Stella Academy

mechanics Module

Interactive Simulation Screen

SYS_OK

Lesson Directive // Gears & TorqueREF_CORE

\text{Ratio}

=

N_{\text{driven}}

N_{\text{driver}}

=

\omega_{\text{driver}}

\omega_{\text{driven}}

Hover over a variable in the formula above, or see glossary below:

\text{Ratio}

Gear Ratio

Unitless

N_{\text{driven}}

Driven Gear Teeth

Count

N_{\text{driver}}

Driver Gear Teeth

Count

\omega_{\text{driver}}

Driver Speed

RPM or rad/s

\omega_{\text{driven}}

Driven Speed

RPM or rad/s

Gears are used to transmit rotational motion and torque between shafts. When two gears mesh, they rotate in opposite directions.

INSIGHT: Gears allow us to trade speed for torque, or torque for speed.

The gear ratio is found by dividing the number of teeth on the driven gear by the number of teeth on the driver gear.

INSIGHT: A ratio > 1 means the output is slower but has more torque.

If a small gear drives a large gear, the large gear turns slower but can provide a much stronger twisting force (torque).

INSIGHT: Speed and torque are inversely related in a gear train.

●Telemetry Control Console

CAL_SYS

Adjust Simulator Parameters

Gear Teeth Ratio:2:1 Ratio

Syllabus Worked Example

Q: Find the output torque (\tau_{\text{out}}) if a motor drives a 12-tooth gear at 5 Nm, meshed with a 36-tooth gear.

1.Find the gear ratio: \text{Ratio} = \frac{36}{12} = 3.0.

2.Remember that torque multiplies by the gear ratio.

3.Calculate output torque: \tau_{\text{out}} = \tau_{\text{in}} \cdot \text{Ratio} = 5 \cdot 3.0.

Result:\tau_{\text{out}} = 15 \text{ Nm}