POV-Ray : Newsgroups : povray.general : How would you design an involute gear tooth : Re: How would you design an involute gear tooth Server Time
24 Apr 2024 21:52:34 EDT (-0400)
  Re: How would you design an involute gear tooth  
From: KEBman
Date: 29 Mar 2018 17:55:00
Message: <web.5abd5f56aa9ea79bf7923d990@news.povray.org>
Thanks for your help, guys!

Alain <kua### [at] videotronca> wrote:
> You are correct about the isosurface : IF you can come out with some
> function for your gear, it will make the ideal gear. It problem is
> devising that function.

I'm no math expert, but here are two similar equations for making the involute
of a circle.

x(u) = d_b(cos u + u sin u)
x(u) = d_b(cos u - u sin u)
Where d = diameter (d) of the base circle (_b), and I assume u is
some unit of measurement.
Source: Tutorial: How to Model Geometrically Correct (Involute) Gears in Blender
https://youtu.be/DqBOva04lcE

X(t) = r(cos t + (t - a) sin t)
Y(t) = r(cos t - (t - a) sin t)
Where r = radius and t = time, and a some constant where 0 represents the
"azimuth" of the circle.
Source: https://en.wikipedia.org/wiki/Involute#Examples

I tried this, but it didn't work:
isosurface {
 function { r*(cos(t)+(t-a)*sin(t)) } // does not work...
 max_gradient 4
    contained_by { box { -2, 2 } }
 pigment {
  color rgb <1, 0, 0>
 }
 rotate y*20
}

However this function {1*(cos(tid)+(tid-0)*sin(tid))} does yield a box when
'tid' is #declare tid = -3; 3, 4, 5, or above 9, which just seems odd to me...
These numbers for tid yielded nothing: -2,-1,0,1,2,7,8,9, though the renderer
seems to hit some kind of treshold at 9.317, gradually slowing down as decimal
places are added. So again, I'm not really that good with mathematics... Still
an isosurface for this would be ideal.

Any help would be much appreciated!


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