Where:
The primary goal in the early design phase is determining the "travel" or displacement based on the pinion's rotation. Module ( rack and pinion calculations pdf
$$v = \frac\pi \times d \times n60,000 \quad (\textif d \text is in mm, v \text in m/s)$$ $$v = \frac\pi \times d \times n12 \quad (\textif d \text is in inches, v \text in ft/min)$$ Where: The primary goal in the early design
Used to calculate the bending strength of the gear teeth: rack and pinion calculations pdf
v equals the fraction with numerator pi center dot cap D center dot n and denominator 60000 end-fraction is rotational speed in RPM and is diameter in mm) Pitch and Module:
$$\textTravel = \pi \times d$$