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Unit 2. Mechanism and machines


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1. Introduction2. Rectilinear movement into an equivalent:Levers. Pulleys and Hoist. Sloping flat. Wedge. Screw

3. Circular movement intoi. Rectilinear: Rack and Pinion , handle-winchii. An equivalent: gears, wheels, pulleys and strap.iii. An alternative rectilinear: Crank-connecting rod, cam4.Thermal machinesi. Steam engineii. Explosion engineiii. Reaction engine

Unit 2. Machines and mechanisms


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Which one of

these objectsis a mechanism andwhich one is a structure?


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2.1 Introduction

Structures and mechanisms resists forces

and transmit them, but mechanism cantransform these forces and movement inour benefit.


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A machine is a group of elementsthat help us do a job. Inside we can

find, mechanism, engines andstructures

Unit 2. Machines and mechanisms


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2.2 Rectilinear into an equivalent

Rectilinear Rectilinear


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In this group we will find machines thattransform a rectilinear movement intoanother rectilinear movement. Thesimplest one is the lever


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Lever: It is a mechanism made up of arigid bar and a point of support which isalso called a fulcrum.



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Archimedes said once:Give me a place to stand

on, and I will move theEarth


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Resistance (R) is a force (normally the weight of anobject) that has to be overcome by the use of theapplied Force (F).

2.2 Rectilinear into an equivalentLever elements

The point of support, or fulcrum, is the point on whichthe lever swings. The arms correspond to the distancebetween the fulcrum and the applied force or theresistance.

Fulcrum

ForceResistance

dRarm dFarm


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2.2 Rectilinear into an equivalentLever elements

Fulcrum

ForceResistance

dRarm dFarm

The lever's LawR!dR=F!dF


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In physics we define mechanical work as

the amount of energy transferred by aforce acting through a distance

W= Fdd= distance between A and B

F= Force applied to move theobject

F

d


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Levers behave according to a law of physics,called the LAW OF THE LEVER, that isderived from the

Newtons second Law.

Equilibrium means that all forces applied toan object are neutralized

!F=o



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Therefore, if we apply the Newton's law, weget that, when there is an equilibrium, allforces and works applied to an object areequal to cero

Equilibrium !Fd=!W=0!W= Wr+Wf=0

Wr= Wf



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Wr= Wf

The lever's Law

R!dR=F!dF


Units:

R,F= [N]

D=[m]W=[Nm]=[j]


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Exercise: Calculate the weight of the man tobe able to raise the old lady.

Data:

Mans distance to fulcrum= 1 m

Ladys distance to fulcrum= 2 m

Ladys weight= 90 Kg

1Kg= 9,8N

1 Ex 2.2 Rectilinear into an equivalent

Solution


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1. We read the text2. We identify the mechanism, and write

all the related formulas

3. We draw the diagram of thismechanism

How to do an exercise

LeverRdR=FdF

Fulcrum

ForceResistance

dRarm dFarm


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4. We write all the data that we need tosolve any exercise. Change all units toIUPAC: Meters, Kg, Newtons, etc..

5. We read the text again and write thevalue of the magnitudes needed.

F=? R= 882N DR=2m DF=1m4. We calculate the magnitude

How to do an exercise

Distance Mass Force Time

Meters Kilograms Newtons Seconds


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Exercise: Calculate the force that has to beapplied to break this nut.Extra data:

Dstance between the nut and fulcrum =2cm Nut weight= 15gr Nut Break limit Resistance= 1 N Force distance to fulcrum= 15cm Resistance distance to fulcrum= 5cm

Resistance

Force


Solution


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Exercise: What must the distance bebetween the ant and the fulcrum in orderto rise an elephant that weights 1 ton.

Extra data:

Distance between elephant and fulcrum =1cm Ant weight= 1gr Fulcrum weight= 30kg Ant height= 1m


Solution


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There are three classes of levers and eachclass has a fulcrum, load and effort whichtogether can move a heavy weight.



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First Class lever: Fulcrum is situatedbetween the Force and Resistance


Force

Resistance

Arm Arm


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Second Class lever: the Resistance issituated between the Force and the Fulcrum


ForceResistance

Arm Arm

Resistance

Force


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Third Class lever: the Force is situatedbetween the Resistance and the Fulcrum


Force

ArmArmResistance

Force

Resistance


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Pulleys: A pulley is awheel with a slot. Itmakes easy toovercome a

resistance offeredfrom an object



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A pulley is a group of mechanisms forming amachine. And as a machine a lever is able todo work

But what is work?


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Pulleys: A pulley is awheel with a slot.There is a rope,chain or strap that

goes around its axle


Wheel

Slot: gap

where therope goesaround

Axle: it holds the wheel

Force

Resistance


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Fixed Pulleys: they have only onewheel therefore they only changethe direction of the Force


It is used to raise and lower weight easily. Forexample in wells


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If we analyze the Fixed pulley we see that is alever with equal distance to the fulcrum, so wecan apply the Levers law


RRdR=FFdFSince dR=dF R=F

balance


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Mobile Pulleys: It is groupof two pulleys, one of themis fixed and the other onecan move linearly.


In this case we only have to apply half of theresistance to get the balance


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Multiple MobilePulleys: If we canhave severalcombinations of

this mechanism.


In this case, this is the formula used to definethe equilibrium (where n is the number ofmobile wheels)


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Hoist: It has multiple mobilewheels that decreaseexponentially the Forceneeded to achieve the

balance


Where n is the numberof mobile wheels


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Exercise:We want to rise a fixed pulley that has awater bucket hanging from the hook. Whatis the force that we have to apply to get

balance?


Data:Water volume: 5l

Wheel diameter: 30cm

Well depth: 15m1L=1kg

1kg=9,8N


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Data:Water mas=5L x 1kg/L=5Kg

R=5kg x 9,8N/kg= 49N

F=?

R=F

49N=F


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Exercise:We have this hoist and we want

to raise a heater. What is theforce needed to get at least

balance?


Data:

Heater weight: 50kg

Heater volume: 39L

Heater Brand: Fagor


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Sloping flat:Its a flat that forms an angle thathelps to raise an object.


The smaller the

angle is, lessforce will beneeded to raisethe object and

the distance willbe longer


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The formula is obtained using the trigonometrylaws

!

b

a

!

F

b


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Wedge: Its a double Sloping flat. Theforce applied is proportional to the faceslength.


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Screw: Its a multiple Sloping flat rolled up.The force applied is proportional to thenumber of teeth.


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2.3i Circular into Rectilinear

Circular Rectilinear


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Handle-winch:A handle is a bar joined tothe axle that makes it turn. A winch is a

cylinder with a rope around it that is used to

raise an object



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This mechanism is equal to a lever, sowe can apply the same levers law:


F

R

DFDR

RDR=FDF


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Calculate the force needed to raise a water bucket that has 10L of

fresh water. Name the mechanism, draw its diagram and theformulas applied

Extra data:

Handle size Df =30cm

Bar radius Dr= 15 cm

Water density 1kg/L

1Kg= 9,8N

Bucket material: iron

Bucket color: Black

solution

2.3i 1 Ex Circular into Rectilinear


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Rack and Pinion: This mechanism isused to transmit high efforts like a cartransmission or a lift:



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2.3ii Circular into an Equivalent

Circular Circular


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GEARS: Wheels with teeth that fit intoeach other, so that, each wheel moves theother one.

Used in cars, toys, drills, mixers, industrialmachines, etc



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Both wheels turn in the opposite direction.

All the teeth must have the same shape andsize.


driven geardriver gear


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Gears with chain system: It consists of twogears placed at a certain distance that turnsimultaneously in the same direction thanksto a chain that joins them.


The most common use is inbicycles and motorbikes.

Both gears turnsimultaneously inthe same

direction


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The gear that provides the energy is calleddriver gear and the one that receivesdriven gear


Force is applied in this gear

driven gear

driver gear

!


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2.3ii Circular into an EquivalentFriction wheels: System with two or more wheels that arein direct contact.

These wheels can't transmit high forces but theycan resist vibration and movements


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2.3ii Circular into an EquivalentPulleys and strap system: Group of pulleys placed at acertain distance that turn simultaneously thanks to astrap that joins them

These wheels can't either transmit high forcesbut they can resist vibration and movements


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2.3ii Circular into an EquivalentPulleys and strap system are used also to changemovement direction in many mechanism like motor engines,industrial mechanism, etc


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Pulleys and strap system shown in thispicture has driven pulley A and five drivenpulleys. Indicate each wheel movementdirection.


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The speed of the wheel is measured in rpm(revolutions per minute) that describe the

angular speed"

v =rw

"= angular speed

r= radio

v= linear speed


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Gears are used to increase or decrease theangular speed. To describe the equilibriumwe have to know the number of teeth andangular speed

E= driver S=driven


WS=

ZS=


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WS=

ZS=


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In these mechanisms the ratio between thespeed of the driven wheel and speed of thedriver wheel is called transmission ratio i

DriveN

DriveRDriveN

DriveR DriveN

DriveR


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Exercise:We have a pulley and strap system formedby two wheels as you can see in thepicture. Which is the angular speed of the

driver wheel?

2.3ii Ex 1 Circular into an Equivalent

Sol


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Exercise:We have a gear system formed by two gearswith 20 and 40 gears teeth (driven anddriver wheels respectively). Calculate:

Which is the transmission ratio?If the driver gear is moving at 300 r.p.m.,how fast is the driven gear moving?


Sol


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The transmission ratio I indicates if thegear increase or decrease the driven gearspeed


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I>1indicates that the mechanism increasesthe driven gear speed, but decreases itspower

F

driven

driver


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I


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Exercise. This pulley and strap system its used to modify

the speed of a drill, changing the pulleys combination.


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a.Which positions allows us to get themaximum speed on the drill?.

b.If the engine speed is 1400 rpm, Whatis the smallest speed of the drill?

Si el motor gira a 1400 rpm Cul es la mnima velocidadque se puede obtener en la broca?

Si se elige la posicin que aparece representada en lafigura A qu velocidad girar la broca?

idad de giro en la broca?

Si el motor gira a 1400 rpm Cul es la mnima velocidadque se puede obtener en la broca?Si se elige la posicin que aparece representada en la

figura A qu velocidad girar la broca?Solution


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Gears are also used to raise heavy objectsapplying a low force at a low speed.

This mechanism isalso a lever, if wewant to raisesomething heavy weneed a small drivergear and a bigdriven gear


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2.3ii Circular into an EquivalentTherefore, we canapply the levers law

RDR=FD

F


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2.3ii Circular into an EquivalentMechanical associations

We can create a mechanical associationconnecting several elements. With thisassociation we can decrease or increase theout speed or the force applied


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When we analyze this mechanism we study how theenergy and the movement is transmitted in each step


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So, when we have a mechanical association, thetransmission ratio between the first andthe last one is:

itotal=

D1" D

3" D

5" " "

D2" D

4" D

6" " "

=

WS

WE

itotal

=

D or Z drivers

D or Z driven=

WS

WE

itotal

=i1#2

" i3#4

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