This question has been bugging me ever since kamocat started this thread over 2 weeks ago. So this afternoon I had a block of free time and worked out the math.
I wrote a short paper "equation for bump-less mecanum roller" and posted it here:
http://www.chiefdelphi.com/media/papers/2390
The paper presents the derivation of a set of parametric equations for designing the roller profile.
Much thanks to compwiztobe and kamocat for verifying the output of the equations in their CAD programs.
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