Gears & VEX
Agenda
gear testing
apparatus
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Essential Terminology
Gear Types
Gearing Up/Gearing Down
Direction
Gear Ratios
Example
Application: Sumo-Bot Competition
Essential Terminology
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Driver – gear attached to a motor
Follower – gear doing useful work
Idler – gear between the driver and follower
Gear Train – a row of gears
Geared Up – the follower moves faster than the
driver
• Geared Down – the follower moves slower than the
driver
• Compound gears – a gear train with multiple gears
on one axle
Do you get it?
B
A
motor
• Which gear is the driver (A or B)?
• Which gear is the follower (A or B)?
Do you get it?
B
A
motor
• Which gear is the driver (A or B)? → A
• Which gear is the follower (A or B)? → B
Do you get it?
wheel
motor
A
B
C
• Which gear is the follower (A, B, or C)?
• Which gear is the driver (A, B, or C)?
• Which gear is the idler (A, B, or C)?
Do you get it?
wheel
motor
A
B
C
• Which gear is the follower (A, B, or C)? → C
• Which gear is the driver (A, B, or C)? → A
• Which gear is the idler (A, B, or C)? → B
Gear Types
spur gears
differential
bevel gears
rack & pinion
worm gear
Spur Gears
12 tooth
24 tooth
84 tooth
36 tooth
60 tooth
Worm Gears
Worm gears allow axles at
right angles to transfer
rotational motion.
worm gear
Bevel Gears
Bevel gears allow
rotational motion to
be transferred at
right angles.
Rack & Pinion
pinion
rack
Racks and pinions are used to translate rotational motion into linear motion.
Differential
Differentials are devices that allow each of the axles to rotate at different speeds, while
supplying equal torque to each of them.
Sprockets & Chains
Sprockets inside the same chain rotate in the same direction.
Sprockets outside the chain rotate in the opposite direction.
Pulleys & Belts
Pulleys and belts are not available for VEX
Sometimes tank treads can be used as belts.
Direction
follower
• even number of gears:
driver & follower turn in
opposite directions
• odd number of gears:
driver & follower turn in
same direction
driver
driver
follower
follower
driver
Did you get it?
driver
Would the follower gear move clockwise or counterclockwise?
Did you get it?
driver
Would the follower gear move clockwise or counterclockwise?
Did you get it?
driver
Would the follower gear move clockwise or counterclockwise?
Did you get it?
driver
Would the follower gear move clockwise or counterclockwise?
Geared Up
• large driver turns
small follower
• increases speed
• decreases torque
(turning force)
follower
driver
driven gear
follower gear
Geared Down
• small driver turns
large follower
• increases torque
(turning force)
• decreases speed
driver
follower
driven gear
follower gear
Gear Analysis
To analyze any gear train you need to:
1. Locate the driver gear
2. Locate the follower gear
3. Calculate the Gear Ratio
Use the following rules to calculate gear
ratios.
Gear Ratios
(determining what a gear will do)
follower t eeth
gear ratio 
driver tee th
Example Gear Ratio:
– ⅓ or 1:3
– read as 1 to 3
– 1 turn of the driver will turn the follower 3 times
What is the gear ratio?
84 tooth driver
60 tooth follower
What is the gear ratio?
driver
follower
gear ratio 
follower t eeth 60 teeth 5


driver tee th
84 teeth 7
Long Gear Trains
The gear attached to the motor is the driver.
The gear doing work is the follower.
All in-between gears are idlers.
Ignore the idler gears!
Follower
Driver
Idlers
Gear Ratio = 24/40
= 3 /5
3 turns of the 40
tooth gear will
turn the 24 tooth
gear 5 times.
Compound Gears
(Multiple Gears on One Axle)
1.
2.
3.
Pair up drivers and followers
Start a new driver/follower pair if an axle has a second gear attached.
Multiply the gear ratios of all the driver/follower pairs.
D2
Gear 1 = 12 teeth
Gear 2 = 36 teeth
Gear 3 = 12 teeth
Gear 4 = 60 teeth
Compound Gears
(Multiple Gears on One Axle)
1.
2.
3.
Pair up drivers and followers
Start a new driver/follower pair if an axle has a second gear attached.
Multiply the gear ratios of all the driver/follower pairs.
Gear 1 & Gear 2:
follower 36 3


driver
12 1
D2
Gear 1 = 12 teeth
Gear 2 = 36 teeth
Gear 3 = 12 teeth
Gear 4 = 60 teeth
Compound Gears
(Multiple Gears on One Axle)
1.
2.
3.
Pair up drivers and followers
Start a new driver/follower pair if an axle has a second gear attached.
Multiply the gear ratios of all the driver/follower pairs.
Gear 1 & Gear 2:
follower 36 3


driver
12 1
D2
Gear 3 & Gear 4:
follower 60 5


driver
12 1
Multiply the gear ratios:
Gear 1 = 12 teeth
Gear 2 = 36 teeth
Gear 3 = 12 teeth
Gear 4 = 60 teeth
3 5 15
x 
1 1 1
Compound Gears
(Multiple Gears on One Axle)
1.
2.
3.
Pair up drivers and followers
Start a new driver/follower pair if an axle has a second gear attached.
Multiply the gear ratios of all the driver/follower pairs.
Gear 1 & Gear 2:
follower 36 3


driver
12 1
D2
Gear 3 & Gear 4:
follower 60 5


driver
12 1
Multiply the gear ratios:
Gear 1 = 12 teeth
Gear 2 = 36 teeth
Gear 3 = 12 teeth
Gear 4 = 60 teeth
3 5 15
 
1 1 1
15:1
Calculate the Gear Ratio
(Assume the last axle does the useful work)
60t
36t
12t
12t
4
12t
1
36t
2
3
Calculate the Gear Ratio
(Assume the last axle does the useful work)
60t
Pair 1:
36t
follower 36 3


driver
12 1
12t
12t
4
12t
1
36t
2
3
Calculate the Gear Ratio
(Assume the last axle does the useful work)
60t
Pair 1:
36t
follower 36 3


driver
12 1
12t
12t
4
12t
1
36t
2
3
Pair 2:
follower 36 3


driver
12 1
Calculate the Gear Ratio
(Assume the last axle does the useful work)
60t
Pair 1:
36t
follower 36 3


driver
12 1
12t
12t
4
12t
1
36t
2
3
Pair 2:
follower 36 3


driver
12 1
Pair 3:
follower 60 5


driver
12 1
Calculate the Gear Ratio
(Assume the last axle does the useful work)
60t
Pair 1:
36t
follower 36 3


driver
12 1
12t
12t
4
12t
1
36t
2
Pair 2:
follower 36 3


driver
12 1
3
Pair 3:
follower 60 5


driver
12 1
Multiply the gear ratios:
3 3 5 45
  
1 1 1 1
45:1
Team Unlimited’s
2-Speed Transmission
Calculate This:
60 tooth
36 tooth
60 tooth
36 tooth
60 tooth
60 tooth
Is this transmission currently geared up or down? → geared down
What is the current gear ratio of this transmission? → 60:36 = 5:3
What is the gear ratio of the other set of gears? → 60:60 = 1:1
Calculate This:
60 tooth
36 tooth
60 tooth
36 tooth
60 tooth
60 tooth
Is this transmission currently geared up or down? → geared down
What is the current gear ratio of this transmission? → 60:36 = 5:3
What is the gear ratio of the other set of gears? → 60:60 = 1:1
Sumo-Bot
• All robots are placed in a 10’
x 10’ field
• If any part of a robot touches
the field wall, it is removed
• The last robot left on the field
wins!
Good Luck!
Hint: use gears to get the perfect combination of speed & torque
Thanks/Resources
• Teaching Gear Theory to Students
• CMU's Vex Curriculum: Gearbox Lesson