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car's trajectory

Discussion in 'Electronic Design' started by Mark-T, May 23, 2008.

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  1. Mark-T

    Mark-T Guest

    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
     
  2. Nate Nagel

    Nate Nagel Guest

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

    nate
     
  3. Rich Webb

    Rich Webb Guest

    Who's Ackermann? One of the profs at Stanford?
     
  4. Think he wrote a paper on"nerds dont need condoms"


    martin
     
  5. Nate Nagel

    Nate Nagel Guest

    I was referring to Rudolph Ackermann

    http://en.wikipedia.org/wiki/Ackermann_steering_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
     
  6. Rodan

    Rodan Guest

    :

    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.
     
  7. Guest

    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.
     
  8. Guest

    Yes, and well said.

    Harry C.
     
  9. Den

    Den Guest

    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.
     
  10. Gib Bogle

    Gib Bogle Guest

    I would never get a physicist to fix my car.
     
  11. Guest

    Wise decision Gib, If you did have a physicist to fix your car, you
    like me would end up driving 20 and 30 year old vehicles that reliably
    and cheaply get you where your are going, but are not the greatest
    girl magnets in the world! :) This is about the only advantage I see
    to owning a brand new BMW (as beautiful as they are), which comes with
    monthly paments that are often top $300.

    By the way, New BMWs are real chick magnets, but so are gourmet
    dinners in a top rated restaurant and a $60 bottle of wine. Somehow
    the girls to fail to realize that they are being driven to dinner in a
    1996 Cadillac Cimarron. Quite honestly, when driving an old but well
    mainained classic car from 25-years back, you save enougn money to
    afford occasional weekend junkets to Bermuda. I can tell you that
    girls like weekend junkets to Bermuda, or Paris, much more that their
    attraction to the wheels that you drive on a daily basis.

    Harry C.
     
  12. Guest

    Wow, you are really into cars which sadly I am not. For me, cars are
    simply boxes with wheels that get me from where I am to where I need
    to go. Still, I am not knocking your passion. I believe everyone
    needs a hobby or side interest in which they can become passionate
    about. Mine is surpsingly, fireworks manufacture and electronics, plus
    a small interest in machine tools (lathes, milling machines, and
    shapers) on the side. Different strokes for different folks.

    During highschool and college, super-powered street rods where all the
    rage, It never became my thing, but I admired the talent and work that
    typically went in to the conversion of an old, rusty Ford pickup truck
    into a machine that could beat track records. Back the, the guys that
    could afford to build them machines would replace everything but the
    truck body with new mills, transmissions, rear ends, shifter and
    brakes. Literally, nothing original remained except for the body,
    which they would of course restore to new condition. What amazed me is
    that these care guys would put thousands of hours of work into
    restoring and enhancing a rusty old wreck that they had purchased for
    $300, and then spend $25,000 or more on the project. Wow!

    While the car guys got their rocks off on this, I spent far more money
    than I could afford on rockets and fireworks and metal working
    equipment. Trust me, there is no greater rush than building a home
    comstructed rocket that will break 100,000 feet altitude, and send he
    coastal defense people (NORAD) searching for the source. I also once
    enjoyed making display quality fireworks as a challenge. Another rush
    comes from the constuction a 5-break aerial shell where the bottom
    shot fires at an altitude of 75-feet!

    Today I am retired, and work on cars and other this. Mostly other
    things. Yesterday we picked up a 1996 Mercury Sable shipped by a car
    transporter from California. I already have purchased an received the
    Ford dealer service manual (damn thing is 6" inches thick). I really
    don't plan to do any enhancedment to it, because it runs just fine. My
    game plan is simply to check out the many of its automatic details,
    and it has many, then turn it over to my wife for her transportation
    and retire her 1990 Tempon by means of Craig's List.

    Oh, on the physics side, I repair and restore the operation of
    radiation detection devices, plus machine special components for
    vacuum systems and patricle accelerators. As Dr. House would say,
    "this can get boring, and boredom leads to death". Death is bad!!!!

    Oh, Just for your information, Holly has just introduced a new product
    line. Carburetors are of not interest to me, since they are little
    more than atomizers, but you may find some interest in this news line.

    Kindest regards, and I do mean that.

    Harry C.
     
  13. With a reasonable size parking spot you can do it with very few
    positionings of the steering wheel, kind of a bang-bang control, and
    frontwards. But you have to be willing to think out of the box and
    allow one front wheel to pass over the sidewalk. Probably that's a
    big-city technique best used in high density traffice with
    pedestrians, cyclists, streetcars, kamikaze taxis driven by insane
    foreigners, other motorists trying to grab the spot, clueless tourists
    etc.
    Best regards,
    Spehro Pefhany
     
  14. And I find that inevitably if you don't equalize the gap in front and
    back that someone will park in such a way to reduce the larger of the
    two gaps.

    Best regards,
    Spehro Pefhany
     
  15. Mark-T

    Mark-T Guest

    Thanks, I didn't know that. It wasn't supposed
    to be a trick.

    What about front vs. rear wheel drive? It
    might seem to make no difference, but
    imagine the front wheels rotated a full
    90* to the left... there will be a
    difference in path, depending on front
    or rear drive.


    Mark
     
  16. Willem

    Willem Guest

    Mark-T wrote:
    ) Thanks, I didn't know that. It wasn't supposed
    ) to be a trick.
    )
    ) What about front vs. rear wheel drive? It
    ) might seem to make no difference, but
    ) imagine the front wheels rotated a full
    ) 90* to the left... there will be a
    ) difference in path, depending on front
    ) or rear drive.

    Assuming perfect grip, there will not be a difference.


    SaSW, Willem
    --
    Disclaimer: I am in no way responsible for any of the statements
    made in the above text. For all I know I might be
    drugged or something..
    No I'm not paranoid. You all think I'm paranoid, don't you !
    #EOT
     
  17. Phil Carmody

    Phil Carmody Guest

    Yes. The car will go nowhere. Assume perfect grip and
    infinitely narrow incompressible tyres, perhaps?

    Phil
     
  18. Willem

    Willem Guest

    Richard wrote:
    ) Phil Carmody said:
    )> Yes. The car will go nowhere. Assume perfect grip and
    )> infinitely narrow incompressible tyres, perhaps?
    )
    ) In which case it will dig itself further and further into the tarmac, until
    ) the engine dies.

    If the tyres are infinitely narrow, wouldn't the car drop like a brick ?


    SaSW, Willem
    --
    Disclaimer: I am in no way responsible for any of the statements
    made in the above text. For all I know I might be
    drugged or something..
    No I'm not paranoid. You all think I'm paranoid, don't you !
    #EOT
     
  19. N8N

    N8N Guest

    While it would be technically difficult to rotate the wheels of either
    car 90 degrees in either direction, it'd be *more* technically
    difficult to rotate the wheels of a FWD car that far...

    nate
     
  20. DaveN

    DaveN Guest


    Because you don't have sufficient car control to make the space??

    Seriously, I usually drive in because if you have shopping you can get to
    the boot (trunk!) much more easily.
     
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