# Speed Reduction

## Overview

- If you gear your robot too high
- It won’t have enough torque to move (accelerate)
- If you can accelerate, it will be very difficult to control

- If you gear your robot too low
- You will have so much torque, your wheels will slip before you reach max power
- You will move too slow to be effective

- A good robot speed is 8-12 ft/s
- Design your robot so sprockets can be changed easily
- Start at a slow speed, with practice if the driver gets comfortable, change sprockets to increase speed

- Some teams have successfully gone as high as 18 ft/s or as low as 4 ft/s
- Require 2 speed gearbox, cannot rely only on 4 or 18 ft/s speed
- Drivers need a lot of practice to control robots that fast

## Motors

- The CIM motor has an angular velocity of 5310 rpm (+/- 10%)
- Directly using a 6" wheel would convert to 139 ft/s (> 150 km/h)

- Therefore, you must reduce the angular velocity between the motor and the wheel
- This can be done with gears, sprockets, or belts

- Generally, most of the reduction is first done with a gearbox (1 or more stages of gear reduction), then sprockets or belts do the rest
- Coupling motors on the same gearbox increases torque but angular velocity does not change
- This will allow you to accelerate faster and push harder but it will
**not** increase your top speed

## Gear Ratios

- To create a gear ratio using sprockets, the number of teeth on the output of the gearbox should be different that the number of teeth on a sprocket on the driven wheel
- A larger sprocket on the wheel will reduce speed and increase torque
- This is generally what is required to achieve desired speed

- A larger sprocket on the gearbox output will increase speed and reduce torque

- There should not be a sprocket gear ratio between wheels
- The number of teeth on the sprockets that connect the wheels should be the same

- The number of teeth on the sprockets connecting the wheels do not have to be the same as the number of teeth on the sprocket connecting the driven wheel to the gearbox

## Convert motor angular velocity to robot linear velocity

- v = ω ·
*N*_{G} · *D* · π / *x* · *N*_{w} · 720
- ω =
*motor angular velocity (rpm)*
*x* = *gearbox ratio*
- N
_{G} = *# of teeth on sprocket or pulley on gearbox output*
- N
_{W} = *# of teeth on sprocket or pulley on wheel*
- D =
*wheel diameter (inches)*
*v* = *robot linear velocity* *ft/s*

- This equation is very general and does not account for efficiency losses, current, acceleration, etc.