Elliptical gear, module 1.5, 31 teeth, eccentricity 0.5, bore at a focus — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/elliptical-gear-m1-5-31t-e0-5-focus-bore/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)
Basis: Xem Studio design following Brown's figure (1868); true size, no printing allowance
Catalog version: 2026-10-20

Overall (mm): length 52.67, width 46.09, height 12.0
- Pitch curve an ellipse with semi-axes 24.89 × 21.55 mm (eccentricity 0.5, perimeter 31 × π × 1.5 = 146.08 mm), the Ø8 bore at a focus; teeth generated by a 20° basic rack rolled round the pitch curve without slip (addendum m, dedendum 1.25 m), so any two such gears mesh. Outline: every tooth flank and fillet is a spline fitted to the generated curve within 0.008 mm.
- 31 teeth (odd): a pair pivoted at their foci 49.77 mm apart (the major axis) meets tooth-to-space at both ends of the major axis. 12 mm face.
- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).

dimension  value
module  1.5
teeth  31
pitch ellipse  49.77 × 43.11 mm
eccentricity  0.5
bore  Ø8 at a focus
face  12 mm

Files elsewhere (not hosted by Xem Studio; license as stated by the publisher):
- Henry T. Brown (1868, public domain): Five Hundred and Seven Mechanical Movements — scan on archive.org — web — Publisher's page; dimensions are facts — https://archive.org/details/fivehundredseven00browiala
- 507movements.com: Brown's movement No. 33: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_033.html
- Xem Studio: drawing — web — Publisher's page; dimensions are facts — https://xemstudio.com/objects/elliptical-gears-focus-mechanism/

Free files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/elliptical-gear-m1-5-31t-e0-5-focus-bore/index.json
API: https://xemstudio.com/api/geometry?object=elliptical-gear-m1-5-31t-e0-5-focus-bore