Technical Drawing

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V

I DESCRTPTTVE

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E rgeering Stqdents

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CITED SOIIRCES

/ REFERENCES

l. Descriptive Geomehy (krsbuctional Pamphlet). pt:PI"d- by. the Department of Mechanics, United States Air Force Academy, Coiorado, dsat June 1958' (Unpublished) 2. Lecture Notes Taken During Engineering Drawing 228 (Dept of Mech) classes at the US

' _{Air Force Academy, Fall Term of 1964' (Unpublished)}

3. Solid Geomeby. Revised ed- F. Eugene seymour and PaDl smith, MacMillan company' Nerv York: 1959. (ISBN 971-103-168-x)

. 4. Student,s Classroom Exercise Plates in Engineering Drawing at U.P' Diliman, School-Year 1 9 9 5 - 1 9 9 6 .

5. Technical Drmving. 9h ed. Frederick E. Giesecke et al, MacMillan Publishing Company' New York: 1991. (ISBN 971-1055-58-9)

DOCUME,NT

ATION TERMIN OLOGY

1. Source - Minor or no change from the cited material

2. ReGrence - Major or very significant alteration of the cited material

DESCRTPTTVE

GEOMETRY

ond

TECHNTCAL

DRAWING

for

Enginee?ing

Students

I

I t ! &

_r'

R

I _{Compiled, Arranged and Annotated}

i ,

by

ROBERTO S. BARANGAN

B.S. Engineering Science (1966), USAI Academy, USA Lecfu rer, PAF Colle ge of Arronautic s, I97 7 - 197 8

Senior Lecfurer, University of the Philippines Dilim'. College of Engineerin g 1995-1997

and

ROBIN M. BARANGAN

B.S. Computer Engineering (1993X University of San Carlos, Cebu City Insbuctor, Asiaa College of Technolory Masters ia Coryutcr Science Prograrn, 1996

ceteacher, university of san carlos Masters in Eosineering program, lgg6-lggT Faculty Chairman & Computer Insbuctor, Divine Mercy Comprter Collegg 1997

ACKNOWLEDGEMENTS

This booklet cvolvcd initially from a compilation of lccture manuscripts used by onc of the authors in conducting crasscs in Enginecring D**id;iin oilirrl an"t u lirftce number of copies of the first edirion (199G19971** *in" ,uuiiubl" to G? rip-fngineering Pi*int m9""T' very helpful zuggestions were received by the aulhors from the up e"gir,*ri"i.q"*q pcffient facutty which led to significant *pr"*,o*O fi'i"g i"-rp"*t l i" tbe zubfruent editions of lhis booklet'

The authors also wish to acknowledge the temcndous value of the lectures and "poop sheets'' given to the first+ited author by rhe f*"b';ithi rtaon*i-.t' genarrnelt at Jhe Yt oit Force

Academy during his undergradualc (ca.de0 y*r, Jf,if" *ing up tngin-eering Drawing thereat in 1964' The methods and techniques of instruction u*n W tho;faculty members have a very strong bearing in the selection and arrangement of the zubject rr*r rn., in this uoott"t, despite those rong intervening years' chapters 4 lo 7 are dedicated to these people. For chapte r

'z

ia 3' as well as lhe Appendices' TECHNTCAL DRAWTNG by Frederick ol#i".rrr (r;';ittioni*o soiio ceometry by seymour and i*irft @evised edition) were used as the primary reference '

DuringtheschoolYear|997_1998,&coPyofthg.draftofthisbookletwassentiJotheDearrof Engineering of each of the eight major universities and colleges i" lut"tto cebu' with a request

for their cvartration and rccommcndations so es to makc the u."n.t *it"ule for thcir respcctivc engincering drawing subjects. Almost without exception, ea.ch fean endorsed his copy to their Architecture Deparhnent which handles engineering a**ing zubjttts in toi itUu engineering schools' Except for the University of San cJo, and tie Uoiu"rrity oiifr. Vi*yri.*t o. p.uiO.A r"elevant L-mments' the rest of the

schoors pcrceive the book as having ritu"

"ir""*.. or appricability to ttr"ir current

engineering curriculum'

I-astly, we 8I€ proud of thc invaluable contribution of our young€st daughter (of the first{ited author) and younger sistcr (of ffr" ,..o.ri*if"O author)' Tarah Atd in fhe computcr-processing

of the original mantrscriptand its subsequentcditions'

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FOREWORI)

This booklct was initialty madc in orqgrlo providc cnginccring &rwing shrdsnb at Ilp Dilimm witi a singlc rcfc-rcncc matcrial drat contain,s all_&g lasic conccpts and[rr.inciptciUat _{tc sflrdcn6 nccd in} -ordcr- to accomplish_ th9 rcgrhcmcutl of trc frcshan cnginiaing O"r*ltg cunicul'nr- lo fr.f U* booklct is a surnmn'izcd collcction of trc rescrchcd lccturJnotes _{ricd in cliss presentatiors e,rrioi tti} School-Year 1995'1996. _^During fte dweloprned{ arohrtion _{of tris boo\ sevcral materiels tryonj te} nccds-of frc cnginccring frcshmcn wcrc latsr addcd in ordcr to hc$ offrcr cnginccring &awing io'rtuCo* in their own presentations, per zuggcstion of thc insructors themsjbcs.

This cdition 1o^ntainl proccdurcs in thc conskuction of two-dimsnsional gcomctic figurcs (Chsptef 2); review _{9f the principles} and p,roce&nes in drawing Orrhographic projeciion, _tCtmpi&lj; chracteristics md relationships of lines in tlree dimensions (chapter q); ch-aracterisiics md ritationsnipi of plancs/surfaccs in thrcc dimsnsions (Chaptcr 5); gcomcbic consFuctions in tbrcc dimsnsions (Chrpi:; 6)' iltusrative problem-solving tccbniques (Cfaqter ?); tcchniguel mg procedses in making tni sin'gf.-shokc, vsrtical lcttcring (Appcndix _{A); thc basic rcguhemcnts in dimcnsioning cnginccriig e"*fig'} (4pp*dit B); and sclcctcd two-dimcnsional tangcncics and tangenry-bascd Jonsfrrction _iroccdure"s. Claptcr 1, on the other hand, _{-gv:t thc scope} of DESCRIPTfvE boMEIRy ar a ,ubi.cf and diffcrcntiatcs it from othsr rclatcd subjccts. For cxarnplc, whcrcas Analytic Gcomcty _{malpcs fcomeric} problcms tt[ough algcbraic calculations, Dcscriptivc Gcomctry dctErmincs acfiral mcnstna]tion and projective properties of objects through orthographic projections, or precise drawinp of thesc pro;..iio*.

Conccpts and proccdurcs c4plaincd _{in ftis book arc vcry basic and cncapzutatcd but arc csscntial} h 1.. graphical sohrtion _{t9 Tarry levels of engineering probftms. Since enfineering aawint ls n*} graphical mcthod of prccisety stating cngincering facts, through thc application oiOfSCnfoffVf GEOMETRY, the concepts and procedures presented in &is book are, ttr-"rrfore, basicalty useful anJ lelevant io t* production of cngineering. drawings through Computer-Aided Drafting and Desig' (CADD), and in othcr computcr graphic applications.

TABLE OF CONTENTS

TTTLE

INTRODUCTION... Abbreviations and SYnbols

PLA}.IE GEOME1RIC C ONS]}.U CTION S Dividing Lines/Anglee Into Equal Ptrts """"' Drawing Parallel and Perpendiculr Li99s" " " "

Constru"c ti on o f Tri angltt, S quurt u md Re ctangl"s" " " " "' Drawing Tangent Lines to Circles

Drzwing Circles krside/Outside Potygons " " " " " " Conskuction of Ellipses ---"""

PROJECTIONS USED IN ENGINEERING DRAWING Iso mebi c Proj ri cti ons/Drawings

Multi-View Proj ecti onslDrawinP Missing Viewsllines ....-.--'.---.' Auxilia'y Views """"":""""' PAGE CHAPTER t IL I 4 5 9 t 2 1 6 1 9 23

u.

IV.

v.

76 3 3 3 9 4 3 47 Sectional Views LINES IN SPACE s,, Classification ofl.ines Je

Prallel,Intersectinf p"tp""aif"lr and Skew Lineg 54

PLANES IN SPACE _6A.

Definition ofPlanes

Relationships of Lines andPlanes 65

FUNDAMENTAL C ONSTRUCTIONS IN SPACE

Line Parallel to a Given Line and ffougl a Given Point '.U, True-Length View andPoint View of aline t t Line From , cirr"n poiot rerpendicd-;;; ci*,.n Line ...---. .. 781 q

Estsblishment ofPlmes in SPace '',

Plane Parallel to One Line I to Tlvo Skew Lines 8?'o ?

EdgB View andTruo Shrye Visw ofPluree oJ IncatingPiercingpoint ofatitre on aPlane 86

Line Perpendiculr to aPlure 88

PlaaeThougbaPointandPerpendicularts aline 89 Constuction of

" Sofia (Cir*io Cone)

90

PROBLEM-SOLVINC

Intersection of Two Planes (Touching aad NON-Touching)

True Angle Between a Line and aPtire / Between T\ro Plues """"""""' Snortegtbishnce Between Point-md-LinelPoist-and-Plane

92 95 97

!

f

*

I

I

I t

l

Shortest Distance / Eorizontal Line Between Tlvo Skew Lines

Plaas Prallel to a Given Plae and Tkough aPoint ... 102 Plane Perpendicular to a Given Plme .... 103 Line of IntersectionBetweenPlme aad Solid (Pj'ranid) ... 104 Plane Perpendiailarto aGiveo Line .,... ... 106 APPENDIX A (Single-Sboke, Gothic Vertical Letters mdNumerals) ... APPENDIX B @imensioning)

APPENDI X C (Two-Di mens ional Tange nci es and Tange ncy-B as e d Conshuctions) ... AI B1 c l

I

I

I

.I

A. BASIC STUDENT REQINREMENTS ( CLASSROOM ) 1. Drawing Board, Desh or Table

2. Drawing orMechanical, Pencils:

a. ZWmlead for initial construction lines b. HB/F lead for final drawing lines

5W6H lead for work requiring extreme accuracy B/2B lead for free-handiketching and lettering

c. d. a J . 4 . 5 . 6 . 7 . 8 .

Pencil Erasers: Rubber, or rubberized plastic Straight-edge with millimeter scale

Compass Divider Protractor

Irregular, or Frenctr, Curve

COMPUTER-AIDED DRAWING AND REQUIREMENT D E S I G N ( C A D D ) N t r N n d u M B . I

r

t E

r

t

i

-N

DESIRABLE ADDITIONAL EQUIPMENT ( HOME ) l. T-Square

2. Triangles: 30" - 60" and 45o ( 4" to 6" sides ) 3. Metric Triangular Scale

4. Erasing Shield C .

l. Computer ( Minimum Spec: 486 or better ) . 2,. Digiiizer/Graphics Tablet, Lightperg Trackball' or loystick 3. Monitor: with Raster Scan, 6r Vector Refrestr, Display device 4. Dot-Matrix/Laser Printer. OR Plotter

5. Alphanumeric KeYboard

l-CHAPTER I

INTRODUCTION

Mmy engigeering problemr cm be solved moro easily by grryhical tran by mathematical solutions. For example, a sheet mehl prt can bs laid out graphically on a flat surface fairly easily, whereas it would be more difficult (and less &scriptive) to describe the outline of that part mathematically. The clearance between conbol c$les of a machine can be determined and described graphically, and again it might be more difficult (and less easy to visualize) to describe tre clearance between tre cables mdhematically. The grryhical solutions to geomehic problems is call ed DESCRIPTIVE GEOMETRY.

To more ftlly appreciate the relationship behveen Descriptive Geomeb;r and Engineering Drawing the following Webster's Dctionary definitions are necessry:

Geomeh-v -- That branch of mathematics which investigates relationships, properties and measurements of solids, surfaces, lines and angles; be science ftat heats on the properties and relations of spatial magnitudes; the theory of space and figures in space.

Plane Geomebv -- That branch of geomehy dealing with plane figures. Solid Geomebv -- The geomeby of solid figrrres.

Analytic Geomebv -- The branch of geomeb-y in which position is indicated by algebraic symbols, and solutions are obtained by algebraic analysis.

DESCRIPTIVE GEOMETRY -- The theory ofgeomeh-y heated by means of projections, specifically, the theory of projecting an exactly defined body so as to deduce both projectirre and mebical properties from irc projection

Graphics -- The art of making drawings in accordance wi0r mathematical rules and dreories.

Perspective Dra,vinq -- The r-t of pichring objects, or a scene, in such awwy a.s to show. them as they appear to the eye with reference to relative distance or

dep$-Oblique Draving -- The art of picturing objects in such a way as to show drem in bue shape in only one (frontal) view, uftile slanted by 45 degrees on the other two dimensional a,\es.

Isometric Drawing -- A method of drawing figures md maps so that thee dimensions are shown not in perspective, but in their achral meafirements.

Orthonraphic Projection -- A projection in which 6e projection lines are perpendicular to Sre plane ofprojection.

Sketches -- Free-hand draring using only pryer and pencil, and uzually re not made to any scale.

Drawin$ -- A term applied generally to all drafting activities, but more specifically to t op u.ilgsrdiory scale, .r difrtroiiated from trose using special scales (or actual projections), or to those done fee-hmd (sketches).

projections _{-- The representation} of fre surfaces of m object on apichre plane- Behind every dr"*i"g

"f an object iJa space relationship involving fotn imaginary things: 1. The observer's eyes, or tre station point

2. The object

3. The plane orplanes ofprojection

4. The projectors, also called visual rays or lines ofsight

Wtrere the observer is relatively close to the objec! and ttre projectors form a "cone" of projectors, Sre resultingprojection is known r".p."rp".tit". If the observeC.s.eye is imagined as infinitely distant fromlhe o-bject and the plane o-p-iotion, the projectors will be parallel, so the q,'pe ofirojection is lqrown as parallel roiection If the projectors, in addition to being parallel to each other, are perpendicula'(*"r.D i" th" pt-e of projettion, dre result is an qrhe^sgph!!, or ri$t-angle. proj""iion. If fte projectors a-e parallel to each other but oblique to the plane of projection, tre result is an oblique projection

It can be said therefme ttrat orthosaphic proiection (multi-view or a:(onomebic) is a method of representing spatial urr*gr@ descriptive gqomet--v is the method of interpretrrg (or A"#iUiogl the shapes, sizes and positions of solids, surfaces, lines and angles which are so repesented- In-making lhese interpretations, the theorems and concepts of geomeby re applied.

Since engineering drawing is Sre graphical method of precisely stating engineering facts^ concerning three dimensional objece o"

"puti"t arangements, it involves the application of descriptive geomehy.

Just as there 6.e certain findanental theorems of geomeh-y, there are also certain fundamental conshuctions, or processes, of descriptive geomety upon vrhich the subject is developed These re:

1. Consbruction of a line 0nu a point prallel to a given line 2. Conskuction of a line tbru a point perpendiculr to a given line

3. Constiuction of a line tfrru a point intersectiqg a given line at a specified point 4. Establistrnent ofaplane in space

5. Consb:uction of a line parallel to agiven plare; aplane parallel to agiven line

6. Conskuction of a line perpendicular to a given pi-r; a plane perpendiculr to a given line

7. Detennining the point at uihich a line pierces a plane 8. Determining the line of intersection ofhro planes

9. Determining the shortest distance beturcen two SIG\M lines

11. Construction of aplane parallel to agiven plae

12. Construttioo of aplme perpendioltar to agiven plaoe 13. Determiningthe bue angle betweentwo intenecting lines i+. pttt*inini tne gp rqgle between a line ad aplme iS. pututtioiol thu angle (dihedral) betweeo two planes 16. Establishment of a solid in sPrce

The above processes pimrily require he execrfion of the following graphical operations uti lizing corrosponding goomohi-c concepts:

l. Co*t*tEitiof theNormal (orTirue I-ength) Vi* of aline; 7. Consruction of the Point View' orEnd-View' (PU oftre line; 3. Cons[uction of 6e Blge View (EV) of

aplanel-4. Conshction of the Noimal View (finre Slrye View) of a_plane; md

5. Construction of First, second, rrriio, and otirer Auxiliry views, as needed, in order to aftain the requirements oftbe problem at hatrd

Thispanrphletcoverssomeofthefundamentalsofdescriptirregeomehyandsomeofthe

practicalapplicatioril.;;;;fi

;-q:,gl""::t*:',,i:"'*3"*i;f

_T.ltr*t*:f

_*

ilHilt ffi'o#iti; ##Jr'ffirobr",o, .* b, readily

solved

tbrougb

manual

drar'rdns

or

through corrputor-AidJ;*fting anaDesign (CADD) using softwa-e

zuchrdAiltocaD:---=--\-r{K(JC'

-

RS. Barangan

l-!"^,

R.M. Barang# July 1996

CP DS/TS EV LOI LOS PP PV RP FRP PRP HRP T (or PT) TA TL TS

A B B R E V I A T I O N S

A N D

S Y M B O

L S

CuttingPlane

Didort€d/ForEshorterrd Dirnrrsiorr of obj ed Edge View of a plane

Line of Intersedion

Lineof-Sight" cr direction of view PiercingPoint of a line tlnougfr a plme Poirt View, cr end view, of a line Reference Plarn

Frortal ReferencePlur Profile Reference Plane Hcrizontal Referere e Pl an e Poirt of Tmgency

Tn-re Angle cr- Ditre&al True Lengtlr of a line

True Shape (and Size) of a plane surface

Poir:t in space _{(also A B. P. Q. X dc )} Inlersection of trpo rcs

Finite end-poirt of a lir€

I

J

Perpendiculr lines Center line; Axis of rotdion

R P _{Referenct Plarrc, dirrrrniorc rneasured r:pward} RP Reference Plare, dirrersiorn rrreasured downward

Hidden lircfidersion linetine of Intersectior(t id&n) Irnagrrary lire;Corsh'udion lirre; Projection line . . _{Probable line}

____€_

f,tffJt

Point of a line cfier€in left-side pcrtion is visible, while right-side is ' - ' Visible lirre of inlersection

A.

CHAPTER II

BASIC

GEOMETRIC

CONSTRUCTIONS

BISECTING AGI\TEN LINE AB:

L Using poirt A as center md any radius R grcdcr thm onehalf of the lengh of Une AB, &aw an rc e$cnding to both sides of Une AB'

Z. Using poirt B as center and the srrp raditrs & draw a second rc irtersecting the first ec at Poin! C and at Point D.

3. Draw a line corrrectjngPoints c and D irtersecting Line AB aL Point E (Lirr cD is perpendicular to Line AB).

(Source: Reference 5, Page 122)

B

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B

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./ b'

1 . UsingPoiri E as crigin, draw another lirre EG making an angle of 30 to 45 de grees with Line EF'

?.. Starti"ng from Poirt L and using any conveniert length lay or:l points l, 2, and 3 on Line EG af equal dis:nces.

3. Draw a line connectingPoint F a-rdPoinl 3

4 . Draw a fouth line pa.utt.l to lirc 3F, passing tlroudt p9h ?, a-rd intersecting Line EF d. Point 11 5. Draw a fifth line also parallel bo Line if, p.*tit g tt-ugh Poinl l, and inta-secting Lirre EF' alPointIC

(Sorrrce: Relerence 5, Page 125)

\ \ \ F I I

l+

\ _ t \ \

c.

I . Locate certc (Poirt O) of Arc AB, aod draw e tmgert (LitE lp d' Poirt' B' z. Draw ctrcd li"" AB

"Ja.*-,a ir L poirt c, m"tia ab t-+rl t" ure'half of AB'

3. UsingPoirtCasccr&rurdndi.5eq'.raltotLdistieeC,&as-a."offingturgertLineBFd'Poirt D.

(Source: Rcfercncc 5, Fe$ l4l)

F , . \ t k

-v-

_{t , Y}

) e c

O / / D

divieion pointr asPoints l, 2. md 3.

7. UsingPoirt 1 as ctnter, andradus equal to 1'A draw the Arc AC' 3. Arc BC is PracticallY eqal !o AB'

(Sor:rcc: Refercnce 5, Page 14l)

x

O

-

rO

-\

1, Draw line AB tangert to Arc BD atPoirt B. Divide Urr AB irrto four eqtral segmerls'

E

AB. DIVIDING AN ANGI,E INTO EQUALPARTS:

I . Usingpoirt A as center end any radius & drsw an rc o.dling Si& AB at Poirt' D and Si& AC at Poirt F. 2. using poirt o as ceffcl. and any radius Rl , &as a e econd 8rc asay horn Point A 8nd beturecfi sides AB

sndAC. 3 . ;;G tt

" ,'.* rediw Rl md

poin! F ar ccr{cr, &aw a third rc that irkr:seds the sccond arc al Poirt G. 4. Line AC UiseCs Angle BAC and Arc DF'

(Sourcc: Rcfccncc d Page 123)

L Usingpoiri O as center md any radius R, draw an rc cuBing Si& OM *PointN and Side OP alPoinl L.

Z. Cornectingpoirt N Lo Poirt L, divide the resulting chordlirr (Chcd tN) irfo tlrce eqr:al segrrnnts. 3. Designstc tlr [wo new points e*ablishcd on Chord LN as Poinl 3 and Poird' T. Corrst Poirts S and T

with Poirt O.

4. Line OS and Line OT divide Angle MOP, Ctrcrd I.,}{, and Arc LN into tlree approximatety equal parts. (rd

( z - a )

I I t J

G.

AC. DEF1INING A CIRCI.E OR AN ARC

ffi

poir,tr

(poirrs

I P,:1 I

t*:T

n:trK.from

each

other

as

possible'

Itsfaousu u[lt el rvq lrys'

prit*o _{chordlirrscorrrctingPoirtAbryk . . ..} X. Or* p.tp.ndiorlar biuotttt, * and GItr to the chrd line'

3. The irnrrsecri."ortr,.illffi,a;i;;J*,PoirtD, is the ccrrtcrof th rc'

(Sourcc: Rcfcreocc I Pagc l3a)

DRAWDIG A CIRCLE ltlKuu\rl1 rrrrrle r \

l. coru.recl poin! A to point B, 'd poirt B to c. Draw perpendiculr

b'ise<tccs, DF 'd GE to Line

mdto Line BC.

Z. TheirterseciionofDFmdGHatFbittOisttEcenterofthecirclemdthedid'af,IceOAistheradirs' (Source: RefereDc. d Page l3a)

ir AB

.{'n

/ _{- \ - - '}

- t \

A P r c \ r . / A J t . / c B r l -} t ' I P * ' l I / 1 1 l R I B. ' _ - _ ' ) I a I I I I ft lb I l -I I I I I I I

I

I h I I ---I--Ftt

t l \ .

r t ' S t 1 /

t l

l t

_ G

A B

h

B BB. DRAWNG PARALLEL LINES: LINE PASSINC TIIROUGH POINT P A}qD PAIT]\LLEL TO LINE AB:

l. UsingPoirtP as center md anyradius R gfealer than ttte digtarce FcrnPoinlP !o LirE AB, draw m rc crd,irry Lirr AB at Point C.

Z. UsingPoirtCascenterandthesarrrradirs&drammothrrcpassingtlroughPoirtPmdo.rtingLine AB atPoinlD.

3. UringPoirtCaeainascerterandthedistarebehreenPointPandPoirt,DrradiusRl,drawathirdrc cr.dting tlx frst erc d Point F,

4. The line cornedingPoirt P to Poirn F is parallel to Une AB. (Source: Refcreoc€ 5, Page l?4)

LINE pAR.0U..EL TO. AIID AT A GIVEN DISTAIICE FROM. LINE AB:

l. UsingPoirt A (of Line AB) as center and the given did.ance ! as raditx, &aw an arc on orr si& of Line AB.

Z. UsingPoirt. B (of Lirr AB) as center and the srne disterre S r radiu, draw a second sc on ttr saf,ne si& of Une AB.

3 . Draw a line tangent bo both ttE fn$ and the second acs. 4. the new line is parallel to Une AB'

(Source: Refecoce 5, Page 125)

a-

_s

\ \

c.

BC. DRAWING PERPENDIqULAR LINES

/ b / ' D P

+

U . 1 3 . I I a A

J<

t D

l

-I I I I I I

x

x

l. Usingpoirtp as centcr and any radiu R greater than tlp distsre betweenPointP and Line AB, draw en arc cr.illing Line AB al Point C and 8t poitt D (two Poirfs).

2. UsingPoirt C (E st), md Poirf. D (net) o

".rlr" and arly radius Rl, draw two zuccessive

srcs on that si& of une AB avav fromPoinlP; tie two rcs intcrsecting d. pointF.

3. The line connedingPoirts P & F is perpendiculrto LirE AB. (Source: Refertncc d Page l4

\ ^ - * , | ; . I I

X

Fxtend Lig AB beyondPoirt B. UsingPoirrlB as cenler and any raditx R' draw an a'c cuiling Line AB at Point C ard tlre ertsnsion lirE atPoint D.

UsingPoirt C (first) and Point D (nef.) c cert€N a-rd any radius.Rl i" lonh operdiors, &aw two arcs on the srrr side of Lirr AB (eithcr si&); the two EcE intr€ecting 8t Poirr' F'

The line conneclingPoid B to Poirt F is pe-pendiculr to LirE AB'

/ 1

, l c . L D

\

E

BD, CONSTRUCTION OF A GIVEN ANGLE: TO LAYOUT A$I ANGLE O:

l. Draw Side AB to any cornenicnt leryth in the rrnrltiplc of l0 unit* Find tlr SD{E of Argle 0, tom any table of naural lirrs.

2. Using poirt B (of Side AB) as cenbr and thc didancc F XI0SINE 0 as radit's, &ev an rc on eitlrr side of Line AB.

3. Drarp Line AC tangenl to this arc and also Pesing tlroush Foirt A' 4. Angre 0 is fcrnnd by ttn int€rsedion of Line AB and Line AC' (Sourccl Rcfcnocc 5, Pagc l23)

/{-/ \ / R

a g

TRA}ISFERRING A GIVBI P'}JGLEBAC TO A}JOTHERPOSITION ORINCAfiON:

l. l,ay out Lirre Ats' in the desire d rrw position/locdjon Using any radius R, andPoirt A (first) then Poirt .f( ned, as certa:, draw two a'cs; the fnst rc cufting Line AC atPoirt P and Lirre AB at Point D; the second ac cutiry Lirr AB' at PoinrD.

Z. UsingPoirt D' as center and the distance from Point P to Point. D s radiu, draw a third rc interseding the second arc atPoint C''

3. The line connecting Poirt.pt' to Poirt C' forrm the given angle BAC in the new peition as Angle B'A'C'. (Sor:rce: Referenct 5, Page 124)

t B B A _{10X (+0 lnn)} += 10" S i n e S = 0 . 5 n = ( l O X ) S i - e 4 > I = {OSire 10-] l = 2 O m

0

CC. CONSTRUCTION OF TRIANGLES :

Iey out Si& A in the desired pcition

U s i n g o n e e n @ i a @ n d P o i r t l ) o f s i d e A a s c c r t e r r r d t h c l c n $ h o f S i & B a s r a d i u s , d r a w s f i a r c o n

iffi#d:XT*r,* A and the rengh of side c a radius, draw a second rc intcrsectins the 6rd rc

at Poinl3.

4, ConnectingPoirt 3 with Points I dld 2 e*ablishes Triangle ABC' (Sorrrce: Refercncc 5, Pagc l??)

S i l e A

\

(t- z)

1. usingthe lengh of the given hypotenuse (side aB) * djlTg' draw a sernicircle'

Z. Using one endpoirt (E ,Soirt A) of tlrc f"lp".,G1side AB) as cenbef and the length of Side AC radir-t!, &aw an a'c inbsectirylt}r scrni'circle atPoirt C'

3. corurecrirypoirt c with En$oi*s A a-rd B .Juti"tes tlp &sired Right TrienS,le ABC'

(Souce: Refersnce 5, Page 128)

- - - \ 1 S i d e F o (HYPotenuse) A _ S i d e € C

(r)

1 . 2 . 3 . ?. 3 s i d e C S i d e F 7 2 ( i ) (B.

(+)

( ' ) l 2

pRA\rlntc ,Jq EQUTIAI{GULIiIr TRIAT|IGLE VJTIH ONE SIDE ON GMI{ Ln{E AB:

L Drarr a straidrt Lim AB, md designate rPoint, O ner cne end Using Poirt, O a certer, md any conveniertradir.rs R, draw an arc cuting LirE AB etPoirf, C; end efend thc rc W b 90 degrccs (fr,om Poirt O) in ttr d$ired si& of Une AB'

2,. UsingPoirt C as crnter, rrd the sarrr radiun & &aw a second arc irferxdingthe Ent rc atPointD. 3. CorrrectPoint O !o PointD md Poirt C !oPoirtD to compl& the egiangular tsimglc.

(Sourcc: Rcfcreoca 5, Pagc 129) ₁

INSCRIBING A}.I EOTILATERAL TRIANGLE IN A CIRCI.E OF RADIUS R:

l. Desigrrate anyPointAinthe circurnfererre of the circle;PointD is located althe opposibe md of the dia'neier lirn.

Z. Using Poirt A as cenLer, and radius R equal to the radiu of the circle, dr;ur 8n arc cr-tting tlre circumference of tle circle atPoinlB and at Point C'

3. ConnectPoint D to Point B, Point B to Point C, and Point C bo Poirt D to complde the biangle. (Sor:rce: Reference 4)

-g

e--.

-F \

cD. CoNSTRUCTION OF PARALI.g,oGRAI\{S ffouR-sIDD POLYGON$: DRAWING A SOUAREWITII SIDE AB GIVEN:

1. Draw Side AB in the desirt pcition CorEhuct Une BE perpendiculr to Side AB ard originating fr'om Poirt B,

Z. UsingPoirn B as center rrd AB as radius & draw m rc cr:Eing Une BE at Poid C' Using Points A and C as centtrs, and the sarrr radirs R in both oper*iorn, draw two arcs irrtcrsecting each other d'Point D' 3. Cornect Point C to Point D and Poirt A to Poirt D'

(Sotnce: Refercnce 5, Page 129)

NSCRIBING A SOUARE IN A CIRCLEWTH RADIIJS R;

l. Draw the circle withPoirt E as centJer. Draw Line AB tlnough Point E cutring the circle d Points G and It

?. Draw Line c.D perpendicutr to Lirr AB, and passin3 tlrough Poinl E, cr-ilting ttrc circle ar Pohts M a-rdN.

3. ConnectPoints GtoI4 Mto }1 H!o N, mdNto G' (Source: Reference 4) I

),1(

B

z<

_I

I

_I

I

I --.1 \ B A" I F , l - ' r

)T;

. l I I

J}

I I I 1 4

\a.

t 7

3 .

Draw the diagonal BD md bisect it af Poirt O. UsingPoinr O as centef,, &av a circle passing tlroudr Poirt B urd Poiri D. Lirn BD ig a dirndcr'

urirg p"irr" B urd D as c€ntert, md lcnglh of side Bc as radiu, draw two rcs cttting the circle * Point C rrdPointA

Cgnn{fgnrBb-Point C, C-!o D,D,!o A _1d AtoB tolltaeUerectaull

B - C

- - - - \

( s )

r t

rL

1, Draw Side AB in the dcired crierialion Corsbruct Angle 0 d. Point B, a-rd desigrate Lire BF as the si& makingthe Angle 0 with Si& AB'

Z. Usingpoiri B as cenLer and lenglh of Si& BC as radiw R, draw an arc cuting Lbte BF aLPoirn C. 3. Usinlfoirt A as center and si& BC as radits R, &aw s second arc on the sarne side (of Une AB) as

Poirt C.

4. Usingpoirt C as cenber and length of Si& AB as radiu Rl, draw a third rc inlersecling tlc second erc at Point D.

5. Conned Poinl A to Point B, B to C, C to D, srd D t'o A

(.)

( s - s)

( - r )

A

DD. DRAWINGLINFS TANGE}.TT TO CTRCLFS

Frqn the certer of the circJc @oirt, O), draw a line pcsing tlrough Poirt A and e*ending to Point B' making the lengh of AB eqrul to OA'

UsingPoirt O fr$, rrd Poud, B rr4 es ccnters with a radir.rs R eqr:al !o my lengh greater thrr AB in both ipcrations, &av two arcs which intersect d Poinl C snd Point D'

The line connerlingPoirt C toPoirtD (perpendicrrtar Uitectcr of Une OB) is tangentto Circle O at Point

A

(Source: Relerence 5, Page 135)

1. Frcrn tlre certer of tlE cbcle @oint O), draw a line to Poirt P' Bisect Line OP md desigrrate the midpoint as Point M

?. Using Poirt M as ceriler md the lengih of OM as radius, daw ert aa'c cttting ttr circle at Poirt Tl and T2' 3. LinePTl andPT2 reta-rgenttothe circle.

(Sorrrce: Refcreoce 5, Page 135')

-)a \

\ T I T A 2 . 3 .

x

D 1 B l - - ] - - - - ' o 1 6

3

_i, L

LINE TANGENT TO TWO DIFTRENT CIRCLES ON TIIEINSIDE (CROSS.BE.TI:

Draw Line Ol -O2 conneding the ocrtcr o-f the fir*.drcle (Circle l) !o tnc certer of the second circle (Circle 2). Erom the centers of both chcter, erect perpcndicular lirBs b tjne Ol-O2, irtcrsecting the circurnferencc of Chcle I d Point A urd the circunfcr,ence of thc otlr circle (Circle 2) d Poirt B. ConnedPointAwithFointB by a brcken lirn intfnectingLine Ol-O2 atPointP.

UsingPoirtP as e.corrtrnon point or.tsi& of bcth chctes, _{and thc proced:re fa &tcrnrining poirt of} tangency of a line to a circle @roced:rt B above), locaie PoinL Tl on Circle I crd Poinl T2 on Circle 2. The line conneding Poirt Tl !o Point T2 is tangert bo both Circle I and Circle 2.

(Sorrrce: Rcfcreoce 5, Page 136)

L , 3 . 4 . t - 2 )

-l-I ' l

+

' x , .($z oz \ l t / \ , :l o l Y '

\.D.

1 . Draw Line BD perpendiorlr to Lire ABC er Point B'

z. Frcrn poirf, B -a *ine t!* givcn radir-s & &aw a shqt rc irtcrsgcti"g LiT Pg *?oirt o' 3. Usingpoirt O as cer# ana-,"aius & &aw the desired circle passingtlrough Point B'

(Source: Rtfertnce 5' Pagc 135)

v

1 . 7.

Draw Line BD perpendicular io Line ABC atPoint B'

Conned point B to point p; Con$nrd. a perpenaicil".r bisecbcr GH of Une BP; desigrrate tk irfersection

of Une BD rrd Line GH as Poirt O'

3. UsingPoirt O as center and a radius equal to OB, &aw the &sired circle or rc'

(Source: Reference 4)

o'l

M. EIRCLFS INSIDE ^P$ID OUTSIDEIRI.AiI'IGLES l. Biscct Angle A by Line AD Qdcnding this lirr bqrcnd thc middls of the kimglc.

Line BE intersecting LitE AD at Poirt O.

2. Draw Line FG ttrough Poirt O perpendictrlr !o Si& AB al Poinl If 3. Usi4Poirt O as ccntcr rrd radiur equal to OH, draw the dcshed circle. (Sourcc: fufcrcnce 4)

Biscct Angle B by

CIRCI'MS CRIBING A C IRCLE .{ROIIND TRIANGLE ABC : I. Draw a perpendicular bisecLcn (Jne DE) bo Side AB'

Z. Draw a perpendictrlar bisectcr (line FFI) to Side BC intcrseding Line DE (first bisector) atPoint O. 3. Usingpoirt O as cenber and OA(orOB) as radiu, drawthe desir€d cim:rrscribedcircle.

(Source: Referarcc 4)

tt

IF. CIRCLES INSIDE A}TD OUTfIIDERECTA}IGLES:

L Draw the given si& AB zuchthalPoirt. A and Foirt B bcth lies on the circr'rnference of tbe circle' 2. Frqn bothPoint A end Poirt B, craw one f irr .J pcrPendiculr t'o Side AB md intcrsccting thc circle d

Poirt D and Poinl C.

3. ConnectPoirrtAtoPointD,PoirtDtoPointC.6dPoirtC!oBincrdcrtocorrpldctlerectangle'

A # e

, c

(r)

CR.CLE D{SIDE A SQUART/ CIRCLE .AROUND A SQUARE:

l. Draw the given squa-e &sigrating each ccrner as Points A B, C and D, respectively; &aw a diagonal from Poini A to Point C.

2. Draw a perpendicular bisectcr (Line FQ to Side AB irtersecting the dia3onal ilne AC at Point O' and cr-dling Side AB at Poirrt G.

3. UsingPoirt. O as certcr and OG as radius, &aw the irscribed circle' UsingPoirt O as cerd€f and OA as radius, ,&aw the desired circurnscribing circle.

(Source: Reference 4)

( r )

( l l

r)

D.

( z )

F I i t I D c

.i)

{o

Xt,)

_b t 6 A

-t-20

/\ rq , l--]'J

EG, HD(AGON INSIDE A EIRSI.,E/ AROUND A CIRCI-E HEKAGON IMTIDE A CIRCLE OF tu\DIUSR TACROSS CORI'IERS):

l. Drar diarneter line AD across thc givm circle; AD cquals 2R RomPoint Aand using radir.rs _{\ &aw} rr rc a.dting ttr circlc at Poirt B and Point F'

Z. Frcrn point, D and using the sarne radius R, &aw anoth€r rc o-ltingthe circle * Poirt, C andPoint E 3. Draw Lines AB, BC, CD, DE, S, FGto co'npldc th hcxagon

(Sourcc: Rcferencc d Pagc 130)

( r )

( z )

(r)

HEXAGON AROUND A CIRCLE OFRADruS R (ACROSS FLATS)

l. Draw dirneter Line AD across tle given circle. Usiry radits R as length urd strting from Point A' mark offpoints B, C, E, and F, at equal di$ances around the circurnference of the circle (six points totat). ?., Frcrn the certer of tle circle @oinr O), draw radiating tines Q.ine OA' OB, -- OF), erch line extending

beyond the circr-trnference of the circle.

3. Draw one perpendicula- line to each radialing lirr, making tlee pcrpendiculas tangent to the cide d. Poirts A B, C, D, E & F.

4. The intersectiorx of these perpendiculars are the corn€rs of *te circumscribed hexapn

- X

_f

l /

-x-I I , \ I \ ,

)S

, , \ \ Y._{- t}

,fr

X - t \

(2-r)

E ot.i , - F T I I . , / \ I -

,C-( r)

(r-4)

r.d

l . ,

d ^ft crrfing the &cumfere*e of the Draw two diamders of the circle rrhich re perpendicular to each other'

;,[5l#e,

},s,k ff H**?

*ilng the

di

*ance

berween

po

inr

p and

po

i nr A as

rad

ius,

draw m rc cutingradius ON atPoirtX

3. Frmr point A *d;i"g tl* distare bctweenPoirt A and Point X a raditx, draw a the circle at Poirlt B' DraT Line AB, -a *t ;ttttngth to daerrnine Points C' D' circr-nnference of the circle'

(Source: Refarmct 5, Pagc 130)

second rc cuting ard E around the

I

( 1 )

l. Draw the diarretcr Lirrc Ali divide this dirrrter line into five (fcr Perfagon) equa'l

segments'marking

&aw lhe c'ther four sides. (Source: Rcfercocc 5, Page 130)

( r )

( , )

L

><

H.

z. $:ffi,iT'f;illli,iRt;rt"i.,HX.,u

* cbcre

dianpter

as

radius,

&aw

rwo

rcsintersecting

e*h

otlrr atPoirt O. Draw a lire connecthg P"; ;;;oir,tZ 6'' tf'" ai"'na"r "f tlr circle) and extend this

3. #iffit*';*t.i"it.iti si& of the &sired regular pcntagon usins the lensth of Line AB'

lt

- I I t I

(z-r)

A t - \ I E! I I I I x \\-- o P H I I t I

t

I I I b I ' l _, ' J l ' t

]>.

,t)t. 22

_

-A

FF. EONSTRUCTION OF ELUPSES DRAWING AREAL (FOCD ELLIPSE:

l. Drar the majr axis ss Line AB, md thc mina qis as Linc CD (pcrpendicula to Line AB); tlr fr7o lirnr intcrsecting dPoint O.

2. Locale Focus E and Fanrs F by draving acs fromPoints C and D (ends of tlr mina ncis) with radiu both egal to orr-half of the majc uir (errylh of OA). Intcrsectiors are the foci.

3. Between Focr:s E md Point O on tlr majc axis, rnert e randcrn irtervals a nunber of poirts, spacing thce points rrr Focrx E rncre closely. Five poirfs should h thc minimrm Mark offthe sdrr nurnber of points, sith identjcal soacings, between Pointc E md O.

4. Using Focus E and Faus F as certers and redii A-3 and B-3, respectively, draw rcs irtcrscCing at Poirrl 3' in the leB half.

5. Using the sarrr procedrre above rith radii A-5 (A4, A-2 ard A-l) ard B-5 @4, B-2 and B-l) resp€ctively, locde Poinis 5t,4t,Z', and I' in the let half.

6. Dr.rplicate all operatiorn fcr tlre right half and corrrd all poids rsing inegular curve, (Sourcc: Rcfetmcc t Pagc la3)

B

J-xtr

>t-

t t - - r

-YYr/

- _{a ' \ , / t} _r _/J,

B.

ffie AB rrd the minc axis as une cD (perpendictrlr to une AB) intcrsecting

al Point O.

Draw Line AC: using poirs, o r cerfcr md oA (semi-m{or ais) as radius' &aw an arc cttLing t}re odension of Une OC *PoinlE

fsowce: Refercoce 5' Page l4?)

(s -+)

2 .

ffi;ffi';"::;;'d;;dius, &aw a second rc c'tinsline-Ac atPointF'r :-^ aar zs*-mnicr ax

'^:lHilgffisilftr#[i'H'ff&:::Ha;;:i**:":r,ns*Poin'!Kand'ihe

ffiii"'3?:'S;

iffi ilt; ffii ; ;il; ;J-*;K

1t T-"111'J:'X';';

ffi"#Xffi

n ST'ffi: #'#:&;;M

r or on

the

Jier si&

or

tlr majc

and

mincr

5. ffi* .x.r,aed lirps cornerting Point M to K Y to L' J.' K^ ld 't tY to detrr{nine

poirts of tangency

Cf);[h are the limits of the rcsto be *"y 1"".,"-:l llTS;

g*":H*rff'lt*Xfl,,l$*nilft,il;;ry

_ffl

e ends

or

tlr mincr

a:<is

(F.m

7 . Draw arcs trofil lrre loLr celrsl-i uuuru' @ I q\

Centss J and ]O; *d tl,t ner en& of majcr axis (from Cerfers K and L)'

q

24

CHAPTER III

METHODS

OF PROIECTION

USED

IN ENGINEERING

DRAWINGS

l. Forr tlryes of.projection are gerrally used in rruking technical 6awings; all are Pictcrial except the Multi-Vicw. In Multi-view end in Isornetric projections, the p'rojection _{lines (cr vistral rays) re prallel to each ot5cr,} and these projedion lirrs re pcqpendictrlar!o the plrn of pnojection; th& Nfuti-view and Isonnuic projections re classified as OrthoFaphic Pr,ojections, Ttrese re the two rrxtly urd in cngirrcring drawingr.

2, The main difrerence between the M:lti-view and Isorrdric projedionr is that in the Isorndric projectiorq the object is pictrred as irnlinsd !o ttr plarr of projectior\ nEh thaf dirrnsionr ar" foreshqterrd

3. In Oblique projeaior5 projection lines are also parallel _{to erch cther Qike in orthographic projecion) brr} these lines are rnt prpsndiculr to the projection plane.

4. The fouth tlTe is the Perspective. kr this projectiort the obsenler is considered !o be d, a FINIIE di*.ance Fom the object thus, projedion lirps ae not parallel to each otlrr, irstead these lines fcrm a corp with the vertrx at tlr obsererb eye,

(Source: Rcfecncc 5, Page 602)

MULTI-VIE1J ISOI.IETRIC B

l./

)A

'o'

\ E \ T ")\

-l

c c L -

---.---t\<l

lt

ll

_--.---\ (F-ront ) // / SP

./

\tr-:>l

/ /'1

>;,/

_\

\B (nisht S r d e ₎ . D/ \

>\

, o "

f , / " " r / c / -\___:-G"fl-no")- .,

S

\ D OBLI qTE (45' Caveller gpe) / D '

-A ISOMETRIC PROJECTIONIDR-AWING:

l. In rr Isometric , the objec is prrojedcd srrh thd its prircipal elft' :. T:' -l:-:#.::5:t55

pr.n. or fi3#il-ffft: fitii;oilo;'rl*- is sr rsorrrcrii unl r uie which r - - ^ - l - - T - - . * e i a D l mi8 nct prallel to nv isorndnc

"*;; ffi;;'t*d hr* 'e,ry;*.;.*uJ io 'ny of tt e Isonrtric Axes _{| -}

t*f:,ltT-;:^;ff

il'#;";iifr;ffi;;:,;;;il;;;i;;."i""carewhereinaudistarresre0'8165

tirrps tsrE lenglh/size. An isonraric drarring is &awn using crdinary scale, or full size'

; :'"ffi ;"; #;X ;il#i ffi}i;;ffiJ;ffi"J ;r'{aq "'"T

1T*: If ,YH

thaf are parallel !o any edge in thc nnrh,i-vi.* a*'h"g *iff Ue prallel, rcspectively, to thc ccrresponding edge in the isorndric drawing

oltlfi*.

strfrcs

in isorrptric

cm

be

&awn

bv

estabtishins

_{q 1111.*T:ti' :lu:]flT"It*}

tr,. i*.rJi";H::io

esablish

the

obliqt'e

_{pt-.' tr,. u,,o,'id ?t F "!tlq::li,::#l*:r'ili}

ffiffi:$#?

;:,}Hffi;ffi;

ffi;#"d.*

*"*, uy

the

rse

_"rtrirute

ororanerism:f

h3;

- r L ^ ^ . . a 6 r r c l r f r e t f

J. The Isornetric Axes may be plrced in [fty desired poeition; btt ttE angle bCween th a:<es mu* r€tnaln 120 degrees.

6. Hidden lirps re crnitted in Isondrics unless very nec€ssry fcr clariby' (Source: Referettcr 5, Pages 603 emd 6M)

ISOMETRIC PROJEITION DIMETRIC PROJECTION

I s o r e t r i c b Y R o t a t i o n o f S i d e V i e n TRII{Ef,RIS PROJECTIOR R P _Y

1"*<b+<c

o x * o 1 f ow

Isonettlc Front Tieu

f

3 o "

+

\ ' 6 0

_I

Y o x = O Y = o ' 4 A q = ( b = ( c o Y Lb

-=_ J

ri=.-.-l.o

I

I

26

A ISOMETRIC DRAWING f.Cort'd,): iSOME:HC DRAWING OFNORMAL SURFACES

-(Source: Rcference 5, Pagl 600

along cdges-. -/ 4, 3o' \ t ) -I T

!*

_\ IIr

-l--

-T-".'1

f \

A ISOMETRIC DRAVJING (Conf d'): lsoMETRIc DRAWING oF INCLD{D SURFACES (I., M and }Q

(Source: Refcracl $ Pages 606 md 607)

All rcllu:lcncrtr mlt to thr rrln tdgc6 b. cf perelkl tbo

I F:-_l

' \

_{M I}

: \i;J

T l.^.l

1'F

+

L

N-=-D * \ 3 o ' 4 3 o

-l"

+ _

".a13etrg ber ffiGoFoBLIQtIEsr'RFAcES(SrrrfacecreatedbypassingC\.dtingPlaneXYCt}nough Points A. B and C)

OFFSET LOC ATION MEASUREMENT

H:

E,

h

A EOMETRIC DRAWING (Cort'd.):

?, Objeds re more easily drawn by meru-of Isonrtric Box condrrrtjon This consids mainly in enctosing th,e object in a rectangrlar box wtrose sides coincide rith the otternnst pointsrfaces of the object

8. Since the only lirrs thal re true len$h in an isqnetric drawing are.the isonrtsic ares (and tlx lines paratlel to these axes), NON-isorrrtric line will NOTbe hte lengih

9. Angleswillprojecttsr"resi.agdlghetttheplamoftheangleisparalleltotheplarrofprojcctiorr. Since the various surfmes of an object in ISOMEIRICS re uzually irclined to the plane of projection, angles gerrerally are NOTtn:esize. Incrdertosctoffanglesinisonrdrics, lirrrmerurerrrntsoftttcsidcsremadealongisorrrbiclirs.

10. If the general shape of tk object does rnt readily mrfcrm to the redrrgular fcrrrt il cm $.ill be dravm using an inccrnpletc Isornetric Box

I l. Ornaes can be drawn in isornetric by rneans of a series of otfset rrnasrenterts. Enough points on the cr.nre should be establislred to rcuralely fix the path of the cr.rnte; t}r rrnre poirts used, t}r grealer th acoracy. Offset isornetric lines re then drawn from each poirt prallel to tlre isorrrtric axes.

(Sourcc: Rrfercace d Pags 608)

EOX CONSRI]CTIOII HTIrH

F---l

l-"

-j

T-D

I

ISO}iEIRTC LINES I I T

I

q ---T----T-b !_l_----r-c

\-<

, r ' \ . 2

- w

H

-<tY')-\\,./

\t

30"

+

//

T_

u

J

+

a

----:r

t F 3o" t

rv

I T I

A ISOMETRIC DRAWING (Cont d'): BOX CONSTRUCTION WIIH NON-ISOIVIETRIC LINES

(Sourcc: Refcrenct 5, Pagc 609)

( Y

.y

( r o P) \

"-2\

s

.-1-\b

\

_7--I

FS-\l/);

_-1-I 9t

/7-

^,-j-l,

Y,

l--'

:x

_{_1_}

\ \

-bi<{

l

>K

,r

1,{

5i\

\ - \ \ 30

A, ISOMETRIC DRAWING(ConI d): ANGLE IN ISOMETRTC

(Source: Rcferenc! d Page 610)

./ \ _{,; ----{} \ \ \ {

r [ \

\c

tr\

,/\

il-.

.1

\l

IIr

A

I . Using very liglt lines, corblnEt g'r Isonpbic Box on any available EPs€, s follows:

& Draw a long hcrizontal line md mart ie midpoint a Poinr d; this spot will beccrne the bofiorn' rigtrl'front ccrner of the conplde Isometic Bor

b. Frcrn point o, &aw a vertical lirn vihich will becorrn tlp heich! axi1.lomPoint o also' mrk'off upward the heigtt of the Isonraric Box using tr,. a**iffir the highest pirt in the lhont a'rd Side Views. This second poirt will becorrn ,h" ;;, right-front lrrnst-fcrwaflcf) corrrcr of ttp complete bor

c. Using Poirt O again as Yert.,q &e$t a line to ,l* ti4tt and to tlr- left' bcth of which shall be 30 degrecs above the htrizontsl ti',". tt. lirr towards d;ttgta will become the profile (depth) axis; while the lirr towudsthe left will becorrp tlE F,ontsl (width)

axis_.-d. Frqn point o, mark off lowards the rigfrt, ard aong the profile -(de$h) axis' tlE &pth of the Isorrrtric Box rsingthe dinpnsiors of the deeped p"iit qfro* tf'e Font plane) in tlE Top View' or e. ***jJf,Ifi'"o"**ds rhe left, and alons rhe Fortal (width) axis, the wi&h of tlp Isorrpbic

Box usin3 dirnensions Laken fromthe farth€* poinr Qo th ten or*re ;ght profile plane) in tlre Front View, or ToP View.

f. Complde tlre Isorreb'ic Box rrsing onlv lines that are all parallel F tl" tlre.e iscrnetric €xes'

.2. Starting Fom one coner (cr face) of I5e Isomeric Box, ttu*fo srfaces (cr lines) hom *re Multi-view projectiors, one d. a t ime. I&ntify surfaces (cr lines) in accordance *itn tr,.ii ..ientd'ion (parault' incline' or oblique) io ti," primrry planes (plarrs prallel to the axes) of tlp Isornetric Box

3. Hiddm lines and poinLs will NoT be shown in Isomdric drawing except when very nec€ssry to cla'ify ambiguous strfaces in the drawing

-T-I I D

I

{ B GIVEN I'IULTI-YIEV ( T o p Y l e w ) n

f-- ',

--J

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(n-s vrew)

32 l4t!.,

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I I (Front viev) c

B. IvfIJLTI-VIEril OF A GIViEN ISoMETRIC DRAWING:

L Confuct the srnalle* isornctric box whictt een errctosc all prb of thc isandric Egure, using ligtt lirrs: e" Draw vertical parallel lines pasring tlru all visible poinb. the* lines re pcallel to the vertical

(heid$) qis of the figure'

b. Draw a semnd set of parallel lims, all 30 &grees from the hcriantal, passing tbru dl virible points aln. These lirns re prallel t'o the profile (defh) axis of tle figurt.

c. Draw a hird s€t of parallel lines passing thn-r dl points, all 150 degees Fom the hrizontal. These lirre ae parallel to the Frontal (wieh) ais of t}e figure.

d" lhe box should bemrrn apprert tlnr tle irtersediors ofthc lirrs.

Z, Condnrct. a quadril*eral in a certral rca, sith the sidth taken Fsn thc hontal uit of the isonrtsic box and the height tak€n F,om the vertical axis. lhis is tlE Flort view bor

3. Confr:ct another quadrilateral above, and a ghort distsrce Font ti€ Frort View box with tlp sane width; but the degh is taken Fom the profrle aris of the isonrdric bor Thil is the Top View box

4. Con$nrct a third qua&ilateral a shcrt di*.mce !o the (drawer'tridt of the F|ront View box sith the sarrx height; br* the &pth is taken from the pofilg axis. Ttris is the Righl Sidc View box

-- --v- '

5. Starting from ttn rrnst conveniert view (ncmrally tte Frort View), transfer all poins (cr lines) visible in that isorrrric view, !o t6 corresponding rrruhi-vie.v box (Fronr View), using the heighr and width dimensiors taken ;i;;li;r pa-allel bo tlre vertical-md frontal a:<es, respeciively, Conract comsponding points right away.

6, Locate points (cr lines) that may be hidden from the frort view, and coru'rect tlpse points (cr corntrut the lines) with broken lines'

':'. _{koceed to the Top View, a"rd then to the Riglt Si& View'}

9rE8N ISOI{EIRrC TSOHETRIC BOX

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STDE Vlev HINTI-VI$T DRA}TI}G V l e v (srae vtev)

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(Front Vlcv)

B. MI}LTI.VIE:W PROJECTION:

1. A Multi-Vicw projection is obtained by drawing parallcl projcction lines from a[ poins in thc contours of ttrc objec[, making thcsc lincs pcrpcndicular to trc pranc _{#;tt I;F ;. inc} picrcirg.pgTtt^:l thcse projcction lincs on thc projcction ptanc form bognduics, oioagti, of nt obig$ as projcctcd in thc projcction planc. Thc planc ofprojcction on wtrich thcFront Vic*is"pro;cctcd is ttlt:d thc frontal planc; that planc on which thc Top Vicw is projcctcd, ttrc haizontal pil; *i ttttt on which thc Sidc Vicw is projected".thettfrfft*T'of

projcction can bc imagincd to form a gfass box cnclosing trc objccl thc observer is alwrys considered to bc outsidc the box do6ng in Since th"c bor has sir siles' six vicws of thc objcct can bc madc. In all ttrcsc vicws, howcvsr, thc objlCtts otfy tfncc principal-dimcnsions: WIDTII' HEXGHT, and DEPTH, regardless of the shapc of thc objcct Tht'ror rRoNt' llAR and BoTTOM views have the sarne 1IIDTIL The REA& LEFT-SIDE, FRONi, LO iUCUI-SIDE vicws all have the samc IIEIGHT. Thc TOP, RIGIIr-SIDE, BOTTOI', *a f,fff-JDlEt i"t"t havc thc srnc DEPTII Thc front surface s of the uir*r'r*o*ding the FRONT View are faced toward the Front Vrcw'

3. Folding lines between thJ views conesponds to nrr ilinir lines of ttre glass box of projection plures. Instcad of using folding lincs, ho*ru.r-as ,.r*n.. *tt i*. tt-T^*--q[9-0fo measurcments in thc

irp

"rO ,id. ui.*r, tSe"frontal il*. .- bc uscd

as a rcfcrencc planc in cdge vicw'

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REl(t view L-s view FRoNr Vie'^l R-S Vrew

Folctius tlaes /-goTToM vteuJ

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5-Degree l ' l i t e r

(Sor.rce Peferenc-e 5,Page 2@)

B. MULTI'VIEV/ PROJECfioN (9ort d);

4. Since all desh dirnensions in t}e Top andside view muc ccrrespond poirr, fcr point, rct:rate rrdho& of rursfcrring tlcse d*Elcrs rrnst bc uscd. A45-&gtEc milcr-lirr .T b" rnilized forthe PuPose'

j. ivt * tlrre views of m object b to be drawn, a ru.rnbering sy*crn fcr cvery point is necessrlr Each' *rr.. of O" object should be given a ntnnber, .f ,h" poi* is visible in r gven view, the rn:rnber is plrced orlside thc ;; il if tp point ii uaaltr" the rn:rrsal b plcd irui& the eorrrcr. Thir syslan where poirts rt identified by numbers in all views, ir

"..y ,16.iuf in projeciing known points in trro giveo views to unlmown

positions in a third view (miseingview)'

6. A view may be drawn only to show what is needed to dearly describe tl,e obj".t, or arry part thereof. prtial view c', theref*, be made tt-rgtr the rse of techniqrs nrh as Break Lines, HElf'views, or Broken€ut' Views.

7. Multi-view projectiorn can be effecively malyzr,d by considring the mmponert elerrpnts that makc r:p most solids. A strface <pi-l> may be bor:nded by $raidt lirns cr by crrved lirns; or a combindion ttseof. A plare ;*f.*alwaysprojeaslalneqanc*hersurfaceofthegrneforrn Adraightlirralwaysprojectsasarpttsffai$t i,* ;;., . ioi.r A qorrt€t., cr poirq is tlp mnrncn irtersection of tlree of rnone surfaces cr edges; and, il always appears as a Point in everY view'

(Source: Refcrmce 5, Page 210)

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-/' 2 2.z 7 I 1 ) EV TS FS PV TL FSI - Point(orEnQ View - Truelen#h - Foreshcrtened Length - Edge View

- True Size and Shape - Foreshcrtened Size

B,

8. Anormal rurface is a plar thd, is prallel to a plure of projectiur' It ryee1s l'r b'"t size rtd shape ort the plane !o which it ie puallel, srd as.a verticat a hcriarfal iine on _"{*t"t pltt ts oi projection A normal edge is a lirr thai is perpendiorlarlo a plure of projeAion e wif gPp€r . _"'piitt J" th plrr of prqieCion !o which it

is perpendicuir, and as a lire intnx lenglh on adrer1.plaps of pr$eCion

g. An inclir*d $rface ir a plene nrfrcc that ie p.rp*aJ* to ore plarc of projedion'-bd' irrlined to acljacert plarns. It will project e a draiglt line on the'plure to wtrictr it is perpcndiculr' and it will Ppear fcrcshatcrpd on planes to which it is irrlined. An inclired idge is " f it* *,"t is paraliel t93 dare of projection' but inclined to a,ctjrcrnt plarns. It will apper trrr lengh on the ptariro *fri"tr it is prallel' mj foreshcrteffd on adjacent planes. The t',. length view of sr irrlined fi* ir"rr*ryr ir*fim{ *Hi;th. faeshortened views are eittrer vertical or horizorial lirrs,

I O, An oblique gnrface is a plane thd is irElined !o s[ primary plqo-o!{-oJ^:tion Il CANNOT apper as a line in any principal view. Sincc il is NOT PorX"l !o '.y Princip* p[-", it CA]'D{bT 4P"o tnr size in my of t}re prirnipal planes. It is NOT perpendicr.rlar *, poAta ti i"y Itii*ipJ pf"*; therefre, I uppta.t fcneshcrterrd in

every principal view. _{^t _t-_^ ^c --io.+inn tn wfiinh it} '

. _{I 1. If an angle is in a rprmal plarr, tlr angle will be shown trrr} size on tlre plane of projection bo which it,rs prallel. r tlr ffrgJe is in m irrlirpd plure, it miy project either smaller t ltgt than tle trrr size of tlr mgle' depending on its pcsition

12. The views of a space crrve re &awn by the pmjections of poirts along the curve; the rrnre poirts ued' the rnqe acclxd,e will be t}e cun'e.

l{u,}'ti-Vic*r.of Norcral Surfaces and' Ed8es ( R e f e r e a c c l R e f . 5 , P q , e 2 l ) )

B. MULTI-WEW PROJECIION (-Cont'd) :

Multi-Vierr of Inclined $:rfaces and Edges (Sourcc: Rcfcrance d Page 214)

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45-DEcREE rNGr,Es (+) (Referancet Ref 5o Paee 717)

Multi-View of Oblique Strrfaces and Edges

(Source: Reference 5, Page 215)

ReferEnc€ S,Page 217)

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8. MULTI'WET/PBOJECTION(Coni'd'):

l d. A cylindcr b &awn by strowing its cirnrlr edges and contou elerpnts. A cortor:r elerrrrt is a $raight lirp on tlrc clinder surftre, prallel to the longitudinal axis-of the cylinder. The circular edges will appear in one cr two views; while the cortor.nelcnrcrts will appea es horiantal cr vertical lincs. The contour etcmerts will appear as poirts in the views where the circulr edges appear.

1 ?. Intemections and Tmgencies:

& No lirc *rould be drawn where a cuved srrface is tmgent to sr:rfacc irfcrsects a ptane srfre, a de0nitc cdge is forrned b. If the irtersection between a small cytinder md a large one is

a plane sr.rface; but, whm a currred very srnatl, a sraight line js used to repercnt, the irter:ect ion

c. if the irtcrsection is lrgc, bd still rnt largp enough to juSify plctting the:,n:, tttt liT 1f *e"t"y is approximated by draiing an arc whosc iadius is'equal bo tH radir.s R of tle lrge cylinder'

d, If the two cylinders re of [o sarne radirs, tf. ngr"'.f the irtcrsection consi$s of two semi'ellipse thal arppea as *raigfuintersecting lirrs (V) in one view.

Sorrce: Reference 5, Page 221

CYLINDRICAL SURFACES

Source: Refererce 5, Pages 218 and 220)

Bight Ciroular Cylinder Interecotlon Cyllnclrloa]. Eele T:ngcnoy InterscotLon of Cyllnilrrs

Sowce: Reftrence 5, Paget 2ZZ sttd223

C. MISSING VIEIII: Proiecting A Third View

l. If the missingvies to bc draurri is eithrthiTop View (rittr ttr Front rrd Si& views Ervm), c tlp Si& View (with the Ihont ard lo'p viers given), the tectrri$.ns md proced-ut applicable to the construction of Aturiliry "i.*, _{-gf. O-p.ia"'lar)} ; fu[y applicable. Inthe mnsr:ction of citts of thee Missing vicms, the linebf*ig]t (Loq is Ercd at ridtt_{to the projedion try betrreen the two giren views. Thertfcre, t}e pmject'ion lires from tle} l,1rdl'emr) viewio the mirting

"i.r *ill also be Ferpcnaicutr to these pmjecion lino. {s in the mrstnrction of en auiliary

"i"*, *.ogonnnt of distarpes from a cosurnn refererrce

plrre will bc taken frcrn thc adjacert' given view, and transferred to the lvfssingView'

1., If the missing view to be drawn is the Frort View (with Top and Side views Fvm), the pocedure nec€ss8ry is mrrh simpler La *iu onlyrequire that the projectior lirns Fcrn the Top View rrd from the side Vies be dr"wn perpendiculr to each other. The intersection of these projeciion tircs, for each poirt in the objed" deErmirn the locdion md position of a particular poiri in tie Mssing Front View.

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_{F % * a}

Sorrce r Refercnce 5, P age 322 T o A 'l'o? Sowce:'Rcfercncc 5, Page 202 t{iiltng gide Ylas llieein3 ., Iront Yic* R - r 3 D e F @ o A T R - s , D € _ Sor:rce: Refercnce 5, Page 203

lttsrlng Top Yiev A q x I L r A & ) l{J'asing rrrrllia:qf Ylcrr -t I I -l l I o o

n

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ll

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D. MSSINGLINES:

a. Using Vizualizatic,n and Andysis. (Source: Refercoce d Pagc 209)

I{ISSIIGt Irtna AE Ln thc troat Yicv Llnc EE ln thc ToP YleY A F T o ? e e F B O N T B - s l D e To?

b. Using'Rule ofParallclisrrf of Lines. (Source: Relerence 5,Page2l7)

a

F H

u.

KISSIilGT tlrc -{D anA Ltne CG I'ri tbc lroat YLcv

R - s r D e I \ r D - - , | ,-i 40

*'s' fr, .";ti tj;' i : *a; s;

s

D. MISSING LINES:

l. When tbree incorplete vieun of anobject re given md missing lines are to be formd in one viap onln the technique applicable in &e conskuction of missing views (i.e., apriryipd vi.ax, is to be constucted fiom two given pnncipal vieun) can be used to Itipply the missing lines. The missing lines can be located by making projection lines fom he neaest (a cenhal) view and taking o,rar.pments of the end-points_ofthese linee from the o$rer (or adjrent) view, reckoning such measurements fiom a common reference plme'

Z. When three vierrs are given" md missing lines re to be established in more than one vien6 ttren the Rule ofparallelism oflines must be resorted to; othenrise, a coherent vizualization and methodical analysis ofthe planes and lines &fining the object must be resorted to. Each plrre or n'face constihrting the object must be meticulously examined to detennine &at all si&s of each s'rface are completely define4 or are in place. The orientation of each plane surface shall be determined.and vizualized, using two adjacent views at a time. Points, lines, and planes have definite roles in defining m object in space. These roles conform to the following relationships:

a A plane surface camot exist by itse$ it must be srryported by, at least three oher plane surfaces to form a solid

(atehahedron)-b. A line cannot exist by itselt it must be connected to, at leret two other lines to form the sides of a plane surface. On the other hand, the boundary of two plane surfaces always forms a sbaight line (an edge).

c. A point cannot exist by itselt it must be cormected to, at least one other point to form a line in space. Points represent intersection of two or more lines, a corner of an objecf or Sre point view of aline/edge,

d- The sides of a surface always form a closed polygon. A nrrface bounded by curved lines may be enclosed by only one line (circle or ellipse). A cuved surface may rypeer. as a flat surface with curved sides in one viav, or ils a curued surface with straight sides. In any way, it must show a cun ed side in, at least one view given two or three PrinciPal

via'vs-e. A. plalre surface will retain tte same general shape (same number of sides) in all y1eavs &aum, orwill become a straight line (ifshown on edge); however, the length of their sides may become disproportionately foreshortened A circle may become an ellipse, or an edge (shaight line).

f A sgrface can neitrer bend nor wqp; therefore, all sides of a plane surface will remain sbaight lines; and &e sides of a curved surface will maintain a continuous flrve wittrNO breaks nor kinks, A plae urface, therefore, cannot have a line (or' edge) widrin its normal

boundarY-g. A line in one view may become apoint (in ar end vian); on fite other hand it may represent a surface in edge.

tL A point may be an intersection o{, at leasf thee plane surfaces; on, it may represent tre point view of an edge. A point in one view may also repesent two or more ' _{points that are digned in ftat view.}

D. MISSINGLINB9: a, Similr Adiaccrt Areas: $ornce Refercncc 5' Pagc 2l t)

1

c

A

T O P V t € W

b. Similar Fitrres of Same Areas: (Source: Reference I Page ?l l)

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_{rR,xT '}

N

Fc.oAf

E. AIIXILIARY VIEII/S:

l. en Ar.priliary View is dtained strcn an objec is projected on any plane dhcr thm the horizorfat, frrontal, and p,ro6le projection plures. A Primry A.odliary View is p,rojeded on a plur that is perpendicr-rlr to o6 of ttre prircipal planes of projec'tion A Secondry Au.tiliry Viev is a projedion frqn a fimry ^gr.uriliary View, and on a plme irclirrd to all thce primry planes. In many casct, a Tertiary Auriliary View mqy becorrr nec€ssary to solve problerns in DESCRIPITVE GEOMEIRY.

Z. When the objectto be &asn has an inclined sr:rfacc that docs _{NOT appea tsrr size (and shqe) in any of} the regular (principaf) views; and the tsrr size ard sh4e of this irrlird srrfee is !o be daermirE4 an arxiliary projection plane parallelto t}e strfact can be imagined (i.e, a plarn perpcndiarlar!o ttre desired lineof-sigh).

3. Plars prallel to the prircipal planes of projection re rnrmally nsed as refertnce, cr datr:rq plrr fcr lrrrsferring dimensions from one view to another view wfrich uses the sarne _{refsrnce plane. The reference plane may} mirride with a projection plane, it may crl tlrough the object, a il may coirri& with tle back sr:rfacc of the object

(Source; Relerene 5, Pages 317 to 318)

a- Folding-Line Method b. Reference-Plane Method (Normal)

T 6 ? _{R e F . - r ^ " c f l o * .} ( E d g e \je..,) A

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c. Reference-Plarre Metiod ($vrnrnetricaD

E d 3 eYiew o* ee o{ P r,Srr*n e P l q n e

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d Reference-Plane _{Method Gtnsyrrrnetsical)}

T

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+

. E AIJIGLIARy VIEIIIS:

4. Depth A-uilirv Viry. Apdliary plrrs of p,rojed.ion that, are pcrpendiorlr to the ftortal projedion plane will *pw one

"rn"*r O"-rlon..r *t"r"e, tom any plane parallei !o the hontal projection.pl*t:,.frb corr11Dn principal dimengion is DEPrE hencr, all views projeced Fcrn the Front View are ryh At'Eriliary Views' includingthe Top and Side Views.

i. Heidt AuxiliaryView. tu)dliary plane of projection that re PTP*f"yo.to t}r haiaontal plane of projection will show or*

"ffi-airr"rr"i*, * di*.r,"", 6om cry plan. p."ilul to trrg haj3ntal plane of

projection This conrrmn principal dimernbn is HEIGIIT; hcrce, all views-projeaea frcrn thc Top View a'e lIcidt 'au'o<iliry Views.

. _{6. Width Ar-uilirv Vies. nr"xiliary projedion planes} that re perpendicularto the Profile projection planes will show ore colrurpn dinEnsion from any pi*. pa.ahl b tlr p-fil; p-3"aiott pt-"' This corrrnon prirnipal dimersion is WIDTII; hence, all views pmjeaca Fom ttre sidc view re widh AD(iliary views'

7. The principal dirrpnsion shown in m armiliry view is that one cfiich is NOT shocm in the certral view from which the auxiliry view was projeded

Heieht G{) Arr:( Views

(Sowce: Reference 5, P age 321)

J(

1"

Depth CD) Aux Views (Souree: Referencc 5, Pagc 320)

Width 0lr) Ao< Viess (Sourcc: Rcfercoce 5, Pagc 321)

Auxiliar.v Sectjon (Sor.rrci: Rcfetence d Page 326)

fRorrq'

M

E. ATJJOLIARY VIETIS:

g. Dihe&al Angl€s. thc rrgle between hrb plrres is a dihedral angle. One of tle p,rincipal rses of auiliary views is to show aineAl angles in trrr aize. Tectrriqrns in ddcrrniningtrlE sia of ditrdral rrgles include:

a. To get the edge view of .a plare, nnd tln poirn view of any lim in that plane;

b. To get the trtr angle between two plarrs, find the poirt, view of the line-of-intersection of tle rwo planes; and

c. To draw a view showing a tnre dihe&al angle, assurrn a [neof*igh (LO$ parallel.lo the line of intrrsection of the two planes making thc mgle'

9. Usesofanarxiliaryview:

& To debermine tle tnr lenethCiL) of lines, b. To obtain the point view @V) of lims, c. To obtainthe edge view @V) of planes' and

d. To find the tnE size ard shape CIS) of a plane(s*'L"'1. a Dihe&als / Angles (Sourcc: Refcrence i Pagc 323)

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b. Successive Auxiliarv Views: (Sorrce: Refermce 5, Page 328)

F o l d i n g L i h e s AUX.7 Aux 3

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Q u x a ) *-AUX 1

E CONSTRUCTION OF AIIJfiLI,ARY VIETIS:

l. Drnr two views of tbe object, if mt gjven Desigrale the view fr,om wtrichthe ar-niliary will be projected (cr &asn) as the Certral Vieq md the othevierr-frrcrn wtrichrnea$.r€rnerts will b€ tak€n as Adiacenl

?. Drar projection lines htween iderfical poirrs in ttr Adjacert and Ccrtral views, making stre that these lirrs re all prallel to each cther.

3. Draw a reference plane (RP) lirc bebreen these two views, making tlr ItP line perpendiorlr t'o the projedion lirns.

4. Delernrine the desire lineofeigtrt (LOS fa the Arxiliry view, and indicatc this IOS by an arrow indicdingthe dirtction of looking at the objed

i^^ fm oll rnirtc in i lel to' br'rt opilosile in i. Draw a second seiof pmjdion lines frorn all poiras in the Central View, parall

direction of, the LOS arow. This set of pojection lines shali edend towards the rea where the axiliary View will be corstnrted

6. Drsw the second RP line pcrpcndiarlr to the second set of projection lines' -.

7. Using rrreasrrernents From the Adjacent View, transfer all bi;ts b thc .p,uxiliry View along respective projection lircs (from Adjacert bo Central thencc to *,xilia-y).

8. Conned alivisible poirrs by solid lines; while -hidden poirts shall be connected by broken lines'

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