Gear Rack Ratio Calculator
Calculate linear rack movement from gear rotation. Essential tool for mechanical design, CNC systems, and robotics applications.
Gear Parameters
Gear module (tooth size)
Teeth on the gear
Direction of gear rotation
Calculation Results
Enter gear parameters and click "Calculate Rack Travel" to see results
Engineering Note
These calculations provide theoretical rack movement. Actual travel may vary due to backlash, manufacturing tolerances, and system compliance.
What Is a Gear Rack Ratio?
A gear rack ratio explains how rotational motion from a gear converts into linear movement of a rack. This fundamental relationship is crucial in many mechanical systems where you need to transform rotary motion into straight-line motion.
Think of a car's steering system - when you turn the steering wheel (rotary motion), the rack moves linearly to turn the wheels. Or consider a CNC machine where rotary motor motion becomes precise linear axis movement.
This calculator helps you determine exactly how far a rack will move for any given gear rotation, making design and troubleshooting much easier.
How the Gear Rack Ratio Works
The relationship between gear rotation and rack movement is surprisingly simple. As the gear rotates, its teeth engage with the straight teeth of the rack, pushing it linearly.
The distance the rack moves depends on three key factors: the gear's module (tooth size), the number of teeth on the gear, and the angle of rotation. Larger gears with more teeth move the rack farther per degree of rotation.
This linear relationship makes rack-and-pinion systems predictable and reliable for precision applications.
Formula Used in the Calculator
Rack Travel Calculations
For Full Revolution: Rack Travel = π × Module × Number of Teeth
For Partial Rotation: Rack Travel = (π × Module × Teeth × Rotation Angle) ÷ 360
Where:
- π = 3.14159... (pi)
- Module = Gear module (mm)
- Teeth = Number of teeth on gear
- Rotation Angle = Angle in degrees
The formula represents the circumference of the gear's pitch circle, which determines how far the rack moves per revolution.
Example Calculation
Gear Parameters
| Parameter | Value |
|---|---|
| Module (m) | 2 mm |
| Number of Teeth (z) | 20 |
| Rotation | 1 Revolution (360°) |
| Rack Travel | 125.66 mm |
Understanding the Result
The rack moves 125.66 mm when the 20-tooth gear completes one full revolution. This equals the circumference of the gear's pitch circle (π × 2 mm × 20 teeth).
Final Note
The Gear Rack Ratio Calculator turns complex motion relationships into clear, usable results. Whether you're designing a system or troubleshooting an existing one, this tool delivers accurate linear movement data in seconds.
Remember that these calculations provide theoretical values. Real-world systems may have slight variations due to manufacturing tolerances, backlash, and system compliance.