Planetario: Print-in-Place Split-Ring Planetary Fidget (4 speeds, multicolor)

The animation (GIF) shows the real motion, rendered from the same 36 positions that were collision-checked in code.

Planetario is a print-in-place split-ring planetary fidget with four speeds that are powers of two. Hold the blue ring and turn the sun with one finger. The sun turns at ×1, the planets spin backwards at ×½, they orbit at ×¼, and the gold crown creeps round at ×1/16. Sixteen turns of the sun move the crown once. It comes off the bed already assembled, in one piece.

Why it is different

• Most split-ring fidgets print the upper ring floating on a thin gap above the lower one. This one is printed upside down: the gold crown, the four planets, the sun shaft and the blue ring all start on the bed. A 45° chamfer lets the blue ring close over the crown. Nothing floats and there are no supports.

• Each planet is compound: a small 12-tooth layer meshes the gold crown and a large 18-tooth layer meshes the sun and the blue ring.

• Spirals are inlaid in the sun and the planets. They pulse and swirl as the parts turn at different speeds, which gives the hypnotic look.

Details

• Size: Ø79.2 × 22 mm. Fits the A1 mini and any bed of 80 mm or more.

• Real involute teeth: module 1.25, 20° pressure angle. External gears are generated by a rack and internal gears by a rolling pinion cutter, so the meshing flanks are true conjugates.

• Teeth: sun 18 + 2 × planet 18 = blue ring 54. Gold crown 48 meshes the planet's 12-tooth layer at the same 22.5 mm centre distance. Assembly condition (18+54)/4 = 18, a whole number, so all four planets are identical.

• Herringbone teeth at 30° (overhang at the tooth tip is 34°, under 45°). The V traps every part, so nothing can slide out.

• Clearance: each flank is pulled back 0.20 mm, which leaves at least 0.32 mm of real 3D gap between moving parts.

• 72 grip flutes around the blue ring, 16 dots on the gold crown so you can watch it creep, and a small HANMA inlaid in the rim.

Print

• A1 mini + AMS lite, 4 colours: navy #1f3263 (body), gold #e3a82b (crown and lettering), coral #ea5f3c (sun), cream #f4ead6 (planets).

• Colour is only in the first 1.6 mm (8 layers), which is the face you see on top. Everything above that is navy, so there are only about 25 filament changes.

• Sliced with Bambu Studio, 0.2 mm layers, no supports: 3 h 06 min, 49.5 g (navy 40.6 + gold 3.3 + coral 2.5 + cream 3.1).

• Keep elephant-foot compensation on, or your first-layer squish low: the gaps on the first layer are 0.35–0.4 mm. After printing, hold the ring and twist the sun firmly once to free it.

• The 3MF is print-ready with colours assigned. The Python source (manifold3d) is included.

How it was checked

• Speeds from the Willis equations match the simulation: sun +1, orbit +0.25, planet spin −0.5, crown +0.0625.

• 36 positions over 2 sun turns: 0.000 mm³ collision volume between all 7 parts. The smallest gap was 0.322 mm and the mesh phase error was 3e-14 teeth. Controls that fail as they should: one planet shifted half a tooth collides (59 mm³), the crown driven at 1/12 instead of 1/16 collides (32 mm³), and zero backlash leaves a 0.000 mm gap. With 5 planets the assembly condition fails (0.40 tooth off).

• Perfect loop: after frame 36 the shape is identical to frame 0 (difference 0.000 mm³). Twenty degrees earlier it differs by 8,576 mm³.

• In the print pose every part is one solid touching the bed, with at least 0.328 mm to its neighbours, so nothing fuses. Controls: a part lifted 0.5 mm is flagged as floating, and a 0.05 mm backlash is flagged as fused.

• Herringbone: the sun, the crown and the planets each collide if pushed ±1 mm in height. With straight teeth the crown slides out (control).

• Overhangs over 45°: 0.00 mm² on every part. Without the planet chamfer: 209 mm² (control).

• The colours do not overlap (0.0000 mm³), and every inlay passes a 0.4 mm minimum-width test.

About this design

Designed with AI assistance and checked in code before release (see above). Pictures are 3D renders and the slicer preview, not photos. Not printed yet: makes and feedback are very welcome.

Español

GIF del movimiento real. Fidget planetario de anillo partido impreso de una pieza: sujetas el aro azul y giras el sol. El sol va a ×1, los planetas giran a ×½ hacia atrás, orbitan a ×¼ y la corona dorada a ×1/16. Se imprime boca abajo, todo apoyado en la cama y sin soportes. Tiene dientes evolventes reales en espiga y 4 colores. 3 h 06 min, 49,5 g.

العربية

صورة GIF للحركة الحقيقية. لعبة تروس كوكبية تطبع قطعة واحدة مركبة جاهزة: أمسك الحلقة الزرقاء وأدر الشمس. الشمس ×1، والكواكب تدور حول نفسها ×½ بالعكس، وتدور في مدارها ×¼، والتاج الذهبي ×1/16. تطبع مقلوبة دون دعامات، بأسنان حقيقية على شكل حرف V وبأربعة ألوان. 3 ساعات و6 دقائق، و49.5 غراما.