# Calculating rack and pinion

Hi cd,

Our team is trying to figure out how to calculate the measurements of the rack that we’re designing for a mechanism. Could anybody help us out?
Thanks

Could you elaborate on “measurements”? As in designing tooth profiles? Calculating forces on teeth? Larger mechanism scope style measurements for a rack and pinion?

p= diametal pitch (typically 20 with frc gears)

Circular pitch = Pi/p

Addendum = 1/p

Dedendum ~ 1.25/p

Tooth thickness at pitch line = Pi/(2*p)

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Designing tooth profiles
We’re going to use a westcoast 10 dp for our mechanism, and are trying to design it in onshape

So the easy solution is to pull the tooth profile for the rack from a CAD model, i.e. mcmaster carr, and make your own part. This is excellent for testing and may be sufficient.

You could lay it out yourself, just take your time, maybe check your results vs a commercial product for validation.

Grabbing a model and using the profile from that is probably the most efficient use of your time, but there is a loss of learning experience. Just something to think about.

Thanks for the help

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As a quick aside:
Placing a chamber on the edge of the teeth of straight cut spur gears (axis parallel to length of rack, the edge that is closest to the word “Dedendum” in the figure in chadr03’s post) will help with 3d printed stuff running smoothly.

We normally do this using the SolidWorks toolbox add-in. You can create a gear/rack with a specified pitch, number of teeth, and a few other parameters, then save it as a part and edit it. We have used this to great success to make curved racks for hoods in previous years