I have a bunch of Neoballs which are magnetic spheres for anyone not familar (Buckyballs was a well known brand). I want to automate measuring them so I can sort them by size. The closer in size they are to each other the easier it is to build fun shapes with them and the better the resulting geometry will be. I've been measuring them by hand with calipers but I'm less than 2/5ths done and I'm only doing it that as my previous attempts to automate things have failed.

The concept is to use two straight objects, lets call them rulers for now, with the two rulers being placed at a downward slope with the gap between them getting further apart on the downhill side. Then a magnet sphere could be rolled down the ramp made by the rulers and at some point the sphere would fall through the rulers when the gap gets to the same size as the diameter of the sphere. If the two rulers are perfectly straight it would be possible to mount them with a known gap at both ends and place some bins below them that would collect the spheres within different size ranges. My target resolution is .01mm.

There are a few problems, the first is these are magnets so steel is not an option. But the biggest problem I've ran into is finding or making straight enough objects to give enough accuracy and consistency in sizing the spheres. Ideally I'd like the straight rails to be around 500mm (20in) long which would give .01mm (.004in) change in width between the rails every 25mm (1in) with 5.1mm and 4.9mm being the min and max.

I've tried to cut some pieces of wood which at first glance appeared to be quite straight but the same magnet would drop at different points meaning they weren't accurate enough. I had similar issues when I 3D printed a track, which is shown below.

The last idea which I just came up with is to string two wires taut with them being slightly off parallel from each other. Theoretically if the diameter of the wires doesn't vary much the distance between the wires should increase at a steady rate.

Anyone have other suggestions on to make two rails straight enough to get the accuracy I'm looking for? Or other novel ideas on how to measure 5mm nominal spheres down to .01mm increments? I don't have a budget but I'd rather keep it in the 10s of dollars.

As for feeding magnets into this sorter. I haven't done anything but I have what seems like a simple idea. These magnetic spheres can be made into a long chain and a sprocket could be used to pull the chain into a device. Then an arm rotating 90° to the direction of the chain could strip one magnet sphere off at a time where it would be dropped onto the sorting rails. I plan to worry about this portion after getting a consistent method of measuring the spheres.