Thread: calculating with circles View Single Post 2014-07-11, 22:48 #1 diep   Sep 2006 The Netherlands 22×173 Posts 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  