Long Vehicle Kinematics
Han de Bruijn
http://hdebruijn.soo.dto.tudelft.nl/jaar2011/rotonde.pdf
Sources:
http://hdebruijn.soo.dto.tudelft.nl/jaar2011/rotonde.zip
Executables:
Find the Any Key and press it.
Han de Bruijn
Jacob
I looked through five pages.
What point does this paper make?
Han de Bruijn
Mathematical truth, what else?
Han de Bruijn
alie...@gmail.com
> Document:http://hdebruijn.soo.dto.tudelft.nl/jaar2011/rotonde.pdf
Overly complicated.
Consider a conventional caterpillar tracked vehicle. Describe it on
and exiting a traffic circle in terms of the relative angular
velocities of the L and R tracks. Define rate of turn change during
exit.
You apparently assume the diameter of the circle to be much larger
than the L and R tire separation on a given axle.
As the circle shrinks the tracked vehicle will eventually pivot on
its inside (braked) track, then end up in a neutral steer (tracks
counterrotating).
Describe it exiting the circle in both situations.
Note the tracks have mass and cannot change angular velocity
instantaneously.
Mark L. Fergerson
Jacob
Have you heard this formula?
1. Tell them what you're going to say.
2. Say it.
3. Tell them what you said.
I suppose you covered #2 about something, Why might I want to know how
a car turns without a rear differential? What does this paper tell me
about how it turns?
Han de Bruijn
> On Mar 2, 2:58 am, Han de Bruijn <umum...@gmail.com> wrote:
>
> > Document:http://hdebruijn.soo.dto.tudelft.nl/jaar2011/rotonde.pdf
>
> Overly complicated.
What's complicated about the following?
The velocity of the rear wheels is the projection of the velocity of
the front wheels on the vector that joins the rear and the front of
the vehicle.
With a velocity, a first order derivative is involved, automatically.
This is the whole mathematical model. No dynamics, _only_ kinematics.
So my theory is as simple as possible. But not simpler.
> Consider a conventional caterpillar tracked vehicle. Describe it on
> and exiting a traffic circle in terms of the relative angular
> velocities of the L and R tracks. Define rate of turn change during
> exit.
>
> You apparently assume the diameter of the circle to be much larger
> than the L and R tire separation on a given axle.
>
> As the circle shrinks the tracked vehicle will eventually pivot on
> its inside (braked) track, then end up in a neutral steer (tracks
> counterrotating).
>
> Describe it exiting the circle in both situations.
>
> Note the tracks have mass and cannot change angular velocity
> instantaneously.
Talking about overly complicated .. I've read this several times and
couldn't understand anything of it.
Han de Bruijn
Han de Bruijn
Why should I add #1 and #3 to no more than 4 or 5 pages of #2 ?
And if you don't want to know, why didn't you simply ignore ? Do you
think that I mind whether you are interested or not in a free gift ?
Shrug.
Han de Bruijn
Michael Stemper
>On Mar 4, 1:12=A0am, Jacob <a...@hsu.edu> wrote:
>> On Thu, 3 Mar 2011 00:05:51 -0800 (PST), Han de Bruijn wrote:
>> >On Mar 3, 5:51 am, Jacob <a...@hsu.edu> wrote:
>> >> On Wed, 2 Mar 2011 02:58:10 -0800 (PST), Han de Bruijn wrote:
>> >> >http://hdebruijn.soo.dto.tudelft.nl/jaar2011/rotonde.pdf
>> >> I looked through five pages.
>>
>> >> What point does this paper make?
>>
>> >Mathematical truth, what else?
>>
>> Have you heard this formula?
>> 1. Tell them what you're going to say.
>> 2. Say it.
>> 3. Tell them what you said.
>>
>> I suppose you covered #2 about something, Why might I want to know how
>> a car turns without a rear differential? What does this paper tell me
>> about how it turns?
>
>Why should I add #1 and #3 to no more than 4 or 5 pages of #2 ?
Really, I do believe that the #2 that you've given us is sufficient.
--
Michael F. Stemper
#include <Standard_Disclaimer>
Nostalgia just ain't what it used to be.
alie...@gmail.com
> On Mar 3, 3:41 pm, "n...@bid.nes" <alien8...@gmail.com> wrote:
>
> > On Mar 2, 2:58 am, Han de Bruijn <umum...@gmail.com> wrote:
>
> > > Document:http://hdebruijn.soo.dto.tudelft.nl/jaar2011/rotonde.pdf
>
> > Overly complicated.
>
> What's complicated about the following?
>
> The velocity of the rear wheels is the projection of the velocity of
> the front wheels on the vector that joins the rear and the front of
> the vehicle.
Front wheel steering system quirks are irrelevant if you stop
ignoring the role of a differential. Consider a front-wheel drive car
with unpowered independent freewheeling rear axles.The two rear wheels
will have different velocities (different number of revolutions per
trip around the circle regardless of what the front wheels are doing,
hence different distances traveled per unit time) while the vehicle is
on the circle. Ignoring this is nonphysical.
It is a simplification of the fact that in your discussion of
exiting the circle, you gloss over the fact that the front wheels will
have different speeds while on the circle (because they're at
different radii), and the same speed upon exiting it. This requires a
velocity change (acceleration). Considering a tracked vehicle clears
away the clutter of "more, less, and 'perfect' " Ackerman.
> With a velocity, a first order derivative is involved, automatically.
"A" velocity? On the circle, four different velocities (one per
wheel) plus a fifth if you like, the center-of-mass of the vehicle
ground speed. Off it, they're all one. Deltavee all over your model.
> This is the whole mathematical model. No dynamics, _only_ kinematics.
The only way to ignore the forces involved in exiting the circle,
is to ignore exiting the circle.
Exiting the circle requires reducing to zero that component of the
vehicle's velocity transverse to the new course (the occupants will
perceive a right turn). Changing velocity = acceleration. No force, no
acceleration.
Ignoring exiting, note that with real-world steering systems, you
have to apply constant force (torque) to the steering wheel to stay on
a constant-diameter circle. Your model is thus still inherently
dynamic, unless you claim an asymmetrical steering linkage that has a
zero-force point on a circle of a particular radius fixed by the
geometry.
> So my theory is as simple as possible. But not simpler.
IMO that which it ignores nugates much of what it addresses.
(my elaboration brevity-snipped)
My point was that deltavee requires an energy transaction. Energy
difference between on- and off-circle is related to circle size.
What's the difference between the kinematics of being on a circle of
apparently (but not quite) infinite diameter, and being on a straight
line?
> Talking about overly complicated .. I've read this several times and
> couldn't understand anything of it.
Replace "tracks" with inside and outside front wheels.
Your model is inherently dynamic. Get over it.
Mark L. Fergerson
Han de Bruijn
> On Mar 8, 7:00 am, Han de Bruijn <umum...@gmail.com> wrote:
>
> > On Mar 3, 3:41 pm, "n...@bid.nes" <alien8...@gmail.com> wrote:
>
> > > On Mar 2, 2:58 am, Han de Bruijn <umum...@gmail.com> wrote:
>
> > > > Document:http://hdebruijn.soo.dto.tudelft.nl/jaar2011/rotonde.pdf
>
> > > Overly complicated.
>
> > What's complicated about the following?
>
> > The velocity of the rear wheels is the projection of the velocity of
> > the front wheels on the vector that joins the rear and the front of
> > the vehicle.
>
> Front wheel steering system quirks are irrelevant if you stop
> ignoring the role of a differential. Consider a front-wheel drive car
> with unpowered independent freewheeling rear axles.The two rear wheels
> will have different velocities (different number of revolutions per
> trip around the circle regardless of what the front wheels are doing,
> hence different distances traveled per unit time) while the vehicle is
> on the circle. Ignoring this is nonphysical.
Agreed. But I'm only assuming that the axis joining the rear wheels is
perpendicular to the (vector joining rear and front of) the vehicle.
> It is a simplification of the fact that in your discussion of
> exiting the circle, you gloss over the fact that the front wheels will
> have different speeds while on the circle (because they're at
> different radii), and the same speed upon exiting it. This requires a
> velocity change (acceleration). Considering a tracked vehicle clears
> away the clutter of "more, less, and 'perfect' " Ackerman.
>
> > With a velocity, a first order derivative is involved, automatically.
>
> "A" velocity? On the circle, four different velocities (one per
> wheel) plus a fifth if you like, the center-of-mass of the vehicle
> ground speed. Off it, they're all one. Deltavee all over your model.
So you want a more refined model? I'm the first one to applaud! Indeed
my model implements sort of a long _bicycle_ instead of a long vehicle
because the two front wheels as well as the two rear wheels are "taken
together". So it's rather long bike kinematics instead of long vehicle
kinematics. Right?
> > This is the whole mathematical model. No dynamics, _only_ kinematics.
>
> The only way to ignore the forces involved in exiting the circle,
> is to ignore exiting the circle.
Oh well, it's an approximation for slowly moving vehicles, I suppose.
> Exiting the circle requires reducing to zero that component of the
> vehicle's velocity transverse to the new course (the occupants will
> perceive a right turn). Changing velocity = acceleration. No force, no
> acceleration.
>
> Ignoring exiting, note that with real-world steering systems, you
> have to apply constant force (torque) to the steering wheel to stay on
> a constant-diameter circle. Your model is thus still inherently
> dynamic, unless you claim an asymmetrical steering linkage that has a
> zero-force point on a circle of a particular radius fixed by the
> geometry.
>
> > So my theory is as simple as possible. But not simpler.
>
> IMO that which it ignores nugates much of what it addresses.
>
> (my elaboration brevity-snipped)
>
> My point was that deltavee requires an energy transaction. Energy
> difference between on- and off-circle is related to circle size.
> What's the difference between the kinematics of being on a circle of
> apparently (but not quite) infinite diameter, and being on a straight
> line?
>
> > Talking about overly complicated .. I've read this several times and
> > couldn't understand anything of it.
>
> Replace "tracks" with inside and outside front wheels.
>
> Your model is inherently dynamic. Get over it.
I think your point is that my model is _too_ simple. I'm not enough of
an expert to deny it (just encountered this puzzle and had a nice try)
Han de Bruijn
Jacob
Finally some clue on what generated so many pages of effort.
Han de Bruijn
Does "four and a half" compare with "many" in your country?
Han de Bruijn
Jacob
I can't speak for the country. It looked like a substantial amount of
work to me. It wasn't and isn't clear to me what question it was
trying to address or where that question might arise.
It arose in a puzzle you encountered.
Maybe the question will arise in some situation I will encounter. The
only way I have to file it in my memory is to recall that Hans showed
something about a long wheelbase that would seem to be different from
the situation where the wheelbase is shorter.
I apologize for not elaborating more. It just looked like something
that significant thought had gone into. I might need it some day, but
I might not make the connection because I don't know what problem it
tried to solve.