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Old 2014-07-11, 22:48   #1
diep
 
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Sep 2006
The Netherlands

677 Posts
Default calculating with circles

hi!

I'm trying to draw in cad in a 'mathematical correct" manner a small part for 3d printer for GT2 belt.

Yet i probably missed some lessons in math here and there.

A good example of the picture is here: http://www.adafruit.com/blog/wp-cont...2/gt2tooth.jpg

I'm trying to get the math right for 1 part of a tooth.

As we see we have 3 circles, yet i just worry about the 2 larger ones.
Let's focus upon the circle which i'll put at O :
That one had diameter r.

y ^ 2 + x ^ 2 = 0.555 ^ 2

then if i interpret the drawing correct the other circle is at

(x + 0.4) ^ 2 + (y - 0.195) ^ 2 = 1

Of course for the same tooth there is also y + 0.195

If i try to calculate now where the circles touch each other, then i get in troubles with limited mathskills...

Where is the mistake?

I'm first trying to write it in the highschool form of y = ...

I get then to : y = +- sqrt( -x^2 + 0.555^2 )
and y = +- sqrt( -x^2 -0.8x + 0.84) + 0.195

Now i want to solve this to see where they hit.
I square both y's then and get to:

-x^2 + 0.555^2 = - x^2 - 0.8x +0.84 + 0.195^2 +- 0.195 sqrt(-x^2 -0.8x + 0.84)
<=> 0.8x -0.57 = 0.195 sqrt( -x^2 -0.8x + 0.84)
now squaring that again i get :
(0.8x -0.57)^2 = 0.195^2 * ( -x^2 -0.8x + 0.84)

0.678025 x ^ 2 - 0.88158x + 0.292959 = 0

D = b^2 - 4 ac = -0.17350808

Now my skills working with i are not so high as i get then to:

x1,x2 =( 0.88158 +- 0.131722464 i ) / (2 * 0.678025)

In short i didn't manage to find where the 2 circles touch each other (and where they should also have the same vector going up)

Anyone?

Thanks,
Vincent
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