I get the same values given your input values.

> I don't know why but I was expecting less power.

Must it really be able to slam the steering from full right to full left in
1/4 second?  That sounds fast.  Even so, you will need a substantial motor.
To actually get 1/4 second you need more than your 273W at startup and to
overcome inertia.  The energy you put into the inertia gets wasted and is
not recoverable.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
Danny Sauer wrote:
> Having operated an ATV manually for years, a linear
> actuator for steering, a solonoid or two for shifting, and a servo for
> throttle would be my first instinct...

>From the yahoos I've seen driving ATVs around here you don't need a servo
for the throttle.  Just a brick would do.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
Olin wrote regarding 'Re: [OT] Calculating torque' on Wed, Jan 18 at 16:41:
> >From the yahoos I've seen driving ATVs around here you don't need a
> >servo for the throttle.  Just a brick would do.

Yes, the PWM method of throttle (and brake) control does seem popular
with some of the younger crowd - both off- and on-road... :)

--Danny
part 1 1197 bytes content-type:text/plain; format=flowed; charset="iso-8859-1"; (decoded 7bit)

From: "Neil Baylis" <neil.baylisgmail.com>
> Yes, if you can attach to the steering rods directly, you can drive them
> with leadscrews. A leadscrew driven by a stepper motor will be simplest to
> control. Otherwise, a leadscrew driven by a servomotor will be faster, but
> more complex to design. Do the rods move in the same direction? If so, you
> can drive them with a stepper motor that has a leadscrew passing through
> the
> center of the motor (double ended). This will cut down on friction,
> allowing
> for a smaller motor.
>
> Neil
>

Interesting, I've heard somewhere that steppers are not for variable load
torque. Is that true?
I'm not entirely sure if I understood your question, the rods are attached
to this table that is rotated by the steering column, when the steering
colum is rotated to the right, it pushes the left wheel rod and pulls the
right wheel rod. I'm not sure but I believe it is ackerman compliant. I'm
attaching a small gif with a top view representation of what I just said.
I'm thinking about replacing the whole steering axis/table with your
suggestion.

part 2 2247 bytes content-type:image/gif; (decode)

part 3 35 bytes content-type:text/plain; charset="us-ascii"
(decoded 7bit)

Yes, it looks as though it could work. It will become similar to a rack and
pinion steering mechanism, except the rack is replaced by leadscrew, and the
pinion is replaced by stepper motor.

Neil

{Quote hidden}

> -
Neil Baylis wrote:
> and the pinion is replaced by stepper motor.

Why a stepper motor and not a servo motor?  Trying to track the steering
position open loop when it's getting banged around sounds like trouble, and
the holding torque will need to be large.  Isn't the steering inside some
other feedback loop anyway so that the low level control doesn't need
absolute position?

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
Certainly a servo would give better control. I don't know if the double
ended leadscrew motors are available as servos, but no matter. It still
should be possible to do it with a single leadscrew with two nuts.  Well..
wait, actually no. You would need two leadscrews coupled together with a
timing pulley that would be driven by the servo, or the servo would have to
drive one end of a common leadscrew. The double ended stepper design has
only one moving part.

I didn't suggest that it should be open loop. When I said servo, I was
referring to a type of motor, not a type of control system. If you close the
loop around a stepper, then it's also a servo. But it's not a servo motor. I
suggested stepper motor because of the ease of driving it, and the
possibility of the double ended leadscrew arrangement.

Neil

On 1/18/06, Olin Lathrop <olin_piclistembedinc.com> wrote:
{Quote hidden}

--
http://www.pixpopuli.com
I've had a little experience with such things (like working on the
DAVe, the UMass Dartmouth vehicle for DARPA grand challenge.) We used
a rack and pinion setup, with a DC motor turning the pinion gear.
There was a US digital optical encoder(\$80! since it was custom..) and
used a PIC for controlling the motor via PWM and feedback into the
counter.. the index on the encoder was aligned with the wheels
straight.  I still have the code if anyone is interested.. (controlled
over RS232 port with a second PIC for the DC motor drive control[via
PWM].  The steering controller could send the wheels L/R to R/L as
fast as the wheels could slip on cement.. I also had worked on the nav
and route following system

andrew

You may find that the original steering system does not connect both of the
steering rods directly 'inline' with one another. There will often be a
non-180 degree angle between them in the neutral (central) position. If you
compute their motion you may find that the two wheels do not turn the same
number of degrees for each incremental rotation of the steering shaft. This
is done to provide varying geometry as you turn the wheels, including
perhaps a tendency for the wheels to want to center themselves. For this
reason, I would try to keep as much of the original mechanism as possible,
perhaps cutting off and driving the original steering shaft via gearing or a
chain. A worm gear on a motor driving  a gear on the steering shaft would
seem to be attractive.

Bob Ammerman
RAm Systems

{Original Message removed}
On 1/18/06, Robert Ammerman <rammermanverizon.net> wrote:
> You may find that the original steering system does not connect both of the
> steering rods directly 'inline' with one another. There will often be a
> non-180 degree angle between them in the neutral (central) position. If you
> compute their motion you may find that the two wheels do not turn the same
> number of degrees for each incremental rotation of the steering shaft. This
> is done to provide varying geometry as you turn the wheels, including
> perhaps a tendency for the wheels to want to center themselves. For this

Well, wouldn't a scaled down version of a car's rack and pinion
steering w/ tie rods accomplish this?  It would allow you to set
toe-in (as in FWD cars), which I believe allows them to seek center by
themselves..  Also, the angle to the center would not need to be
straight inline because the inner and outer tie rod ends provide for
some amount of angular difference out of a straight line. (think, a
wheel turns around the ball joints and the tie rod is at the end of
the rim inside, and the angle the tie rod makes to the straight-line
of the axis of the rack is not always constant)

> reason, I would try to keep as much of the original mechanism as possible,
> perhaps cutting off and driving the original steering shaft via gearing or a
> chain. A worm gear on a motor driving  a gear on the steering shaft would
> seem to be attractive.

True, but also depends on how much work and how solid you want the
steering to be..  Ah.. the trade-offs.  Both ways have mechanical
issues that must be accounted for in the design of the steering, and
both would be in my opinion about as hard to do as the other...
(unless parts availability is an issue and also skill of the
fabricator)

> Bob Ammerman
> RAm Systems

andrew

Olin Lathrop wrote:

>> The distance from the steering column axis to the point in the
>> handlebar where I took the measurements (I tried to apply force to
>> the tangent of that point) is 0.34m, so I take that the torque
>> necessary to steer my robot is 43.35Nm. Is that correct?
>>
>> There is also the issue of how fast I want to turn it from lock to
>> lock, and I believe 250ms would be appropriate (60rpm). From that
>> I've calculated that the motor needs to have a power rating of no
>> less than 273.4W (roughly 1/3HP).
>
> I get the same values given your input values.
>
>> I don't know why but I was expecting less power.

Look at the graph in this data sheet:
http://www.casaferreira.com.br/pdf/CEP453042.pdf

It shows the typical relationship between torque, power, rotational speed
and current for an electric servo motor. It also shows where the rated
numbers typically are located on the graph.

And don't forget that this is not a constant movement; you'll have an
acceleration phase, you may or not have a phase with constant maximum
speed, you'll have a deceleration phase and you'll have a "move in on the
target" phase where your position controller is active and the torque goes
up and down around 0.

Maybe this helps you for the controller:
http://www.compumotor.com/whitepages/ServoFundamentals.pdf

> Must it really be able to slam the steering from full right to full left in
> 1/4 second?  That sounds fast.  Even so, you will need a substantial motor.
> To actually get 1/4 second you need more than your 273W at startup and to
> overcome inertia.  The energy you put into the inertia gets wasted and is
> not recoverable.

It could be, probably, partially, but the effort is not worth it :)

In any case, it's this inertia that you need to accelerate and decelerate.

Re linear actuator: for these calculations, it doesn't matter much whether
you use a gear motor that has a rotating output or a linear actuator that
is a motor with a screw gear that then gets translated back into a rotating
movement. The torque, force, power calculations are pretty much the same;
the only things that change are the friction losses and that the
translation back into a rotating movement usually is not linear -- both
often negligible effects.

A linear actuator needs to do exactly the same a rotating actuator needs to
do: accelerate, move along, decelerate, move in on the target, and provide
the same torque/rotational speed (at the steering column) in the various
phases.

Gerhard

andrew wrote regarding 'Re: [OT] Calculating torque' on Wed, Jan 18 at
22:38:
> Well, wouldn't a scaled down version of a car's rack and pinion
> steering w/ tie rods accomplish this?  It would allow you to set
> toe-in (as in FWD cars), which I believe allows them to seek center
> by themselves..

There are a few minor things wrong with this. :)  First, toe-in is
adjustable on almost all RWD cars too (I'd say all, but then there'd
be *something* obscure which isn't).  Second, toe-in affects stability
at speed, and to an extent, steering effort.  It has little effect
(within a reasonable range of adjustment) on self-centering.  The
centering is mostly controlled by the caster angle, which isn't

> Also, the angle to the center would not need to be straight inline
> because the inner and outer tie rod ends provide for some amount of
> angular difference out of a straight line. (think, a wheel turns
> around the ball joints and the tie rod is at the end of the rim
> inside, and the angle the tie rod makes to the straight-line of the
> axis of the rack is not always constant)

Here again, the angle between the tie rod ends and the steering rack
is pretty important when turning, as the thing being pushed/pulled by
the tie rods is moving in an arc.  When you change the angle of the
tie rod arms with respect to the steering knuckle, you mess with the
rate of change across the arc, and can greatly affect steering effort
as you approach the extremes.  If you don't get the rack in the right
place with the proper length tie rods, you'll screw up the ackerman
angles of the front wheels and end up dragging the inside or outside
tire while turning, which results in jerky, imprecise steering.  It's
like bump steer, but different (though they're both caused by the rack
positioning and tie rod length relativel to the steering knuckes).
There's some freedom to play around, but not a lot.

Basically, if the vehicle handles acceptably now, it would probably be
best to try to maintain as much of the original steering geometry as
possible - maybe by attaching a linear motion device to the existing
pitman arm / idler arm / steering rack.

--Danny
From: "Danny Sauer" <piclistdannysauer.com>
<snip>
>
> Basically, if the vehicle handles acceptably now, it would probably be
> best to try to maintain as much of the original steering geometry as
> possible - maybe by attaching a linear motion device to the existing
> pitman arm / idler arm / steering rack.
>

I thought about that too. In my RC monster truck, ackermann is implemented
with bended horns on each wheel, and the steering rods slide from side to
side. In this ATV, the rotating platform is the one that "supposedly"
implements the ackerman.
But riding the ATV, it doesn't turn nicely on full lock (chinese
"japanese-wannabe brand"), which prompted my to check to see if the ackerman
geometry is right. If it's not, then I'd go to leadscrew on a blink... I
checked this morning and I believe it would be easier to do mechanically.

Another idea that crossed my mind was to cut the steering axle (as I was
going to do one way or another) and install a lever perpendicular (or
almost, since there's some rake angle to the steering column) to the
steering axle and use it as a lever, but thinking better, levers, pulleys
and gears aren't the same thing mechanically in terms that all of them
distribute power differently? Is there any advantage of using one over the
other?

Cheers

From: "Gerhard Fiedler"
>
> Look at the graph in this data sheet:
> http://www.casaferreira.com.br/pdf/CEP453042.pdf
>

Thanks for the link Gerhard, I'll digest them.

<snip>
> And don't forget that this is not a constant movement; you'll have an
> acceleration phase, you may or not have a phase with constant maximum
> speed, you'll have a deceleration phase and you'll have a "move in on the
> target" phase where your position controller is active and the torque goes
> up and down around 0.

I remember something about it from my robotics class, I think I still have
my simulink programs (can I call them that?) that simulate a motor and a pid
controller using triangular and trapezoidal profiles.

<snip>
{Quote hidden}

So if I'm reading right, no matter what the power required will always be
the same (assuming all losses are equal), what should define the type of
motor and gearing (linear or rotating) is the platform?

From: "andrew kelley" <leetslackergmail.com>
> I've had a little experience with such things (like working on the
> DAVe, the UMass Dartmouth vehicle for DARPA grand challenge.) We used
> a rack and pinion setup, with a DC motor turning the pinion gear.

First of all congratulations on DAVe, now that I've been working on
autonomous rovers for a little longer than 1 year, I know how difficult is
to build such a beast, especially when you make your own platform. Can you
share some info on your motor/gear/controller combo (such as manufacturers,
models)?

> There was a US digital optical encoder(\$80! since it was custom..) and
> used a PIC for controlling the motor via PWM and feedback into the
> counter..

You mean USB? Or US digital is the name of the company?

> the index on the encoder was aligned with the wheels
> straight.  I still have the code if anyone is interested.. (controlled
> over RS232 port with a second PIC for the DC motor drive control[via
> PWM].  The steering controller could send the wheels L/R to R/L as
> fast as the wheels could slip on cement.. I also had worked on the nav
> and route following system

Since I'm starting on this task, I'd be very interested in taking a look at
your code for learning purposes, since we'll probably buy the controller off
the shelf. We want to be done with actuators as fast as possible and start
to play with the "fun" stuff such as navigation and vision as soon as
possible.

Are you guys further developing DAVe?

Hello,
> to build such a beast, especially when you make your own platform. Can you
> share some info on your motor/gear/controller combo (such as manufacturers,
> models)?

I will be able to once I get up back to school (I'm 920 miles away
from it right now, leaving monday night)

> > There was a US digital optical encoder(\$80! since it was custom..) and
> > used a PIC for controlling the motor via PWM and feedback into the
> > counter..

> You mean USB? Or US digital is the name of the company?

US Digital is the name of the company.  http://www.usdigital.com.  Quadrature
encoder with index.  We got the size to fit the output shaft of the
motor that we used.

{Quote hidden}

Sure.. It still had bugs at its last testing but I have some visio
diagrams of the software flow.. it was pretty simple..

> Are you guys further developing DAVe?

Perhaps, I don't know since we didnt win the competition....  We may
just to be able to have a base to be able to experiment with AI and
obstacle avoidance.

--
andrew (with my 7 month daughter playing with the keyboard and mouse
as I try to type.)

"andrew kelley" <leetslackergmail.com>
>> Are you guys further developing DAVe?
>
> Perhaps, I don't know since we didnt win the competition....  We may
> just to be able to have a base to be able to experiment with AI and
> obstacle avoidance.

That's our goal. We hava another project going on with a smaller platform
(an RC car), but there are many limitations using such platform (limited
payload capacity, not enough energy to have a decent autonomy, less capable
of dealing with rough terrain, etc), but it still has its usefullness.

Cheers

>> A linear actuator needs to do exactly the same a rotating actuator needs
>> to do: accelerate, move along, decelerate, move in on the target, and
>> provide the same torque/rotational speed (at the steering column) in
>> the various phases.
>
> So if I'm reading right, no matter what the power required will always
> be the same (assuming all losses are equal), what should define the type
> of motor and gearing (linear or rotating) is the platform?

Mechanical design and availability... In some instances, it is easier to
work with a linear movement, in other it's easier to work with a rotational
movement, in some cases you can position a linear actuator better, in
others a rotational one.

In some cases, you need a linear movement but can't find a suitable linear
actuator, so you use a rotating actuator with a lever on its shaft, or
maybe an external screw gear. In others, you need a rotating movement but
don't find a suitable rotating actuator, so you put a lever on the shaft
you need to rotate and drive it with a linear actuator. Sometimes, you need
to put the actuator sideways of the shaft to rotate, which can make a
linear actuator look good. Sometimes you need to rotate an output shaft
more than some 120°, which pretty much disqualifies a linear actuator (at
least for simple mechanic constructions). And so on...

For the range you're looking at, they are pretty much the same. Gear motors
with rotational output and output speeds/torques in your range usually have
a screw gear inside that drives the output gear, whereas linear actuators
have a similar screw gear inside that drives the output clamp (or whatever
this thing is called that clamps around the screw gear, has a corresponding
thread inside and drives the output). If you look at them from that angle,
they are both quite similar: the output gear of the rotational output is
simply replaced by the output clamp of the linear actuator. Both get driven
by a screw gear.

The requirements at your steering column are the same for both (obviously),
and they simply get translated into motor requirements by the overall
movement ratio. (The overall movement ratio includes all gear ratios and
any lever ratios and similar you may have between the motor movement and
the steering column movement.) Once you have chosen a particular motor and
construction, you can go the other way and use the motor characteristics
and the overall ratio of that construction for example to calculate the
torque applied to the steering column from the motor current. For this, it
doesn't matter whether that's a linear actuator or a rotational one. The
only thing that matters is the (possibly nonlinear) overall ratio between
motor shaft and steering column.

(You get a nonlinear ratio for example if you use a linear actuator to
drive a lever mounted to the steering column -- unless you only work only
with really small angles, the overall ratio will change with the angle of
the lever, and the max. torque at the steering column will be much higher
in the middle than at the end points; by factor of 2 for +-60°.)

Gerhard
Gerhard,

On Fri, 20 Jan 2006 10:01:17 -0200, Gerhard Fiedler wrote:

>...
> whereas linear actuators
> have a similar screw gear inside that drives the output clamp (or whatever
> this thing is called that clamps around the screw gear, has a corresponding
> thread inside and drives the output).

"Nut" !  :-)

Or "drive nut".  In some cases it may be a half-nut so that it can be lifted off to remove the drive, such as
on lathe feed-screws.

The type of rotary-to-linear motion convertor that I like is the "ball screw", where the screw and the nut
have matching half-round helical grooves, which within the nut are filled with ballbearings, which
"recirculate" as the nut moves along the rotating screw.  It acts like a really coarse thread (2 tpi isn't
unusual), but with extremely smooth operation, low friction, and very little backlash.  The only disadvantage
is that they are darned expensive!

Cheers,

Howard Winter
St.Albans, England

I would consider a mechanical system that has self-locking characteristics.
Whether it be a worm drive or a screw drive...a system that has
anti-backdrive
properties maybe of benefit. Consider bumps, ruts in the road or all
attempting
to backdrive the input.

A worm is an excellent candidate as most are 0% backdrive and can be simply
driven via a stepper.

Milosz Kardasinski wrote:

> I would consider a mechanical system that has self-locking
> characteristics. Whether it be a worm drive or a screw drive...a system
> that has anti-backdrive properties maybe of benefit. Consider bumps,
> ruts in the road or all attempting to backdrive the input.

That's probably a good idea.

> A worm is an excellent candidate as most are 0% backdrive and can be
> simply driven via a stepper.

Maybe most but not all... for example the gear motor I sent the data sheet
link in a previous message has a worm drive, but it's not self-locking.

I'm not sure how to see that easily if it's not specified.

Gerhard

From: "Gerhard Fiedler"

> Maybe most but not all... for example the gear motor I sent the data sheet
> link in a previous message has a worm drive, but it's not self-locking.
>
> I'm not sure how to see that easily if it's not specified.

Unfortunatly, there isn't a concrete rule of thumb. Theoretically, a worm
drive will not back drive if the friction angle is greater than the worm
lead angle. However, the actual surface finish (AGMA spec) and choice of
lubrication may reduce this significantly; among many other factors.
More importantly, vibrations may cause motion at the points of mesh
with further reduction in friction angle.

Now for the good news, generally speaking, if the worm lead angle is 5
degrees or less there is reasonable expectation of self-locking. Between
(5,11] degrees of worm lead there is a percentage of back drive. Over 11
degrees back driving can be expected.

Milosz Kardasinski wrote:

> Now for the good news, generally speaking, if the worm lead angle is 5
> degrees or less there is reasonable expectation of self-locking. Between
> (5,11] degrees of worm lead there is a percentage of back drive. Over 11
> degrees back driving can be expected.

Thanks for the rule of thumb :)

FWIW, the gear I've been talking about has around 7°. This makes it fall
into your "grey zone", and so it's not surprising that it does back drive.

Gerhard

More... (looser matching)
- Last day of these posts
- In 2006 , 2007 only
- Today
- New search...