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...
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Originally posted by agrysonOk....... what If you had the same axle length for two sets of wheels
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...
(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 Rš affect the dia. of cicles C or Z
Effectively, the ratio X:YI think the above answers that question though?
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
Provided the axle is constant, the ratios relationship with the circle should be this.
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Originally posted by agrysonThis does probably answer my question, except I'm having trouble conceptualizing this ( highest Mathmatics course Basic Algebra)........
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
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.
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Originally posted by agrysonHey...... 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! š
P.S.
What you thought I was saying is... exactly what I was saying! So you've got the idea.