Paradoxical Cones – the Uphill Roller

I came across an account of the “uphill roller” in a book by Julian Havil, “Nonplussed!”. The basic idea is that two cones, joined at the bases, will appear to roll uphill on a pair of diverging rails if the combination of the angles of the cones, slope of two rails and divergence of two rails is within certain margins. Julian’s article explains the mathematical analysis and gave a simple inequality.

That looks cool, I thought, and the challenge of machining two con-joined cones appealed too.

I decided to design an adjustable set-up that would demonstrate conditions when the cones would appear to behave paradoxically and conditions when the would not. Somewhat to my surprise the finished article worked as inteded.


  • CAD Drawings – Draft-it format
  • CAD Drawings – GIF Images
  • Machining notes

I’ll upload a video when I have one…