# descibing a circle diameter help needed

• posted

Hi all

I need some help if i might ask

I need to Model a chainwheel and drive its diameter by the pitch of each tooth.

the pitch is 12.5 mm or 0.492" for our american buddies

what i need to do is describe diameter as a result of the tooth pitch x the number of teeth

im puzzled this is probably really easy to some of you guys i can only describe the diameter of the circle using dimensions and not the circumference

any help

• posted

diameter = (number of teeth) x pitch / pi

• posted

That equation can come close, especially for large sprockets with a lot of teeth, here is a more accurate forumala: diameter=2*pitch*SIN((90-180/#_of_teeth)*ATN(1)/45)/SIN(360/ #_of_teeth*ATN(1)/45)

This equation includes the conversion to radians as solidworks requires (all SWX trig functions input/output radians)

• posted

I just answered a similar post on eng-tips.com. Is this the same poster???

Anyhoo, for a chain, look at the problem as a circle circumscribed about a polygon with "n" equal sides and length equal to pitch "p". Draw a line from the endpoints of one segment to the center, and calculate the radius by bisecting the resulting isoceles triangle.

The result: diameter = pitch / sin(180°/n)

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