Rack & Pinion Displacement
Compute the linear travel per revolution and total displacement of a rack from pinion module m, teeth Z and number of revolutions.
Inputs
Formula
Fundamentals
Compute the linear travel per revolution and total displacement of a rack from pinion module m, teeth Z and number of revolutions.
This tool computes Rack & Pinion Displacement from the formula: travel/rev s0 = π·m·Z; total s = s0·n
History
Design theory of gears, threads and bearings matured with machine tools and standardisation (AGMA, ISO) since the Industrial Revolution.
Engineering applications
Used for transmission design, joint strength checks and component selection.
Glossary
| Module m | Input parameter |
| Pinion teeth Z | Input parameter |
| Revolutions n | Input parameter |
| Travel per rev | Output result |
| Total travel | Output result |
How to use
- Fill in Module m, Pinion teeth Z, Revolutions n in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Travel per rev, Total travel in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：travel/rev s0 = π·m·Z; total s = s0·n
输入变量：
- Module m
m— mm - Pinion teeth Z
Z - Revolutions n
n
输出结果：
- Travel per rev
s0— mm - Total travel
s— mm
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 travel/rev s0 = π·m·Z; total s = s0·n，取 Module m = 3 mm；Pinion teeth Z = 20；Revolutions n = 10。
代入计算得：Travel per rev = 188.5 mm；Total travel = 1,885 mm。
Key Points
- Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
- Compare stress with allowable stress and keep a safety factor (≥1.5, ≥2 for critical parts).
- For high speed/load also check lubrication, heat and fatigue life, not just static strength.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Module m (mm) | m | mm | 3 |
| Pinion teeth Z | Z | 20 | |
| Revolutions n | n | 10 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Travel per rev | s0 | mm |
| Total travel | s | mm |
Applications
- Common engineering use cases