I don't know

The trick is to stop thinking in three dimensions, look along the table and draw lines on a sheet of paper that show what you see.
. .
. / .
. / .
. / / . A
.__/_________/_____._____

On the left is one wheel, on the right another, the dots are the imaginary sides of your triangle, where they meet the ground is the centre of your circle (A) After you see this, you should be able to work the trigonometry yourself.


EDIT; Ok, it's really hard to draw pictures when your formatting is completely ignored! Sorry, I tried...

Originally posted by agryson
The trick is to stop thinking in three dimensions, look along the table and draw lines on a sheet of paper that show what you see.
. .
. / .
. / .
. / / . A
.__/_________/_____._____

On the left is one wheel, on the right another, the dots are the imaginary sides of your triangle, where they meet th ...[text shortened]... it's really hard to draw pictures when your formatting is completely ignored! Sorry, I tried...

Ok....... what If you had the same axle length for two sets of wheels
(set A) and (set B) the only thing that changes are the radi of the wheels.............compare the dia. of the traveled circles of (set A) to (set B)..... as they too, will turn circles with different dia. the only variation lies in the wheel radius.......so, you have wheel (set A) with its variable diameters (x)& (Y) the will turn circle (C) and wheel (set B) with dia. (R) & (D) turn circle (Z) how does the ratio of X:Y or R😀 affect the dia. of cicles C or Z

That Smiley is supposed to be 😀

ahhhhhh R to D

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

I think the above answers that question though?
Provided the axle is constant, the ratios relationship with the circle should be this.

Originally posted by agryson
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

This does probably answer my question, except I'm having trouble conceptualizing this ( highest Mathmatics course Basic Algebra)........
here's what I think it might mean though...... As it tends to 1, the radius of the circle turned approaches infinity........ so as the ratio of x:y become's 1:1 it creates a straight line ( infinity)? As it tends to 0, the radius of the circle turned approaches 0, .....The greater the differential between x & y shrinks the dia (infinately)....... What I expected to see when asking this question was a formula using the difference of x & y to calculate how how x will lead y or vice versa derriving the circumference of the turned circle with the circumference of x & y.

Yes it will, but it also depends on the length of the axle. For instance if you had a huge wheel on one end, with no wheel on the other, the radius can never actually be 0, because the axle is still doing something, that's why we need the length of the axle to get the radius of the circle.

Let me rephrase my earlier analogy. Forget everything and imagine a normal cone spinning on a table on its side, it should be clear, that the radius of the circle is equal to the height along the edge of the cone.
The question you asked is the exact same, but the point of the cone is missing, so to get the hieght of the edge of the cone, we need the size of the two wheels and the length of the axle.
After that, the only math needed is trigonometry...
http://en.wikipedia.org/wiki/Trigonometry
It's a little long, but is a very useful technique for all kinds of problems like this.

P.S.
What you thought I was saying is... exactly what I was saying! So you've got the idea.

One more thing though, there's no relation between the circumference of the wheels and the circumference of the circle other than through the axle. I personally think it's easier to leave Pi out of it and work with the angles.

Originally posted by agryson
P.S.
What you thought I was saying is... exactly what I was saying! So you've got the idea.

Hey...... thanks alot , I'm sure it wasn't easy for you to continue to re-answer my questions, most people would have given up on me........so thanks again! 🙂

No worries, there's no point answering a question unless the answer is understood. Keep up the looking around for problems like that though, that's what makes a person a good physicist, not maths ability. (I'm CRAP at maths!)