Rack and Pinion Tooth Design

Hey everyone, I found this forum while trying to do some research on rack and pinion tooth design. I'm having trouble getting my teeth to match up and I'm hoping I can get some help. My only concern at the moment is making the teeth match so that I can create a 3D model. I was attempting to get dimensions for the addendum and dedendum as well as the tooth thickness based on my pitch circle radius (1 inch), a certain number of teeth (arbitrary for now) and a pressure angle of 20 degrees. If someone could please help me out with finding formulas for my tooth geometry based on the dimensions I have, I would really appreciate it. Also, if you are aware of any useful resources that may help me out, please send them my way.



  • smhale
    I should mention that the formulas I tried to use are as follows:

    Number of Teeth = N
    Pitch Diameter = d
    Diametral Pitch = Pd = N/d
    Addendum = 1/Pd
    Dedendum = 1.25/Pd
    Tooth Thickness = 1.571/Pd
  • rebellionofrebel
    Refer to any standard Machine Design book like R norton or the one by Shigley.. U will get what u r looking for. Also try out AGMA handbooks or standard Design Data books they have all requisite formulae to guide you through. a thoeretical treatise will only be found in the books i had mentioned with authors or the AGMA handbooks
  • Ramani Aswath
    Ramani Aswath
  • smhale
    Thanks for the replies guys. I actually need exact physical dimensions to create a virtual model but that template will certainly help when I attempt to create a physical mockup. The formulas I have were taken from R Norton's Design of Machinery. He does not give much detail into the formulas and I am wondering if these will work for a rack and pinion. Norton called them "standard depth gear tooth deign" formulas. I assume they are true for any type of gear.
  • Ramani Aswath
    Ramani Aswath
    Why are you cutting and pasting the response by rebellionofrebel? Serves no purpose and is a disservice to the person taking time to make a helpful reply.
  • Ramani Aswath
    Ramani Aswath
    An update:

You are reading an archived discussion.

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