Leaving Certificate
Technology
Structures and Mechanisms
Introduction …………………………………………………….....................
2.
Motion ……………………………………………….....................................
6.
Newton’s Third Law of Motion …………………………………………….
8.
Force …………………………………………………………………………… 9.
Load …………………………………………………………………………….
11.
Structures ……………………………………………………………………..
12.
Naturally occurring Structures ……………………………………………
14.
Forces on a Structure ………………………………………………………
16.
Moments ………………………………………………………………………
18.
Calculating Moments ……………………………………………………….
19.
Manmade structures found in Nature ……………………………………
21.
Shell structures in design ………………………………………………….
29.
Beams …………………………………………………………………………
30.
Frames ………………………………………………………………………...
35.
Frame analysis ………………………………………………………………
40.
Factor of safety ……………………………………………………………...
42.
Moments ………………………………………………………………………
45.
Levers …………………………………………………………………………
48.
Lever classification …………………………………………………………
49.
Mechanical advantage ……………………………………………………..
51.
Velocity ratio …………………………………………………………………
52.
Linkages ………………………………………………………………………
53.
Pulleys ………………………………………………………………………...
56.
Pulley advantage ……………………………………………………………
58.
Calculations ………………………………………………………………….
60.
Cams and followers …………………………………………………………
63.
Rotary cams ………………………………………………………………….
65.
Linear cams ………………………………………………………………….
66.
Gears ………………………………………………………………………….
67.
Gear trains ……………………………………………………………………
70.
Power ………………………………………………………………………….
73
Introduction
Structures and Mechanisms
Looking at the image below, it can be clearly seen that the bicycle is constructed around a frame
structure. However, the bicycle also depends on mechanisms to function. The chain and sprocket
is one example of a mechanism.
Structures are a central part of life today and depend heavily on various mechanisms within
machinery for their production. Structures come in countless shapes and sizes, each one with its
own unique and specific function. Can you think of any structures which impact on your everyday
life?
High Rise Building
Vehicle Frame
Bridge Supporting Roadway
Residential Dwelling
We can simplify learning about these structures and their inherent strength, by identifying and
learning about their structural components.
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Machinery is also a central part of life today. As already mentioned, machinery plays a crucial role
in the manufacture of those structures, which we have already identified as being a part of our
everyday lives. It would be impossible to name every machine in existence. How many examples
can you think of?
Drill
Tractor
Car
Exercise Bicycle
Luas
We can simplify learning about these various machines by realising that every machine is made
up of a variety of working parts.
These working parts are called mechanisms
Rack and Pinion
Pulley and Wheels
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Cam and Follower
3
Can you identify and name the mechanism and/or structure in each of the following images?
Bicycle
Wrench
Wheelbarrow
Entrance
Collins Dictionary Definitions
A mechanism is defined as:
A system of moving parts that performs some function
Motion is defined as:
The process of continual change in the position of an object
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Force is defined as:
Exertion or the use of exertion against a person or thing that resists
Motion and Force
What input is required for this drill to work?
Input
The lever of the drill is pulled down
Output The chuck of the drill moves down
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Motion
There are four main types of motion:
1. Linear Motion – movement in a straight line
2. Reciprocating Motion – backwards and forwards movement
3. Rotary Motion – movement around in a circle
4. Oscillating Motion – movement over and back in an arc
Can you think of any everyday examples of these types of motion?
1. Linear Motion
A train on its tracks moves in a linear motion.
Can you give any other examples of linear motion?
2. Reciprocating Motion
Engine pistons and valves move up and down
(reciprocate) continuously.
Can you think of any other examples?
3. Rotary Motion
Rotary motion is also known as circular motion.
The wheels of a bicycle move in a rotary fashion.
What other examples of rotary motion can you think of?
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4. Oscillating Motion
The pendulum of a clock and a child on a swing are both examples of oscillating motion.
Can you think of any other examples?
Newton’s First Law of Motion
Newton’s First Law states:
A body continues at rest or at a constant speed in a straight line, unless it is acted on by an
external force.
This means that without the application of force, a body at rest will not move and a body in motion
will continue at a constant velocity forever, if no force is applied to it.
The above rules are true in theory. In practice, however, a car moving along a level surface will
always slow down, if no force is applied. This is because of frictional forces acting as a brake.
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Newton’s Third Law of Motion
Newton’s Third Law states:
To every action there is an equal and opposite reaction.
In other words, if Object A exerts a force on Object B, then Object B will consequently exert an
equal and opposite force on Object A.
This is demonstrated when a car sits on a road. The car tyres push against the road. The road, in
turn, pushes back on the tyres in the opposite direction. As a result of the forces being equal and
opposite, the car sits on the road’s surface.
It neither floats nor sinks, but rather remains sitting.
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Force
There are five main types of force:
1. Tension
2. Compression
3. Shear
4. Torsion
5. Bending
A Rope in Tension
Columns in Compression
Pipe Bending
1. Tensile Force (Tension)
As demonstrated in a spring, this is where a load pulls an object apart.
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2. Compressive Force (Compression)
This is where a load presses or squashes objects together, as with the cans being crushed by
compression below.
3. Shearing Force (Shear)
This occurs when loads push at right angles to the surface of the object, as demonstrated by the
image of the scissors below.
4. Torsion Force (Torsion)
This occurs when the load causes an object to twist.
5. Bending Force (Bending)
This will occur when a load or force causes an object to bend to an angle.
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Load
As there are different types of forces acting on a structure, so too will there be different types of
load.
Static Load is a load which is fixed at one point,
e.g. a building.
Dynamic Load is a load which is not fixed to any
one specific point,
e.g. a car travelling along a road.
Structures
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A structure can be defined as an arrangement of parts joined together in a manner which provides
strength in order to facilitate the carrying of loads. There are many different types of structure in
existence. Examples of these include; buildings, bridges, cranes and chairs.
The Eiffel Tower
The Golden Gate Bridge
Most objects are arrangements of parts, e.g. atoms, crystals, cells.
Crystals
Atoms / Cells
Similarly, structures are objects made up of parts which, when combined, create solid structures.
What, do you think, contributes to strength in structures?
Hint: Structures are designed to be able to withstand loads, which may distort or break them.
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This picture shows a variety of structures, including;
buildings, a tower crane and scaffolding.
Factors which contribute to strength in structure are as
follows:
•
The strength of the material
•
The shape of the parts
•
The method used to join the parts together
•
The manner in which they are arranged
This Florentine Bridge and Thai Tribal Home incorporate all of the aforementioned factors in order
to contribute to their strength
.
Naturally Occurring Structures
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Nature provides us with the template to many of our strongest structures.
How many can you name?
Spiders Webs
Honeycomb
Trees
These naturally occurring structures must, in order to serve their purpose as structures, be able
to withstand loads. The forces of nature also provide an everyday challenge to these structures.
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Engineers have studied these naturally occurring structures, which have proven their strength and
durability against the forces of nature time and again. They have learned from them and
incorporated many of their features into useful designs with several applications in our various
man-made structures.
Bee’s Honeycomb
Mount Everest
Honeycomb Floor Mat
Egyptian Pyramid
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Forces
Force changes the state of rest or uniform motion of a body.
Force is measured in units of weight.
Point Load – A load acting on a point
Stable pair – When forces are equal
Unstable pair – When forces are not
equal
Stable combination – When opposite forces
are balanced
Universally distributed load – When the load
is spread evenly across a supporting member
The effects of force on a structure
Stress is caused within a structure by any force trying to change the shape of the structure.
Strain is the actual change in shape that is caused.
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Compression – is when something is
squeezed and can result in crushing.
Tension – is when something is pulled and
can result in stretching
Shear – is when something is cut or slides
and results in sliding or shearing
Torsion – is when something is twisted
Bend – is when something is bent and can be
permanently deformed
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Moments
Moments are any movement or action about a point or fulcrum. A moment is obtained by
multiplying the load by its distance from the point being considered.
Moment = F x d
Distance
(d)
Force
(F)
When something is in equilibrium, the moments of a force are balanced.
The Principle of Moments states that for there to be equilibrium, the clockwise moments must
equal the anti-clockwise moments.
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Calculating Moments
Example 1
Clockwise Moments = 20N x 1m
Anti-Clockwise Moments = 10N x 2m
20Nm = 20Nm
Therefore, the scales is in equilibrium.
Example 2
9 kN
2m
1m
RL
RL :
RR
RR x 3m = 9 x 2m
RR :
RL x 3m = 9 x 1m
RR = 9 x 2
RL = 9 x 1
3
3
RR = 6kN
RL = 3kN
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9kn
Example 3
3m
RL
RL :
1m
RR
RR x 3m = 9 x 4m
RR :
RR = 9 x 4
(RL x 3m) + (9 x 1m)
RL =
-9
3
3
RR = 12kN
RL = -3kN
So, in summary, equilibrium can be described as a state of balance which occurs when both
sides are equal.
Observing the picture on the left, each of the stones is of a
different size and non-uniform shape. However, these stones
have been stacked in a manner which allows them to balance
and remain upright. How is this possible?
Explanation: Each of these stones has an individual ‘point of
balance’ which, when placed in line with the ‘points of balance’ of
each of the other stones, allows the stack of stones to remain
upright and unwavering. This ‘point of balance’ is known as the
Centre of Gravity.
The Centre of Gravity is crucial to engineers, when designing large scale structures, such as high
rise buildings. It is vital that the building be in equilibrium, in order to ensure that forces such as
strong winds, earthquake tremors, or even traffic shudders, do not cause the building to shake on
its foundations and collapse.
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Manmade Structures Influenced by Natural Structures
In order to better understand the influence of structures in nature on manmade structures, we will
examine the following natural occurrences, and establish a link between natural and everyday
manmade structures:
•
A grass leaf
•
A water lily
•
A palm tree leaf
•
A sea arch
•
A snail shell
Water Lily
Palm Tree
Grass Leaves
Snail Shell
Sea Arch
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Grass Leaf
Plants often provide structural inspiration for engineers because they manage to achieve
characteristics which are simultaneously lightweight and strong
Grass leaves combine these two characteristics. The area between the two outer surfaces of a
grass leaf is made of a honeycomb or mesh structure. This honeycomb structure creates a
material which is very strong and stable, yet simultaneously thin and lightweight.
Grass Leaf under a Microscope
This image shows how the internal honeycomb
structure of a grass leaf provides it with its
strength
Manufactured Honeycomb Structures
Honeycomb is predominately used as a core in sandwiched structures to meet design
requirements for highly stressed structural components. When sandwiched between layers of
carbon fibre, honeycomb exhibits extreme resistance to shear stresses.
Water Lily
Water lilies are naturally very fine,
yet their structural properties enable
them to maintain their shape,
even in adverse weather conditions.
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On observation, the underside of a water lily consists of a
web-like structure, which grows from the centre of the
leaf outwards. This structure effectively scaffolds or
supports the surface of the leaf.
Supporting Structures
Can you think of any man-made structures which support platforms in the way that the
water lily does?
Sports stadiums, multi-storey car parks and modern factory roofs all use the water lily structure as
a model on which to construct and manufacture their structures.
The Eiffel tower’s giant Lily Pad design of the future.
A structure made with parts
that extend to meet each other.
Palm Tree Leaves
Palm tree leaves can grow to over 10m in length and 1m in width, yet in spite of this magnitude
they are very light in weight. This combination of characteristics allows the palm tree leaves, which
gain their strength from thin corrugated sheets, to be supported by their stalks.
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This cross section of a palm tree leaf shows a zigzag
pattern. This folded characteristic gives the leaf its thin
yet durable and hard-to-tear properties.
Corrugated Structures
Can you think of any man-made structures which take their inspiration from the palm tree
leaf?
Shed and garage roofs and cardboard packaging all use the palm tree leaf as a model on which to
base their corrugated structure, providing strength and durability without the hindrance of excess
weight.
Corrugation used in packaging
Corrugated roofing
In the sections above, we examined the honeycomb structure and the zigzag pattern of the palm
tree leaf. Designers have always tried to recreate these structural forms.
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Task
If you hold a sheet of paper at one end, the other end will flop and bend over.
What happens if the sheet is folded to recreate the zigzag structural form of the palm tree leaf?
In designing and building these structures, engineers have many factors to consider. Engineers
have found that by bending sheets into shapes, as in the above example, they are increasing the
rigidity of the material.
This can also be achieved through the square form.
Recreate these paper forms, as demonstrated above.
Experiment with creating a square form fold, in addition to the zigzag.
Examine, through experimentation, the maximum load each structure can bear.
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Sea Arch
Coastal features, such as pillars, caves and arches, formed naturally by weathering and marine
erosion, have inspired engineers for centuries. One of the most inspirational of all of these is the
arch.
The arch can be described as a curved opening
in a mass of rock resulting from the erosion of
rock by wave activity and chemical weathering.
Structural Arches in Buildings
Can you think of any man-made structures which take their inspiration from the sea arch?
The arch is a central and defining feature of many of our most famous and easily recognisable
building, such as the Colosseum in Rome.
In more everyday applications, arches can be seen in fields and over rivers all over the
countryside in the form of bridges. Builders use stone to form these arch shapes. These bridges
have their origins in Ancient Rome and are, therefore, sometimes known as The Roman Arch
Bridge. The main feature of this style of bridge structure is a keystone, as shown in the image
below.
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Keystone
Why do you think stone-built bridges use the arch as their structure?
What would happen if the keystone were removed?
Task
Using 40mm wooden cubed blocks, cut / shape / form them into a Roman Arch.
Experiment with different means of supporting the stones in place.
In more modern times, as technology has advanced, road bridges are occasionally of the
suspension design, as shown below.
As illustrated, the bridged roadway is carried by wire cables, which are supported by towers.
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Other bridges are constructed using concrete. These are known as beam bridges, an example of
which can be seen below.
As can be seen below, different types of frame structure can be joined together, using a variety of
material shapes, to construct girder bridges.
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Shells
‘Shell’ is a word commonly used to describe the hard covering
of eggs, crustaceans, tortoises, etc. A shell serves to protect
and provide shelter from the elements, whilst also being
lightweight. A shell is usually curved in form.
The snail’s shell, as shown, embodies all of the
aforementioned qualities.
Shell Structures in Design
Can you think of any man-made structures which take their inspiration from the shell?
Man-made shell structures are used in various sectors of engineering. Masonry or stone domes or
vaults in the Middle Ages facilitated the construction of more spacious buildings. Nowadays, the
use of reinforced concrete has made the use of shell-like structures commonplace.
Shell structures can usually be understood as a set of beams, arches and catenaries. They are
capable of carrying large point loads. The shape of a shell, rather than the materials used, is the
key to its strength. There are many examples of shell structure to be found in modern building
design. The Sydney Opera House is one such example. Shell structures play a very important
part in mechanical design as shown below.
Sydney Opera House
Car Shell
Shells serve to protect and provide excellent strength.
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Beams
A beam is a strip or section of material used to span a distance and support a load. They can be
used to add strength to a structure.
beam
Beams come in many different shapes.
Task: How do beams support?
•
Using a standard 300mm ruler and two blocks, arrange the materials as shown in the
diagram above.
•
With the ruler positioned flat on the two blocks, add a weight to the centre of the ruler.
•
Now, reposition the ruler on its edge and add the same weight to the centre of the
repositioned ruler.
•
Discuss the results…what happened and why?
•
What do you think would happen if a number of rulers were to be positioned on the flat on
the two blocks? Repeat the test under these conditions.
•
Replace these with a single piece of wood of equal dimensions
(approx.) to the rulers being removed.
•
Again repeat the test under these new conditions.
It can be concluded from these tests that a beam will bend under a downward load. On close
inspection, it can be seen that the top of the beam is being compressed, whilst the bottom of the
beam is being pulled apart and, is therefore said to be under tension.
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Compression along the top of
the beam
Tension along the
bottom of the beam
As we move from the bottom of the beam to the top, we change from tension to compression. But
what happens at the very centre? The answer is – somewhere in the middle, very little happens.
This area is known as the ‘neutral axis’.
Neutral axis (red
line)
As we know, a beam must work hard on both top and bottom to resist the forces of tension and
compression. Engineers designing beams know that very little happens along the neutral axis. For
this reason, beams are designed in order to be strongest along their top and bottom.
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Beam
Span
Post or
column
Beams are usually used in conjunction with what are known as posts or columns. These compose
the upright element of the structure, as illustrated above.
Why might it be important to have different sections of beam?
1. to save material
2. to reduce cost
3. to reduce weight
4. to maintain strength
In saving material, some beams can be constructed in hollow sections, as illustrated below
Box section
Circular section
Can you identify some of the uses of these sections in everyday life?
One such example of this is a bicycle. It is necessary for a bicycle to be lightweight, in order to
make cycling it easier. For this reason, the amount of material used needs to be reduced.
Therefore a bicycle is constructed using a circular section.
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Classroom tables are often constructed on a square or box section. Reducing the amount of
material used by constructing a hollow beam or beam section, accordingly reduces the cost of the
product, thereby making it more appealing to the consumer.
Classroom Table
Bicycle Frame
These circular or box sections are sometimes referred to as ‘tube’.
Beams can be manufactured in many different shapes and sizes, and when fixed together, they
can lend enormous strength to a structure.
Some examples of different beams shapes are illustrated below:
Angle Beam
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Channel Beam
Tee Beam
Universal Beam or I Beam
Universal Column or H Beam
As already stated, there are many different types of beam section, which have a diverse range of
functions in addition to the construction of buildings and bridges. Strength of beam and weight of
load are important factors to consider when choosing a beam. Beams and columns are not always
constructed using steel. Some beams are manufactured in wood, as seen in timber framed
houses. Beams can also be reinforced to provide additional strength, as illustrated below.
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Beam
Concrete
Steel
Head
Column
Steel
Tie
Base
Can you identify some of the uses of beams in everyday life?
Frames
Frames are structures made from sections of materials.
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Frames are used as the basis for the construction of many different artefacts, such as gates,
stools and picture frames. Their advantage is that they enclose spaces without filling them with
solid material.
However, the question must be asked…Are frames always rigid?
If the frame is examined in more detail:
A member is said to be a part of a complex structure.
The point which the members meet or join is called a joint.
Joints can be either fixed or pivoted. Pivoted joints are not very stable and if a large force is
applied to a corner the frame may lose its shape. A fixed joint is much stronger and can resist
larger forces than a pivot joint.
Member
Joint
A
B
How do you know if joints are fixed or pivoted – apply a force.
As shown above.
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Task
Take thin strips of card, plastic or wood and some pins, screws and nuts.
Make up some polygon frames, e.g. square, rectangle, pentagon, hexagon, etc.
What happens when force is applied to a corner of the constructed frame? Can any conclusions
be drawn from these tests?
A rectangular or square frame is not a rigid structure. It relies on the strength of the joints for its
rigidity.
Now, either remove or add a strut to create triangular shape within the structure. What
happens?...The triangle does not distort. We can conclude from this that triangles are more stable
and rigid structures.
Member
Adding one more member makes the
frame stable.
Joint
Can you identify the main shape which is repeated in the image below?
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A triangle is one of the strongest frame shapes known to man. The implementation of this
concept in design is known as triangulation. The term triangulation is used to describe the
arrangement of triangles together in the formation of a frame. Square, rectangular and other
frames can be made more rigid by bracing. In other words, bracing involves placing a diagonal
piece or strut to create a triangle.
The construction of roof trusses is based on the principle of triangulation.
The parts of a roof truss are identified as ties and struts.
All structures have forces which act upon them.
A tie is the part of a structure which has tensile forces acting upon it.
A strut is the part, which has compressive forces acting upon it.
Identify the struts and ties in the following images.
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Task
Take photographs or make sketches of triangulated structures.
Identify the struts and ties within these structures, bearing in mind that a tie has tensile
forces acting upon it and a strut has compressive forces acting upon it.
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Frame Analysis
The result of a measurement is always a number multiplied by a unit, e.g. 10mm (10 being the
number and millimetres being the unit of measurement). Magnitude is what we call the size of the
quantity being measured.
•
Something with magnitude and no direction is called a scalar quantity, e.g. 5kg
•
Something which has both magnitude and direction is called a vector quantity, e.g. 5kg
acting vertically downwards
•
Vectors can be shown by straight lines. The direction can be indicated by an arrow and
the magnitude by figures.
Calculating the Magnitude of the Perpendicular Components
v
y=v Sin Θ
Θ
Θ
x=v Cos Θ
Θ
If a vector of magnitude v has two perpendicular components, x and y, and v makes an angle Θ
with the component x as shown above, then the magnitudes of the components are as follows:
x=v Cos Θ
y=v Sin Θ
Proof: In the shaded triangle above:
Cos Θ
=
Ö Sin Θ
adjacent
=
hypotenuse
Ö Cos Θ =
x
y
v
Ö
y = v Sin Θ
v
Ö x = v Cos Θ
Sin Θ =
opposite
hypotenuse
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Calculations
Calculation One
Problem: Find the vertical and horizontal components of a vector of magnitude
20N acting at 60o to the horizontal
Solution:
20N
Horizontal component = x = 20 Cos 60o = 10N
Vertical component = y = 20 Sin 60o = 17.32N
Calculation
Two
o
60
Problem: A person pulls a chain which is attached to a trailer
300N
with a force of 300N. The rope makes an angle of 20o with the
horizontal. Find both the effective vertical and horizontal
20o
Solution:
forces on the trailer due to the chain.
Effective vertical force
=
Effective horizontal force
300 Sin 20o
=
(300)(0.342)
=
102.6N
=
300 Cos 20o
=
(300)(0.940)
=
282N
Note: It can be concluded from this calculation that a downwards vertical force of at least 102.6N is
required to keep the trailer on the ground and a horizontal force of 282N is required to prevent the
trailer from moving along the ground.
Calculation Three
Problem: A mass, which is simply supported by a frame, is shown in the
sketch. The pin A on the frame is in equilibrium. Determine the magnitude
of the forces acting on members B and C of the frame.
Solution: In order to firstly calculate the
force of the mass in Newtons, the mass (40kg)
must be multiplied by 10, giving a force of 400N.
The force at B is calculated as follows: 400 Cos 60o = (400)(0.5) = 200N
The force at C is calculated as follows: 400 Sin 60o =(400)(0.866) = 346.14N
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Factor of Safety
Imagine the following scenario; an elevator with a maximum load
capacity of 6 people is carrying a load of 8 people.
What do you think might happen in these circumstances?
The lift should not ‘give way’ as something known as a Factor of
Safety is implemented to ensure that the overloading of a lift will not
result in disaster. Factor of Safety is used to provide a margin of leeway of flexibility over the theoretical
Overcrowding
capacity of the item in question.
This is to allow for any uncertainty in the product.
This uncertainty could be attributable to any number
of things, from the strength of the material to the
manufacture quality to human disregard for regulations.
When allocating a Factor of Safety, the trustworthiness
of the product is examined. The more trustworthy a
product is, the lower its Factor of Safety will be, due to
the fact that the margin of lee-way is less uncertain.
However, the less reliable a product is, the higher its
Factor of Safety will be, due to the uncertain nature
of its maximum functioning capacity.
Disaster!
So, referring back to the previous scenario of the elevator; If the cable supporting the elevator will
break under a load limit of 1000kg, but is listed as having a maximum load limit of 100kg, it is listed as
having a Factor of Safety of 10.
Factor of Safety is crucial in structural design, as component failure could result in substantial financial
loss, serious injury or even death. The use of Factor of Safety does not, however, imply that a structure
or design is safe.
Incidences exist in our past which highlight the importance of factor of safety. One of the many reasons
for the failure of structures is its inability to withstand loading and unloading. For example a crane hook
lifting and dropping heavy loads continually. What should happen if the hook is not up to the job?
Which factors exist that lead to the hook being checked? As with all structures the responsibility of
making sure they are safe falls to the engineer. Tests are carried out to ensure the structure is safe.
This can be easy to do when the structure can be taken away and checked. However, what about the
likes of a bridge? Natural disasters, such as earthquakes, occur all the time, but what about the
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disasters that occur due to the failure of the structure? One such example occurred in 2003 in
Minneapolis, U.S., when the Interstate 35 Bridge collapsed, so tragically, during the height of a
Minneapolis rush hour. Investigators found that two factors contributed to its failure: age and heavy
use. The constant loading and unloading of the traffic across the bridge coupled with the increasing
volumes of traffic led to the eventual collapse of the bridge.
Aerial views of the Interstate 35 Bridge collapse
The factor of safety or Safety Factor, is used to provide a design margin to allow for
uncertainty in the design process. The uncertainty could be any one of a number of the
components of the design process including calculations, material strengths, duty, manufacture
quality. The value of the safety factor is related to the lack of confidence in the design
process. The simplest interpretation of the Factor of Safety is
Factor of safety = Strength of Component / Load on component
If a component needs to withstand a load of 200 Newton’s and a FoS of 4 is selected then it is
designed with strength to support 800 Newton’s...
The selection of the appropriate factor of safety to be used in design of components is
essentially a compromise between additional cost and weight and the benefit of increased
safety and/or reliability. Generally an increased factor of safety results from a heavier
component or a component made from a more exotic material or / and improved component
design
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The factors of safety listed below are based on the yield strength.
Factor of Safety Application
Material properties known in detail. Operating conditions known in detail
Loads and resultant stresses and strains known with a high degree of certainty.
1.25 - 1.5
Material test certificates, proof loading, regular inspection and maintenance.
Low weight is important to design.
Known materials with certification under reasonably constant environmental
conditions, subjected to loads and stresses that can be determined using
1.5 - 2
qualified design procedures. Proof tests, regular inspection and maintenance
required
Materials obtained for reputable suppliers to relevant standards operated in
normal environments and subjected to loads and stresses that can be
2 - 2.5
determined using checked calculations.
For less tried materials or for brittle materials under average conditions of
2.5 - 3
environment, load and stress.
For untried materials used under average conditions of environment, load and
3-4
stress.
Should also be used with better-known materials that are to be used in
3-4
uncertain environments or subject to uncertain stresses.
Task
Investigate the different types of bridge trusses that exist for example – Box girder, or Warren girder.
Construct the trusses from 6mm square wood strips or equivalent.
(The maximum length of the truss to be 600mm and height 60mm.)
Weight suspended from the truss.
1. Add increasing weights as a point load as shown above until the truss fails. Which type of truss
could withstand the greatest load?
2.
Add increasing weights as a universally distributed load until the truss fails. Which type of
truss could withstand the greatest load?
3. This time load and unload the weights at different points and times, attempting the replicate
traffic on the bridge. Record all positions and times. Repeat for all the trusses in the same
order and measure the amount the trusses bend and draw some conclusions.
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Moments
The crane in the image below looks unstable, as though it should topple over. There appears to be too
much of the boom on the left-hand side of the tower.
It doesn’t fall because of the presence of a counter balance weight
on the right-hand side. The boom is therefore balanced.
In order to understand this better, we need to understand pivots,
moments and equilibrium.
The pivot point or fulcrum is the point at which something rotates.
The weights on the scales are at equal points from the pivot point.
When something is balanced it is said to be in equilibrium.
In the example of the see-saw, if one of the people moves backwards
or forwards, the balance is tipped one way or the other.
The see-saw is no longer in equilibrium.
When something is in equilibrium, the moments of a force are balanced.
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The Moment of a Force is calculated as the force multiplied by the distance from the pivot point.
Moment = F x d
Distance
(d)
Force
(F)
This can also be represented as illustrated below:
The Moment of Force can also be called Torque. Torque can be defined as a force that tends to rotate
or turn things.
Torque is generated any time a force is applied using a wrench.
The Principal of Moments states that for there to be equilibrium, the clockwise moments must equal
the anti-clockwise moments.
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Clockwise Moments = F2 x d2
Anti-Clockwise Moments = F1 x d1
If F2 x d2 = F1 x d1 there is equilibrium
Example
Clockwise Moments = 20N x 1m
Anti-Clockwise Moments = 10N x 2m
20Nm = 20Nm
Therefore, the scales are in equilibrium.
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Levers
A lever is a rigid rod, pivoted about a fixed point or axis, which is known as a fulcrum.
•
Fulcrum or pivot – the point about which the lever rotates
•
Load – the force applied by the lever system
•
Effort – the force applied by the user of the lever system
A lever can be used to move a large load with a small effort.
The way in which a lever will operate is dependent upon the type of lever.
There are three types or class of lever, referred to as:
1. Class One e.g. See-saw
2. Class Two e.g. Wheelbarrow
3. Class Three e.g. Shovel
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In each class the position of the Load, Effort and Fulcrum are changed.
Class
One
Class
Two
Class
Three
Can you give three examples for each class?
Class One Levers
•
This is the most common type of lever, with the fulcrum in the middle, the effort on one side
and the load on the other
•
A see-saw is an example of a Class One Lever. Other examples are a crowbar, scissors or
weighing scales.
•
The distance between the effort and the fulcrum, and the distance between the load and the
fulcrum, determine the mechanical advantage and the velocity ratio of the Class One Lever.
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Class Two Levers
•
With a Class Two Lever, the fulcrum is at one end, the effort is at the other end and the load is
in the middle
•
A wheelbarrow is an example of a Class Two Lever. Other examples include bottle openers,
nut crackers and foot pumps
•
A Class Two Lever allows a large load to be lifted by a smaller effort. Because the load is
always closer to the fulcrum, the effort is always less than the load
Class Three Levers
•
With a Class Three Lever, the pivot is at one end, the load is at the other and the effort is in the
middle
•
A shovel is an example of a Class Three Lever. Other examples are a pair of tweezers and a
fishing rod
•
A Class Three Lever allows a small load to be lifted by a larger effort
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Mechanical Advantage
The image below shows a man using a stake to lift a rock. This is an example of a mechanism. As the
man exerts a small amount of effort to the end of the lever, the rock is moved. This gain in effort is
known as Mechanical Advantage.
Mechanical Advantage =
Load
Effort
Mechanical Advantage – Calculation
The mechanism shown is being used to raise a weight of 400N. By adjusting the lever, it was found
that the weight could be lifted with an effort of 100N.
Effort
Load
What is the Mechanical Advantage of this mechanism?
Load
Effort
=
Mechanical Advantage
400N =
4:1
or
100N
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Velocity Ratio
Distance moved
by effort
Lever
Load
Distance moved
By load
The image above shows the position of
weight prior to force being applied. The image on the right
demonstrates the distance moved by the weight on application of force.
When enough effort is applied to the lever, the weight will move. The distance moved by the lever is
greater than that moved by the weight.
The difference is known as the Velocity Ratio.
The Velocity Ratio =
Distance moved by effort
Distance moved by load
Velocity Ratio – Calculation
•
The mechanism shown is being used to lift a weight.
•
The 400N weight is moved with 100N of effort.
•
The lever is moved 85cm in order to raise the weight 17cm.
Distance moved
By lever
85cm
Distance moved
By load
17cm
What is the Velocity Ratio of the mechanism?
Velocity Ratio =
distance moved by effort
distance moved by load =
17cm
=
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85cm
=
5:1 or 5
52
Linkages
A linkage is a mechanism made by connecting two or more levers together.
A linkage can be used to change the direction of a force or to make two or more things move at the
same time.
Windscreen wipers on a car operate using linkages
Reverse Motion Linkages
Linkages can be used to make things move in opposite directions. The movement is reversed by using
a lever to form the linkage. If the pivot point (fulcrum) is at the centre of the connecting lever, then the
output movement will be the same as the input movement, but it will act in the opposite direction
Fulcrum
or pivot
point
A Reverse Motion Linkage
A Clothes Horse
Push-Pull Linkages
Push-pull linkages are used to move the output in the same direction as the input. This consists of
levers with two fixed pivot points.
Pivot point
A Push-Pull Linkage
Windscreen Wipers
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Bell Crank Levers
Bell Crank Levers are used when it is necessary to change the direction of movement or force through
900. If the fulcrum is at an equal distance from the input and output, then the movement of the output
will be equal to the movement of the input. Otherwise, the movement will be different and the system
will have Mechanical Advantage.
Pivot point
Bicycle Brake
A Bell Crank Lever
Parallel Motion Linkage
This linkage can be used to make things move in the same direction at a set distance apart. Parallel
motion is only achieved if the levers at opposite sides of the parallelogram are equal in length.
Parallel Motion Linkage
Toolbox
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Task
How do linkages work?
Reconstruct each of the above linkage types using strips of card and paper pins.
Examine the effect moving the positions of the pins (or pivot points) will have on the movement of the
pieces of card. (Note increase or decrease in distances moved)
Note: If the pivot point of a reverse motion linkage is not in the centre of the connecting levers, then
the movement of the output will not be equal to the movement of the input. It is also possible to design
a reverse motion linkage which will provide mechanical advantage.
Can you observe any similar traits in any of the other linkage types?
Crank and Slider
A Crank and Slider mechanism changes rotary motion to reciprocal motion or vice versa. In a car
engine, the reciprocating motion of the piston caused by exploding fuel is converted into rotary motion,
as the connecting rod moves the crankshaft around.
A pneumatic air compressor uses this principle in reverse – an electric motor turns the crankshaft and
the piston moves up and down to compress the air.
Crank and Slider
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Pulleys
A pulley wheel is a mechanism which helps move or lift objects. Like most wheels, pulley wheels spin
or rotate on an axis. The centre of a pulley wheel features a groove. Nested in this groove is a rope,
belt or cable.
pulley
The man in this image is pulling
downwards on a bar, which is attached to a cable.
Tracing the cable’s path through the machine, it can
be seen that the cable passes through the pulley
wheels, and its opposite end is connected to the
weights at the bottom.
Exercise Machine
Parts of a Pulley System
Effort – the force the man is applying to the bar
Load – the weight being lifted
Fulcrum – the pivot point of the pulley
Direction of Force
Notice that the pulleys change the direction
of the applied force. Although the machine is pulling
sideward’s, the weights are moving
upwards.
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Types of Pulley
There are three basic types of pulley. These types of pulley are classified by the number of pulley
wheels and their positioning.
1. A Fixed Pulley
This does not rise or fall with the load
being moved. It also changes the
direction of the applied effort.
A ski-lift operates on a fixed pulley system
2. A Moveable Pulley
This type of pulley rises and falls with the load being moved.
Pulley on Weight-Lifting Machine
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3. A Block and Tackle Pulley
This consists of two or more pulleys (fixed and moveable). The block and tackle is capable both of
changing the direction and creating a Mechanical Advantage.
Block and Tackle in use on a Boat
Block and Tackle Pulley
The Pulley
The pulley is really a wheel and axle with a rope or chain attached. A pulley makes work seem easier
because it changes the direction of motion to work with gravity. If a heavy load, like a bale of hay,
needs to be lifted up to the second floor of a barn, you could tie a rope to the bale of hay, stand on the
second floor, and pull it straight up. Or you could put a pulley at the second floor, stand at the first floor,
and lift the bale of hay by pulling straight down. It would be the same amount of work in either case, but
the action of pulling down feels easier because you're working with the force of gravity.
The Pulley Advantage
A pulley really saves effort when you have more than one pulley working together. By looping a rope
around two, three, or even four pulleys, you can reduce the effort needed to lift something. However,
as you increase the number of pulleys, you also increase the distance you have to pull the rope. In
other words, if you use two pulleys, it takes half the effort to lift something, but you have to pull the rope
twice as far. Three pulleys will result in one-third the effort — but the distance you have to pull the rope
is tripled!
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Fig. 1 shows a pulley arrangement consisting of one pulley and
a load on one end of the rope. For the load and pulley to remain
in equilibrium, the person holding the end of the rope must pull
down with a force that is equal to the load.
In this simple pulley system, the force is equal to the load, so
the Mechanical Advantage is 1:1 or 1.
100N
Fig. 1
Fig. 2 shows a pulley arrangement consisting of two
pulleys. The upper pulley is fixed in position and the
lower pulley is moveable. The load is supported in two
locations – at the rope end which is attached to the
upper bar and at the end of the rope held by the person
(via the upper pulley).
Each side of the rope carries half the load. Therefore,
100N
the force required by the person to keep the load in
equilibrium is also half the load.
Fig. 2
This system has a Mechanical
Advantage of 2:1 or 2.
Fig. 3 shows a pulley arrangement consisting of four
pulleys. A quick way to work out the Mechanical
Advantage of a system is to add the tension in the
ropes. For example, if one unit of tension is applied to
the rope held by the person (via the large pulley fixed to
the bar), then one unit of tension is applied to each of
the four ropes attached to the load pulley. Therefore,
there are four units of tension on the load.
This system has a Mechanical
100N
Fig. 3
Advantage of 4:1 or 4.
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Calculation
This pulley arrangement features a
4:1 Mechanical Advantage.
How can pulleys assist work?
Just like other simple machines, pulleys
can change the relationship between
force and distance.
For example, pulling the rope 2m in order to lift a load 0.5m, the output distance is divided and the
output force is multiplied by the same factor. Therefore, a load of 60kg can be lifted by only 15kg of
effort!
The Mechanical Advantage is calculated like so:
Mechanical Advantage = Load / Effort = 60kg / 15kg
Mechanical Advantage = 4:1 or 4
As already stated pulleys are used for transferring motion and force from one shaft to another. Many
machines are often driven by round grooved pulleys and rubber belts. The vacuum cleaner uses a
pulley to transmit power from the electric motor to the rotating brushes. If both pulleys are the same
diameter, then they will both rotate at the same speed. If one pulley is larger than another, then
mechanical advantage and velocity ratio are introduced. A large drive pulley will cause a smaller driven
pulley to rotate faster. In situations where no slip between the driven and driver pulleys can be allowed
a vee pulley and vee belt will provide less slippage than a flat belt pulley system. If more positive drive
is required a toothed belt and pulley can be used.
Pulleys and belt
Toothed belt and pulleys
Calculation 1
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If a 120mm diameter pulley drives a 60mm diameter pulley for each revolution of the driver pulley, the
driven pulley does two, as 120mm ÷ 60mm = 2
Calculation 2
The diameter of a motor pulley is 40mm and it revolves at 280 rev/min. The diameter of the driven
pulley is 70mm. What is its rotational speed?
Note: As the driven pulley is larger than the motor pulley, it will revolve more slowly
Speed of driven pulley =
280 x 40
rev/min = 160 rev/min
70
Chain and Sprockets
Chains and sprockets provide direct drive with no slippage. They are usually used on bicycles,
camshafts and motorcycles. When compared to the pulley and belt systems chain and sprocket will be
far more reliable.
Calculation 1
The sprocket on a bicycle has 45 teeth and
the sprocket on the back wheel has 15 teeth. So, for ever
revolution of the front sprocket, the rear one will complete
three full revolutions, as 45 ÷ 15 = 3
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Calculation 2
The sprocket on an engine of a moped has 15 teeth and the sprocket on the back wheel has 120 teeth.
If the engine revolves at 3200 rev/min, what is the rotary speed of the rear sprocket?
Note: The rear sprocket is larger, therefore it revolves more slowly.
Speed of rear sprocket =
3200
x
15
120
=
3200
x
1
8
=
400 rev/min
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Cam and Follower
•
The Cam and Follower is a device which can convert rotary motion (circular motion) into
linear motion (motion in a straight line).
•
A cam is a specially shaped piece of material, usually metal or hard-wearing plastic, which is
fixed to a rotating shaft.
•
There are several different types of cam, but most of these can be placed into two groups,
namely rotary or linear.
•
Many machines use cams. A car engine uses cams to open and close valves.
Follower
Cams
Followers
(valves)
Cam
Cams
•
A cam can have various shapes. These are known as cam profiles.
•
Cam profiles can be pear, heart, circular or drop shaped.
•
Pear
Heart
Circular
•
One complete revolution of the cam is called a cycle.
•
As the cam rotates, there will be one distinct event per revolution.
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Drop
63
Followers
•
A follower is a component which is designed to move up and down as it follows the edge of the
cam.
•
Follower profiles can be knife edge, flat foot, off set or roller.
Knife Edge
Follower
•
Flat Foot
Follower
Off Set
Follower
As the cam rotates, the follower moves accordingly.
The exact distance it moves depends on the
Roller
Follower
Follower
shape and size of the cam.
Cam
•
The cam follower does not have to move
up and down – it can be an oscillating lever,
as shown here.
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Rotary Cams
•
Rotary Cams change rotary motion into reciprocating (backwards and forwards) motion.
•
The ‘bumps’ on a cam are called lobes.
•
The square cam illustrated, has four lobes,
Follower
and lifts the follower four times each revolution.
Examples of other rotary cam profiles
Square cam
Rotary Cams in Operation
This image depicts a cam used in an engine to control the movement of
the valves.
These cams are used in a pump to control the
movement of the valves.
Cam
Follower
Cam and Follower Mechanism of a Sewing Machine
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Cam
Linear Cams in Operation
Follower
Maximum
distance
moved by the
follower
Linear cam
•
The linear cam moves backwards and forwards in a reciprocating motion.
•
Linear cams change the direction (and magnitude) of reciprocating motion
•
The shape of the surface of the cam determines how far the follower moves.
Cylindrical Cams in Operation
•
Cams can also be cylindrical in shape.
•
The cylindrical cam rotates on an axis.
•
The profile of the cylindrical cam decides
the movement of the follower, which is fixed.
Here, we can see the two different displacements represented
by the red and green arrows.
The red arrow shows the displacement of the follower, i.e. the
distance travelled up or down by the follower.
The green, curved arrow shows the angular displacement
travelled by the cam.
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Gears
•
A gear is a wheel with teeth on its outer edge
•
Gears rotate on a central axis and work with other gears to transmit turning force
•
The teeth of one gear mesh (or engage) with the teeth of another, as depicted below
•
Gears are used to transmit turning force
•
They can also change the amount of force, speed and direction of rotation
The rotating force produced by an engine, windmill or other device, needs to be transferred or
changed in order to do something useful.
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Driver and Driven
•
Two meshed gears always rotate in opposite directions.
Driven gear
Driver gear
•
In the above image, the smaller gear is the driver or input gear.
•
The driver’s teeth engage the teeth of the driven gear causing it to rotate.
•
In other words, the driver drives the driven, thus providing the input force; the driven gear
follows the driver, thus yielding the output force.
Direction of Rotation
•
The driver and the driven rotate in opposite directions. This is always the case when two gears
are meshed directly together.
•
Sometimes it’s necessary to reverse the direction of rotation. The reverse gear in a car is a
practical example of this.
•
In other cases, however, it’s necessary for the driver and driven to rotate in the same direction.
•
Inserting an idler gear between the driver and the driven is the simplest way to achieve this.
Driver
Idler gear
Driven
Gear Ratio
•
If a pair of meshed gears has a driver and driven of the same size, then there will be no
change in speed or force of input or output. This is stated as 1:1 Gear Ratio – one turn of the
input yields one turn of the output.
•
Generally, the Gear Ratio is calculated by counting the teeth of the two gears and applying the
following formula:
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Gear ratio =
Number of teeth on driven gear
Number of teeth on driver gear
Gear Ratio – Calculation
A 100 tooth gear drives a 25 tooth gear.
Calculate the Gear Ratio for the meshing teeth.
Gear ratio =
Number of teeth on driven gear
(Velocity Ratio) Number of teeth on driver gear
Gear ratio =
Driven
Driver
=
100
25
=
4
1
This is written as 1:4
Speed of Driven Gear – Calculation
A motor gear has 28 teeth and revolves at 100 rev/min.
The driven gear has 10 teeth.
What is its rotational speed?
Speed of driven gear =
Number of teeth on driver gear x
Number of teeth on driven gear
Speed of driven gear =
Driver =
Driven
100
28 x 100
10
= 280 rev/min
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Gear Trains
•
Multiple gears can be connected together to form a Gear Train
•
If there is an odd number of gears in the Gear Train, the output rotation will be the same
direction as the input
•
If there is an even number, the output will rotate in the opposite direction to the input.
Compound Gear Trains
A compound gear train is one which has two or more gears
attached to the same shaft. In actual fact, it is a combination
of two or more gear trains.
Calculation
A gear of 22 T drives another of 46 T. Attached solidly to the second gear is a 32 T, which drives a
gear of 80 T. If the first gear makes 100 rev/min, calculate the speed of the last.
The middle shaft turns at
100 x 22 rev/min
46
and the last gear makes 100 x 22 x 32
46
80
= 19.13 rev/min
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Worm and Wheel
•
In a simple Gear Train, very high or very low Gear Ratios can be achieved by combining very
large and very small cogs, or by using a worm and wheel.
•
The Velocity Ratio of a Worm and Wheel
is easily calculated, because the worm has
only one tooth. The worm gear is always the
drive gear.
For example, if the wheel gear has 60 teeth and the worm
gear has one tooth, then Velocity Ratio is 1/60 = 1:60
•
A worm and wheel can be seen in everyday use in gear box systems, where large loads are to
be lifted, e.g. bridge lifting mechanism.
•
Its major advantage lies in the fact that the worm is always the drive gear, as mentioned
above. This enables the worm and wheel to lift or lower significant weight without causing
strain on the gearbox.
Rack and Pinion Gears
The Rack and Pinion Gear is used to convert between rotary and linear motion.
Often the pinion rotates in a fixed position and the rack is
free to move – this arrangement is used in the steering
mechanisms of most cars.
Alternatively, the rack may be fixed and the pinion rotates,
moving up and down the rack.
Note:
The distance moved by the rack corresponds directly with the number of teeth on the pinion.
For example, if the pinion has 12 teeth, as in the illustration above, each anti-clockwise rotation of the
pinion will result in a movement to the right of the rack, by a measure of 12 teeth.
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Bevel Gears
•
Bevel gears are used to transfer drive through an angle of 900. If both gears have the same
number of teeth, they are called mitre gears.
•
Bevel gears will provide some Mechanical Advantage or increase in Velocity Ratio.
Bevel Gears
Work exists everywhere, and although it cannot be seen, its effects can be felt all the time. It is only
possible to do work if you have energy, which can be applied. Energy exists and cannot be destroyed,
but energy cannot be created from nothing.
Work comes in a number of different forms. Three of these are:
1. Mechanical Work – e.g. allowing a car to run
2. Electrical Work – e.g. allowing lights to be turned on
3. Heat Work – e.g. providing warmth from a fire
Work = force x distance moved in direction of the force
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Power is the rate at which energy is converted from one from into another. All moving objects and
machines only have limited power. They may be able
to handle lots of energy, but it is only possible to do
this at a certain rate.
Average power used:
total time taken
total work done
A windmill converts wind energy into mechanical energy
The amount of power a machine can produce lots of energy is not the only factor to be considered
when designing a moving object. It is also necessary to consider the efficiency of the machine.
Efficiency refers to the amount of energy lost through work. Some machines are very efficient
because they lose very little energy. Some machines are less efficient, because they lose heat through
friction, which can never be gotten rid of, but can be reduced.
Power output x 100
Efficiency (%) =
Power input
Friction resists the movement of one surface over another.
Friction is increased as:
1. the surfaces become rougher
2. the pressure between the surfaces increases
3. less friction-resistant materials are used
Friction has a number of effects:
1. it produces heat
2. it causes parts to wear
3. it reduces a machine’s power
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The rough surface of the bicycle brake pads, creates friction
when applied to the rubber of the tyre, thus causing the
bicycle wheel to stop turning
Sometimes friction is advantageous, e.g. bicycle or car brakes would not work without friction.
However, when smooth movement is necessary, friction must be reduced. This can be done by:
1. using low friction materials, such as bronze, brass, nylon or white metal
2. using a lubricant, such as oil or grease, to separate surfaces
3. ensuring that surfaces are as smooth as possible
4. using moving bearings, like a roller bearing
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