Sprocket profiles and diameters, CAD

[johnrobholmes]

I finally figured out how to make some chainrings in CAD, but my problem is the diameter of the ring. I can make the tooth profiles for the right pitch and tooth count, but I don't know how to calculate the diameter, nor do I know how to place the tooth profile on the disc.


I made this one as a 36t profile, but it fit 29t exactly. The second set of parallel lines are set 1/2 of the pitch out from the first defining set, which should intersect the middle of the chainring. Didn't work so smooth.

 

[TPA]

If you are just trying to draw in CAD......

I'll try to do this without pics, cause I don't have any :lol:
draw a pic as you read if necessary.

the bottom of each tooth profile is a partial arc of a circle of a diameter with a center point. The distance between center points of these small circles (chord length) is the same regardless of the number of teeth.

as the number of teeth increases, the angle from the center of the sprocket (alpha) changes by a known amount....360deg/n.

This creates a triangle from the center of the sprocket to the center of a small hole (side b), to another small hole center (chord length side), back to the center of the sprocket (another side b).

So known information is.....angle alpha, and chord length.
since the other two angles of the triangle are equal, they can be known.
beta=(180deg-alpha/2).

so to get the other two sides (b), use the law of cosines.

[sin(alpha)]/chord length = [sin(beta)]/b......solve for b
b=[sin(beta)]/[sin(alpha)/chord length]

that way, you can always calculate the BCD of the small holes for each successive number of holes....then add the geometry for the tooth between each hole, and CAD will tell you the overall diameter.


After re-reading your post....this may not be what you were after.
....well maybe its useful

 

[johnrobholmes]

I figured out the easy way to do it. Chain pitch x number of teeth = diameter at middle of chain. Basically just measure the chain that would go around the sprocket once.


Tada. Chamfer there for show, I don't know what is normal yet.

 

[purplepeopledesign]

Use the (very common) polygon function. Set the number of sides = number of teeth, then scale one of the sides to exactly the chain pitch... assuming it's bicycle that's 1/2". The resulting polygon will have each corner at the center of the drilling hole. Put a circle centered at each corner and cut the rest out to suit. The center of your bolt circle will be the center of the polygon.

ensen.

 

[Miles]

It's quite a simple construction - you were almost there:

 

[johnrobholmes]

I tried your method using half pitch, but it wasn't working right for some reason. I need to retry it again tomorrow, I have a CAM project due tomorrow so I will be in the manufacturing lab for a while.

Enson, ingeniously simple method. I like!