Rack And Pinion Calculations Pdf [work]
Rack and Pinion Calculations: A Comprehensive Guide
- r = pinion pitch radius (m)
- d = pinion pitch diameter = 2r (m)
- N = number of teeth on pinion
- pr = circular pitch = π·m (m) where m = module
- m = module (mm per tooth) — metric sizing
- P = pitch (for imperial systems often inches per tooth)
- b = face width of gear (m)
- L = rack linear travel (m)
- θ = pinion rotation angle (rad)
- v = linear velocity of rack (m/s)
- ω = angular velocity of pinion (rad/s)
- T = torque on pinion (N·m)
- F = linear force on rack (N)
- i = transmission ratio between pinion rotation and rack travel: L = r·θ for pure rolling
Module ($m$)
The is the ratio of the pitch diameter to the number of teeth. It is the primary metric for gear sizing.
- Gear Ratio: 2:1
- Linear Motion Output: 62.8 mm per rotation
- Torque: 10 Nm (assuming a force of 100 N)
- Select material and compute allowable stress; Safety factor = allowable / computed stress. Typical SF = 1.5–3 depending on application and load variability.