Simple machines
Year 1 Design for Industry
John Errington
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Simple Machines
A simple machine is any device that only requires the
application of a single force to work. They change the
direction and/or size of forces.
The traditional list of simple machines is:
* The inclined plane
* The wheel and axle
* The lever
* The pulley
* The wedge
* The screw
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Mechanical advantage
Ideal Mechanical Advantage (IMA) or distance ratio
IMA = distance moved by effort / distance moved by load
Actual mechanical advantage (AMA) or force ratio
AMA = load / effort
Efficiency = AMA / IMA *100%
Work Input = Useful Work Output + Work to Overcome Friction
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Friction
Friction is the resistive force that occurs when two surfaces
slide along each other when forced together. It causes
physical deformation and heat build up. The frictional
force is a function of the force pressing the surfaces
together and the coefficient of friction of the two
materials.
Ff = Fp * μr
where:
Ff is the frictional force
Fp is the force perpendicular to the contact surface and
μr is the coefficient of friction
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Static Friction
Static friction (sometimes called stiction)
occurs when the two objects are not moving
relative to each other (like a desk on the
ground).
The coefficient of static friction is typically
denoted as μs.
The initial force to get an object moving is
often dominated by static friction.
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Examples of static friction
In the context of hard disk drives, stiction refers to
the tendency of read/write heads to stick to the
platters, preventing the disk from spinning up and
possibly causing physical damage to the media.
Some hard drives avoid the problem by not resting
the heads on the recording surfaces.
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Kinetic Friction
Kinetic friction occurs when the two
objects are moving relative to each
other and rub together (like a sled on
the ground). The coefficient of kinetic
friction is typically denoted as k, and is
usually less than the coefficient of static
friction.
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Examples of kinetic friction:
* Sliding friction is when two objects are rubbing against each other.
Putting a book flat on a desk and moving it around is an example of
sliding friction.
* Rolling friction occurs when the two objects are moving relative to
each other and one "rolls" on the other (like a car's wheels on the
ground). The coefficient of rolling friction is typically denoted as μr.
* Fluid friction is the friction between a solid object as it moves
through a liquid or a gas. The drag of air on an airplane or of water
on a swimmer are two examples of fluid friction.
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For our initial treatment of simple machines
we will assume friction is negligible.
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Inclined Plane
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Inclined plane
Inclined plane is a device used to
Operating
lever
raise heavy loads with relatively
small forces. For example, pushing a
load up a ramp onto a platform
requires less force than lifting the
load onto the platform.
• Ramps and steps are forms of
inclined planes.
• An eccentric cam is another form of
inclined plane – often used to clamp
materials.
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Lever
Lever consists of a rod or bar that rests
and turns on a support called a fulcrum. A
force or effort is applied at one end of the
rod to lift a load placed at the other end.
A lever can help lift a weight with less
effort. Prying something loose with a
crowbar is using a lever. Some machines,
such as a catapult, use a lever to hurl
objects.
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Three Classes of Levers
First-class levers – the fulcrum is in the
middle like a seesaw, crowbar, or balance
scale.
Second-class levers- the load is in the
middle like a wheel barrow, or a nutcracker.
Third-class levers – the effort is in the middle
– like a pair of tweezers.
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First-class Lever
Effort
Load
Fulcrum
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Lever
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Wedge
A wedge is a device that has two or
more sloping surfaces that taper either
to a sharp edge or to a point. Wedges
are used to split, clamp or pierce
materials, and to adjust the positions
of heavy objects.
Knives, chisels, axes, pins, needles,
and nails are wedges.
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Wedge
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Pulley
Pulley is a wheel
over which a rope or
belt is passed for the
purpose of
transmitting energy
and doing work.
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Pulley
Change Force Direction
Same Force Size
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Block and Tackle
Imagine that you have the
arrangement of a 100 pound weight
suspended from a rope, as shown.
If you are going to suspend the
weight in the air then you have to
apply an upward force of 100
pounds to the rope. If you want to
lift the weight up 10 feet, you have
to pull in 10 feet of rope to do it.
100lb
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Block and Tackle
Now imagine that you add a
pulley. 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 to
keep the weight suspended,
and you still have to reel in 10
feet of rope to lift the weight 10
feet
100lb
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Block and Tackle
Here you can see that the weight is
suspended by two ropes rather than one.
Each rope holds only half the weight, or 50
pounds. That means that if you want to hold
the weight suspended in the air, you only have
to apply 50 pounds of force (the ceiling exerts
the other 50 pounds of force on the other end
of the rope).
If you want to lift the weight 10 feet higher,
then you have to reel in twice as much rope 20 feet of rope must be pulled in. This
demonstrates a force-distance tradeoff. The
force has been cut in half but the distance the
rope must be pulled has doubled.
100lb
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The mechanical advantage of a block and tackle is simply found
by counting the number of ropes from the bottom pulley system.
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More pulleys
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Screw
A Screw is an
inclined plane
wrapped in a
spiral around a
shaft.
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Screw
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Wheel and Axle
Wheel and axle is a
mechanical device used in
lifting loads. It is one of the
six simple machines
developed in ancient times
and ranks as one of the
most important inventions in
history. Sometimes teeth or
cogs may be placed around
the edge of the wheel, as in
a cogwheel, or on the
sprocket wheel of a bicycle.
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Wheel and axle
D
d
A large wheel on a small
axle reduces the frictional
force at the bearing by an
amount equal to the ratio of
their diameters.
FD = Fd * d / D
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Gears
An adaptation of a
wheel and axle
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Gear teeth
For gears to mesh together the tooth spacing has to be
the same on each gear. So we can calculate the
mechanical advantage (or the speed reduction) as
R = N1 / N2
where N1, N2 are the number of teeth on each gear.
Example:
A gear of 50 teeth is driven by a gear with 10 teeth.
This gives a mechanical advantage of 5 (and a speed
reduction of 5)
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‘A’ frame
Side
view
A simple lifting machine (just a
lever with force and effort at the
same point) used to change the
direction in which a pull force is
applied. Used in ancient times for
raising heavy stones.
Front view
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Examples of simple machines
• Inclined plane: wheelchair ramp, slide, hill, roller coaster
• Wedge: chisel, screwdriver, door wedge, thumbtack, pins
• Lever: see saw, wheelbarrow, hammer, crowbar, bottle
opener, oar, fork, baseball bat
• Pulley: flagpoles, clotheslines, blinds, crane, fan belt
• Wheel and axle: doorknob, roller skates, eggbeaters,
pencil sharpener, skateboard
• Screw: nuts and bolts, jar lid, corkscrew, screw jack
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Worked example: lever
• A guillotine as shown below is used to cut brass bar which is 1cm
thick.
• If a force of 20kg (196N) at the cutting edge is required to cut the
bar, how much force will need to be applied at the handle?
• How far will the handle move while making the cut?
• What will be the force F in the support?
60cm
Fulcrum Hinge joint
4cm
Handle
F
(note the use of two wedges to cut the bar)
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Worked example: lever
If a force of 120kg (1176N) at the cutting edge is required to cut the bar,
how much force will need to be applied at the handle?
Fhandle = 1176 * 4 / 60 = 78N
• How far will the handle move while making the cut?
Blades move 1cm handle moves 1 * 60/4 cm = 16cm
• What will be the force F in the support?
F = 1176 up plus 78N down = 1098N
60cm
4cm
Fulcrum
Hinge joint
Handle
F
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Worked example – pulley system
• A block and tackle is used to lift a car engine
weighing 90kg (882N). The bottom pulley block
has six ropes.
• What is the distance ratio?
• If it takes a pull force of 180N to lift the engine,
what is the actual mechanical advantage and
the efficiency?
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Worked example – pulley system
• A block and tackle is used to lift a car engine
weighing 90kg (882N). The bottom pulley block
has six ropes.
• What is the distance ratio? 6 (six ropes)
• If it takes a pull force of 180N to lift the engine,
what is the actual mechanical advantage
(force ratio = load / effort = 882 / 180 = 4.90
• and the efficiency η?
η= force ratio / distance ratio * 100%
η = 4.9 *100 / 6 = 81.7%
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