← 3D Prints · Print-in-place · Bambu A1 Mini
A print-in-place fidget bearing is a lovely object with nothing to say. Give its concentric rings logarithmic scales and it stops being a toy — it becomes a circular slide rule, and the spinning becomes the arithmetic. Turn the rings below before you spend any filament.
Drag the inner ring to set the multiplier · drag the hairline to read a value off it.
Mark the numbers so that distance around the circle is proportional to the logarithm, not to the number. One sits at the top. Two lands about a third of the way round, five at roughly seven-tenths, and ten arrives back at the top having gone exactly once around.
Once the scales are laid out that way, adding angles is multiplying numbers, because that is the one thing logarithms do. Rotating the inner ring by some angle adds that angle to every reading at once — so a single turn locks in a multiplier and the whole ring becomes a times table for it.
And because ten closes the loop, the scale repeats forever. The instrument gives you the digits; you carry the decimal point yourself. That is not a defect — it is the reason a three-inch disc can multiply numbers of any size.
A natural question, and the answer is pleasing: changing the base just stretches the whole scale by a constant factor, and since both rings stretch together, every answer comes out identical. Base ten is chosen only so the scale closes at ten, which makes a decimal shift exactly one full turn and therefore free.
Where the base does show up is if you want to read logarithms off directly. For that you add a plain evenly spaced ring beside the logarithmic one — line them up and you read base-ten logs. Scale that even ring by about 2.303 and you read natural logs instead. Those are exactly the L and Ln scales on a real slide rule.
This is the part the printer decides, not the design. Every nesting level costs you one wall thickness plus two clearance gaps of radius — roughly 1.5 mm on a 0.4 mm nozzle. That single number governs the whole object.
Geometric ring widths are the right law and not merely the pretty one: with a constant ratio between neighbours the object looks self-similar as it spins, and the inner rings shrink gracefully instead of collapsing into slivers the printer cannot resolve. Drive it below the wall minimum and the slicer quietly drops the ring — you get a solid puck and no warning.
Your three-quarter-inch disc holds three rings. Take it to three inches and it holds seven — and they spin better, because an outer ring that size carries real angular momentum instead of being ruled by friction.
A good spinner wants almost no friction. A slide rule wants just enough friction to hold its answer while you read it. Those are opposite requirements on the same clearance number.
The resolution is to stop treating every ring the same. Print the calculating rings tight — clearance near 0.25 mm, so they turn deliberately and stay where you put them — and leave one outer ring loose at 0.40 mm purely for the spin. You get an object that fidgets and an instrument that holds still, in the same 30 grams of filament.
There is a second, subtler tension worth knowing before you slice. Print-in-place clearances are anisotropic: the gap in the Z direction is set by layer height and comes out clean, while the gap in XY is set by extrusion width and tends to close up. If a ring seizes on the first print, the fix is almost always to widen XY clearance by one increment — not to reprint at a finer layer height.