ENG H191 Hands-on Lab
Lab 6: Gears
INTRODUCTION
Background
Gears are important components in a large variety of devices. Music boxes,
clocks, cars and CD players all have gears. The typical type of gear is a
pinion gear however there are many other types of gears each of which meet
the needs of certain applications.
Purpose
The purpose of this lab is to familiarize you with the concept of torque and
rotational speed, and how these quantities may be manipulated using various
types of gears. The uses of several types of gears will also be investigated.
Lab
Experience
The lab experience will encompass:
1. Applications of Worm Gears,
2. Application of Bevel gears and Rack & Pinion
3. Application of Spur gears and Sprockets.
TORQUE AND SPEED
Introduction
Gears are used to perform mechanical work. A common application of gears
is to convert from one rotational speed to another through a gear train (or gear
box or speed reducer). For example, a clock has two or three hands, each of
which spin at different speeds but there is only one motor or power source
turning the hands. The clock takes the speed of the input motor, gears it
down and drives the second hand, gears it down again to drive the minute
hand and down further to drive the hour hand. Several gears allow one power
source to drive a variety of objects.
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Torque
When rotational speed is changed through gearing, the rotational force that
can be applied also changes. Consider a car traveling on a highway; the car is
in high gear traveling fast but with low acceleration ability. When the car
approaches a steep incline it down shifts, putting the car in a lower gear,
which produces more torque but the car cannot go as fast (the engine must
turn much faster to maintain speed).
The transmission in a car transfers power from the engine to the drive train
and moves the car. Power (or energy) is always conserved in any system, so
this must also be true for a car's power train. Power, in a rotational system is
represented by rotational speed and rotational force (or torque).
Interplay of
Torque and
Speed
In linear motion the relationship of Power, Force, Work and Speed are as
follows:
Power = Work / time
Work = Force * Distance
Power = Force * Distance / time
In rotational motion the formulas are identical; we just have some different
terms. Rotational force is called Torque and rotational distance is measured
in radians or degrees.
Power = Torque * (Rotational Speed)
A car is equipped with an engine capable of delivering a certain horsepower;
the gear that the car is in determines how the power is converted into speed
and torque. For a fixed power, if you need more torque the speed must go
down or if more speed is needed then the torque available must decrease.
A bicycle is another perfect example of how gearing controls torque and
speed. Shifting gears on a bicycle is done to make the rider as efficient as
possible. Low gear is for going up hills, high gear is used to go fast on
smooth flat land.
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TYPES OF GEARS
Spur Gears
A pinion or spur gear is a simple gear used to mesh with another gear in the
same plane. The smaller gear is commonly referred to as the pinion, while
the larger gear is simply called the gear.
Figure 1: Spur Gear
Figure 2: Symbolic Representation
The symbolic representation is used to simplify diagrams. The value, Dp, is
optional. Dp is the pitch diameter, which can be used to find the gear ratio,
(Dpgear / Dppinion). Gear ratio can also be found counting the number of teeth
on each gear:
Dp gear
Dp pinion
Bevel Gears

NumberOfGearTeeth
NumberOfPinionTeeth
Bevel gears are designed to mesh with each other at different angles
(commonly 90°). This type of drive is used to change the axis of rotation. A
differential (which is discussed later in this lab) uses bevel gears to control its
motion.
Figure 3: Bevel Gears
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Rack and
Pinion
A pinion turns and moves a rack in order to convert rotational motion into
linear motion. Rack and pinion steering is just one of many applications of
this gear set.
Figure 4: Rack and Pinion Gear Set
Worm gears
This type of gear, like the bevel gears, converts the axis of rotation by 90°. A
worm gear is used for high ratio speed reduction. When a worm rotates, it
moves just one tooth on its meshing gear. (Double helix worms move two
teeth.) Because of the shape of worm gear, the driven gear must be specially
made in order to mesh properly.
Figure 5: Worm Gear
A note on gear When expressing the ratio of some gearbox, the convention is normally to
write the output rotational speed over the input rotational speed. So high gear
ratios
would be used for faster speeds in a car or on a bicycle for example, and low
gear would output more torque.
GearRatio 
OutputSpeed
InputTorque

InputSpeed
OutputTorque
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LAB EXPERIENCE
Make sketches of all equipment used in class; include them in your lab report.
Applications
of Worm
Gears
Automobile Window Lift Motor
Take the gear assembly apart. Watch out for messy grease!
Observe how the given gear head motor unit would move and which
gears are the input/output, respectively.
Determine the gear ratio. # of teeth on the output gear : # of worm gears.
Using Legos™
Observe the motion of the Lego™ robot gripper that is given.
Use the robot gripper to grab items. Notice how the worm gear is used to
provide holding power without energizing the motor.
Questions
What is the gear ratio of the window lift motor? How did you determine
this?
How does the Lego™ worm gear robot gripper still hold objects without
a continuously applied force? Compare this mechanism to a crescent
wrench. Use the word 'back-driven' in your answer.
Bevel Gears
and Racks
A differential is used to transfer power from the drive shaft to the wheels of
the car. When a car turns a corner the wheels travel different distances and so
move at different speeds. Move the Lego™ differential unit provided to
prove this to yourself. A differential provides equal force to each wheel while
allowing different speeds at each wheel. For more information on
differentials, a very good description with animations can be found at
http://www.howstuffworks.com/differential.htm.
Questions
Understanding a differential: Explain what would happen to the simple
differential used in lab if one tire is sitting on ice and the other tire is on
clean pavement and the drive shaft is spinning? Will the car move?
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Pinions and
Sprockets
Bicycle Gearing
A bicycle demonstrates the trade off of speed and torque. Experiment with the
speed and force attainable at different gear ratios. Since a bicycle uses a
chain the direction of rotation of the output shaft (sprocket) is not reversed as
it is with a pair of gears. For the given bicycle, find the gear ratio (sprocket
combination) for:
a) Max Torque
b) Max Speed
c) Redundant combinations
For this experiment, create a table that shows all the possible gear
combinations. Show which ones are redundant. (Measure wheel diameter
and length of pedal arm).
Gear Boxes
Using the Legos™ set provided build a simple gearbox that has a gear ratio of
1:75.
Questions

Draw a sketch of the gearbox you made for the 1:75 gear ratio. Be sure
you could reproduce the gearbox from this sketch.
(Advice: Use symbolic representations for the gears (no teeth), and use
a top view.)

If a rider can pedal no faster than 5 revolutions per second, what is the
fastest he/she can make the bicycle in the lab go.
Hint: determine the diameter of the rear tire and the length of the pedal.

A biker weighs 175 lbs and his bike weighs 25 lbs. What is the steepest
hill the rider can climb? (Assume the rider can put all of his/her weight
on the pedal.)

Would a wrench driven by an electric motor have a very high or a very
low gear ratio?
Hint: Read the note on gear ratios earlier in this write up.
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LAB REPORT
Format


General
Guidelines

Include sketches of all mechanisms studied and built.

Be sure to provide answers to all questions presented.
Lab report format (INDIVIDUAL or TEAM) will be announced in lab.
Follow the sample lab report format provided.
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