Industrial Engineering Presets
Kinematic Parameters
Live Mechanical Telemetry
- Pitch Circle Dia. (dp)72.0 mm
- Circular Pitch (p)12.57 mm
- Linear Pitch Speed (v)0.226 m/s
- Tangential Force (Ft)416.7 N
- Radial Separating Force (Fr)151.7 N
- Resultant Tooth Force (Fn)443.4 N
- Mechanical Power (P)94.2 W
- Travel per Turn (Srev)226.2 mm
Physics & Governing Equations
A rack and pinion converts rotational torque into linear drive force through intermeshing gear teeth.
- Pitch Circle Diameter ($d_p$):
dp = m × Z where m is gear module and Z is pinion tooth count.
- Circular Pitch ($p$):
p = π × m (Distance between consecutive teeth centers along the rack).
- Linear Speed ($v$):
v = ω × rp = (2π N / 60) × (dp / 2000) in m/s.
- Tangential Drive Force ($F_t$):
Ft = 2000 × T / dp in Newtons.
- Separating Radial Force ($F_r$):
Fr = Ft × tan(α) pushing pinion and rack apart.
- Line of Action & Pressure Angle ($\alpha$):
The normal contact force acts along the pressure angle vector ($\alpha = 20^\circ$).
Primary Industrial Uses
Rack and pinion systems provide high positioning accuracy, zero slip, and unlimited linear stroke capability.
- CNC Routers & Laser Cutters: High-speed fixed rack drives enable long travel gantries without the rotational whip of lead screws.
- Automotive Steering Gearbox: The steering wheel rotates the pinion, sliding the tie-rod rack left and right to turn wheels.
- Mountain Cog Railways: Steep mountain trains use a center rack track and driven pinion cog to prevent sliding on steep grades.
- Linear Actuator Lifters: High load vertical lifting shuttles and heavy industrial transfer tables.