Rack & Pinion Servo Actuator

This mechanism converts the rotational motion of a servo motor into linear motion using a rack and pinion gear system. Designed for hobby robotics, makers, and students

1. Gear Specifications

A. The Pinion (Motor Gear)

Standard: Spur Gear
Pressure Angle: 20°

Module: 1.5M
Teeth: 14T
Pitch Diameter: 21 mm

B. The Rack (Linear Rail)
Pressure Angle: 20°
Module: 1.5M
Pitch Line: 15 mm
Total Length: 61.2 mm

2. Theoretical Calculations

A. Mounting Center Distance

This is the vertical distance from the Servo Center to the Rack for perfect gear meshing.

D= Rack Pitch Line+ Pitch Radius = 25.5 mm

The Pitch Circle of the pinion is tangent to the Pitch Line of the rack.


B. Linear Displacement & Resolution

The General Formula: To calculate the travel distance for any angle:

D= (Angle/360)*pi*Pitch Diameter

C. Recommendation (Best Settings) For the best stability, do not rotate more than 125 degrees.

• Why: This keeps the movement smooth and safe.

• Result: At 125 degrees, the slider moves about 20.5 mm (Measured).

3. Hardware 

• 7x Screws: M3 x 10mm

• 5x Screws: M3 x 8mm

• 3x Screws: M3 x 12mm

• 5x Heat Inserts: M3 (OD 4.2mm, Length 3-4mm).

• 10x Ball Bearings: 693ZZ (3x8x4 mm).

• 5x Washers: M3 Flat Washers