Matching surface to roll a low poly sphere on

What it is

A matching complex surface to smoothly roll a low poly sphere on.

Why

• To point out that there is nothing wrong with the world (@Chuck)
• To add a remix to rookiebwoy’s Low poly sphere
• Just playing around with math and CAD

How

Normally you have a complex (round, high poly) object that rolls and a primitive surface to roll it on (maybe single poly). Once you reduce the complexity of your rolling device, that complexity needs to go somewhere. With the condition of only having two interacting objects, this complexity has to go into the surface that is rolled on.

With a little math, you will discover that the surface to roll a six sided sphere on has to have catenoid proportions. The 2D expression simply is f(x)=-cosh(x) along a single straight contactline. This also is true in 3D and the basic shape is formed. The last step is to repeat that shape to get more than just a hill from which the shere will tip over…

Does it work

Nope, not as well as I had hoped. → Welcome to the difference between theory and reality. Too little friction, low contact pressure and indifferent equilibrium states sabotage us here…

How to print

The provided model is designed for six sided spheres with a diameter of 10mm. A matching six sided sphere is given, for other sizes just scale it. → rookiebwoy's Low poly sphere has a diameter of 15mm => scale to 150%

If intended to try it out, a smooth finish is desireable = small layer height, I used 0.12mm.

What next

Tell me in the comments how useless this is… or maybe, take a look at my other designs ;-)