# Gear Ratio Calculation

Please note that this document attempts to cover a strong range of scenarios that are likely to be encountered, however it is still likely that subtle changes may be required to suit a particular problem.

## High torque, low speed Applications

### Method

- Determine the minimum gear ratio
- Round the ratio up to the nearest available reduction
- Note, some scenarios might result in the rounded reduction being too great in which case a compromise on the driving motor may have to be made.

- Recalculate output torque to ensure it is greater than required maximum output torque.

### Determining the Minimum Gear Reduction ratio

- Determine the maximum load torque the gear system will have to overcome.
- Determine the maximum torque output the chosen motor can provide for the maximum allowable current; For motor data seek data from the manufacturers website, http://motors.vex.com/ offers a good source of data for FRC legal motors.
- The ratio between the maximum load torque required to the maximum torque output of the chosen motor is the minimum gear ratio required.

**Examples**

**A Gearbox to Drive a Winch to Pull up the Robot**

Suppose a system was considered with the following properties:

- Heave (robot): 40 kg
- Winch diameter: 35 mm
- Driven by a CIM motor
- Breaker: 40 Amps @12V

From the specifications above the maximum load torque can be calculated to be 13.734 Nm (= 20*9.81*0.035).

*CIM Motor data:*

CIM motor power curves

Examining the current draw plot (blue dotted), it can be determined that the motor will spin approximately 3800 RPM or 63.33 RPS or 10.080 radians per second. By examining the torque curve (solid yellow), an output torque of approximately 0.65 Nm.

By applying the the data from above the method described previously the reduction ratio is 21.129; From Vex Pro, the best suited planetary gearbox to this design problem is a 25:1