Download Mechanisms Levers Class 1 levers:

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Mechanisms
A mechanism is simply a device which takes an input motion and force, and outputs a
different motion and force. The point of a mechanism is to make the job easier to do. The
mechanisms most commonly used in mechanical systems are levers, linkages, cams,
gears, and pulleys.
You need to know how to calculate the mechanical advantage obtained by using levers,
the velocity ratio in levers and pulley systems, and gear ratio and output speed when
using gears.
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Levers
Linkages
Cams
Gears
Pulley systems
Types of motion
Levers
A lever is the simplest kind of mechanism. There are three different types of lever. Common
examples of each type are the crowbar, the wheelbarrow and the pair of tweezers.
All levers are one of three types, usually called classes. The class of a lever depends on
the relative position of the load, effort and fulcrum:
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The load is the object you are trying to move.
The effort is the force applied to move the load.
The fulcrum (or pivot) is the point where the load is pivoted.
Class 1 levers:
A class 1 lever has the load and the
effort on opposite sides of the fulcrum,
like a seesaw. Examples of a classone lever are a pair of pliers and a
crowbar.
For example, it would take a force of
500N to lift the load in the animation
below. But using a lever - a rod with
the fulcrum placed closer to the load
than the point of effort - it only
requires a force of 100N.
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Class 2 levers:
A class 2 lever has the load and the
effort on the same side of the fulcrum,
with the load nearer the fulcrum.
Examples of a class-two lever are a
pair
of
nutcrackers
or
a
wheelbarrow.
In the diagram below, the wheel or
fulcrum on the wheelbarrow is helping
to share the weight of the load. This
means that it takes less effort to move
a load in a wheelbarrow than to carry
it.
Mechanical advantage and velocity ratio
Class 1 and class 2 levers both provide mechanical advantage. This means that they
allow you to move a large output load with a small effort. Load and effort are forces and
are measured in Newtons (N). Mechanical advantage is calculated as follows:
Mechanical advantage = load ÷ effort
In the example above, where the load=500N and the effort=100N, the mechanical
advantage would be: 500N ÷ 100N = 5
Velocity ratio
The mechanical advantage gained with class-one levers and class-two levers makes it seem
like you are getting something for nothing: moving a large load with a small effort. The
catch is that to make the effort smaller, you have to move a greater distance. In the first
diagram the trade-off is that you need to push the lever down further to move the load up a
smaller distance. This trade-off is calculated by the velocity ratio:
Velocity ratio = distance moved by load ÷ distance moved by effort
Class 3 levers:
A class 3 lever does not have the mechanical
advantage of class-one levers and class-two
levers, so examples are less common. The effort
and the load are both on the same side of the
fulcrum, but the effort is closer to the fulcrum
than the load, so more force is put in the effort
than is applied to the load. These levers are good
for grabbing something small, fiddly or dirty, or
picking up something that could be squashed or
broken if too much pressure is applied. The
common example of class 3 levers is a pair of
barbeque tongs or a pair of tweezers. The
latter are shown in the diagram.
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Linkages
Linkages are mechanisms which allow force or motion to be directed where it is needed.
Linkages can be used to change:
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•
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The direction of motion
The type of motion
The size of a force
A linkage consists of a system of rods or other rigid materials connected by joints or pivots.
The ability of each rod to move will be limited by moving and fixed pivots. The input at one
end of the mechanical linkages will be different from the output, in place, speed, direction
and other ways.
1. A reverse-motion linkage changes the
direction of motion. In the diagram below, note
how the linkage looks a little like a "Z". See
how the central rod moves around a central
fixed pivot. By pulling (or pushing) the linkage
in one direction, it creates an exact opposite
motion in the other direction. If the fixed pivot
was not central, it would create a larger or
smaller motion in the opposite direction.
2. A parallel-motion linkage creates an identical
parallel motion. In the diagram below, note
how the linkage looks a little like an "n". This
time, it is the two side rods that move around
two central fixed pivots, while the top of the
"n" moves freely. By pulling (or pushing) the
linkage in one direction, it creates an identical
parallel motion at the other end of the linkage.
3. A bell-crank linkage changes the direction of
movement through 90°. A bell-crank linkage
tends to look a little like an "L" or, as shown in
the diagram below, a mirror image of an "L".
By pulling (or pushing) the linkage in one
direction, it creates a similar motion at the
other end of the linkage. For example, a bellcrank linkage could be used to turn a vertical
movement into horizontal movement, as in a
bicycle breaking system.
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4. A treadle linkage shows how
linkages can be used to change
one type of motion into another.
In this case, the rotary motion of
the cam moves a parallel-motion
linkage.
The
parallel-motion
linkage controls the identical sideto-side, or oscillating motion, of
two windscreen wipers
Cams
A cam is a shaped piece of metal or plastic fixed to a rotating shaft. A cam mechanism has
three parts: cam, slide and follower.
The cam shaft rotates continually, turning the cam. The follower is a rod that rests on the
edge of the turning cam. The follower is free to move up and down, but is prevented from
moving from side to side by a slide or guide, so the follower can only do three things:
1. Rise (move up)
2. Fall (move down) or
3. Dwell (remain stationary)
The follower's pattern of movement depends on the profile or outside edge of the cam that
it follows. If the cam is perfectly round and the fixed shaft is in the centre of the cam, the
follower will dwell. But if the cam is a different shape, and/or the shaft is not central, the
follower will rise or fall. How often and how quickly the follower moves is determined by the
shape of the cam and the position of the shaft.
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Cams come in many different shapes - for example pear-shaped, triangular or
square.
The cam may have a chunk or chunks removed, so that the follower falls into a gap
and is then is pushed out again.
Whatever the shape of the cam, positioning the shaft off-centre will alter the
behaviour of the follower.
1. Pear-shaped cam
The pear shape of this cam means that for half the cycle,
the follower will dwell. Then, as the pointed part of the cam
approaches, the follower is pushed up (rises), then, as the
point passes, falls and dwells - and the cycle starts again.
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2. Eccentric cam
The eccentric cam is perfectly circular, but the rotating
shaft is off-centre, which affects how it turns. This type of
cam produces a smooth, symmetrical rise and fall motion in
the follower, which never pauses to dwell.
3. Drop cam
With a drop cam the shaft is central in a perfectly round
cam, which has a chunk removed. The follower will dwell for
most of the cycle, until it suddenly falls into the removed
section, then rises again as the cam regains its circular
shape.
Note that if the size of the cut-out portion was larger or the
incline smoother, the follower would behave differently.
Gears:
Gears consist of toothed wheels fixed to shafts. The teeth interlock with each other, and as
the first shaft (the driver shaft) rotates, the motion is transmitted to the second or driven
shaft. The motion output at the driven shaft will be different from the motion input at the
driver shaft - in place, speed, direction and other ways.
A number of gears connected together are called a gear train. The input (eg a motor) is
connected to the driver gear. The output, (eg the wheel of a buggy) is connected to the
driven gear.
Spur gears
The photograph shows a simple gear
train made up of a couple of spur gears.
These are the common gears (or cogs)
that look like wheels with teeth around
the rim. Next to the photo is a diagram
showing how you would draw this gear
train in an exam.
In the drawing, the centre of each gear is shown by a cross. Each gear is drawn as two
circles, one slightly larger than the other to show where the teeth would be. Teeth do not
have to be drawn, but the number of teeth is written next to the gear, in this case 60 teeth
and 15 teeth. Arrows indicate the direction that the gears are moving. Note that with two
connected gears, they will be rotating in opposite directions.
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Gear ratio and output speed
Where there are two gears of different sizes, the smaller gear will rotate faster than the
larger gear. The difference between these two speeds is called the velocity ratio, or the
gear ratio, and can be calculated using the number of teeth. The formula is:
Gear ratio = number or teeth on driven gear ÷ number of teeth on the driver gear
So the gear ratio for the simple gear train above, if the smaller gear is the driver gear, is:
Gear ratio = 60 ÷ 15 = 4. In other words, the driver gear revolves four times to make the
driven gear revolve once.
If you know the gear ratio, and the speed input at the driver gear, you can calculate the
speed output at the driven gear using the formula:
Output speed = input speed ÷ gear ratio
So if the gear ratio is 4 and the driver gear is revolving at 200 rpm then the output speed
= 200 ÷ 4 = 50 rpm
Compound gear train
Where very large speed reductions are required,
several pairs of gears can be used in a compound
gear train. A small gear drives a large gear. The
large gear has a smaller gear on the same shaft.
This smaller gear drives a large gear. With each
transfer, the speed is significantly reduced.
Worm gears
Another method of making large speed reductions is to use a
worm gear. This is a shaft with a thread like a screw. This
connects at 90° to a large gear (the thread shaft points along
the outside edge of the larger gear). Each time the shaft spins
one revolution, the gear turns forward by only one tooth. If the
gear has 50 teeth, this creates a gear ratio of 50:1. Worm
gears are a good option when you wish to alter direction or
rotary motion through 90° and reduce the speed. The
photograph below shows a worm gear powered by a motor.
Bevel gears
Bevel gears, like worm gears, change the axis of rotation
through 90°. The teeth have been specially cut so the gears will
mesh at right-angles to each other, where spur gears must be
parallel.
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Rack and pinion
A pinion is a round cog and the rack is a flat bar with teeth. The
driver cog either moves along the rack, as in a rack and pinion
(funicular) railway - or else the driver cog moves the rack, as
in the steering system in cars. Rack and pinion changes rotary
motion into linear motion - as shown in the diagram below.
Pulley systems
Pulleys are used to change the speed, direction of
rotation, or turning force or torque.
A pulley system consists of two pulley wheels each on
a shaft, connected by a belt. This transmits rotary
motion and force from the input, or driver shaft, to the
output, or driven shaft.
If the pulley wheels are different sizes, the smaller one will spin faster than the larger one.
The difference in speed is called the velocity ratio. This is calculated using the formula:
Velocity ratio = diameter of the driven pulley ÷ diameter of the driver pulley
If you know the velocity ratio and the input speed of a pulley system, you can calculate the
output speed using the formula:
Output speed = input speed ÷ velocity ratio
Worked example
Work out the velocity ratio and the output speed of the pulley shown in the diagram above.
Velocity ratio = 120mm ÷ 40mm = 3
Output speed = 100rpm ÷ 3 = 33.3rpm
Torque
The velocity ratio of a pulley system also determines the amount of turning force or torque
transmitted from the driver pulley to the driven pulley. The formula is: output torque =
input torque x velocity ratio.
Pulley drive belts
Drive belts are usually made of synthetic fibres such as neoprene and polyurethane, with a
V-shaped cross section. It is possible to reverse the direction of the driven pulley by twisting
the belt as it crosses from input to output. Pulley belts have the advantage over chains that
they do not need lubrication (though unlike a chain, a belt can slip).
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Types of motion
There are four basic types of motion in mechanical systems:
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Rotary motion is turning round in a circle, such as a wheel turning.
•
Linear motion is moving in a straight line, such as on a paper trimmer.
•
Reciprocating motion is moving backwards and forwards in a straight line, as in
cutting with a saw.
•
Oscillating motion is swinging from side to side, like a pendulum in a clock.
Many mechanisms take one type of input motion, and output it as a different type of
motion. Below are some examples.
1. A chain and sprocket changes
rotary motion to linear motion or vice versa. A wheel-and-axle,
rack-and-pinion, rope-and-pulley,
screw
thread,
or
chain-andsprocket could also be used for
this.
2. A cam-and-follower changes rotary motion to
reciprocating motion. A crank, link and slider or
rack-and-pinion could also be used for this.
3. A peg-and-slot changes oscillating motion to
rotary motion. A crank, link and slider could be
used for this, and also to change rotary to
oscillating motion.
4. A crank, link and slider will change rotary motion
to oscillating / reciprocating motion
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5. A rack-and-pinion changes rotary motion to
reciprocating motion. A crank, link and slider could
also be used for this. A cam-and-follower will change
reciprocating to rotary motion.
Mechanical systems and sub-systems
Small systems can be combined to make more complex systems. A cam which is turned by
an electric motor can operate a micro switch which could be used to turn a light on or off.
Two mechanical systems can be connected together to give complex movements.