Gear Library
Production-ready gear profiles. Mathematically exact.
Generate involute spur gears, helical gears, rack & pinion pairs, and worm drives directly inside Fusion 360 — as sketch profiles, extruded solids, or helical sweeps. Every profile is computed from first principles: true circular arcs at root and tip, conjugate tooth flanks, and real-time derived values shown as you type.
Supported profiles
Five gear types. One add-in.
Each type has its own tab in the Gear Library dialog. Parameters are validated in real time and derived values update as you type.
Involute Spur Gear
General-purpose parallel-shaft power transmission
The workhorse of mechanical design. True involute tooth flanks are generated as separate splines per flank — never one continuous spline — with genuine circular arcs at tip and root cusps. Profile shift support prevents undercut on low-tooth-count gears.
Helical Gear
Smooth, quiet operation; reduced noise vs. spur
Identical to the spur gear engine with an additional helix angle parameter. The helix angle controls the direction and pitch of the face-width sweep. When paired with a rack, the helix angle auto-syncs between tabs so the rack-and-pinion geometry is always consistent.
Rack & Pinion
Rotary-to-linear motion; CNC drives, actuators
The rack tab generates a linear rack with straight pressure-angle flanks — the mathematically exact conjugate to the involute pinion. Body height, tooth count, and total rack length are all configurable. Module and pressure angle must match the mating gear; mismatches are flagged on generation.
Worm & Worm Wheel
High-ratio reduction; self-locking mechanisms
ZA (Archimedean) worm geometry with straight flanks in the axial cross-section. The worm pair tab generates both the worm and wheel in a single workflow. Lead angle is auto-calculated from starts and diameter quotient; center distance is derived automatically.
Cycloidal Gear
Coming SoonClocks, instruments, low-backlash robotics
Math is already implemented — epicycloid for the addendum flank, hypocycloid for the dedendum flank, with rolling circle radius = m/2 for standard cycloidal gearing. The UI tab ships in Phase 2.
- ① Module (m) — tooth size1 module = 1 mm pitch radius per tooth. Standard series: 0.5, 0.8, 1, 1.5, 2, 2.5, 3. Imperial: m = 25.4 ÷ DP.
- ② Teeth (z) — tooth countMin 3; below 8 triggers undercut warning. At 20° PA, z ≥ 17 avoids undercut with zero profile shift.
- ③ Pressure angle — flank contact angle20° global standard; 25° for heavy load; 14.5° legacy. Must be identical on all mating gears.
- ④ Profile shift (x) — pitch circle offsetPositive shift reduces undercut on small tooth counts. Mating gears need sum-of-shifts correction to maintain center distance.
- ⑤ Flank resolution — spline accuracyPoints per tooth flank. 20 = fast preview; 40 = standard; 80 = large gears or fine detail.
- ⑥ Build — output geometrySketch drops a curve. Extrude adds face-width. Helical sweep adds helix angle (set to 0 for spur; 15–25° for helical).
- ⑦ Hub hole — center boreMust be smaller than root circle diameter. Leave unchecked if the gear mounts on a separate boss.
- ⑧ Pitch diameterPitch dia = m × z. This is the meshing reference circle.
- ⑨ Base circleBase circle = Pitch dia × cos(PA). Involute flanks unwind from this circle. Must be smaller than root circle or tooth profile becomes undercut.
- ⑩ Center distanceC = m × (z₁+z₂) / 2. For matched-module gears. Profile shifts affect this — consult the sum-of-shifts formula if x₁+x₂ ≠ 0.
- ① Module (m) — shared moduleBoth the worm thread pitch and the wheel tooth size use the same module.
- ② Worm starts (z_w) — thread starts1 = highest reduction, self-locking tendency. 2–4 = good back-drivability. Max 6. Lead angle increases with more starts.
- ③ Wheel teeth (z_g) — gear ratioGear ratio = z_g / z_w. 40 teeth ÷ 2 starts = 20:1 ratio.
- ④ Diameter quotient (q) — worm slendernessq = worm pitch diameter / m. Standard range 4–25; q=10 is typical. Higher q = fatter, stronger worm; lower q = more slender.
- ⑤ Pressure angle — tooth flank angle20° standard for worm gearing.
- ⑥ Lead angleLead angle = atan(z_w / q). Must be > ~6° for back-drivability. Below 4° the gear is self-locking (cannot be back-driven).
- ⑦ Gear ratioGear ratio = z_g / z_w. High ratios in a single stage are the worm's key advantage over spur geartrains.
- ⑧ Center distanceC = m × (q + z_g) / 2. The physical center-to-center distance between worm shaft and wheel shaft.
- ⑨ LeadLead = π × m × z_w. Axial distance the worm advances per wheel revolution.
Real-time computation
Derived values update as you type
Every parameter you enter immediately updates a panel of computed geometry values. No manual calculation needed — the wizard does the math.
What gets computed
- Pitch diameter — m × z — the reference circle for meshing calculations
- Base circle — pitch dia × cos(α) — the origin of the involute curve
- Tip & root circles — addendum and dedendum applied to pitch circle, adjusted for profile shift
- Circular pitch — π × m — arc length per tooth on the pitch circle
- Center distance (spur pair) — m × (z1 + z2) / 2
- Worm lead angle — atan(z_w / q) — auto-calculated, shown read-only
- Rack total length — n_teeth × π × m — updates with tooth count
Parameter reference
Parameters at a glance
All parameters accept decimal input. Module is always in millimetres.
| Parameter | What it controls | Typical range | Notes |
|---|---|---|---|
m — Module | Tooth size; scales the entire gear proportionally | 0.5 – 10 mm | Imperial: DP = 25.4 / m. All outputs in mm. |
z — Tooth count | Number of teeth; sets pitch diameter for a given module | ≥ 3 (≥ 8 recommended) | Warning below z = 8. Undercut risk below z = 17 at 20° PA with x = 0. |
α — Pressure angle | Flank angle; affects tooth strength and separating force | 20° (standard) | 14.5° legacy; 25° heavy loads. 20° is ISO/ANSI standard. |
x — Profile shift | Radial offset of the gear cutter from the pitch circle | −0.5 to +0.5 | Positive shift reduces undercut. Mating gears need matching corrections. |
β — Helix angle | Tooth wrap angle over face width | 15° – 30° | Helical gears only. Higher = smoother but more axial load. 0° = spur. |
z_w — Worm starts | Number of worm thread starts; sets gear ratio with z_g | 1 – 6 | 1 start = self-locking tendency. 4+ starts = easier back-drive. |
z_g — Wheel teeth | Worm wheel tooth count | ≥ 6 | Gear ratio = z_g / z_w. Larger z_g = higher reduction. |
q — Diameter quotient | Worm pitch diameter relative to module: d_w = m × q | 4 – 25 (ISO) | q = 10 is a typical starting point. Controls lead angle via atan(z_w / q). |
| Body height (rack) | Depth of rack body below the pitch line | ≥ 1 × m | Dedendum + structural margin. Does not affect tooth geometry. |
Engineering guidance
Things worth knowing
Practical notes for getting useful gears, not just geometrically valid ones.
Profile shift and undercut
Undercut occurs when the tip circle of the mating gear digs into the root of this gear below the base circle. At 20° pressure angle with zero profile shift, undercut begins below z = 17. Below z = 8 the Gear Library shows a warning.
A positive profile shift (x > 0) moves the pitch circle outward, eliminating undercut on low-tooth gears. The catch: the mating gear needs a matching negative shift, or centre distance and meshing geometry must be recalculated. Always check both gears in a pair together.
Module vs. Diametral Pitch
Module is the metric standard (ISO): m = pitch diameter / tooth count. Diametral Pitch is the US customary equivalent: DP = tooth count / pitch diameter (inches). The conversion is m = 25.4 / DP.
The Gear Library works exclusively in module. To match an imperial gear, convert its DP to module first and verify the pressure angle also matches — metric and imperial gears are not interchangeable even if module converts cleanly.
Pressure angle selection
20° is the global standard for most applications — strong tooth, reasonable separating force, available off-the-shelf. 14.5° is legacy (pre-1950s); avoid for new designs. 25° gives a stronger tooth with more separating force; useful for high-load gearboxes where bearing loads are already accounted for.
Every gear in a mating pair must share the same pressure angle. There is no correction factor that makes 20° and 25° gears mesh correctly together.
Center distance (spur/helical pairs)
For a standard (zero-shift) pair: C = m × (z1 + z2) / 2. With profile shift, centre distance changes and both gears must be designed together — use the mating gear fields in the Gear Library dialog to keep geometry consistent.
For worm pairs: C = m × (q + z_g) / 2. This is shown read-only in the derived values panel once module, diameter quotient, and wheel teeth are set.
Helical gear angle selection
15° – 30° is the practical range for smooth, quiet operation. Lower angles approach spur gear noise levels; higher angles increase axial thrust load on bearings. 20° is a good default for most applications.
Double-helical (herringbone) gears cancel the axial thrust but cannot be generated directly — produce two mirrored helical bodies and merge.
Worm back-drivability
Lead angle (γ = atan(z_w / q)) determines whether the worm drive can be back-driven from the wheel side. Below ~4°: self-locking (wheel cannot drive worm). Above ~6°: back-drivable. Between 4° and 6°: ambiguous — depends on lubrication and material friction.
Self-locking is useful for hoists and positioning mechanisms but back-drivability is required for any application that needs to be manually adjusted or powered from the output side.
Why separate splines per flank matters
A common shortcut in parametric gear generators is to fit one continuous spline across the full tooth profile — from root fillet through the flank to the tip. This works visually but overshoots at the root cusp, producing a tooth that is geometrically incorrect (the spline pulls away from the true involute near the base circle).
The Gear Library uses separate splines per tooth flank joined by true circular arcs at the tip and root. The root fillet is a circular arc that is tangent to the dedendum circle and the flank spline — not a single curved segment trying to do everything. The result is geometrically correct, interference-free tooth geometry that CAM tools can use directly for gear hobbing simulation or mesh analysis.
Installation
One add-in, two tools
The Gear Library ships inside EqSketch. Installing EqSketch gives you both.
Download EqSketch
Download the .zip from the link below. It contains the full add-in including
the Gear Library, EqSketch, and the saved gear library file.
Extract to the Fusion 360 add-ins folder
Unzip into your Fusion 360 add-ins directory:
Windows: %APPDATA%\Autodesk\Autodesk Fusion 360\API\AddIns\
macOS: ~/Library/Application Support/Autodesk/Autodesk Fusion 360/API/AddIns/
Enable in Fusion 360
Open Fusion 360 → Tools → Add-Ins → Scripts and Add-Ins → select EqSketch → Run. Tick "Run on Startup" to keep it active between sessions.
Access the Gear Library
In a sketch: Sketch → Create → Gear Library.
For direct solids: Solid → Create → Gear Library.
saved_gears.json inside the add-in folder. Back this file up before
uninstalling if you want to keep your saved profiles.
Troubleshooting
Common errors & fixes
GearParameterError: Tooth count z must be >= 3
The minimum physically realisable involute gear is three teeth. Set z to at least 3. For anything functional, z ≥ 8 is strongly recommended — the add-in shows a warning between 3 and 7 but still generates the profile.
Tooth tip vanishes on the rack
Occurs when the combination of pressure angle and positive profile shift makes the half-width of the rack tooth tip zero or negative. The geometry literally has no tooth left. Fix: reduce the pressure angle (try 20° if you are using 25°) or reduce the profile shift toward zero.
Module m must be positive
Module must be a positive non-zero number. Check that the module field is not blank, zero, or contains a non-numeric character. If you are importing parameters programmatically, verify the value before passing it to the wizard.
Starts z_w must be 1–6
Worm start counts above 6 are outside the ISO manufacturing norm and are not supported. 1 start gives the highest reduction with the most self-locking tendency; 4–6 starts are easier to back-drive and have higher efficiency. If you need more than a 6-start worm, redesign as a helical gear stage instead.
Diameter quotient q must be 4–25
Per ISO 6336, the diameter quotient for worm gears is constrained to the range 4–25. A value of q = 10 is a sensible starting point. Values outside this range produce worms that are impractical to manufacture with standard tooling.
The gear and rack don't mesh cleanly in the assembly
Module AND pressure angle must match exactly between the gear tab and the rack tab. Check both fields. A rack generated at m=2, α=20° will not mesh with a gear generated at m=2, α=25° — the flanks make point contact at the wrong angle. If you changed one tab, re-check the other.
Helical sweep fails in Fusion 360
Two common causes: (1) face width is zero or negative — enter a positive value in the face width field. (2) Helix angle is at an extreme — keep it strictly between 0° and 90° exclusive; exactly 0° falls back to a spur extrude automatically but values very close to 90° may cause geometric failures.
The gear profile looks wrong at the root — it's not a straight line
This is correct. The root of an involute gear tooth is a fillet arc, not a straight line. The circular arc at the root connects the two tooth flanks tangentially to the dedendum circle. A straight-sided root would be incorrect geometry (and much weaker). If you are comparing against a reference and the shapes don't match, check that the reference is also using full fillet root geometry rather than a simplified "full-depth" approximation.
Get EqSketch
Includes the Gear Library, EqSketch sketching tools, and all future gear types — in a single Fusion 360 add-in.