An important abbreviation is DoF, which means degree of freedom and refers to one coordinate of angular motion. All driveline rotational DoFs are measured with respect to a single absolute coordinate system at rest.
Standard symbols for angular motion analysis include the following:
| Symbol | Meaning (Units) |
|---|---|
| r | Gear radius |
| N | Number of gear teeth |
| g | Gear ratio |
| θ | Angle |
| ω | Angular velocity |
| τ | Torque |
For a pair of coupled, coplanar gear wheels, the gear ratio g21 of gear 2 to gear 1 is defined as the ratio of the second gear wheel radius to the first. This definition is equivalent to the ratio of the number of teeth on the second gear wheel to the number of teeth on the first.
g21 ≡ r2/r1 = N2/N1
The gear ratio is the ratio of torques and the reciprocal of the angular velocity ratio.
g21 = τ2/τ1 = ω1/ω2
For gear boxes made of more than two gear wheels, the gear ratio is defined to be the ratio of torques or the reciprocal of the ratio of angular velocities, between the output and input shafts.
If the gear is reversing, the output ω and τ have opposite signs from the input ω and τ.