Tusi Couple Astrolabe - 8 Beads in Straight Lines Roll as a Circle

Eight beads. Eight straight slots. Each bead only ever moves back and forth in a straight line - yet together they roll around the dial as one perfect circle.

This is the Tusi couple, a mechanism found by the Persian astronomer Nasir al-Din al-Tusi in 1247 at the Maragheh observatory. A disc of half the radius rolls inside a larger circle, and every point on its rim travels in a straight line. Copernicus later used the same trick in his planetary models. Here it is packed into an astrolabe-style dial: 64 degree ticks, eight-point star engraving, a throne (kursi) with hanging ring, and a sunburst disc you can see turning through the centre window.

Push any bead with a fingertip and the whole circle rolls. Hang it, keep it on a desk, or hand it to someone and watch them try to work out how it moves.

Parts (4 STL files):

- tusi_body: dial + wall + kursi, 76 x 99 x 9.4 mm. Print cover side down (as oriented).

- tusi_disc: rolling disc with 8 pegs, 34 mm.

- tusi_floor: bottom plate, 67.7 mm.

- tusi_beads: 8 beads, 8 mm.

Assembly: hold the body face-down, drop the disc in with the pegs through the slots, press the floor in against the inner ledge (drop of glue), flip it, press a bead onto each peg (small drop of CA glue).

Print notes: PLA, 0.2 mm layers, no supports, 3 walls, 15-20% infill. Clearances are 0.4 mm per side on the pegs and 0.8 mm above the disc; checked by simulation through a full turn with zero collisions. Two colours look best (beads in a contrast colour). Not test printed yet. Not for children under 3 (small parts).

Material: PLA. Layer 0.2 mm, no supports. 4 parts + 8 beads, glue for floor and beads. Size 76 x 99 x 17 mm assembled.

Also on Cults3D: https://cults3d.com/en/creations/tusi-couple-astrolabe-8-beads-in-straight-lines-roll-as-a-circle

License: you may print this model and sell the printed objects. You may not share, distribute or sell the digital files. Designed by Black (BlackSpectre).