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I am looking at designing a rack and pinion system that will be laser cut out of some plastic. While the cad system that I am using has a spur gear generator, I was looking at the design of the rack gears. I thought that it needed an involute type profile, but many of the references that I see have a flat profile instead of an involute type profile. For example, this metal rack gear from McMastercarr has a seemingly flat profile.

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Is this common? Is the reason that it has a flat profile due to the fact that the radius of the base circle for racks is theoretically infinite?

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  • $\begingroup$ You are correct. One of the few details I remember from the kinematics course I took years ago was that involute profile of a rack has straight lines because, as you observed, the radius of the base circle is infinite. This is a comment, not an answer because I can't quickly find any web sites that show that with any certainty. If I find my kinematics book (or a web site), I'll add an answer that says the same thing. $\endgroup$
    – user1683793
    Apr 10, 2020 at 2:36

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Standard (circular) involute gears have a stationary contact normal. It is usually a line, that is tangential to the base radii of the two gears. When you replace one gear with a rack, then for the meshing to be the same on the gear, the rack needs to be compliant to the given contact normal. From the stationary contact normal you can easily follow, that the contact surface must be flat.

The observation of an infinite base radius (on the rack) may be misleading, because the (theoretical) involute of the racks (infinite) base circle would be a point.

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I found my old Machine Design (Machine Design by Norton) textbook, and this is how it puts it:

If the diameter of the base circle of a gear is increased without limit, the base circle will become a straight line. If the "string" wrapped around this base circle to generate the involute were still in place after the base circle's enlargement to an infinite radius, the string would be pivoted at infinity and would generate an involute that is a straight line.

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