Download MECHANISMS I: SIMPLE MACHINES INDEX 1) PRELIMINARIES a

MECHANISMS I: SIMPLE MACHINES
INDEX
1)
PRELIMINARIES ....................................................................................................................... 1
a) Mechanical advantage .............................................................................................................. 2
b) Conservation of energy ............................................................................................................ 2
c) The three (six?) Simple machines ............................................................................................ 2
2) LEVER ......................................................................................................................................... 3
a) First-Class Lever. ..................................................................................................................... 3
b) Second-Class Levers. ............................................................................................................... 3
c) Third-Class Lever. .................................................................................................................... 3
3) WHEEL AND AXLE .................................................................................................................. 4
4) PULLEY ...................................................................................................................................... 4
a) Fixed pulley .............................................................................................................................. 4
b) Moveable pulley ....................................................................................................................... 4
c) Block and tackle ....................................................................................................................... 5
How does a Block and tackle work? ............................................................................................ 5
5) INCLINED PLANE ..................................................................................................................... 6
6) WEDGE ....................................................................................................................................... 6
7) SCREW ........................................................................................................................................ 7
1) PRELIMINARIES
All machines have in common the following things:
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they involve a kind of motion
they involve a kind of force
they make a job easier to do
they need some kind on input to make them work
they produce some kind of output
The four basic kinds of motion are:
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Rotary: going round and round. This is the most common kind of movement
Oscillating, swinging backwards and forwards
Linear, in a straight line
Reciprocating, backwards and forwards in a straight line
A machine is a device that helps make work easier to perform. (Remember, Work
= Force X Distance). A machine makes work easier to perform by accomplishing
one or more of the following functions:
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transferring a force from one place to another,
changing the direction of a force,
increasing the magnitude of a force, or
increasing the distance or speed of a force.
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a) Mechanical advantage
When a machine takes a small input force and increases the magnitude of the
output force, a mechanical advantage has been produced. If a machine
increases an input force of 10 newton to an output force of 100 newton, the
machine has a mechanical advantage (MA) of 10. This is shown below:
MA = Output Force/Input force = 100/10 = 10
b) Conservation of energy
No machine can increase both the magnitude and the distance of a force at the
same time. When a machine produces an increase in force, there is always a
proportional decrease in the distance moved. Conversely, when a machine
produces an increase in distance, there will be a proportional decrease in force.
Another way to state this concept is that no machine can produce more work
than the amount of work that is put into the machine. In fact,
This concept can also be put into the form of an equation. (Remember that work is
equal to force times distance.)
F1 X D1 = F2 X D2
Where:
F1 = Input Force, F2 = Output Force
D1 = Input Distance D2 = Output Distance
c) The three (six?) Simple machines
You are probably familiar with many different machines. Some of these machines
appear highly complex. However, all machines, no matter how complex, are
made up of one or more of the six simple machines. The six simple machines are:
Lever
Wheel and Axle
Pulley
Inclined Plane
Wedge
Screw
Individually, each of these machines is a simple machine. When two or more
simple machines are combined in such a way that they work as a single
mechanism, the device is classified as a complex machine.
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2) LEVER
A lever is a rigid bar that rotates around a fixed point called the fulcrum. The bar
may be either straight or curved. In use, a lever has both an applied force and a
resistance force.
There are three different classes of levers. The class of a lever is determined by the
location of the applied and resistance forces relative to the fulcrum. Each of the
three classes of levers will be discussed next.
a) First-Class Lever.
The fulcrum is located at some point between the effort
and resistance forces. Common examples of first-class
levers include crowbars, scissors, pliers, tin snips and
seesaws.
When the fulcrum is nearer the weight, you have to apply a
smaller effort, and reversely when the fulcrum is nearer
where you apply the force, then this force must be a bigger
effort to balance the weight
b) Second-Class Levers.
With a second-class lever, the resistance is located
between the fulcrum and the effort force. Common
examples of second-class levers include nut crackers, wheel
barrows, and bottle openers.
This levers are said to be always “advantageous” because
you always have to apply a smaller effort to balance the
weight
c) Third-Class Lever.
With a third-class lever, the effort force is applied between
the fulcrum and the resistance force. Examples of third-class
levers include tweezers, ice tongs, and shovels. Common
examples of third-class levers include a fishing pole.
This levers are said to be always disadvantageous because
you always have to apply a bigger effort to balance the
weight
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3) WHEEL AND AXLE
The wheel and axle is a simple machine consisting of a large wheel rigidly secured
to a smaller wheel or shaft, called an axle. When either the wheel or axle turns, the
other part also turns. So that, one full revolution of either part causes one full
revolution of the other part. If the wheel turns and the axle remains stationary, it is
not a wheel and axle machine.
The mechanical advantage of a wheel and axle is the ratio of the radius of the
wheel to the radius of the axle. In the wheel and axle illustrated below, the radius
of the wheel is five times larger than the radius of the axle. Therefore, the
mechanical advantage is 5:1 .
The wheel and axle can be used to increase speed. This is done by applying the
input force to the axle rather than a wheel.
4) PULLEY
A pulley consists of a grooved wheel that turns freely in a frame called a block. A
pulley can be used to:
 simply change the direction of a force
 or to gain a mechanical advantage, depending on how the pulley is
arranged.
a) Fixed pulley
A pulley is said to be a fixed pulley if it does not rise or fall with the
load being moved. A fixed pulley changes the direction of a
force; however, it does not create a mechanical advantage. A
fixed pulley is illustrated below.
b) Moveable pulley
A moveable pulley rises and falls with the load that is being moved.
A single moveable pulley creates a mechanical advantage;
however, it does not change the direction of a force.
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c) Block and tackle
In many applications, both fixed and moveable pulleys are used in combination to
form a device known as a block and tackle. A block and tackle is capable of both
changing the direction of a force and creating a mechanical advantage.
How does a Block and tackle work?
A block and tackle can contain as many pulleys as you like, although at some
point the amount of friction in the pulley shafts begins to become a significant
source of resistance.
Imagine that you have the arrangement of a 100
pound (45.4 kilogram) weight suspended from a
rope, as shown on the right.
Here you have to apply an upward force of 100
pounds to the rope. If the rope is 100 feet (30.5
meters) long and you want to lift the weight up 100
feet, you have to pull in 100 feet of rope to do it.
This is simple and obvious.
Now imagine that you add a pulley to the mix, as
shown on the right.
Does this change anything? Not really. The only
thing that changes is the direction of the force you
have to apply to lift the weight. You still have to
apply 100 pounds of force but maybe more
comfortably.
The following figure shows the arrangement after
adding a second pulley. That is a block and tackle
system.
The force has been cut in half but the distance the
rope must be pulled has doubled.
The following diagram adds a third and fourth
pulley to the arrangement. This makes even easier
to lift the weight (you have to apply just 25
pounds), but having to lift it more distance (if you
want to lift it 100 feet, you have to pull 400 feet.
Detail to see how the rope
surrounds the third pulley
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5) INCLINED PLANE
An inclined plane is an even sloping surface. The inclined plane may slope at any
angle between the horizontal and the vertical. The inclined plane makes it easier
to move a weight from a lower to higher elevation. An inclined plane is illustrated
below:
The mechanical advantage of an inclined plane is equal to the length of the slope
divided by the height of the inclined plane.
While the inclined plane produces a mechanical advantage, it does so by
increasing the distance through which the force must move.
6) WEDGE
The wedge is a modification of the inclined plane. Wedges are used as either
separating or holding devices. Like and axe to cut off trees or a wedge to hold a
door open.
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7) SCREW
The screw is also a modified version of the inclined plane. While this may be
somewhat difficult to visualize, it may help to think of the threads of the screw as a
type of circular ramp (or inclined plane). It is like having to walk up a longer
distance with a smaller effort (like the inclined plane) but doing it in s small space.
Examples of application of this simple machine are the screws, spiral staircases or
the Archimede’s screw for transporting things.
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