CONEJURE - the cone that rolls uphill

Put a double cone at the bottom of the ramp and let go. It rolls uphill. Then lift the ramp one more step on the riser and it rolls back down — and a line engraved on the riser tells you, before you try, exactly which step that will be.

How it works (no magnets, no tricks — the rails do it). The two rails spread apart as they climb. As the cone rolls toward the wide end it rests on the rails ever closer to its points, so its middle sinks faster than the rails rise. The heavy middle actually goes down while the cone visibly goes up. Cone angle × rail spread sets the threshold: for this set it is 11.07°. Lips 1 and 2 on the riser (4° and 7°) are below it — the cone climbs. Lips 3 and 4 (13° and 17°) are above it — it rolls back. The engraved line on lip 3 is the predicted stop height. A plain cylinder is included: put it on the same rails and it never climbs. Ask a kid why.

Zero hardware. The two cone halves print base-down and lock onto a printed stud with a quarter turn (push the lugs into the slots, twist to the stop). No glue, no magnets, no screws. The tips are 4 mm spheres and every edge is chamfered — safe for small hands; the smallest part is the Ø14 × 44 mm stud.

What's in the box

• Cone half × 2, stud × 1, ramp × 1 (216 × 120 mm), riser × 1, control cylinder × 1 (optional). PLA, 3 perimeters, 15 % infill, no supports on any part in the exported orientation. ~350 g total.

• Ballooned exploded assembly sheet and a fit/print guide.

The receipts (this model was engineered, not just modelled). Every claim below is a number in a receipt file shipped with the source:

• The climb threshold is derived in closed form, checked five ways, and then checked against the actual CAD: the cone posed 0.15 mm above its predicted height clears the rails by 0.13 mm at both ends of the run, and the same pose lowered 0.5 mm cuts into the rails.

• The bayonet joint: locked, it clears by 0.24 mm everywhere; pulled while locked it interferes (the lugs sit on 1.5 mm of floor); every printed fit is checked at ±0.15 mm printer extremes.

• Pull-apart strength: 100 N on the lugs → 14.7 MPa band-corrected FEA peak, safety factor 2.06 against the across-layer PLA allowable.

• The assembled cone is balanced to 0.0095 g·mm.

Print notes

• Cone halves base down (the seam chamfer is the elephant-foot relief; no brim there). Stud standing, with a brim. Ramp plate down. Riser base down.

• If the cone stalls on lip 2, run fine sandpaper once along the inner top edge of each rail — that edge is the running surface — and make sure both halves are twisted fully to their stops.

• Fits 220 × 220 beds (ramp 216 × 120 mm).

Honest limits. The 11.07° threshold ignores rolling resistance, so the real stop sits a little below it; the riser steps bracket it by 4° below and 2° above. No drop test has been done; the joint is rated for pulling, not throwing. PLA softens in a hot car.