Wand Through the Wall — a Straight Wand Passes Through a Curved Slit

A straight wand passes through a curved slit. Twice per turn. Without bending.

The wand stands on a small turntable, leaning a little to the side. In front of it is a wall with two curved slits. Swing the wand round and it slides through the slit on the left, comes round the back, slides through the slit on the right, and returns. Then hand the wand over: it is dead straight. Roll it on the table to prove it. Now ask how a straight thing fits a curved hole.

The secret (it is geometry, not a gimmick). The wand is skew to the turntable axis: offset 15 mm from it and tilted 30° sideways, not toward the centre. Spin a straight line about a skew axis and it sweeps a hyperboloid of one sheet, the cooling-tower shape. The wall is a flat plane through the axis, and a plane cuts that surface in a hyperbola:

y² = r² + z²·tan²α

That curve is the slit, and it is engraved on the base so the answer is sitting there the whole time. Every point of the wand travels a horizontal circle; higher points of the tilted wand ride bigger circles, so the slit flares outward as it climbs.

Parts (4 printed, all flat, no supports):

• base ×1 — plate with the turntable post, two leg sockets, engraved formula

• wall ×1 — flat portal, two legs and the slitted panel

• hub ×1 — turntable disc; a bore underneath rides the post, a skewed hole on top takes the wand

• wand ×1 — Ø5 × 80 mm rod with a flat so it prints lying down

Print: PLA, 0.2 mm, 3 walls, 15 % infill, no supports. Print the wall with 4 walls or 100 % infill so the slit edges are solid. A small brim under the wand is cheap insurance. Paint the last 8 mm of the wand white, or print the wand_tip_print part (in the included .scad) in white and glue it on.

Assembly: hub onto the post, wand pushed into the skewed hole (press fit, or a drop of glue), wall legs into the two sockets. Illustrated steps below.

Step 1 — drop the hub onto the base post, bore down. It spins on a small ring.

Step 2 — push the wand into the skewed hole until it bottoms out. It leans sideways, not inward. That sideways lean is the whole trick.

Step 3 — stand the wall in the two sockets. Swing the wand a full slow turn: it threads both slits without touching.

Parametric. One OpenSCAD file. Change the tilt alpha, the offset r_off or the wand length and the wall, base and slit curve all follow. The slit is not drawn: it is literally the volume the wand sweeps, subtracted from the wall.

Child-safe: no sharp parts, no springs, no magnets, nothing to swallow but the wand itself, which is 80 mm long.