Marble track - Tautochrone curve

thingiverse

This is a marble track with two identical tracks side by side, each following a specific curve known as the Tautochrone curve, distinct from a circle or ellipse. The Tautochrone curve is defined as "the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve." This definition comes directly from the Tautochrone curve Wikipedia page. The model has been designed specifically to visualize this unique property of a Tautochrone curve, allowing both marbles to fall simultaneously from different positions along the curve and reach the bottom at exactly the same time. Regarding printing and using this model, it's worth noting that 1) no supports are required; 2) smaller layer heights will result in better performance, as the curve will have more detail and be closer to an actual Tautochrone curve; and 3) common marbles (16mm diameter) work perfectly with this design. Watch how it works in action at https://youtu.be/m1iNnWqxr1M.