Wave Robotics
Gear Ratios
Objective:
Use Vex parts to understand how gear ratios work. Learn how to
calculate a gear ratio, and how RPM translates to robot speed.
Team:
4- 6 per team
Supplies:
Assortment of Vex Parts: 2.75” wheels, 12, 36, 60 and 84 tooth gears.
There are many different ways to use gears to increase the speed or torque of a motor. Speed
and torque are related as follows: An increase in speed decreases torque and an increase in
torque requires a decrease in speed. All of the principles discussed in this activity apply to
chain and sprockets the same as gears.
Simple Gear Ratios
A simple geartrain uses just two gears. The difference in gear teeth between the two gears
makes the ratio. For example, a 36 tooth gear driving a 12 tooth gear creates a 1:3 gear ratio.
This means that for every one turn of the 36 tooth gear, the 12 tooth gear turns 3 times. For
calculation purposes, 1:3 can also be displayed as 3/1.
Compound Gear Ratios
Below are two examples of compound gear ratios. One is linear, the other uses multiple shafts
in tandem. When calculating a compound ratio, the result is the product of each simple ratio.
GR1 x GR2 = GR
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Gear Ratios
Activity 1
Use five of the gears provided to create a gear ratio of 1:5. You may not use more than two
gears of any one size. Show your math. Mount them to a vex frame and add a wheel to the
shaft of the last gear.
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Gear Ratios
Activity 2
Construct an assembly similar to the one above. Install a hand crank in place of the motor.
Select the appropriate gears to create a 1:21 gear ratio. Show any math you did to determine
what gears you chose.
Change the assembly above to a 1:7 ratio by only changing one gear. Keep this assembly for
Activity 3.
RPM and Linear Speed
When we define requirements for our robot, often we define a specific speed that we need the
robot to move at. We then select motors that can withstand the constant use and abuse. From
there we need to figure out what gearing we need to use to get the desire speed. Based on the
RPM of the motor, and the required speed we can determine our gear ratio using the following
equation.:
Df x π x RPMgeared x 1/60 =Speed (ft/sec) OR 1/(Df x π) x 60 x 1/Speed (ft/sec) = RPMgeared Definitions Df x π 1/60 RPMgeared = Diameter of wheel in feet times pi = Distance in feet travelled in one revolution = 1 minute per 60 seconds = RPMmotor x Gear Ratio The diagrams below show how the units cancel to convert Diameter (ft) x RPM into ft/sec:
ft rev rev min min sec = ft/sec 1 60 = ft/sec OR
Df x π 1 Page | 3 RPMgeared Wave Robotics
Gear Ratios
Based on the formula, if I have a motor that does 100 RPM, a wheel that is 2.75” (.20833ft), and
a required speed of 5 ft/sec, the calculation would look like this:
.20833 x RPMgeared = 5
5/.20833 = RPMgeared
RPMgeared = 24
Now calculate the Gear ratio:
RPMmotor / RPMgeared
100/24 or 25:6
Activity 3
Using the 1:7 compound geartrain from activity 2, calculate the speed of the wheel in ft/sec.
Motor RPM = 100
Gear Ratio = 1:7
Df = 2.75” (.20833 ft)
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