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Contents
Introduction to Gear System 1
Basic in Gear Ratio 3 Exercises with Gear Ratio 4 Gear Ratios Word Problems 6 Exercises with Gears Ratio & RPM (Inverse
Proportion) 7 Exercises on RPM and Distance Traveled
9 Experiment 10
Compound Gear System 12 Exercises 13
Wheels Diameter vs. Distance Traveled 16 Examples 16 Exercises 18
Chassis Turning vs. Encoder (Rotation sensor)
19 Example: 20
Name:
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INTRODUCTION TO GEAR SYSTEM
What is it for?
A gear is a set of toothed wheels (gear wheels or cog -wheels) that work together to
transmit
movement.
Many of the everyday mechanisms and devices we commonly use contain gear wheels.
These
include bicycles, cars, and can-openers.
Gears are used to create these effects:
1. To change the position of a rotating movement. (This is sometimes cal led
applying the
rotation at a distance.)
2. To change the direction of rotation.
3. To increase or decrease speed of rotation.
4. To increase turning force (Th is is sometimes cal led torque.)
Basic Key Words
Driver/Input
The name for a gear wheel that is turned by an outside force (such as that from a
motor or from a person turning a handle) and that also turns at least one other gear
wheel.
Driven/ Follower/Output
The name for a gear wheel that is turned by another gear wheel.
Gear Ratio
A proportion used to compare how two meshed gear wheels move rel ative to each
other. For gears, use the number of teeth for calculation. For pu l leys, use its
diameter for calculati on.
Gearing Down
An arrangement in which a small driver turns a large fol lower, resulting in a slowing
down of the turning. Gearing down produces a powerful turning force (torque).
Gearing Up
As arrangement in which a large driver turns a small fol lower , resulting in a speeding
up of the turning. Gearing up reduces the turning force.
Idler Gear
The name for a gear wheel that is meshed between a
driver and a fol lower. It does not mean it does not move.
It is cal led idler gear because it does not affect t he final
gear ratio.
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Torque (twisting or turning force)
This is inversely proportional to speed . In order to determine both the speed and
force of rotating axles, we need to calculate the Gear Ratio.
Warm up information
speed,
regardless of their sizes. speed and torque speed Gears have a trade-off with turning
force (torque) and turning speed.
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BASIC IN GEAR RATIO
The gear ratio is the ratio of the number of teeth on each ge ar. Here is a gear with 8
teeth
meshed with a gear with 40 teeth.
What does this gear ratio tell us?
The Input/driver g ear wi l l rotate 5X when the output/fol lower gear rotates 1X
The Input/driver gear wi l l rotate 5X faster than the output/fol lower gear.
This contraption is meant to increase torque
Assume 40-t == driver
gear
8-t == driven gear
Gear ratio== 8
40
Or 1
5
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Exercises with Gear Ratio
Based on the information provided about the gears shown on this page, answer the
fol lowing questions.
1. What is the gear rat io for the combination?
2. How many times must the driving gear go around for the Driven (or cal led
Fol lower) gear to make one revolution?
3.
Note that the driving gear is always on the r ight. Possible gear sizes are 40, 24, 14
and 8 tooth gears.
e.g.example 1: 24-tooth gear driving an 8-tooth gear . Gear Ratio = 8
24 =
1
3
It means : driver gear turns 1x == Driven gear turns 3x
example 2: 40-tooth gear driving an 24-tooth gear . Gear Ratio = 24
40=
3
5
It means : driver gear turns 3x == Driven gear turns 5x
It means:
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It means:
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It means:
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It means:
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It means:
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Gear Ratios Word Problems
Mary and Tim are designing robots with different gear ratios to complete various
tasks.
1) Mary and Tim want to design a robot with as high a gear ratio as possible in order
to cl imb the greatest possible slope. They have 40, 24, 14, 12 and 8 tooth gears
avai lable.
a. - What gear should they choose as their Driven gear?
b. - What gear should they choose as their driving gear?
c.
d. - What would be the gear ratio of this robot?
e.
2) Mary and Tim want to design a robot with as low a gear ratio as possible so that i t
can reach the greatest possible speed. They have pul leys with diameters of 5, 7
and 9 centimeters avai lable.
a. - What diameter pul ley should they choose as their Driven pul ley?
b. - What diameter pul ley should they choose as their driving pul ley?
c. - What would be the gear ratio of this robot?
3) Mary and Tim want to design a robot with a gear ratio of 2, using a 16 tooth
Driven gear. They have 40, 24, 16, 14 and 8 tooth gears avai lable. What gear
should they choose as their driving gear?
4) Mary and Tim want to design a robot with a gear ratio of 3/2, using a 6 cm
diameter Driven pul ley. They have pul leys of 3, 4, and 9 cm diameter avai lable.
Which should be their driving pul ley?
5) Mary and Tim want to design a robot with a gear ratio of 2/3, using a 60 tooth
driving gear. They have 10, 20, 40, and 90 tooth gears avai lable. What gear
should they choose as their Driven gear?
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Exercises with Gears Ratio & RPM (Inverse Proportion)
(Understanding the concept of Inverse Proport ions.)
For each set of gears first determine the gear ratio, and reduce that to its smallest
proportion. Use the reduced gear ratio for problems A and B.
In problem A assume that the dr iver gear moves at a constant 100 RPM. At what
speed is the driving gear rotating?
In problems below, assume that the Driven gear moves at 100 RPM. At what speed is
the driving gear rotating?
Note: The driving gear is always on the right Possible gear s izes are 40, 24, 14 and 8
tooth gear.
Sample question:
Sample Answer:
Gear Ratio = 5
1 .
8-t driver turns 5 x == 40-t driven turns 1x
For Problem A:
Given: 8-t driver gear turns = 100 times
40-t driven gear turns = 100 times /
gear ratio
= 20 times
For Problem B:
Given : 40-t driven gear turns = 100 times
8-t driver gear turns = 100 times * gear ratio
= 500 times
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Exercises on RPM and Distance Traveled
Resolve the fol lowing questions using the fol lowing gear system.
Note:
1. Driving gear is always on the right. Possible gear sizes are 40, 24, 14 , and 8
tooth gears. 2. Leave the PI as a symbol in your answer. Do not need to resolve PI.
3. Review : Gear Ratio = Driven gear / Driving gear
1. Assuming the circumference of the wheel and the RPM of the motor are
exactly the same for al l experiments, which gear ratio would create the
most speed. A, B or C? Why did you choose that answer?
2. If the driving gear is moving at 100 RPM, how fast wi l l the Driven gear
move for pictures A, B and C?
3. If the driving gear moves at 1oo RPM and the circumference of the wheel
is 5.0 cm, how far wi l l the robot move in 2 minutes for pictures A, B and
C?
4. If the driving gear moves at 200 RPM and the diameter of the wheel is 2
cmon, how far wi l l the robot move in 3 minutes for pictures A, B and C?
5. If the driving gear moves at 200 RPM and the radius of the wheel is 5 cm,
how far wi l l the robot move in 3 minutes for pictures A, B and C
8-
t
24-t
24-t
14-t
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Experiment
WHAT IS THE BIG DEAL ABOUT GEAR RATIO?
- Strength …
- Speed …
- Distance, of course.
- One more… _______________________
Let ’s do a simple experiment . Bui ld a robot (preferably just a vehicle chassis, not
walking chassis). Make sure you can easi ly change the gear ration at ease.
Hypothesis: _Gearing down wil l yield high accuracy_
Independent Variable: Time in seconds
Dependent Variable: Distance in cm
Control Variable: Gear Ratios
Test 1
a. Create a configuration with the first gear ratio.
b. Program it to run for 5 seconds.
c. Run it for 3 times, and measure the distance it travels for each time.
d. Write down the error margin for each run.
e. Take an average.
f . Plot i t on the graph.
Test 2
a. Modify the gear ratio to gearing down.
b. Program it to run for 5 seconds
c. Run it for 3 times, and meaure the distance it travels for each time.
d. Write down the error margin for each run.
e. Take an average.
f . Plot i t on the graph.
Test 3
a. Modify the gear ratio again to gear it down.
b. Program it to run for 5 seconds
c. Run it for 3 times, and meaure the distance it travels for each time.
d. Write down the error margin for each run.
e. Take an average.
f . Plot i t on the graph.
For example:
Gear Ratio : 5: 1 . Duration: 5 seconds
# of trial Error Margin (after calculating the
average
1s t : 13 cm 1
2nd : 12 cm 0
3 rd : 11 cm -1
Overal l Average : 12cm
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Terminate the robots in 5 seconds. Measure the distance.
Special Note:
Students are expected to use the fol lowing procedure:
Identi fy gear sizes by counting teeth
* Determine the gear ratio of each pair of gears
* Identi fy the information required by the question
* Reconstruct the equations provided as an example
* Enter the data provided into these equations
Dis
tan
ce
Gear Ratio
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COMPOUND GEAR SYSTEM
When a system consists of more than one pair of gears is called a compound gears
system.
A compound gear ratio is the overal l gear ratio of compound system .
Before you calculate, you must find the “pairs”. Pair = one is driving another one, but
not on the same axle.
Free hand Sketch of a Top View of a Compound Gear System
Reduce Gear Train
Extreme gear ratios can be achieved by
stacking gears in a gear box.
Incredible changes in both speed and
torque can be achieved with a l i tt le
ingenuity.
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Exercises
Instruction:
On your worksheet, you should do a free-hand sketch of each compound gear system,
and then fol lowed by answering the gear ratios for al l pairs and final gear ratio.
1) Calculate the gear ratio of the fol lowing identical compound gear system with
reverse roles:
Final Output Shaft Main Driver
Pair 1 Gear Ratio =_________
Pair 2 Gear Ratio = ________
Final Gear Ratio = _________
Main Driver Final Output Shaft
Pair 1 Gear Ratio =_________
Pair 2 Gear Ratio = ________
Final Gear Ratio = _________
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2) What are the compound gear ratio of these gearboxes? The input axle is on the
left, and the output axle is on the right.
3) What is the compound gear ratio of this gear box:
G.R. for Pair 1:
G.R. for Pair 2:
Final G.R.
G.R. for Pair 1:
G.R. for Pair 2:
Final G.R.
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4) What is the compound gear ratio of this gear box:
Note:
a) The worm gear must be the driver gear.
b) Worm drivers the 24-t . This is on the axle with this 40-t.
c) The same 40-t drives another 40-t .
d) 40-t and 16-t are on the same axle.
e) The 8-t is driven by the 16-t .
f) The same 8-t is on the same axle with another 8-t inside. This 8-t drives an
24-t.
g) This 24-t – the Final Output Shaft.
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WHEELS DIAMETER VS . DISTANCE TRAVELED
Examples
Example 1:
There is a wheel mounted onto this axle. This wheel measures 14 cm diameter.
Calculate the distance traveled when motor turns 360 degrees:
Step 1) calculate gear ratio: 8
24 =
1
3
Step 2) Distance = 14cm *PI / Gear Ratio.
= 42*PI cm
Calculate the distance traveled when motor turns 180 degrees:
Step 1) calculate gear ratio: 8
24 =
1
3
Step 2) Distance = 14cm *PI / Gear Ratio * 180
360.
= 21*PI cm
Example 2:
The Motor mounts onto this axle. This wheel measures 14 cm diameter.
Calculate the distance traveled when motor turns 360 degrees:
Step 1) calculate gear ratio: 24
8 =
3
1
Step 2) Distance = 21cm *PI / Gear Ratio.
= 7*PI cm
Wheel mounts on the 24-t axle.
The wheel measures 21cm
diameter.
Motor mounts on the 24-t axle.
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Example 3:
Calculate the distance traveled when motor turns 360 degrees:
Step 1) calculate gear ratio: 40
8∗24
3∗24
8 =
3
1∗3
1∗5
1 =
45
1
Step 2) Distance = 9 cm *PI / Gear Ratio.
= 0.5 *PI cm
Example 4:
Calculate the distance traveled when motor turns 360 degrees:
Step 1) calculate gear ratio: 8
24∗
8
24∗
8
40 =
1
3∗1
3∗1
5 =
1
45
Step 2) Distance = 9 cm *PI / Gear Ratio.
= 405 *PI cm
This axle on the 24-t is the final
output shaft.
A wheel measures 9 cm diameter
mounts through this axle.
Motor mounts on the 8-t axle. This is the Main Driver gear.
Motor mounts on the 24-t axle. This is
the Main Driver gear.
This axle on the 8-t is the final output
shaft.
A wheel measures 9 cm diameter
mounts through this axle.
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Exercises
Note: You should leave the answer in expression with PI. For example, i f the answer
is 3PI, you should leave your answer as 3PI, instead of approx.. 9.42.
1) Ashley and John recorded that the wheel diameter was 10cm and that the robot
was programmed to move 2 wheel revolutions. How far did their robot move in cm?
2) Ashley and John recorded that their robot moved 120 cm and that the robot was
programmed to move 4 wheel revolutions. What was the diameter of the wheel in
inches?
3) Ashley and John recorded that their robot moved 250 cm and that the wheel
diameter was 5 cm . How many wheel revolutions was the robot programmed to
complete?
4) Given: Tire diameter = 10cm GR = 1:1 :
1 Tire Rotation Revolution= 16 counts
Question: Distance to travel = 200cm. How many counts should the robot need
to travel ?
5) Given: Tire diameter = 10cm GR = 2:1 :
1Rotation Revolution= 16 counts
Question: Distance to travel = 200cm. How many counts should the robot need
to travel ?
6) Given: Tire diameter = 10cm GR = 1:2 :
1Rotation Revolution= 16 counts
Question: Distance to travel = 200cm. How many counts should the robot need
to travel ?
7) Given: Tire diameter = 10cm GR = 2:5
1Rotation Revolution= 16 counts
Question: Distance to travel = 200cm. How many counts should the robot need
to travel?
8) Given: Tire diameter = 10cm GR =5:2
1 Rotation Revolution= 16 counts
Question: Distance to travel = 200cm. How many counts should the robot
need to travel ?
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CHASSIS TURNING VS . ENCODER (ROTATION SENSOR)
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Example: