introduction to gear system 1they have pulleys of 3, 4, and 9 cm diameter available. ... not on the...

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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

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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.



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.



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



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?



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



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.


e. Take an average.


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.


e. Take an average.


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



Page

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.



Page

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



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.



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:



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:



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 ?


1Rotation Revolution= 16 counts


to travel ?




to travel ?

7) Given: Tire diameter = 10cm GR = 2:5



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:


introduction to gear system 1they have pulleys of 3, 4, and 9 cm diameter available. ... not on the...

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