📚 Gear Calculator Help & Documentation

🚀 Quick Start Guide

Basic Gear Calculation

1. Select Units: mm / module or inch / DP
2. Choose Known Type: Usually Module + Teeth
3. Enter Value A: Your module value (e.g., 0.5 mm)
4. Enter Teeth (z): Number of teeth (e.g., 12)
5. Set Pressure Angle: Usually 20° (standard)
6. Click Compute

📐 Gear Formulas Explained

Core Formulas

What it means: The diameter of the pitch circle where gear teeth mesh. This is the fundamental size reference for a gear.

Example: Module 0.5 mm × 12 teeth = 6.000 mm pitch diameter

What it means: The maximum diameter of the gear, measured at the tooth tips (addendum circle). This is what you measure with calipers.

Example: PD 6.000 + 2 × (1 + 0) × 0.5 = 7.000 mm

What it means: The diameter at the bottom of the tooth spaces (dedendum circle). Used for stress calculations.

Example: PD 6.000 − 2 × (1 + 0.25 − 0) × 0.5 = 4.750 mm

What it means: The distance along the pitch circle from one tooth to the next. Must match between mating gears.

Example: π × 0.5 = 1.571 mm

What it means: The diameter of the circle from which the involute tooth profile is generated. Critical for proper meshing.

Example: 6.000 × cos(20°) = 5.638 mm

What it means: Imperial measurement of gear size (teeth per inch of diameter). Higher DP = smaller teeth.

Example: 12 / (6.000 / 25.4) = 50.8 DP

Variable Definitions

Symbol	Name	Description	Typical Values
m	Module	Ratio of pitch diameter to teeth count (metric)	0.3 to 10 mm
z	Teeth	Number of teeth on the gear	8 to 200+
PA	Pressure Angle	Angle of tooth force transmission	14.5°, 20°, 25°
x	Profile Shift	Tooth thickness/center distance adjustment	-0.5 to +0.5
c	Clearance	Gap between tooth tip and root (×module)	0.25 (standard)
DP	Diametral Pitch	Teeth per inch of diameter (imperial)	12 to 120

🔍 Section-by-Section Help

📚 Library & Persistence

Purpose: Save and manage your gear calculations for future reference.

Features:

• 💾 Save XML: Export all saved gears to an XML file for backup or sharing
• ⬇️ Download CSV: Export as spreadsheet-compatible CSV file
• 🗑️ Clear Library: Delete all saved gears (cannot be undone)
• 📥 Import from paste: Paste CSV data to import gears in bulk

CSV Import Format:

note,mode,valA,z,PA,c,x,m,d,OD,rootD,p,baseD,thick_at_pitch,addendum,dedendum,DP
Idler Gear,module,0.5,12,20,0.25,0,0.5,6,7,4.75,1.571,5.638,0.785,0.5,0.625,50.8

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🧮 Single Calculation

Purpose: Calculate all dimensions for a single gear based on known parameters.

Input Modes:

Mode	Value A	When to Use
Module + Teeth	Module (m)	Designing a new gear from scratch (metric)
Diametral Pitch + Teeth	DP	Designing a new gear (imperial)
Outside Diameter + Teeth	OD (mm/inch)	Reverse-engineering an existing gear
Pitch Diameter + Teeth	PD (mm/inch)	When you know the mesh diameter

Profile Shift (x):

• x = 0: Standard gear (most common)
• x > 0: Positive shift - thicker teeth, stronger, larger center distance
• x < 0: Negative shift - thinner teeth, weaker, smaller center distance

🔧 Auto-Match Profile Shift:

If you measured a gear's OD but don't know the profile shift:

1. Set mode to Module + Teeth (NOT "Outside Diameter" mode)
2. Enter the module and teeth count
3. Enter measured OD in "Measured OD" field
4. Click 🔧 Auto-match
5. Calculator finds the best x value to match your measurement

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🔄 Orientation Assistant

Purpose: Determine the best print angle for 3D printed gears.

Priority Options:

• Tooth profile accuracy:
  • Tilt 10–15° from vertical
  • Place supports on hub/face edges
  • Avoid supports on tooth flanks
  • Use fine layer height (0.03–0.05 mm)
• Print success (reduce peel/suction):
  • Tilt 30–40° from vertical
  • Orient concave faces away from build plate
  • Add chamfered drain holes if hollow
  • Reduces layer area and peel forces
• Surface finish (hide support marks):
  • Tilt 20–30° from vertical
  • Place supports on back/hidden face
  • Avoid outer tooth rim

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🧪 Resin & Post-Cure Notes

Purpose: Compensate for resin shrinkage during post-cure.

How to Use:

1. Select your Material
2. Enter known Shrinkage % (or use ring method below)
3. Enter Target OD (auto-filled from compute)
4. Click ⚖️ Apply shrinkage scale
5. Calculator shows scale factor and projected final size

Typical Shrinkage Values:

Resin Type	Linear Shrinkage
ABS-like (Grey/Black)	0.5% - 1.5%
Tough Black	1.0% - 2.0%
Siraya Tech Blu	0.3% - 0.8%
Clear	0.8% - 1.5%

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📏 Calibration - Ring Method

Purpose: Measure actual shrinkage for your specific resin and process.

Procedure:

1. Model a simple ring with 20.00 mm OD and 10.00 mm ID
2. Print the ring (flat orientation recommended)
3. Post-cure following your standard process
4. Measure the OD with calipers
5. Enter measured value and click 📏 Compute shrinkage
6. Calculator determines exact shrinkage % and scale factor
7. Use this scale factor in your slicer for all future prints

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🔗 Mating Gear Checker

Purpose: Calculate center distance for gear pairs.

Standard Gears (x₁ = x₂ = 0):

Profile-Shifted Gears:

Example:

• Gear A: 12 teeth, x₁ = 0.2
• Gear B: 24 teeth, x₂ = -0.1
• Module: 0.5 mm
• Center distance: 0.5 × (12 + 24)/2 + 0.5 × (0.2 - 0.1) = 9.050 mm

⚙️ Common Workflows

Workflow 1: Design New Gear from Scratch

1. Determine required module based on torque/strength needs
2. Choose teeth count for desired speed ratio
3. Set PA = 20°, c = 0.25, x = 0 (standard values)
4. Click Compute
5. Use Orientation Assistant for print setup
6. Apply Shrinkage compensation if 3D printing
7. Click ➕ Add to Library to save

Workflow 2: Reverse-Engineer Existing Gear

1. Count teeth on the gear
2. Measure OD with calipers
3. Set mode to Module + Teeth
4. Estimate module (try common values: 0.5, 1.0, 1.5, etc.)
5. Enter measured OD in "Measured OD" field
6. Click 🔧 Auto-match profile shift
7. Calculator finds the x value that matches your measurement

Workflow 3: Design Gear Pair (Gearbox)

1. Choose module (same for both gears)
2. Choose teeth counts (ratio = z₂/z₁)
3. Compute Gear A and add to library
4. Compute Gear B and add to library
5. Use Mating Gear Checker to verify center distance
6. Apply same shrinkage compensation to both

Workflow 4: Calibrate Your 3D Printer

1. Model 20mm calibration ring
2. Print and post-cure with your standard process
3. Measure with calipers
4. Use Ring Method to calculate shrinkage
5. Apply scale factor in slicer
6. Print test gear and verify dimensions
7. Adjust if needed and document final settings

🔧 Troubleshooting

❌ "Invalid: z + 2*(1+x) must be > 0"

Cause: Extreme negative profile shift makes the calculation impossible.

Solution: Use x > -0.5 for most applications. Very negative shifts are unusual.

⚠️ "Auto-match requires: measured OD..."

Cause: Missing required fields for auto-match.

Solution: Fill in all fields: module/PD/DP, teeth count, PA, clearance, AND measured OD.

⚠️ "Auto-match works with Module, PD, or DP modes only"

Cause: Trying to use auto-match in "Outside Diameter + Teeth" mode.

Solution: Switch to "Module + Teeth" mode first. Auto-match solves for x, so you can't start with OD.

🔢 Calculated OD doesn't match my measurement

Possible causes:

• Wrong module assumption - try adjacent values (0.4, 0.5, 0.6...)
• Wrong pressure angle - try 14.5° or 25° instead of 20°
• Non-standard clearance - try c = 0.2 or 0.3
• Worn or damaged teeth - measure at multiple points
• Imperial vs metric confusion - check your units

🖨️ My 3D printed gear is the wrong size

Checklist:

1. Did you apply shrinkage compensation?
2. Did you use the ring method to calibrate?
3. Did you post-cure the same way as your test ring?
4. Is your slicer scale set correctly?
5. Did you account for both X/Y and Z shrinkage?

⚙️ Gears don't mesh smoothly

Common issues:

• Center distance wrong: Use Mating Gear Checker to verify
• Backlash needed: Scale one gear slightly smaller (99.5-99.8%)
• Pressure angle mismatch: Both must use same PA
• Module mismatch: Both must use same module
• Surface roughness: Sand or polish contact surfaces

📚 Glossary of Terms

Term	Definition
Addendum	Height of tooth above the pitch circle. Formula: m × (1 + x)
Backlash	Clearance between mating teeth to prevent binding. Achieved by reducing tooth thickness or increasing center distance.
Base Circle	Circle from which involute tooth profile is generated. Diameter = d × cos(PA)
Clearance (c)	Radial gap between tip of one gear and root of mating gear. Prevents interference.
Dedendum	Depth of tooth below pitch circle. Formula: m × (1 + c - x)
Diametral Pitch (DP)	Imperial measure of tooth size. Teeth per inch of pitch diameter. DP = z / (d / 25.4)
Involute	Mathematical curve used for gear tooth profile. Allows smooth power transmission at varying center distances.
Module (m)	Metric measure of tooth size. Pitch diameter divided by teeth count. m = d / z
Pitch Circle	Theoretical circle where two gears mesh. Diameter = m × z
Pressure Angle (PA)	Angle at which teeth make contact. Standard values: 14.5°, 20°, 25°. Higher PA = stronger teeth but more radial load.
Profile Shift (x)	Offset of cutting tool during manufacture. Positive shift = thicker teeth, negative = thinner. Used to prevent undercut or adjust center distance.
Root Circle	Circle at bottom of tooth spaces (dedendum circle). Diameter = d - 2 × (1 + c - x) × m
Tooth Thickness	Dimension of tooth at pitch circle. For standard gears: p / 2 (half the circular pitch)
Undercut	Weakness at tooth root caused by cutter interference. Occurs in small gears (z < 17 at PA=20°). Prevented by positive profile shift.

📞 Support & Resources

For additional help:

• Check the main calculator for built-in notes
• Review the CHANGELOG.md for recent improvements
• Consult gear design handbooks for advanced topics
• Test prints are always recommended before production

👥 Credits

This tool was developed with assistance from:

• Claude (Anthropic) - AI assistant for code development and documentation
• Microsoft 365 Copilot - Initial development assistance

Version: 4.12-fixed-v3

Last Updated: 2024

Open source contributions and improvements welcome!