Structures and Mechanisms Booklet

7/28/2019 Structures and Mechanisms Booklet

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Leaving Cert i f icate

Technology

Structures and Mechanisms


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Introduct ion ..................... 2.

Mot ion ..................................... 6.

Newtons Third Law of Motion . 8.

Force 9.

Load . 11.

Structures .. 12.

Naturally occurr ing 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 classi fication 49.

Mechanical advantage .. 51.

Veloc ity ratio 52.

Linkages 53.

Pulleys ... 56.Pul ley advantage 58.

Calcu lations . 60.

Cams and fol lowers 63.

Rotary cams . 65.

Linear cams . 66.

Gears . 67.

Gear trains 70.

Power . 73


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Galway Education Centre2

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.

Introduction


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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 Cam and Follower


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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 funct ion

Motion is defined as:

The process of con tinual change in the position of an object


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Force is defined as:

Exertion o r 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?

Newtons First Law of Motion

Newtons 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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Newtons Third Law of Motion

Newtons 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 roads 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. Tensi le 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 ofload.

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, cont ributes to strength in st ructures?

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 asfollows:

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 asstructures, 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.

Bees Honeycomb Honeycomb Floor Mat

Mount Everest 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 itsdistance from the point being considered.

Moment = F x d

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.

Distance(d)

Force(F)


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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

RL : 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

2 m

9 kN

1 m

RL RR


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Example 3

RL : RR x 3m = 9 x 4m RR : (RL x 3m) + (9 x 1m)

RR = 9 x 4 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.

RL RR

3m 1m

9kn


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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 Snail Shell

Grass Leaves 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 ormesh 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.

Support ing Structures

Can you think of any man-made structures which support platforms in the way that the

water lil y 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.

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.

The Eiffel towers giant Lily Pad -design of the future.


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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.

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.

Corrugated roofing

Corrugation used in packaging


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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 snails shell, as shown, embodies all of the

aforementioned qualities.

Shell Structures in Design

Can you think of any man-made structures which take their inspi ration 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.

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 resultswhat 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.

beam


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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.

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.

Tension along the

bottom of the beam

Compression along the top ofthe beam

Neutral axis (redline)


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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.

Beam

SpanPost orcolumn


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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 orI 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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Can you identify some of the uses of beams in everyday life?

FramesFrames are structures made from sections of materials.

Head

Column

Steel

Tie

Base

Concrete

Steel

Beam


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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 askedAre frames always rigid?

If the frame is examined in more detail:

A memberis said to be a part of a complex structure.

The point which the members meet or join is called a jo int.

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

A B

How do you know if joints are fixed orpivoted apply a force.As shown above.

Joint


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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 conclusionsbe 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

Joint

Adding one more member makes theframe stable.

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 scalarquantity, e.g. 5kg

Something which has both magnitude and direction is called a vectorquantity, 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

If a vector of magnitude v has two perpendicular components, x and y, and v makes an angle

with the component x as shown above, then the magnitudes of the components are as follows:

x=v Cos y=v Sin

Proof: In the shaded triangle above:

Cos = adjacenthypotenuse

Cos = x

v

x = v Cos

Sin = opposite

hypotenuse

Sin = y

v

y = v Sin

vy=v Sin

x=v Cos


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Calculations

Calculation One

Problem: Find the vertical and horizontal components of a vector of magnitude

20N acting at 60oto the horizontal

Solution: Horizontal component = x = 20 Cos 60o = 10N

Vertical component = y = 20 Sin 60o= 17.32N

Calculation Two

Problem: A person pulls a chain which is attached to a trailer

with a force of 300N. The rope makes an angle of 20owith the

horizontal. Find both the effective vertical and horizontalforces on the trailer due to the chain.

Solution: Effective vertical force = 300 Sin 20o

= (300)(0.342)

= 102.6N

Effective horizontal force = 300 Cos 20o

= (300)(0.940)

= 282N

Note: It can be concluded from this calculation thata 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 pinA 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

60o

20N

20o

300N


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t4 Galway Education Centre42

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 lee-

way 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 thelikes 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 Newtons and a FoS of 4 is selected then it is

designed with strength to support 800 Newtons...

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 SafetyApplication

1.25 - 1.5

Material properties known in detail. Operating conditions known in detailLoads and resultant stresses and strains known with a high degree of certainty.

Material test certificates, proof loading, regular inspection and maintenance.

Low weight is important to design.

1.5 - 2

Known materials with certification under reasonably constant environmental

conditions, subjected to loads and stresses that can be determined usingqualified design procedures. Proof tests, regular inspection and maintenancerequired

2 - 2.5Materials obtained for reputable suppliers to relevant standards operated innormal environments and subjected to loads and stresses that can bedetermined using checked calculations.

2.5 - 3For less tried materials or for brittle materials under average conditions ofenvironment, load and stress.

3 - 4For untried materials used under average conditions of environment, load andstress.

3 - 4Should also be used with better-known materials that are to be used inuncertain 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 doesnt 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 orfulcrum 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

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.

Distance(d)

Force(F)


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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 leveris 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.

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.

ClassThree

ClassTwo

ClassOne


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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 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.

What is the Mechanical Advantage of this mechanism?

Load

Effort

Mechanical AdvantageLoad = 400N = 4:1 or 4Effort 100N

Mechanical Advantage = Load

Effort


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LoadLever

Distance movedby effort

Distance movedBy load

Velocity Ratio

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 .

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.

What is the Velocity Ratio o f the mechanism?

Distance movedBy lever

85cm

Distance movedBy load17cm

The Velocity Ratio = Distance moved by effortDistance moved by load

Velocity Ratio = distance moved by effort = 85cm = 5:1 or 5distance moved by load = 17cm


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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

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.

A Push-Pull Linkage Windscreen Wipers

Fulcrum

or pivotpoint

Pivot point


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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.

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

Pivot point


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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.

The man in this image is pulling

downwards on a bar, which is attached to a cable.

Tracing the cables 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 o f Force

Notice that the pulleys change the direction

of the applied force. Although the machine is pulling

sidewards, the weights are moving

upwards.

pulley


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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 PulleyThis 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 pulldown 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.

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,

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

Fig. 3 Advantage of 4:1 or 4.

100N

100N

100N


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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!

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

The Mechanical Advantage is calculated like so:Mechanical Advantage = Load / Effort = 60kg / 15kgMechanical Advantage = 4:1 or 4


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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 befar 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 Followeris 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 orlinear.

Many machines use cams. A car engine uses cams to open and close valves.

Cams

A cam can have various shapes. These are known as cam profiles.

Cam profiles can be pear, heart, circular or drop shaped.

One complete revolution of the cam is called a cycle.

As the cam rotates, there will be one distinct event per revolution.

Cam

Follower

Cams

Followers(valves)

Pear Heart Circular Drop


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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.

As the cam rotates, the follower moves accordingly.

The exact distance it moves depends on the

shape and size of the cam.

The cam follower does not have to move

up and down it can be an oscillating lever,

as shown here.

Knife EdgeFollower

Flat FootFollower

Off SetFollower

RollerFollower

Cam

Follower


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Follower

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,

and lifts the follower four times each revolution.

Examples of other rotary cam profiles

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 and Follower Mechanism of a Sewing Machine

Square cam

Follower

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.

In the above image, the smaller gear is the driveror input gear.

The drivers 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 its necessary to reverse the direction of rotation. The reverse gear in a car is a

practical example of this.

In other cases, however, its necessary for the driver and driven to rotate in the same direction. Inserting an idlergearbetween the driver and the driven is the simplest way to achieve this.

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:

Driver gearDriven gear

Driver

Idler gear

Driven


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Gear Ratio Calculation

A 100 tooth gear drives a 25 tooth gear.

Calculate the Gear Ratio for the meshing teeth.

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?

Gear ratio = Number of teeth on driven gearNumber of teeth on driver gear

Gear ratio = Number of teeth on driven gear(Velocity Ratio) Number of teeth on driver gear

Gear ratio = Driven = 25 = 1Driver 100 4

This is written as 1:4

Speed of driven gear = Number of teeth on driver gear x 100Number of teeth on dr iven gear

Speed of driven gear = Driver = 28 x 100Driven 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 isfree 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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Poweris 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 takentotal 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.

Efficiency (%) = Power output x 100

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 machines 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

Structures and Mechanisms Booklet

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