Christoph Hormann wrote:
>If you don't want to do an accurate physical simulation you can start with
>some basic rules (for a 2 wheel trailer):
>
>- the wheels of the trailer have a fixed distance to one another.
>- the wheels of the trailer have a fixed distance to the link.
>- the wheels can only move on the ground in their current direction.
>- the wheels' directions are always orthogonal to the line between them.


Hmmmm this might be usefull, but I was looking for something more physical
correct.

Just re-reading your four lines there seems to suggest that the trailer can
not make a curve at all since they only can move in there current
direction. Or is that just me mis reading it.

Thomas

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Thomas wrote:
> 
> >- the wheels of the trailer have a fixed distance to one another.
> >- the wheels of the trailer have a fixed distance to the link.
> >- the wheels can only move on the ground in their current direction.
> >- the wheels' directions are always orthogonal to the line between them.
> 
> Hmmmm this might be usefull, but I was looking for something more physical
> correct.

The limited physical correctness of this approach is just in terms of
dynamics.  Taking this into account would complicate the problem quite a
lot.

> Just re-reading your four lines there seems to suggest that the trailer can
> not make a curve at all since they only can move in there current
> direction. Or is that just me mis reading it.

The emphasis is on *current* direction.  You will probably have to weaken
this requirement a bit (i. e. not use it as a strict rule) to make sure
the distance between the wheels stays the same.

Christoph

-- 
POV-Ray tutorials, IsoWood include,                 
TransSkin and more: http://www.tu-bs.de/~y0013390/  
Last updated 13 Aug. 2002 _____./\/^>_*_<^\/\.______

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Christoph Hormann wrote:
> 
> [...]
> 
> > Just re-reading your four lines there seems to suggest that the trailer can
> > not make a curve at all since they only can move in there current
> > direction. Or is that just me mis reading it.
> 
> The emphasis is on *current* direction.  You will probably have to weaken
> this requirement a bit (i. e. not use it as a strict rule) to make sure
> the distance between the wheels stays the same.

BTW, you can also think of it a different way: The two wheels and their
axis always move on a circle with it's center somewhere on the axis.

Christoph

-- 
POV-Ray tutorials, IsoWood include,                 
TransSkin and more: http://www.tu-bs.de/~y0013390/  
Last updated 13 Aug. 2002 _____./\/^>_*_<^\/\.______

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Christoph Hormann wrote:

>BTW, you can also think of it a different way: The two wheels and their
>axis always move on a circle with it's center somewhere on the axis.


That's what someone here at work suggested as well, but the truck is moving
along a spline and I don't think that it is easy to determine the radius of
the spline at any given point.

Thomas

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Thomas wrote:
> 
> >BTW, you can also think of it a different way: The two wheels and their
> >axis always move on a circle with it's center somewhere on the axis.
> 
> That's what someone here at work suggested as well, but the truck is moving
> along a spline and I don't think that it is easy to determine the radius of
> the spline at any given point.

That's not the point, the trailer won't follow the same path as the truck
anyway, it was just meant to give an idea how things are supposed to work.

BTW, taking a piece of paper and drawing the trailer and it's movement
will be quite helpful for finding a good method calculating it's movement.

Christoph

-- 
POV-Ray tutorials, IsoWood include,                 
TransSkin and more: http://www.tu-bs.de/~y0013390/  
Last updated 13 Aug. 2002 _____./\/^>_*_<^\/\.______

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"Thomas" <tho### [at] gmxnet> wrote in message
news:web.3d6b9ebba31ba4aabbe30ae0@news.povray.org...
> Christoph Hormann wrote:
>
> >BTW, you can also think of it a different way: The two wheels and their
> >axis always move on a circle with it's center somewhere on the axis.
>
> That's what someone here at work suggested as well, but the truck is
moving
> along a spline and I don't think that it is easy to determine the radius
of
> the spline at any given point.
>


    Then the best way to do it would be the small-step physical simulation
kind of approach that Christoph suggested - you'll need to work out the
direction and magnitude of the movement at the link between the car/truck
and trailer and remember that the car/truck and trailer are fixed distances
from that point, oh, also the trailer will pivot around it's center of
gravity (which you can probably safely assume is at the intersection of two
diagonals of the bounding rectangle of the plan view of the main body of the
trailer (unless it's a really oddly shaped trailer))...

--
Pandora/Scott Hill/[::O:M:C::]Scorpion
Software Engineer.
http://www.pandora-software.com

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"Pandora" <pan### [at] pandora-softwarecom> wrote in
> also the trailer will pivot
> around it's center of gravity (which you can probably safely assume is
> at the intersection of two diagonals of the bounding rectangle of the
> plan view of the main body of the trailer (unless it's a really oddly
> shaped trailer))... 


hmmm I thought it would turn on it's axle. Otherwise the wheels would still 
move sideways.


Thomas

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"Thomas van der Veen" <tho### [at] gmxnet> wrote in message
news:Xns### [at] 204213191226...
> "Pandora" <pan### [at] pandora-softwarecom> wrote in
> > also the trailer will pivot
> > around it's center of gravity (which you can probably safely assume is
> > at the intersection of two diagonals of the bounding rectangle of the
> > plan view of the main body of the trailer (unless it's a really oddly
> > shaped trailer))...
>
>
> hmmm I thought it would turn on it's axle. Otherwise the wheels would
still
> move sideways.
>


    hmm... you could be right... no, center of gravity... no axel... no
c.o.g... no, axel... but what about trailers with 4 wheels.... no c.o.g...
no... Ah, damn it, when I wrote that I was certain I was right, now I just
don't know.... I think it's round the center of gravity, and the wheels do
move sideways - think about the case where you've got a trailer with 4 (or
more) wheels, but I'm not certain anymore...

--
Pandora/Scott Hill/[::O:M:C::]Scorpion
Software Engineer.
http://www.pandora-software.com

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On Tue, 27 Aug 2002 16:40:17 -0400, Pandora quoth:

> "Thomas van der Veen" <tho### [at] gmxnet> wrote in message
> news:Xns### [at] 204213191226...
>> "Pandora" <pan### [at] pandora-softwarecom> wrote in
>> > also the trailer will pivot
>> > around it's center of gravity (which you can probably safely assume
>> > is at the intersection of two diagonals of the bounding rectangle of
>> > the plan view of the main body of the trailer (unless it's a really
>> > oddly shaped trailer))...
>>
>>
>> hmmm I thought it would turn on it's axle. Otherwise the wheels would
>> still
>> move sideways.
>>
> ... but what about trailers with 4 wheels

In general, the trailer will pivot around the point halfway between the
front axle and the back axle.  Also in general, the path of the pivot
point of the trailer will inside the path of the trailer hitch.

-- 
Mark

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First off a 4 wheel trailer has a second pivot point, think of a childs wagon
and it will become obvious.  Secondly the hitch and axle are the only places
free to pivot normally, center of gravity shouldn't matter unless there is a
crash.
If you are turning a simple curve with the tractor, the trailer axle should
follow
a curve with a radius bigger than the tractors turning radius by the distance
from the hitch to the trailers axle. So if the tractor turns with radius R1, and
D is
the distance from hitch to trailer axle, the axle should travel a curve with
radius
R2 = R1 + D

--
Tim Attwood

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