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Unit 3
Mechanisms
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Mechanisms
A mechanism is the arrangement of connected parts in a machine. A bicycle,
a car, a corkscrew are all mechanisms.
Types of motion
Rotary motion is motion in a circle the starting point for many
mechanisms. It is the type of motion provided by dc motors.
Oscillation is back and forth motion about a pivot point. It is measured
in terms of both the angle of throw (amplitude) and the period of time
for one complete cycle (periodic time) or the number of cycles in a
given time (frequency).
Linear motion is the most basic of all motions. Uninterrupted objects
will continue to move in a straight line indefinitely. Under every day
circumstances gravity and friction conspire to bring objects to rest.
Reciprocating motion is back and forth motion. In the example below
the reciprocating motion of the piston is converted to the rotary
motion in the crank.
http://www.flying-pig.co.uk/mechanisms/pages/reciprocate.html
The flying-pig website is
a fantastic resource for
demonstrating the
different forms of motion.
It can provide solutions
for many different
mechanical problems
encountered when
designing systems
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Levers
“If you had a lever long enough and a suitable fulcrum you could move the
earth”. The lever is the most basic mechanism and has been used for
thousands of years.
There are three classes of levers, and each one performs a particular job.
Class 1 Lever
Load
Effort
Fulcrum
Products made from this class of lever.
The crowbar is a single lever but the pliers make use of two levers joined
together at the fulcrum.
Activity:
In this space can you draw another product that makes use of the class 1
lever?
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Class 2 Lever
Load
Fulcrum
Effort
You will notice the arrangement has altered in this case. The fulcrum is on the
end, and load in the middle. The Effort or force is on the end.
Activity
Draw in the space below a product that makes use of a class 2 lever.
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Class 3 lever
Load
Effort
Fulcrum
In the case above the load and effort change places. Can you think of a
product that makes use of a class 3 lever? Draw your thoughts below.
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Mechanical Advantage (Leverage)
Levers are used to change the direction, distance or velocity of movement
or to decrease the effort required to lift a load. This latter reduction of effort
was called leverage. Nowadays and in terms of the WJEC syllabus it is known
as MECHANICAL ADVANTAGE.
Mechanical advantage is the RATIO of the LOAD in measured NEWTONS
and the EFFORT required to lift the LOAD also measured in NEWTONS.
Mechanical Advantage
=
LOAD
EFFORT
1N
10N
10cm
100cm
In the example above the FORCE (EFFORT) of 1Newton is required to lift a
load of 10N.
So Mechanical advantage is:
LOAD
EFFORT
10
1
Therefore this system has a MA of 10. There are no units because it is a
ration of the same units
MOMENTS
To design a lever to lift a particular load you will need to know about
MOMENTS. These are a way of calculating what effect a force will have when
it is applied to a lever. A MOMENT is calculated by multiplying the FORCE
with the DISTANCE the FORCE is from the fulcrum.
For a lever to be balanced, the clockwise moments and the anti-clockwise
moments must be the same. In that condition the lever is said to be in
equilibrium.
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Try this experiment.
Take a lever 1200mm long place a fulcrum somewhere in the middle and
balance the lever with a 10N Load with a 2N Effort.
2N
10N
D2 _______cm
D1 _______cm
When the lever is in EQUILIBRIUM (balanced) the CLOCKWISE moments
equals the ANTI-CLOCKWISE moments.
F1 x d1 = F2 x d2
10 x ______ = 2 x ________
You can use this method to find an unknown quantity when designing a leveroperated system.
For example what force is required to open the lid of a tin of paint?
100N
Effort in N
200mm
5mm
Clock wise moments = Anticlockwise Moments
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Conventions
When you draw a lever as a parallel line then you will need to follow the
correct conventions or symbols. For example a lever can be bent through 90
degrees and connected to a backboard, see below. In the diagram the type of
lever is called a bell crank lever. It is designed to move linear motion through
90 degrees.
The FREE or moving pivots can be seen as a
The FIXED pivot however is seen
non-shaded circle.
as a shaded circle.
This pivot passes through the backboard and connects the lever securely to
the backboard
Backboard
Push/ Pull
FIXED PIVOT
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Exam Question Activity
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HINT – think about ratios
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CAMS
Direction of
rotation
Rise
Fall
Dwell
Cams are used to convert rotary motion into reciprocating motion. The
motion created can be simple and regular or complex and irregular.
As the cam turns, driven by the circular motion, the cam follower traces the
surface of the cam transmitting its motion to the required mechanism.
Cam follower design is important in the way the profile of the cam is followed.
A fine pointed follower will more accurately trace the outline of the cam. This
more accurate movement is at the expense of the strength of the cam
follower.
Snail CAM
The snail cam will produce a gradual ‘rise’ and then a sudden fall during it’s
rotation. The dwell is extremely small as the CAM is lifting almost as soon as
it falls.
Follower height
One full rotation
Cam
Rotation
Cam Rotation
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Pear shaped cam
Heart shaped cam
Eccentric Cam
Pear Shaped cam will produce a regular rise and fall with a dwell for
approximately 180 degrees during rotation. The rise and fall will not be
regular, instead there will be a rapid rise and fall which relates to the shape of
the cam.
One full rotation
Fall
Rise
Dwell
Rise
Follower height
Fall
Steady fall
long dwell
steady rise
Cam Rotation
Dwell
Heart shaped cam will produce a linear rise and fall but with no dwell time
and the follower path will be a rising and falling continually.
Rise
Follower height
Fall
Linear rise
no dwell
linear rise
Cam Rotation
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The eccentric cam or circular cam produces a regular rise and fall with no
acceleration of rise or fall. There will be a uniform follower action.
Activity
Design and make a cam in 2D design and cut out on the laser cutter with the
following specifications.
A snail cam with a dwell diameter 30mm and a peak diameter of 50mm; the
first 90 degrees drops from radius of 25 to 22, to 180 degrees it drops from
radius of 22mm to 20mm, to 270 degrees the radius drops to 18 and finally to
a radius of 15mm.
360o
90o
270o
180o
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Specific Mechanisms
Crank and Slider
Connecting rod
Crank
Rotary
Reciprocating
Slider
The crank and slider mechanism can convert rotary motion into reciprocating
motion and vice versa.
Rotary to reciprocating – The input turns the shaft that causes the slider to
move forwards and backwards. Examples of reciprocating motion used are
the drive systems for saws or the pumping system for hydraulic or pneumatic
systems.
Reciprocating to Rotary – The input pushes the slider that causes the crank
to turn. The crank must be away from the bottom dead centre (BDC) if the
mechanism is to start. These systems make use of a flywheel. A flywheel is a
disc with a large mass so that when the slider is pushed the flywheel builds up
inertia which keeps the system running.
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Gears
The gear wheel is a toothed disc that engages or meshes with another
toothed disc. A gear wheel is a basic mechanism. Its purpose is to control
and transmit ROTARY motion. A shaft passes through the centre of a gear
wheel and the gear is connected to a shaft by using a key.
Keyed onto
shaft
Gear wheels that mesh together are known as a gear train. The gears that
are shown are called SPUR gears.
It is extremely difficult to draw two gears with teeth meshing as in the diagram
below and to the left. In order to draw gears more accurately it is necessary to
draw their symbols, the diagram to the right.
Meshing
Centre
lines
Symbols for Spur Gear
Spur gears 12 per gear
NON symbolic
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Transmitting Rotary Motion
The figure below shows two meshed gears.
Gear A is the DRIVER
and turns clockwise.
EFFORT
Gear B is the DRIVEN
and turns anticlockwise.
LOAD
Gear A has 12 teeth.
Gear B has 12 teeth.
When the DRIVER gear rotates once all of its 12 teeth mesh with all 12 of the
DRIVEN gear’s teeth and so the driven gear will also rotate once.
In this gear train the DRIVER transmits the effort while the DRIVEN gear is
the load.
Velocity Ratio is given as =
=
distance moved by effort (RPM)
distance moved by load (RPM)
1 revolution
1 revolution
Therefore the velocity ratio of this gear train is 1:1
NOTE that for this train of two gears the velocity ratio can also be given as
Gear Ratio =
number of teeth on DRIVEN
number of teeth on DRIVER
=
12
12
=
1:1
Note the VELOCITY RATIO of a gear train is sometimes called the ‘GEAR
RATIO’, and they are EQUAL. Sometimes you will see VR written as 1 but
it is more common to write it as 1:1
1
Now the next example shows how the speed of the transmitted motion can be
controlled.
VELOCITY RATIO = GEAR RATIO
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Controlling the speed
Gear A is the DRIVER
and turns clockwise.
Gear B is the DRIVEN
and turns anticlockwise.
Gear A has 10 teeth
and turns at 20rpm
Gear B has 20 teeth.
What speed will the
DRIVEN gear turn at?
What is the Gear Ratio for this system?
Gear Ratio =
Gear Ratio =
Therefore the Gear Ratio is _______________
•
or
____:_____
Put the formula for Velocity Ratio in…
But Velocity Ratio is also given by =
The distances moved are referred to in the Revolutions made Per Minute
(RPM)
So VR =
2
1
=
20 rpm
? rpm
Cross multiply
? rpm =
•
20 rpm x 1
2
Therefore the speed the driven gear rotates at is 10 rpm
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An easier way of representing this formula is to combine the Velocity Ratio
and Gear Ratio calculations in one
Remember GEAR RATIO and VELOCITY RATIO are EQUAL
So the formula can be used as follows:
Rpm of DRIVER x Teeth on DRIVER = RPM of DRIVEN x Teeth on DRIVEN
This one formula can be used with gear train calculations.
YOUR TURN
Calculate the speed of the driven gear.
Gear A is the DRIVER
and turns clockwise.
Gear B is the DRIVEN
and turns anticlockwise.
Gear A has 15 teeth
and turns at 1500rpm
Gear B has 45 teeth.
What speed will the
DRIVEN gear turn at?
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IDLER GEARS
What do Idler gears do?
IDLER
Driver
Driven
The idler gear will change the direction of motion of a gear box, which enables
the output DRIVEN gear to rotate in the same direction as the input DRIVER
gear.
Does it matter how many teeth there are on the IDLER gear?
1. Using the gears board shown below set up a DRIVER and DRIVEN
gear so that the gears mesh together.
2. Next move the Driven gear out and introduce the IDLER gear.
3. Try different sized gears for the idler. What are the results?
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SAQ Exam Questions – Have you really got it?
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Compound Gears
The TEP gearbox shown makes use of a
compound gear train. This consists of two
pairs of meshed gears where the gear
shafts are parallel. The gear train has a
driver gear and driven gear, but the
intermediate gears are fixed together on
one common shaft. The gears are not idle
since one becomes the driver and the other
the driven. They will affect the output
speed of the gear train.
When calculating velocity for a compound gear, calculate the gear ratios and
multiply them to give an overall gear ratio for the gearbox. Use this to
calculate the overall velocity ratio.
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Transmission of FORCE
Gears are not only used to transmit motion they also need to transmit force.
But, the force acts at a distance from the centre of rotation. Consider a
spanner used to tighten a nut below.
Force applied F
distance r
When a spanner tightens a nut a force F is applied by hand at a distance r
from the centre of the nut (centre of rotation). The turning moment on the nut
is the product of force F x distance r. The Turning moment F x r is called
TORQUE.
Torque is measured in Newton Metres because the applied force is in
NEWTONS and the distance is measured in METRES.
The formula for TORQUE is:
Torque = F x radius
What would happen to the ‘tightness’ of the nut if the spanner was made
longer?
If the spanner was longer …………………………………………….……….
So when gears mesh they also
transmit torque.
Look at the example a small gear
with a small radius transmits its force
to the larger gear. Now the force is
transmitted further away from the
centre of rotation, and so the torque
is increased.
The more gears, the more torque.
The less gears the less torque.
So the compound gearbox bought
from TEP will ________________ the torque applied to output shaft. However
an increase in torque means a ____________ in speed.
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Designing Gearboxes
Input
Process
DC Motor
No load speed
240rpm
Gearbox
Output
10 rpm
to turn an
advertising
display
So the gearbox must produce a velocity reduction of 240rpm to 10rpm, i.e. a
velocity reduction of 240:10 or 24:1
Solution 1
A small driver pinion and a large driven wheel. The pinion could have 10 teeth
and the driven wheel _______ teeth?
The problem with this solution is that only one transmission of force is
taking place and so the TORQUE of this system will be ________(high or low)
Solution 2
By finding the PRIME factors of 24 a gearbox with more than one
transmission of force can be designed which will increase the torque of the
system.
The prime factors of 24 are 4 x 3 x 2.
A velocity reduction of 4:1, followed by 3:1 followed by 2:1 would provide an
overall reduction of 24:1 and provide 3 transmission of force which in turn
increase output torque.
3:1
2:1
4:1
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Other mechanisms using gears
Worm and Wheel
A worm is used to reduce speed. For
each complete turn of the worm shaft the
gear shaft advances only one tooth of the
gear. In this case, with a twelve-tooth
gear, the speed is reduced by a factor of
twelve. Also, the axis of rotation is turned
by 90 degrees.
Unlike ordinary gears, the motion is not
reversible, a worm can drive a gear to
reduce speed but a gear cannot drive a
worm to increase it.
As the speed is reduced the power to the drive increases correspondingly.
Worm gears are a compact, efficient means of substantially decreasing speed
and increasing power. This is ideal for use with small electric motors.
Symbol for the Worm and Wheel.
A gear that has one tooth is called a worm. The tooth is in the form of a screw
thread. A wormwheel meshes with the worm.
As the worm acts like a single toothed gear the, so the ratio of the worm and
Wormwheel =
number of teeth on wormwheel
1
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Rack and Pinion
The rack and pinion is used to convert between rotary and linear motion. The
rack is the flat, toothed part, the pinion is the gear. Rack and pinion can
convert from rotary to linear of from linear to rotary.
The diameter of the gear determines the speed that the rack moves as the
pinion turns. Rack and pinions are commonly used in the steering system of
cars to convert the rotary motion of the steering wheel to the side to side
motion in the wheels. Rack and pinion gears give a positive motion especially
compared to the friction drive of a wheel in tarmac. In the rack and pinion
railway a central rack between the two rails engages with a pinion on the
engine allowing the train to be pulled up very steep slopes.
In the space below draw the symbol for Rack and Pinion.
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Bevel Gears
These gear wheels have teeth cut on a cone
instead of a cylinder. They are used in pairs to
transmit rotary motion and torque where bevel
gear shafts are at right angles (90 degrees) to
each other.
A hand drill makes use of a bevel gear
arrangement to transmit the turning action of
the crank to the chuck.
Here a DC motor is used with
bevel gears to transmit motion
through 90 degrees. In this case
no velocity change is taking
place.
Draw the symbols for bevel gears here.
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Ratchet and Pawl
The ratchet can be used to move a toothed wheel one tooth at a time. The
part used to move the ratchet is known as the pawl.
The ratchet can be used as a
way of gearing down motion. By
its nature motion created by a
ratchet is intermittent. By using
two pawls simultaneously this
intermittent effect can be almost,
but not quite, removed.
Ratchets are also used to ensure
that motion only occurs in only
one direction, useful for winding
gear that must not be allowed to
drop. Ratchets are also used in
the freewheel mechanism of a
bicycle, and on the handbrake
lever of a car.
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SAQ
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Pulley Systems
Pulleys can be used to transmit
motion instead of gear wheels.
Pulleys offer an advantage over gear
wheels in that the pulley belt can slip
across the pulley when transmitting
motion. This can be useful if a motor
is connected to a pulley driving the
chuck of a pillar drill. If the drill bit
becomes stuck in the material being
drilled the motor can still drive and
the belt will slip. If gear wheels are
used then the motor could stall,
which might burn out the coils of the
motor, or the teeth could be stripped off of the gear wheels themselves.
DRIVER
DRIVER
Speed increase
Speed decrease
Straight connection
Same rotation
Belt drives are also used with
lawnmowers for the same reason. The
picture above illustrates the action of the
pulley and its effect on driving speed.
Pulleys are attached to the shafts
(axles) of motors in a similar way to
attaching gears, i.e. by using a KEY.
Here we can see a V pulley system where the keyway is shown cut out of the
pulley. This keyway would engage with a KEY attached (brazed or welded) to
the shaft.
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Pulley Symbols
N
DRIVE
10 rpm
80 mm dia
R
DRIVE
20 rpm
40 mm dia
When the DRIVER pulley rotates 20 times the DRIVEN pulley will only rotate
for the 20 x circumference of the Driver pulley, 10rpm.
In this pulley drive the DRIVER transmits the effort while the DRIVEN gear is
the load.
Velocity Ratio is given as =
=
distance moved by effort
distance moved by load
20 revolutions
10 revolutions
=
2
1
Therefore the velocity ratio of this gear train is 2:1, velocity reduction
NOTE that for this pulley drive the velocity ratio can also be given as
Pulley Ratio
=
Diameter of DRIVEN
Diameter of DRIVER
=
80
40
=
2:1
=
2
1
Since velocity ratios are the same then this formula can be used to calculate
an unknown quantity in a pulley drive system.
Rpm of DRIVER x Dia of DRIVER = RPM of DRIVEN x Dia of DRIVEN
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Activity
Design a pulley drive system.
Specification for your design
•
•
•
VR of 4:1
Driver pulley is 25mm diameter
Distance between the centres of the pulleys is 85mm
Use a compass and ruler and draw your system here.
If the DRIVER pulley rotates at 240rpm calculate the speed the DRIVEN
pulley will rotate at.
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Chain Drive Systems
We have all seen chain drive systems
on our bikes. The crank (pedal) is the
driver sprocket and the chain
transmits this motion to the wheel
where we can select different
sprockets, which in turn will select
different speeds.
Chains combine the positive, nonslip, drive of the gear wheel, with the
flexibility of positioning driver and
driven a distance apart without the
need for any additional idler gears.
Activity
In this table list the advantages and disadvantages of the different types of
drive system.
Pulleys
Gears
Advantages
Disadvantages
Advantages
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Disadvantages
SAQ – Exam Questions
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