car's trajectory

Consider a vehicle of axle-to-axle length L,
and left to right wheel separation W (though
I don't believe this matters).

Assume a X-Y co-ordinate plane, the origin
located at the center of the rear axle.

What is the car's forward trajectory,
if the front wheels rotate left at angle U?
What is its reverse trajectory?

What if the car has front wheel drive?

Why does one park into a space by backing
up, rather than forward?



** BONUS CREDIT **

Use your answer above, to solve the parallel
parking problem.



Mark

Mark-T wrote:
> Consider a vehicle of axle-to-axle length L,
> and left to right wheel separation W (though
> I don't believe this matters).
>
> Assume a X-Y co-ordinate plane, the origin
> located at the center of the rear axle.
>
> What is the car's forward trajectory,
> if the front wheels rotate left at angle U?
> What is its reverse trajectory?
>
> What if the car has front wheel drive?
>
> Why does one park into a space by backing
> up, rather than forward?
>
>
>
> ** BONUS CREDIT **
>
> Use your answer above, to solve the parallel
> parking problem.
>
>
>
> Mark

I'm not going to bother solving your problem, but I will point out that
you're disregarding Ackermann.

nate

--
replace "roosters" with "cox" to reply.
http://members.cox.net/njnagel

On Fri, 23 May 2008 18:38:11 -0400, Nate Nagel >
wrote:

>I'm not going to bother solving your problem, but I will point out that
>you're disregarding Ackermann.

Who's Ackermann? One of the profs at Stanford?

--
Rich Webb Norfolk, VA

On Fri, 23 May 2008 18:48:31 -0400, in sci.electronics.design Rich
Webb > wrote:

>On Fri, 23 May 2008 18:38:11 -0400, Nate Nagel >
>wrote:
>
>>I'm not going to bother solving your problem, but I will point out that
>>you're disregarding Ackermann.
>
>Who's Ackermann? One of the profs at Stanford?
Think he wrote a paper on"nerds dont need condoms"


martin

Rich Webb wrote:
> On Fri, 23 May 2008 18:38:11 -0400, Nate Nagel >
> wrote:
>
>
>>I'm not going to bother solving your problem, but I will point out that
>>you're disregarding Ackermann.
>
>
> Who's Ackermann? One of the profs at Stanford?
>

I was referring to Rudolph Ackermann

http://en.wikipedia.org/wiki/Ackerma...ering_geometry

basically, in any modern (within the last hundred years or so) vehicle,
the front wheels will not turn at the same angle for a given steering
input. The alternative would be to use a solid axle with a pivot in the
middle, like a wagon. otherwise, the tires will scrub going around a
corner.

nate

--
replace "roosters" with "cox" to reply.
http://members.cox.net/njnagel

"Mark-T" wrote:

Consider a vehicle of axle-to-axle length L, and left to right
wheel separation W. Assume an X-Y co-ordinate plane,
the origin located at the center of the rear axle.

What is the car's forward trajectory, if the front wheels
rotate left at angle U? What is its reverse trajectory?
What if the car has front wheel drive? Why does one
park in a space by backing up, rather than going forward?
__________________________________________________ _______

It's a trick question. The steering linkage rotates the front wheels
at two different angles. The steering geometry is designed so that
the extended centerlines of the two front axles always meet the
extended centerline of the rear axle at a common point. The sharper
the turn, the nearer this point is to the car.

The trajectory of every point on the car is a circle, centered at
that common point, whether going forward or backward.

Rodan.

On May 23, 7:39*pm, Nate Nagel > wrote:
> Rich Webb wrote:
> > On Fri, 23 May 2008 18:38:11 -0400, Nate Nagel >
> > wrote:
>
> >>I'm not going to bother solving your problem, but I will point out that
> >>you're disregarding Ackermann.
>
> > Who's Ackermann? One of the profs at Stanford?
>
> I was referring to Rudolph Ackermann
>
> http://en.wikipedia.org/wiki/Ackerma...ering_geometry
>
> basically, in any modern (within the last hundred years or so) vehicle,
> the front wheels will not turn at the same angle for a given steering
> input. *The alternative would be to use a solid axle with a pivot in the
> middle, like a wagon. *otherwise, the tires will scrub going around a
> corner.
>
> nate

Nate, thank you for posting this. It's guys like you that bring new
hope to this newsgroup by sharing knowledge with others.
Nate, one minor nit. Ackerman Steering dates back 1800, which is more
like 200 years ago.

This website has a very simple explanation.

http://www.auto-ware.com/setup/ack_rac.htm.

Harry C.

p.s., I'm not a car buff. I simply like to know how things really
works and why. Even though I'm a physicist, the front end steering
mechanism of a care is by definition a "simple machine", but it's
certainly the most complex "simply machine" that I know of. When you
repair you own car, you learn all about king pins, ball joints, tie
rods (not to mention tie rod ends), leverer arms, and worm gears on
the steering box. You also learn about someone mysterious adjustment
such as caster, camber, and toe-in. Some of these I understand, and
others I have only an waving knoledge of. I farm out front end
alignmnet to someone with the proper equipment and who know what they
are doing. (Sadly, many mecahnics don't know what they are doing.)
Strange activity for a physicist, because repairing the from end
steering mechanism is a pretty dirty job, and I really have no love
affair going with cars. The reason that I do this is because when I
was an undergraduate, I simply couldn't affor to pay someone to repair
my 1946 Chevy, so I learned to do it myself. Later, in 1956, my
Pointiac flunked NJ inspection because of excessive steering play.
The estimate to repair the problem was $400 which at the time I didn't
have. With the help of two college friends who wiggled the wheels
while I lay undernearth the car looking for signs of excessive play, a
little device called the leverer arm was obviously the source of the
problem. So we drove to Pep Boys auto supply, purchase a new leveler
arm assembly for the sum of $19.95 and installed in in less than half
an hour. Worn tie-rod ends are another trivial fix, but beware of
replacing ball joints...very difficult to do for an amateur, not to
say that I cannot be done. Leave the ball joint and the kingpins (do
any cars still use kingpins) to the pros.

I really hope that there are still a few college students earning
their degress by their own efforts and financial resources, and not
depending on mom or dad to write their tuition check. It is for these
studients that I post this stuff. To these guys and girls, you have to
how to take care of your transportation in the least expensive way
possible, which means doing most of the repairs yourself. because you
cannot likely afford pricey reapair shops. For us guys, the alernative
is to take the bus and then walk.

Now let me share this with you. Old habbits die hard. While today I
am in a position to drive a new BMW (my wife loves them), I drive two
very differnt cars. One is a 1996 Ford Bronco, and the other is a 1986
Cadillac Cimarron. Our newest vehicle is a 1996 Mercury Sable, with no
rust that we just paid $800 have shiped in from Nevada. Guess what the
very firt thing was that I did. I went to eBay and purchased a Ford/
Mercury 1996 Sable/Taurus service manual. (Damn book is 6" thick, and
cost $40, still money well spent.) This will be my wife's ride, and I
need to know how to repair it, if and when it needs reapir. Far chaper
than paying a dealer or auto shop 10X the price of replacement parts,
which generally need only a half-hour to replace.

I guess my point like Nate's is educatonal, albeit in a slightly
different way. The common point between our posts is that you need to
learn how a steering mechanism, ad a car operates unless you have a
surplus of income. To save up to 9/10 of the repair cost, you need to
learn how to do some simple repairs yourself, and somtimes get a bit
dirty in the process. (Soap is still cheap.)

Now this is for the young couples, if you really want to know why we
drive 10 and 20 year old automobiles, it is simply because that they
take us to the places we want to go, at minimal cost. Over the years,
this has allowed us to own our own modest home in the Massachusetts
suburbs free from any mortage, pay the college expense of three
children who are all now college graduates, operate our sailboat, and
on rare occasions take a trip to Maui (our peferred vacation
destination.)

Take this post for whatever you believe it is worth.

Harry C.

On May 23, 8:09*pm, "Rodan" > wrote:
> "Mark-T" wrote:
>
> Consider a vehicle of axle-to-axle length L, and left to right
> wheel separation W. * *Assume an X-Y co-ordinate plane,
> the origin located at the center of the rear axle.
>
> What is the car's forward trajectory, if the front wheels
> rotate left at angle U? * *What is its reverse trajectory?
> What if the car has front wheel drive? * *Why does one
> park in a space by backing up, rather than going forward?
> __________________________________________________ _______
>
> It's a trick question. * *The steering linkage rotates the front wheels
> at two different angles. * *The steering geometry is designed so that
> the extended centerlines of the two front axles always meet the
> extended centerline of the rear axle at a common point. *The sharper
> the turn, the nearer this point is to the car.
>
> The trajectory of every point on the car is a circle, centered at
> that common point, whether going forward or backward.
>
> Rodan.

Yes, and well said.

Harry C.

> wrote in message
...
On May 23, 7:39 pm, Nate Nagel > wrote:
> Rich Webb wrote:
> > On Fri, 23 May 2008 18:38:11 -0400, Nate Nagel >
> > wrote:
>
> >>I'm not going to bother solving your problem, but I will point out that
> >>you're disregarding Ackermann.
>
> > Who's Ackermann? One of the profs at Stanford?
>
> I was referring to Rudolph Ackermann
>
> http://en.wikipedia.org/wiki/Ackerma...ering_geometry
>
> basically, in any modern (within the last hundred years or so) vehicle,
> the front wheels will not turn at the same angle for a given steering
> input. The alternative would be to use a solid axle with a pivot in the
> middle, like a wagon. otherwise, the tires will scrub going around a
> corner.
>
> nate

Nate, thank you for posting this. It's guys like you that bring new
hope to this newsgroup by sharing knowledge with others.
Nate, one minor nit. Ackerman Steering dates back 1800, which is more
like 200 years ago.

This website has a very simple explanation.

http://www.auto-ware.com/setup/ack_rac.htm.

Harry C.

p.s., I'm not a car buff. I simply like to know how things really
works and why. Even though I'm a physicist, the front end steering
mechanism of a care is by definition a "simple machine", but it's
certainly the most complex "simply machine" that I know of. When you
repair you own car, you learn all about king pins, ball joints, tie
rods (not to mention tie rod ends), leverer arms, and worm gears on
the steering box. You also learn about someone mysterious adjustment
such as caster, camber, and toe-in. Some of these I understand, and
others I have only an waving knoledge of. I farm out front end
alignmnet to someone with the proper equipment and who know what they
are doing. (Sadly, many mecahnics don't know what they are doing.)
Strange activity for a physicist, because repairing the from end
steering mechanism is a pretty dirty job, and I really have no love
affair going with cars. The reason that I do this is because when I
was an undergraduate, I simply couldn't affor to pay someone to repair
my 1946 Chevy, so I learned to do it myself. Later, in 1956, my
Pointiac flunked NJ inspection because of excessive steering play.
The estimate to repair the problem was $400 which at the time I didn't
have. With the help of two college friends who wiggled the wheels
while I lay undernearth the car looking for signs of excessive play, a
little device called the leverer arm was obviously the source of the
problem. So we drove to Pep Boys auto supply, purchase a new leveler
arm assembly for the sum of $19.95 and installed in in less than half
an hour. Worn tie-rod ends are another trivial fix, but beware of
replacing ball joints...very difficult to do for an amateur, not to
say that I cannot be done. Leave the ball joint and the kingpins (do
any cars still use kingpins) to the pros.

I really hope that there are still a few college students earning
their degress by their own efforts and financial resources, and not
depending on mom or dad to write their tuition check. It is for these
studients that I post this stuff. To these guys and girls, you have to
how to take care of your transportation in the least expensive way
possible, which means doing most of the repairs yourself. because you
cannot likely afford pricey reapair shops. For us guys, the alernative
is to take the bus and then walk.

Now let me share this with you. Old habbits die hard. While today I
am in a position to drive a new BMW (my wife loves them), I drive two
very differnt cars. One is a 1996 Ford Bronco, and the other is a 1986
Cadillac Cimarron. Our newest vehicle is a 1996 Mercury Sable, with no
rust that we just paid $800 have shiped in from Nevada. Guess what the
very firt thing was that I did. I went to eBay and purchased a Ford/
Mercury 1996 Sable/Taurus service manual. (Damn book is 6" thick, and
cost $40, still money well spent.) This will be my wife's ride, and I
need to know how to repair it, if and when it needs reapir. Far chaper
than paying a dealer or auto shop 10X the price of replacement parts,
which generally need only a half-hour to replace.

I guess my point like Nate's is educatonal, albeit in a slightly
different way. The common point between our posts is that you need to
learn how a steering mechanism, ad a car operates unless you have a
surplus of income. To save up to 9/10 of the repair cost, you need to
learn how to do some simple repairs yourself, and somtimes get a bit
dirty in the process. (Soap is still cheap.)

Now this is for the young couples, if you really want to know why we
drive 10 and 20 year old automobiles, it is simply because that they
take us to the places we want to go, at minimal cost. Over the years,
this has allowed us to own our own modest home in the Massachusetts
suburbs free from any mortage, pay the college expense of three
children who are all now college graduates, operate our sailboat, and
on rare occasions take a trip to Maui (our peferred vacation
destination.)

Take this post for whatever you believe it is worth.

Harry C.



I found out about Ackermann when I registered a custom build car I made. I'd
shortened the chassis from another vehicle by a foot or two & built a new
body for it. Smart arse vehicle inspector came over and jabbered on about
how "the Ackermann principle had been violated....". The guy who was
actually inspecting the vehicle passed it and told us to go home rip off all
the anti-smog gear and stick a Holley on it. Oh yeah - it went around
corners ok as well, I guess I didn't cut enough out for it to become a
problem.

Nate Nagel wrote:
>
> I'm not going to bother solving your problem, but I will point out that
> you're disregarding Ackermann.


Forrest J. ? ;-)


--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida