1. Gear Ratios
and
RPM
Calculations

2. The most used drive system on a first robot uses sprockets and chains
The most used drive system on a first robot uses sprockets and chains. It is vital to the success of a robot to properly adjust the size of sprockets in order to obtain the maximum speed and power. Balancing speed versus power can be daunting but with a few basic guidelines it can be made easy. Let ‘s examine a couple things to keep in mind while choosing the right gear ratio . . .

3. Two Broad Types of Sprockets
Driver Sprockets are directly driven by a motor
Driven Sprockets mesh with the driven sprocket

4. Gear Ratio Velocity
First, notice which sprocket has the most teeth. This will be the sprocket that completes one revolution. Take the number of teeth on the driven sprocket and divide that number by the amount of teeth on the driver sprocket.
Driver Sprocket: Teeth
Driven Sprocket: Teeth
30/10 = 3:1 Ratio

5. Revolutions per Minute
To calculate the RPM output of a given gear ratio, take the velocity ratio and multiply that number by the RPM output of the motor source.
Ex. 1:
Motor RPM (60 rpm) x gear ratio (3:1)
= 120 rpm
Ex. 2:
Motor RPM (100 rpm) x gear ratio (1:4)
= 400 rpm

6. RPM with a Compound Gear
The easiest way to calculate RPM on a compound system is to split up the problem into two equations or pairs depending on the amount of gears involved. After finding the ratio for each pair, multiply them together with the motor RPM to get your final RPM.
(see next slide for examples)

7. 3:1 Ratio x 2:5 Ratio x 100rpm = 120 rpm
Ex. 1: This example involves 4 gears. Gear A- Driver Sprocket, Gear B and Gear C are Fixed, and Gear D. The motor RPM in this example will be 100 RPM.
Driver Sprocket-Gear A (30 teeth) / Gear B (10 teeth) = 3:1 Ratio
Gear C (20 teeth) / Gear D(50 teeth) = 2:5 Ratio
3:1 Ratio x 2:5 Ratio x 100rpm = 120 rpm
Ex. 2: This example also involves 4 gears. Gear A- Driver Sprocket, Gear B and Gear C are Fixed, and Gear D. The motor RPM in this example will be 60 RPM.
Driver Sprocket-Gear A (20 teeth) / Gear B (15 teeth) = 4:3 Ratio
Gear C (50 teeth) / Gear D (10 teeth) = 5:1 Ratio
4:3 Ratio x 5:1 Ratio x 60rpm = 400 rpm