engineering science-2 .docx

8/12/2019 engineering science-2 .docx

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Engineering Science - 02

HNDCV/MT/02/18 BTEC Higher National Diploma in Civil EngineeringInternational College of Business and Technology Page 1

ACKNOWLEDGEMENT

First of all, I would like to thank my parents for their massive support and guidance to

complete this assignment and also I would like to thank Dr. T.S.S.Jayawardene, who is

who is our assessor lecturer of Engineering Science for the first semester in BTEC HND

in Engineering for guiding us to do this assignment. In addition I would thankful to all of

my friends and specially Mr. Rushantha and Mr. Mahesh who were there with me when I

need them.


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CONTENT

Introduction 03

Bending movements and diagrams 04

Task 1 07

Task 2 13

Task 3 20

Task 4 22

Task 5 32

Task 6 40

Reference list 45


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INTRODUCTION

This assignment briefly describes about static engineering systems and DC-AC theory. In task 1,

task 2 and task 3 questions based on static engineering system and these tasks included aboutbending movements, shear forces, bending movement diagrams, shear force diagrams, how to

identify and draw deflected shapes and how to calculate maximum bending stress.

And in task 4, task 5 and task 6 based on DC-AC theory. These tasks are included V c and i c ,

waveforms and speed control devices.


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CREATE BENDING MOVEMENT DIAGRAMS

The shear force diagram of the above example looks like below:

step-1:Get the Reaction Forces: While creating shear force diagram of the beam you

already have calculated the vertical reaction forces at different points as below:

Rc = 60 KN

Re = -20 KN

These reaction forces will be useful for calculating the bending moments at different

points on the beam.


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Step-3: Calculate the Bending Moments: You need to calculate the bending moments

at the different points on the beam. For calculating the bending moment you need to start

from the extreme left (point A) and gradually you have to approach toward right handside support (point A). You will use the following formula for calculating bending

moment:

Bending moment (M) = (Force)X (Distance between the point of application of the

force and the point at which you need to calculate bending moment)

Bending moment @ A:

Ma = -20 * 0

= 0

Bending moment @ B:

Mb = -20 * 1

=20 KN-M

Bending moment @ C:

Mc = bending moment due to the 20KN force + bending moment due to the 10KN\M

UDL

=20 * (1+1)(10*1*0.5)

=45 KN-M

Bending moment @ D:

Md = bending moment due to the 20KN force + bending moment due to the 10KN \M UDL + bending moment due to the reaction force Rc

=20 * (1+1+1)(10*2X1) + (60*1)

= -20 KN-M

Bending moment @ E:

Me = bending moment due to the 20KN force + bending moment due to the 10KN \

M UDL + bending moment due to the reaction force Rc

=20 * (1+1+1+1)(10*2X2) + (60*2)


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= 0

Step-4: Plot the Bending Moments:Just now you have calculated the bending moment

values at different points of the beam, now plot the values and you will get the bendingmoment diagram like below:


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TASK 1

For the beam shown in the figure below, sketch the deflected shape, draw to scale

the shear force diagram and draw to scale the bending movement diagram. Label all

maximum and minimum values on your shear force and bending movementdiagrams.

4m 5m 5m 6m

A BC

D

70kN10kN/m 5kN m

4m 2.5m 2.5m

70kN50kN 30kN

A B C D

5m 6m

P Q


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Taking movements at B:

;(from (1) )

Then we have to find out bending movements and shear forces for 5 sections. Because

forces are acting on 5 locations.

Section 1

* +

, -

Where (4 9)When


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When

Section 2

Where (9 )When

When


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Section 3

Where (14 )

When

When


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Shear Force Diagram

X (m) V (kN)

0 0

4 63.59 13.5

9 -56.5

14 -56.5

14 30

20 0

-80

-60

-40

-20

0

20

40

60

80

0 5 10 15 20 25

Shearforce(kN)

Distance x (m)


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Bending Movement Diagram

x (m)

M

(kN/m)

0 0

4 0

9 192.5

14 -90

20 0

-150

-100

-50

0

50

100

150

200

250

0 5 10 15 20 25

BendingmomentM(

kN/m

)

DIstance x(m)


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TASK 2

A beam with T cross-section is subject to design loads shown in the following figure. If

the maximum compressive stress of the beam is limited to 50 Nmm2and the maximum

tensile stress to 10 N/mm2, calculate the maximum bending stress of the beam at all

possible locations and check whether the beam will fall.

We have to find out movement of inertia (I) and center of gravity of the T section. For

that we have to calculate the mass, x and y .

According to the figure, 0x .

= uniform density of the section

Object mass

= b1d1=

2

1

2

dd

y

d

b

b

d

x

b1d1


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( ) ( )

, -

Movement of inertia can be found from the parallel axis theorem.

Neutral axis

= b2d2=

2

2d

= (b1d1+ b2d2) =

b2

d2

b2

d2

d1

b1

301.89mm

=118.11mm

=111.89mm


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Then we have to find out the maximum bending movement.

=118.11mm

x x

=111.89mm

10kN 10kN11.25 kN/m

8m5m 5m

10kN 10kN11.25 kN/m


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Taking movements at B:

;(from (1) )

Then we have to find out bending movements for 5 sections (AB, BC, CD).

Section 1

When (0 5)

x (m) M1(kN/m)0 0

1 -10

2 -20

3 -30

4 -40

5 -50

P Q

AB C

D

10kN


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Section 2

When (5 13)

Section 2

Where (13 18)

x (m) M3(kN/m)

13 -50

14 -40

15 -30

16 -20

17 -10

18 0

x (m) M2(kN/m)

5 -50

6 -10.625

7 17.58 34.375

9 40

10 34.375

11 17.5

12 -10.625

13 -50

10kN

10kN


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From this chart we can find out the maximum bending movement.

Maximum bending movement is = 40 kN/m

Upper section of T section is subjected to tension and the lower section of T section is

subjected to compression.

Maximum tensile stress can be found by:

-60

-40

-20

0

20

40

60

0 5 10 15 20

M(kN/m)

M(kN/m)


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Maximum compressive stress can be found by:

.


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TASK 3

A two feet long hollow steel shaft with an outer diameter of 2 inches and an inner

diameter of 1.5 inches is to transmit power while being driven a 3000rpm.

If the allowable shear stress in the shaft is 15000 lb/in2, what is the maximum horsepower

which can be transmitted down the shaft.

()

( )


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The maximum horse power can transmitted = 766.68


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TASK 4

If (0) = 30v, t0, determine expressions for and for t 0 for the circuitshown below,

1stWay

t =0;

t =1;


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t =2;

t =3;

t =4;


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t =9;

t =10;

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12

Vc

Vc

time Vc

0 30

1 23.362 18.19

3 14.17

4 11.04

5 8.59

6 6.69

7 5.21

8 4.06

9 3.16

10 2.46


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time ic

0 2.51 1.94

2 1.51

3 1.18

4 0.92

5 0.71

6 0.56

7 0.43

8 0.34

9 0.26

10 0.21

2nd

way

Appling K.V.L

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12

ic

ic


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For capacitors:

Differentiate:

Substituting values:

Let,

(where k1and k2 are constants)Differentiate:

+ Equaling constants:


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Initial conditions ; t=0, Substituting initial conditions;

30=

Differentiate:

Let

Differentiate:


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Equaling coefficients of ;

Equaling constants:

Initial conditions t=0, Substituting initial conditions:

Q=10

[ ]


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T V

1 23.36

2 18.19

3 14.17

4 11.036

5 8.60

6 6.69

7 5.21

8 4.06

9 3.16

10 2.46

11 1.92


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tci

1 -1.95

2 -1.51

3 -1.18

4 -0.92

5 -0.71

6 -0.56

7 -0.43

8 -2.20

9 -0.26

10 -0.21

11 -0.16


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TASK 5

Often circuits are produce complex waveforms; show how theses can be made up of

different sinusoidal signals. Give typical example for these waveforms.

A basic sinusoid

As shown in the diagram, the amplitude is the difference between the high value and the

low value. The waveform may have different units, depending upon what the waveform

is. If the waveform is measuring a voltage as a function of time, then the amplitude will

be in Volts; if it were current as a function of time, amplitude would be in Amps. The

frequency is equal to and is a measure of how quickly the waveform cycles. If the

waveform is a function of time, then frequency will usually be measured in Hertz (Hz).

Since frequency is a measure of how rapidly the waveform cycles, frequency is

sometimes (usually in older texts) given as cycles.

Making waves

Sine waves can be mixed with DC signals, or with other sine waves to produce newwaveforms. Here is one example of a complex waveform:

A waveform like this can be thought of as consisting of a DC component with a

superimposcompon easy to separate these two components using a capacitor.
http://en.wikibooks.org/wiki/File:Sinus_amplitude_ehttp://en.wikibooks.org/wiki/File:Sinus_amplitude_e


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More dramatic results are obtained by mixing a sine wave of a particular frequency with

exact multiples of the same frequency, (adding harmonics to the fundamental frequency).

The V/t graphs below show what happens when a sine wave is mixed with its 3rd

harmonic (3 times the fundamental frequency) at reduced amplitude, and subsequently

with its 5th, 7th and 9th harmonics:


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The Sinusoidal Waveform. (Horizontal time is in milliseconds, vertical axis -5 to +5

volts)

Examples for waveforms.

Ocean waves

Sound waves

Light waves

Daily temperature(rough sinusoidal pattern

Each day of the yr.)

A cosine wave is said to be "sinusoidal", because cos(x) = sin(x+ / 2),which is also asine wave with a phase-shift of /2.

There are three basic characteristics of sinusoidal waveforms (hereafter sinusoids):

amplitude, frequency, and phase.


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sine wave generator

D.C. stands for direct current i.e. the signal is always a fixed value. A.C. signal

sources can be made up of different types of Waveforms. The most common

waveforms are the

Sinusoidal waveform, the Square waveform and the Triangle waveform. There is

other kind of A.C

waveforms which will be encountered as one becomes more involved with

electronics.

An example of each of these A.C. waveforms is shown below :


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There 3 are three types of wave forms that is The Square Waveform and The

Triangle Waveform


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The Sinusoidal Waveform.

The Sawtooth Wave form

Examples

Sine wave: sin (2 t). The amplitude of the waveform followsatrigonometric sine function with respect to time.

Triangle wave: (t 2 floor ((t + 1) /2)) (1)floor ((t + 1) /2)

. It containsoddharmonics that fall off at 12 dB/octave.
http://en.wikipedia.org/wiki/Sine_wavehttp://en.wikipedia.org/wiki/Sine_wavehttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Triangle_wavehttp://en.wikipedia.org/wiki/Harmonichttp://en.wikipedia.org/wiki/Harmonichttp://en.wikipedia.org/wiki/Triangle_wavehttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Sine_wave


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Sawtooth wave:2 (t floor(t)) 1. This looks like the teeth of a saw. Found oftenintime bases for display scanning. It is used as the starting point forsubtractive

synthesis, as a sawtooth wave of constantperiod contains odd and

evenharmonics that fall off at 6dB/octave.
http://en.wikipedia.org/wiki/Sawtooth_wavehttp://en.wikipedia.org/w/index.php?title=Time_base&action=edit&redlink=1http://en.wikipedia.org/wiki/Subtractive_synthesishttp://en.wikipedia.org/wiki/Subtractive_synthesishttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Harmonichttp://en.wikipedia.org/wiki/Decibelhttp://en.wikipedia.org/wiki/Decibelhttp://en.wikipedia.org/wiki/Harmonichttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Subtractive_synthesishttp://en.wikipedia.org/wiki/Subtractive_synthesishttp://en.wikipedia.org/w/index.php?title=Time_base&action=edit&redlink=1http://en.wikipedia.org/wiki/Sawtooth_wave


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A pulse wave or pulse train is a kind ofnon-sinusoidalwaveform that is similar toasquare wave,but does not have the symmetrical shape associated with a perfectsquare wave.
http://en.wikipedia.org/wiki/Non-sinusoidalhttp://en.wikipedia.org/wiki/Waveformhttp://en.wikipedia.org/wiki/Square_wavehttp://en.wikipedia.org/wiki/Square_wavehttp://en.wikipedia.org/wiki/Waveformhttp://en.wikipedia.org/wiki/Non-sinusoidal


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TASK 6

For speed control device select individual components, you should include product

details and specification. You should include details how you are going to interface the

components and how you will monitor and check the performance of the system.

The purpose of a motor speed controller is to take a signal representing the demanded

speed, and to drive a motor at that speed. The controller may or may not actually measure

the speed of the motor. If it does, it is called a Feedback Speed Controller or Closed Loop

Speed Controller, if not it is called an Open Loop Speed Controller..

Motors come in a variety of forms, and the speed controller's motor drive output will bedifferent dependent on these forms. The speed controller presented here is designed to

drive a simple cheap starter motor from a car. Below is a simple block diagram of the

speed controller.

Theory of DC motor speed control

The speed controller works by varying the average voltage sent to the motor. It could do

this by simply adjusting the voltage sent to the motor, but this is quite inefficient to do. Abetter way is to switch the motor's supply on and off very quickly. If the switching is fastenough, the motor doesn't notice it, it only notices the average effect.


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SCR or thyristor drive

SCR controls for DC motors convertACpower to direct current, with adjustable voltage.

Small DC drives are common in industry, running from line voltages, with motors ratedat 90V for 120V line, and 180V for a 240V line. Larger drives, up to thousands of

horsepower, are powered by three phase supplies and are used in such applications asrolling mills,paper machines, excavators, and ship propulsion. DC drivers are available

in reversing and non-reversing models. The waveform of the current through the motor

by a single-phase drive will have strong ripple components due to the switching at linefrequency. This can be reduced by use of a polyphase supply or smoothing inductors in

the motor circuit; otherwise the ripple currents produce motor heating, excess noise, and

loss of motor torque.

PWM or chopper drives

PWM controls use pulse width modulation to regulate the current sent to the motor.Unlike SCR controls which switch at line frequency, PWM controls produce smoother

current at higher switching frequencies, typically between 1 and 20 kHz. At 20 kHz, the

switching frequency is inaudible to humans, thereby eliminating the hum whichswitching at lower frequency produces. However, some motor controllers for radio

controlled models make use of the motor to produce audible sound, most commonly

simple beeps.

A PWM controller typically contains a large reservoir capacitor and an H-bridge

arrangement of switching elements (thyristors, Mosfets, solid state relays, or transistors).

The speed controller works by varying the average voltage sent to the motor. It could do

this by simply adjusting the voltage sent to the motor, but this is quite inefficient to do. Abetter way is to switch the motor's supply on and off very quickly. If the switching is fast

enough, the motor doesnt notice it, it only notices the average effect.
http://en.wikipedia.org/wiki/Silicon-controlled_rectifierhttp://en.wikipedia.org/wiki/AChttp://en.wikipedia.org/wiki/Three_phasehttp://en.wikipedia.org/wiki/Steel_millhttp://en.wikipedia.org/wiki/Ripple_(electrical)http://en.wikipedia.org/wiki/Ripple_(electrical)http://en.wikipedia.org/wiki/Steel_millhttp://en.wikipedia.org/wiki/Three_phasehttp://en.wikipedia.org/wiki/AChttp://en.wikipedia.org/wiki/Silicon-controlled_rectifier


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The amount of time that the voltage is on increases compared with the amount of time

that it is off, the

average speed of the motor increases.

This on-off switching is performed by power MOSFETs. A MOSFET (Metal-Oxide-

Semiconductor Field Effect Transistor) is a device that can turn very large currents onand off under the control of allow signal level voltage. For more detailed information, seethe dedicated chapter on MOSFETs)

The time that it takes a motor to speed up and slow down under switching conditions is

dependent on the inertia of the rotor (basically how heavy it is), and how much frictionand load torque there is. The graph below shows the speed of a motor that is being turned

on and off fairly slowly:

Inductors

An inductor or a reactor is a passive electrical component that can store energy in a

magnetic field created by theelectric current passing through it. An inductor's ability tostore magnetic energy is measured by its inductance, in units of henries. Typically an

inductor is a conducting wire shaped as a coil, the loops helping to create a strong

magnetic field inside the coil due to Ampere's Law.Due to the time-varying magnetic

field inside the coil, a voltage is induced, according toFaraday's law of electromagnetic

induction,which byLenz's Law opposes the change in current that created it. Inductors

are one of the basic electronic components used in electronics where current and voltage

change with time, due to the ability of inductors to delay and reshape alternating currents.

In everyday speak inductors are sometimes called chokes, but this refers to only a

particular type and purpose of inductor

Choosing a frequency based on motor characteristics

One way to choose a suitable frequency is to say, for example, that we want the currentwaveform to be stable to within p percent. Then we can work out mathematically the

minimum frequency to attain this goal. This section is a bit mathematical so you may

wish to miss it out and just use the final equation.

The following shows the equivalent circuit of the motor, and the current waveform as the

PWM signal switches on and off. This shows the worst case, at 50:50 PWM ratio, and the

current rise is shown for a stationary or stalled motor, which is also worst case.
http://en.wikipedia.org/wiki/Passive_componenthttp://en.wikipedia.org/wiki/Electronic_componenthttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Henry_(unit)http://en.wikipedia.org/wiki/Ampere%27s_Lawhttp://en.wikipedia.org/wiki/Faraday%27s_law_of_inductionhttp://en.wikipedia.org/wiki/Faraday%27s_law_of_inductionhttp://en.wikipedia.org/wiki/Lenz%27s_Lawhttp://en.wikipedia.org/wiki/Lenz%27s_Lawhttp://en.wikipedia.org/wiki/Faraday%27s_law_of_inductionhttp://en.wikipedia.org/wiki/Faraday%27s_law_of_inductionhttp://en.wikipedia.org/wiki/Ampere%27s_Lawhttp://en.wikipedia.org/wiki/Henry_(unit)http://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Electronic_componenthttp://en.wikipedia.org/wiki/Passive_component


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T is theswitching period, which is the reciprocal of the switching frequency. Just

taking the falling edge of the current waveform, this is given by the

equation(shown follow of tha paragraph) is the time constant of the circuit,

which is L / R.

So the current at time t = T/2 (i1) must be no less than P% lower than at t = 0 (i0).

This means there is a limiting condition:


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Speed control circuits

We will start off with a very simple circuit (see the figure below). The inductance of thefield windings and the armature windings have been lumped together and called La. The

resistance of the windings and brushes is not important to this discussion, and so has not

been drawn.

Q1 is the MOSFET. When Q1 is on, current flows through the field and armaturewindings, and the motor rotates. When Q1 is turned off , the current through an inductor

cannot immediately turn off, and so the inductor voltage drives a diminishing current inthe same direction, which will now flow through the armature, and back through D1 as

shown by the red arrow in the figure below. If D1 wasnt in place, a very large voltage

would build up across Q1 and blow it up.


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REFERENCE LIST

http://www.mechguru.com

http://mathworld.wolfram.com/TriangleWave.html

http://homepages.which.net/~paul.hills/SpeedControl/SpeedControllersBody.html

http://mathworld.wolfram.com/SquareWave.html

http://crca.ucsd.edu/~msp/techniques/latest/book-html/node24.html

Hanna, J and Hillier, M (1995) Mechanical Engineering Science. Longman. ISBN0582326753

Bolton(2006).Engineering science.5thedn. Oxford.uk
http://www.mechguru.com/http://www.mechguru.com/http://mathworld.wolfram.com/TriangleWave.htmlhttp://mathworld.wolfram.com/TriangleWave.htmlhttp://homepages.which.net/~paul.hills/SpeedControl/SpeedControllersBody.htmlhttp://homepages.which.net/~paul.hills/SpeedControl/SpeedControllersBody.htmlhttp://mathworld.wolfram.com/SquareWave.htmlhttp://mathworld.wolfram.com/SquareWave.htmlhttp://crca.ucsd.edu/~msp/techniques/latest/book-html/node24.htmlhttp://crca.ucsd.edu/~msp/techniques/latest/book-html/node24.htmlhttp://crca.ucsd.edu/~msp/techniques/latest/book-html/node24.htmlhttp://mathworld.wolfram.com/SquareWave.htmlhttp://homepages.which.net/~paul.hills/SpeedControl/SpeedControllersBody.htmlhttp://mathworld.wolfram.com/TriangleWave.htmlhttp://www.mechguru.com/


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