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Posers and Puzzles

Posers and Puzzles

  1. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 12:05
    I was pushing a bottle cap around and I thought of a problem that I wasn't able to solve..... here it is

    You have a wheel... with a radius (X), attached by an axle you have another wheel with radius (Y) pushing this wheel around it will eventually complete a circle with the radius (R)

    Now,.. the ratio (X:Y) must be directly related to (R) I'm having trouble logically working through this.
  2. 02 Jun '07 12:10
    By the sounds of things, you want like a wonky half of a car? In which case x and y have no baring on r. If you have a 3cm wheel attached by a short bar to a 10m wheel, it will make a small circle. If you have a 3cm wheel attached by a very long bar to a 10m wheel, it will make a large circle.
  3. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 12:30
    Originally posted by doodinthemood
    By the sounds of things, you want like a wonky half of a car? In which case x and y have no baring on r. If you have a 3cm wheel attached by a short bar to a 10m wheel, it will make a small circle. If you have a 3cm wheel attached by a very long bar to a 10m wheel, it will make a large circle.
    I don't understand...... you said x and y have no bearing on r, but then you stated that variable wheel sizes will change (R) if X and Y vary then it does directly affect (R)
  4. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 12:42
    Originally posted by joe shmo
    I don't understand...... you said x and y have no bearing on r, but then you stated that variable wheel sizes will change (R) if X and Y vary then it does directly affect (R)
    wait you said bar lenghts sorry......... You might have missunderstood me..... If the whel size only slightly varies, the resulting path will be a circle with a greater dia. if they vary a great deal the resulting dia. will be much smaller
  5. Standard member agryson
    AGW Hitman
    02 Jun '07 12:47
    Radius X is the radius of the base of a cone, The radius 'R' of the circle made by the two wheel combination is equal to the hypotenuse of the the cone...
    X = radius of base of cone
    R = hypotenuse of cone...
    H = height of cone
    Pythagoras's rule gives you each of these values but your question was about how the length of the axle affects the length of the radius of the turning circle.
    Well, the wheel 'Y' and the axle have a relationship, if one stays constant, but the other increases the size of R increases, because the second wheel 'Y' is effectively a cross section of the cone.
  6. Standard member agryson
    AGW Hitman
    02 Jun '07 12:52
    Effectively, the ratio X:Y
    As it tends to 1, the radius of the circle turned approaches infinity.
    As it tends to 0, the radius of the circle turned approaches 0
  7. Standard member agryson
    AGW Hitman
    02 Jun '07 12:53
    and the radius R refers to the distance between two parallel cross sections of a cone.
  8. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 13:00
    Originally posted by agryson
    Radius X is the radius of the base of a cone, The radius 'R' of the circle made by the two wheel combination is equal to the hypotenuse of the the cone...
    X = radius of base of cone
    R = hypotenuse of cone...
    H = height of cone
    Pythagoras's rule gives you each of these values but your question was about how the length of the axle affects the length of the ...[text shortened]... of R increases, because the second wheel 'Y' is effectively a cross section of the cone.
    can you solve this for me ? This should be my question

    You have one wheel with a radius of 4" and another wheel with a radius of 2" connected by an axle... if you give them a push from point (A) what will be the dia or radius of the outermost circle when the wheels cross point (A) again?
  9. Standard member agryson
    AGW Hitman
    02 Jun '07 13:03
    I need the length of the axle _and_ the second wheel. They're interdependent.
  10. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 13:09
    Originally posted by agryson
    I need the length of the axle _and_ the second wheel. They're interdependent.
    ok thinking about the length of the axle I do see it's importance I totally overlooked that! make it 4", but I gave you the radius of the second wheel?
  11. Standard member agryson
    AGW Hitman
    02 Jun '07 13:12
    Though in this case, the radius of the turned circle is equal to the
    Axle =A
    Radius of turned circle = R

    R = sqrt(16 + 2(A²)
  12. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 13:13
    Originally posted by joe shmo
    ok thinking about the length of the axle I do see it's importance I totally overlooked that! make it 4", but I gave you the radius of the second wheel?
    A short axle with wheels that only slightly vary in dia will turn a relativly large circle?
  13. Standard member agryson
    AGW Hitman
    02 Jun '07 13:14
    so in that case the radius would be the square root of 48 which is about 6.9 or so
  14. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 13:15
    Originally posted by joe shmo
    A short axle with wheels that only slightly vary in dia will turn a relativly large circle?
    WHAT LEVEL OF MATH CAN i EXPECT TO SEE THIS
  15. Subscriber joe shmo On Vacation
    Strange Egg
    02 Jun '07 13:30
    Originally posted by agryson
    so in that case the radius would be the square root of 48 which is about 6.9 or so
    Thanks for trying, I guess I'm just not ready yet!