 Posers and Puzzles

1. 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. 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. 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. 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. 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. 02 Jun '07 12:53
and the radius R refers to the distance between two parallel cross sections of a cone.
8. 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. 02 Jun '07 13:03
I need the length of the axle _and_ the second wheel. They're interdependent.
10. 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. 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. 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. 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. 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. 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!