Lect 03 Points

8/8/2019 Lect 03 Points

1/30

Projections of points, lines, andplanes


2/30

TO DRAW PR OJECTIONS OF ANY OBJECT ,ONE MUST HAVE FOLLO WING INFO RMATION

A) OBJECT{ WITH ITS DESC RIP TION , WELL DEFINE D.}

B) OBSE RV ER{ ALWA YS OBSE RV ING P ERP EN DICULAR TO RES P. R EF.P LANE }.

C) LOC ATION OF OBJECT ,{ MEANS ITS P OSITION WITH R EFFE RENCE TO H.P. & V.P.}

TE RMS ABO VE & BELO WWITH R ES P ECTI VE TO H.P.

AND TE RMS INFRONT & BE HIND WITH R ES P ECTI VE TO V.PFO RM 4 QUADRA NTS .OBJECTS CAN BE P LACE D IN ANY ONE OF THESE 4 QUADRA NTS .

IT IS INTE RESTING TO LE AR N THE EFFECT ON THE P OSITIONS OF VIEWS ( FV, TV )OF THE OBJECT WITH R ES P. TO X- Y LINE , WH EN P LACE D IN DIFFE RENT QUADRA NTS .

ORTHOG RAPH IC PR OJECTIONSOF P OINTS , LINES , P LANES , AND SOLI DS .

STUDY ILLUSTRATIONS GIVEN ON HEXT PAGES AND NOTE THE RESULTS.TO MAKE IT EASY HERE A POINT A IS TAKEN AS AN OBJECT. BECAUSE ITS ALL VIEWS ARE JUST POINTS.


3/30

NOTATIONS

FOLLO WING NOTATIONS S HOULD BE FOLLO WED WH ILE NAMEINGDIFFE RENT VIEWS IN ORTHOG RAPH IC PR OJECTIONS .

ITS FRONT VIEW a a b

SAME SYSTEM OF NOTATIONS SHOULD BE FOLLOWEDINCASE NUMBERS, LIKE 1, 2, 3 ARE USED.

OBJECT P OINT A LINE AB

ITS TO P V IEW a a b

ITS SIDE VIEW a a b


4/30

X

Y

1ST

Quad.2nd Quad.

3 rd Quad. 4 th Quad.

X Y

VP

HP

Observer

THIS QUADRA NT PATTE RN,IF OBSE RV ED ALONG X- Y LINE ( IN RED ARR OW D IRECTION )WILL EXACTLY APP EAR A S S HOWN ON RIGHT SIDE AND H ENCE ,

IT IS FUR THER U SE D TO UNDERSTAND ILLUST RATION PR OP ERLLY.


5/30

HP

VPa

a

A

P OINT A IN1 ST QUADRA NT

OBSE RV ER

VP

HP

P OINT A IN2ND QUADRA NT

OBSE RVER

a

a

A

OBSE RV ER

a

a

P OINT A IN3RD QUADRA NT

HP

VP

A

OBSE RV ER

a

aP OINT A IN4TH QUADRA NT

HP

VP

A

Point A isPlaced Indifferent

quadrantsand it s Fv & Tvare brought insame plane for

Observer to seeclearly .

Fv is visible asit is a view on

VP. But as Tv isis a view on Hp,

it is rotated

downward 900

,In clockwiseDirection (in 1 st

quadrant). TheIn front part of

Hp comes belowxy line.

The HP behindthe Vp is also

rotatedclockwise, and

thereforeomes above the

xy line.

Observe and

note theprocess.


6/30

PROJE CTIONS OF A PO INT IN THE 4 QUAD R ANTS

HP

VP

POINT IN 2 nd QUADRANT

VPHP

P T

P F

HP

VP

POINT IN 3 rd QUADRANT

HP

VP

POINT IN 4 th QUADRANT

VP VP

HP

HP

P T: TOP VIEW

P F: FRONT VIEW

P F

P T

P F

HP

VP

POINT IN 1 st QUADRANT

VP

HP

P T

P F

PT

P

P

P

P


7/30

A

a

aA

a

a

Aa

a

X

Y

X

Y

X

Y

For Tv For Tv

For Tv

P OINT A ABO VE HP& INFRONT OF VP

P OINT A IN HP& INFRONT OF VP

P OINT A ABO VE HP& IN VP

PROJECTIONS OF A POINT IN FIRST QUADRANT.

P ICTO RIAL PR ESENT ATION

P ICTO RIAL PR ESENT ATION

ORTHOG RAPH IC PR ESENT ATIONS OF ALL ABO VE CASES .

X Y

a

a

VP

HP

X Y

a

VP

HP

a X Y

a

VP

HP

a

Fv above xy,Tv below xy.

Fv above xy,Tv on xy.

Fv on xy,Tv below xy.


8/30

SIMPLE CASES OF THE LINE

1 . A V ERTICAL LINE ( LINE P ERP EN DICULAR TO HP & // TO VP)

2. LINE PARA LLEL TO BOT H HP & VP.

3. LINE INCLINE D TO HP & PARA LLEL TO VP.

4. LINE INCLINE D TO VP & PARA LLEL TO HP.

5. LINE INCLINE D TO BOT H HP & VP.

STUDY ILLUSTRATIONS GIVEN ON NEXT PAGESHOWING CLEARLY THE NATURE OF FV & TVOF LINES LISTED ABOVE AND NOTE RESULTS .

PROJECTIONS OF STRAIGHT LINES.

INFO RMATION REG ARD ING A LINE m eansITS LENGT H,

P OSITION OF ITS EN DS WITH HP & VPITS INCLIN ATIONS WITH HP & VP W ILL BE GIVEN .

AIM:- TO DRAW ITS PR OJECTIONS - MEANS FV & TV.


9/30

X

Y

X

Y

b

a

b

a

a b

a

b

B

A

TV

FV

A

B

X Y

H.P.

V.P. a

b

a b

Fv

Tv

X Y

H.P.

V.P.

a b

a bFv

Tv

For Tv

For Tv

Note:Fv is a ve rtical line

Show ing T rue Leng th&

Tv is a point.

Note:Fv & Tv b oth ar e

// to xy&

both s how T. L.

1.

2.

A Linepe r pendic ular

to Hp&

// to Vp

A Line

// to Hp&

// to Vp

Orthographic Pattern

Orthographic Pattern

(Pictorial Presentation)

(Pictorial Presentation)


10/30

A Line inclined to Hpandparallel to Vp

( Pictorial presentation)X

Y

A

B

b

a

b

a

U

U

A Line inclined to Vp

andparallel to Hp( Pictorial presentation)

a b

a

b

BA

X Y

H.P.

V.P.

T.V.a b

a

b

U

X Y

H.P.

V.P.

a

b

a b

Tv

Fv

Tv inclined to xyFv p a r a llel to xy .

3.

4.

Fv inclined to xyTv p a r a llel to xy .

Orthographic Projections


11/30

X

Ya

b

a b

B

A

E

F

For Tv

T.V.

X

Ya

b

a b

E

F

T.V.

For Tv

B

A

X Y

E

F

H.P.

V.P.

a

b

FV

TV

a

b

A Line inclined to bothHp and Vp

(Pictorial presentation)

5 .

Note These Facts:-Both Fv & Tv are inclined to xy.

(No vie w is p arall e l to xy)Both Fv & Tv are reduced lengths .

(No vie w s how s T rue Leng th)

Orthographic ProjectionsFv is seen on Vp c le arly.

To see Tv clearly, HP isrotated 90 0 downwards,

Hence i t com es be low xy.

On removal of objecti.e. Line A B

Fv a s a ima ge on Vp.Tv a s a ima ge on Hp,


12/30

X Y

H.P.

V.P.

X Y

F

H.P.

V.P.

a

b

TV

a

b

FV

TV

b 2

b 1

TL

X Y

E

F

H.P.

V.P.

a

b

FV

TV

a

b

Here TV (ab) is not // to XY lineHence its corresponding FV

a b is not showing True Length &

True Inclination with Hp .

In this sketch, TV is rotated and m ade // to XY line.

Hence its corresponding FV a b 1 Is showing

True Length&

True Inclination with Hp.

Note the procedureWhen Fv & Tv known,

How to find True Length.(Views are rotated to determineTrue Length & it s inclinations

with Hp & Vp).

Note the procedureWhen True Length is known,

How to locate Fv & Tv.(Component a- 1 of TL is drawn

which is further rotatedto determine Fv)

1a

a

b

1

b

F

b 1

UE

b 1

Orthographic ProjectionsMeans Fv & Tv of Line A B

are shown below,with their apparent Inclinations

E & F

Here a -1 is co m ponent of TL ab 1 gives length of Fv.

Hence it is brought Up toLocus of a and further rotated to get point b. a b will be Fv.

S imilarly drawing componentof other TL(a b 1 )Tv can be drawn.

U


13/30

The mo s t importa nt dia gram s how ing g ra phical r e lat ionsamo ng all importa nt param e te r s of this topic.

Stu dy a nd me mor ize i t a s a CIRCUIT DIAGRAM And use in s olving v ar iou s p roble ms.

True Length is never rotated. Its horizontal componentis drawn & it is further rotated to locate view.

Views are always rotated, made horizontal & further

extended to locate TL, U&

Also Re m e m ber

ImportantTEN parameters

to be rememberedwith Notations

used here onward

E

F

U1) True Leng th ( TL) a b1& a b12) Ang le of TL with Hp -

3) Ang le of TL with Vp

4) Ang le of FV with xy

5) Ang le of TV with xy

6) LT V (leng th of FV) C om ponen t (a- 1 )7 ) LFV (leng th of TV) C om ponen t (a -1 )

8) Po si tion of A- Distances of a & a from xy

9) Po si tion of B- Distances of b & b from xy

10 ) Dis ta nce be tween End Proj ec tor s

X Y

H.P.

V.P.

1a

b

F

b 1

LFV

a

b

1

b 1

E U

LTV

Dis ta nce be tweenEnd Proj ec tor s.

E U& Cons truct with a F& Cons truct with a

b & b1 on s am e locus.

b & b1 on s am e locus.

NOTE this


14/30

PR OJECTIONS OF P LANES

In this topic various plane figures are the objects.

W hat will be given in the problem?

1. D escription of the pl a ne figure .2. I ts position with HP a nd VP .

In which ma nner it s po s itio n with HP & VP will be des cr ibed?

1. Inclination of it s S UR FACE with one of the reference planes will be given .2. I nclination of one of it s EDGES with other reference plane will be given

(Hence th is will be a ca se of a n ob jec t inc lined to both r e f e r ence Pla nes.)

To draw their projections means F.V, T.V. & S.V.W ha t is usu a lly a sked in the problem?

S tudy the illustration showing

surface & side inclination given on next page.


15/30

HP

VPVPVP

a dc b

HP

a

b c

d

a 1

d1 c1

b 1

HP

a 1

b 1 c1

d1

CASE OF A R ECT ANGLE OBSE RV E AND NOTE ALL STE P S .

S URF AC E PARA LLEL TO HPPICTORIAL PRESENTATION

S URF AC E INCLINE D TO HPPICTORIAL PRESENTATION

ONE S MALL SIDE INCLINE D TO VPPICTORIAL PRESENTATION

ORTHOG RAPH ICTV-True Sha peFV- Line // to xy

ORTHOG RAPH ICFV- Inc lined to XY

TV- Red uced Sha pe

ORTHOG RAPH ICFV- App ar en t Sha peTV-Pr evi ou s Sha pe

A B C


16/30

PROCEDURE OF SOLVING THE PROBLEM:IN THR EE STE P S EACH PR OBLE M CAN BE SOL VED:( As S hown In Previous Illustration )S TEP 1. Ass um e s uita ble c ondi tions & draw Fv & Tv of initial posi tion.S TEP 2. Now conside r s urfa ce inc linat ion & draw 2nd Fv & Tv.

S TEP 3. Afte r th is,c onside r side/edge inc linat ion a nd d raw 3 r d ( f inal ) Fv & Tv.

ASS UMP TIONS FO R INITIAL P OSITION :(Initial Po si tion me a ns a ss um ing s urfa ce // to HP or VP )1.If in p roble m s urfa ce is inc lined to HP a ss um e i t // HP

Or If s urfa ce is inc lined to VP a ss um e i t // to VP

2. Now if s urfa ce is a ss um ed // to HP - Its T V will s how True Sha pe. And If s urfa ce is a ss um ed // to VP Its FV will s how True Sha pe.

3. Hence begin with draw ing T V or FV a s T rue Sha pe.4. W hile d raw ing this True Sha pe

keep one side/edge ( wh ich is ma king inc linat ion) pe r pendic ular to xy line( similar to pa ir no. on p r evi ou s p a ge i llus trat ion ).A

B

Now Complete STE P 2. By making surface inclined to the resp plane & project it s other view.(Ref. 2 nd pair on previous page illustration )

C

Now Complete STE P 3. By making side inclined to the resp plane & project it s other view.(Ref. 3 nd pair on previous page illustration )


17/30

X Y

a

b c

d

a bcd

a 1

b 1 c1

d1

a bdc

c1 d1

b1 a 14 5 03 0 0

Pr ob lem 1:R ecta ngle 3 0 mm a nd 50 mmsides is resting on HP on one

small side which is

3 0 0

inclinedto VP,while the surf a ce of the pl a ne m a kes 4 5 0 inclin a tion withHP. D r a w it s projections .

R ead p r ob lem a nd a n s wer followi ng qu es tio n s1. Surf a ce inclined to which pl a ne? ------- HP2. A ssumption for initi a l position? ------// to HP3.

So which view will show True sha pe? --- TV4. W hich side will be vertic a l? ---One sm a ll side .

H en ce beg in with T V, d r aw re cta ng le below X-Yd r awi ng one s mall s id e ver tical .

S urface // to Hp S urface inclined to Hp

S ideInclined

to Vp


18/30

CIRCULAR LAMIN A INCLINE D AT A N ANG LE 45 O TO FRON TAL P LANE AND PERPEN DICULAR TO TOP

P LANE (USE IIIRD. ANG LE)(Tutorial 5, qs. 3)

TV

FV

TV

FV

45O

S ince the ci r cular lam ina is to be inc lined at 45 o to the frontal plane (FV),draw it initially parall e l to

the frontal plane.Nex t, rotat e the TV by45 o a nd p rojec t the front vie w from pr evi ou s f igur ea nd ne w top vie w.

For projec tion, divide thetop vie w line in to thes am e n um be r of sec tionsin b oth f igur es

Proj ec t corr esp ondingpoints

a e

g

c

f

b

h

d

a e

g

c

f

b

h

d

a

b,h

c,g

d,f

e

b,h

d,f c,

g


19/30

R ead p r ob lem a nd a n s wer followi ng qu es tio n s1. Surf a ce inclined to which pl a ne? ------- HP 2. A ssumption for initi a l position? ------ // to HP 3. So which view will show True sh a pe? --- TV 4. W hich side will be vertic a l? -------- any side .

He nc e begi n with TV, dr aw pe n t a go n below

X-Y li ne , t ak i n g o ne side verti ca l .

P r ob lem 4 :A reg ula r pen ta gon of 30 mm s id es is re s ting on HP on one of it s s id es with it s s u r fac e 45 0 in cline d to HP.Dr aw it s p r oj ectio n s wh en th e s id e in HP mak es 30 0 ang le with VP

a b d

b 1

d

c1

a

ce

b

c

d1

a 1

a 1

c1 e1

d1

b 1

a 1

e1d1

d

a b

ce

c1e1

b1X Y4 50

3 0 0e

SURFACE AND SIDE INCLINATIONS ARE DIRECTLY GIVEN.


20/30

Exam ples of projec tions of a tr ia ng ular plane(Tutor ial 5 qs. 2)

III r d a ng leTV

FV

X

Y

Z

TV

FV

X

Y

Z

3 c m

3 c m

TV

FV

X

Z

TV

FV

X

Z

Ve rtical plane 3cm from frontal plane

Hor izontal plane 3 c m from top p lane

Inc lined p lanepe r pendic ular to top p lane

Oblique p lane (not pe r pendic ular to a nypr incip al plane)


21/30

Pr ob lem 5 :A regul a r pent a gon of 3 0 mm sides is restingon HP on one of it s sides while it s oppositevertex (corner) is 3 0 mm a bove HP .

D r a w projections when side in HP is 3 00

inclined to VP .

R ea d problem a nd a nswer following questions1. Surf a ce inclined to which pl a ne? ------- HP 2. A ssumption for initi a l position? ------ // to HP 3. So which view will show True sh a pe? --- TV

4. W hich side will be vertic a l? -------- any side . He nc e begi n with TV, dr aw pe n t a go n below

X-Y li ne , t ak i n g o ne side verti ca l .

b

d

a

ce

b 1

a 1

c1d1

e1

b 1

c1

d1

a 1

e1

b1

e1 c1

d

1

a 1X Ya b dce

30

a

b

c

d

e3 0 0

SURFACE INCLINATION INDIRECTLY GIVEN SIDE INCLINATION DIRECTLY GIVEN:

ON LY CH ANGE isthe ma nne r in which s urfa ce inc linat ion is desc r ibed :

One side on Hp & its opp osi te c or ne r 30 mm a bove Hp.Hence r ed raw 1 s t Fv a s a 2nd Fv ma king a bove arra nge men t.

Keep ab on xy & d30 mm a bove xy.


22/30

Part 2: Projections of solids


23/30

SOLIDSTo unde r s ta nd a nd r e me mbe r var iou s s olids in th is s ub jec t prope rly,

tho se ar e c la ssi f ied & arra nged in to two major grou ps.

G roup ASolids h a ving top a nd b a se of s a me sh a pe

C yli nder

Prisms

Tri a ngul a r Squ a re Pent a gon a l Hex a gon a l

Cu be

Tri a ngul a r Squ a re Pent a gon a l Hex a gon a l

C one

T etr ahedro n

P yr amids

( A solid h a ving

six squ a re f a ces)

( A solid h a ving

Four tria ngul a r f a ces)

G roup BSolids h a ving b a se of some sh a pea nd just a point a s a top, c a lled a pex .


24/30

SOL IDSD imension a l p a r a meters of different solids .

Top

R ecta ngul a r Fa ce

Longer

Edge

Ba se

Edgeof

Ba se

Corner of ba se

Corner of ba se

Tria ngul a r Fa ce

Sla ntEdge

Ba se

A pex

S qua re P r is m S qua re Py r amid C ylinder Co ne

Edgeof

Ba se

Ba se

A pex

Ba se

Gener ato r s Imaginary lines

generating curved surfaceof cylinder & cone.

Sections of solids( top & b a se not p a r a llel) Frustum of cone & pyr a mids .

( top & base p

ar allel to e

ach other)


25/30

X Y

STAN DI N G O N H.POn it s b a se .

R EST I N G O N H.POn one point of b a se circle .

LY I N G O N H.POn one gener a tor .

(A xis perpendicul a r to HpA

nd // to Vp.)

(A xis inclined to HpA

nd // to Vp)

(A xis inclined to HpA

nd // to Vp)

W hile observing Fv, x-y line represents Horizont a l Pl a ne . (Hp)

A xis perpendicul a r to VpA nd // to Hp

A xis inclined to VpA nd // to Hp

A xis inclined to VpA nd // to Hp

X Y

F.V. F.V. F.V.

T.V. T.V. T.V.

W hile observing Tv, x-y line represents Vertic a l Pl a ne . (Vp)

STAN DI N G O N V.POn it s b a se .

R EST I N G O N V.POn one point of b a se circle .

LY I N G O N V.POn one gener a tor .


26/30

S TE P S TO SOL VE P R OBL EM S IN SOL IDSPr ob lem i s s olved i n th ree s tep s:

S TE P 1 : A SSUME SOL ID STAN DI N G O N THE PL AN E W ITH W HICH IT IS M AK I N G I N CL I NA TIO N .( IF IT IS I N CL I N ED TO HP, A SSUME IT ST AN DI N G O N HP)( IF IT IS I N CL I N ED TO VP, A SSUME IT STAN DI N G O N VP)

IF STAN DI N G O N HP - ITS TV W ILL B E T R UE SH A PE OF ITS BA SE O R TOP :IF STAN DI N G O N VP - ITS FV W I LL B E T R UE SH A PE OF ITS BA SE O R TOP .B EG I N W ITH TH IS V IEW :

ITS OTHE R V IEW W I LL B E A R ECTAN G LE ( IF SOL ID IS C YLINDER OR ONE OF T HE PRISMS) :ITS OTHE R V IEW W I LL B E A TR IAN G LE ( IF SOL ID IS C ONE OR ONE OF T HE PYRAMIDS):

D R A W FV & TV OF TH AT SOL ID I N STAN DI N G POS ITIO N :S TE P 2: CO N SID ER I N G SOL ID S I N CL I NA TIO N ( A XIS POS ITIO N ) D R A W ITS FV & TV .S TE P 3: I N LA ST STEP, CO N SID ER I N G R EM A I N I N G I N CL I NA TIO N , D R A W ITS F I NA L FV & TV .

A XISVE R TICA L

A XISI N CL I N ED HP

A XISI N CL I N ED VP

A XISVE R TICA L


A XISI N CL I N ED VP

A XIS TO VPer

A XISI N CL I N ED

VP


A XIS TO VPer A XIS

I N CL I N EDVP


G E NE RA L PA TTE R N ( T H R EE S TE P S ) OF SOLU T IO N :

G R OU P B SOL ID.C O NE

G R OU P A SOL ID.CY L IN DE R

G R OU P B SOL ID.C O NE

G R OU P A SOL ID.CY L IN DE R

Th ree s tep sI f s olid i s in cline d to

Hp

Th ree s tep sI f s olid i s in cline d to H p

Th ree s tep sI f s olid i s in cline d to Vp

Th ree s tep sI f s olid i s incline d to Vp


27/30

X Y

a

b c

d

o

o

dc ba

o1

d1

b1c1

a 1

a 1

d1 c1

b1

o1

a 1

(A PEX N EA R ER

TO V .P).(A PEXA W A Y

FR OM V .P.)

Problem 1 . A sq uar e py ram id, 4 0mm ba se sides a nd a xis 6 0 mm lo ng,ha s a tr ia ng ular fa ce on the g rou nda nd the ve rtical plane c onta ining thea xis ma kes a n a ng le of 45 0 with th eVP. Draw its p rojec tions. T a ke a pexne ar e r to VP

S olution S teps :Tr ia ng ular face on Hp , me a ns i t is lying on Hp :1 .Ass um e it s ta nding on Hp.2 .Its Tv will s how True Sha pe of ba se ( sq uar e)3.D raw sq uar e of 40mm sides with one side ve rtical Tv &

ta king 5 0 mm a xis p rojec t Fv. ( a tr ia ng le)4.Nam e all points a s s how n in i llus trat ion.

5.D raw 2nd

Fv in lying p osition I.e. ocd face on xy. And p rojec t its Tv.6.Ma ke visib le lines d ar k a nd hidden d otted, a s pe r the p roced ur e.7 .Then c ons truct r e ma ining inc linat ion with Vp

( Vp c onta ining axis ic the cen te r line of 2nd Tv.M a ke i t 45 0 to xy ass how n ta ke a pex ne ar to xy, a s i t is ne ar e r to Vp) & projec t f inal Fv.

For d a r k an d dotted li nes1 .Dr aw p r op er outli ne of ne w vi ew DARK . 2. Decid e di re ctio n of a n ob s er ver .

3. S elect ne a re s t poi n t to o b s er ver and d r aw all li ne s s ta r ting f r om it-da r k .4. S elect fa r th es t poi n t to o b s er ver and d r aw all li ne s (re mai n ing )f r om it- dott ed .


28/30

Pr ob lem 2:A cone 4 0 mm di a meter a nd 50 mm a xisis resting on one gener a tor on Hpwhich m a kes 3 0 0 inclin a tion with VpD

r aw it

s projections

.

h

a

bc

d

e

g

f

X Ya b d ec g

f h

o

o

a 1

h1

g1

f 1

e1

d1

c1

b 1

a 1

c1

b 1

d1

e1

f 1

g1 h1

o1

a 1 b1

c1d1e1

f 1

g1

h1

o1

o1

3 0

S olution S teps:Res ting on Hp on one gene rator , me a ns lying on Hp :1.Ass um e i t s ta nding on Hp.2.Its Tv will s how True Sha pe of ba se ( cir cle )3.D raw 40mm dia . Ci r cle a s Tv &

ta king 5 0 mm a xis p rojec t Fv. ( a tr ia ng le)

4.Nam e all points a s s how n in i llus trat ion.5.D raw 2nd Fv in lying p osi tion I.e. oe on xy. And

projec t its Tv be low xy.6.Ma ke visib le lines d ar k a nd hidden d ott ed,

a s pe r the p roced ur e.7 .Then c ons truct r e ma ining inc linat ion with Vp( gene rator o1e 1 300 to xy a s s how n) & projec t f inal Fv.

For d a r k an d dotted li nes1 .Dr aw p r op er outli ne of ne w vi e

DARK .2. Decid e di re ctio n of a n ob s er ver.3. S elect ne a re s t poi n t to o b s er ver

and d r aw all li ne s s ta r ting f r omit-da r k .

4. S elect fa r th es t poi n t to o b s er ver and d r aw all li ne s (re mai n ing )f r om it- dott ed .


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X Ya b d c

1 2 4 3

a

b

c

d

1

2

3

4

4 5 0

4

3

2

1

d

c

b

a

3 5 0

a 1

b 1

c1d1

1

2

3

4

Pr ob lem 3 :A cylinder 4 0 mm di a meter a nd 50 mma xis is resting on one point of a ba secircle on Vp while it s a xis m a kes 4 5 0

with Vpand Fv of the

axis

3 5 0

with Hp. D r a w projections ..

S olution S teps:Res ting on Vp on one p oint of ba se, m e a ns inc lined to Vp :1.Ass um e it s ta nding on Vp2.Its Fv will s how True Sha pe of ba se & top( cir cle )3.D raw 40mm dia . Ci r cle a s Fv & ta king 5 0 mm a xis p rojec t Tv.

( a Rec ta ng le)4. Nam e all points a s s how n in i llus trat ion.5.D raw 2nd Tv ma king a xis 45 0 to xy And p rojec t its Fv a bove xy.6.Ma ke visib le lines d ar k a nd hidden d ott ed, a s pe r the p roced ur e.7 .Then c ons truct r e ma ining inc linat ion with Hp( Fv of a xis I.e. cen te r line of vie w to xy a s s how n) & projec t f inal Tv.


30/30

b b 1

X Y

a

d

co

d c ba

o

c1a 1

d1

o1

o1

a 1 b1c1

d1

P r ob lem 4 : A squ a re pyr a mid 3 0 mm b a se sidea nd 50 mm long a xis is resting on it s a pex on Hp,such th a t its one sl a nt edge is vertic a l a nd a tria ngul a r f a ce through it is perpendicul a r to Vp . D r a w it s projections .

S olution S teps :1.Ass um e i t s ta nding on Hp b ut a s s a id on a pex. ( inve rted ).2.Its Tv will s how True Sha pe of ba se ( sq uar e)3.D raw a cor ne r ca se sq uar e of 30 mm sides a s Tv (a s s how n)Show ing all s lant edges d ott ed, a s tho se will not be visib le from top.

4. ta king 5 0 mm a xis p rojec t Fv. ( a tr ia ng le)5. Nam e all points a s s how n in i llus trat ion.6.D raw 2nd Fv keeping oas lant edge ve rtical & projec t its Tv7 .Ma ke visib le lines d ar k a nd hidden d ott ed, a s pe r the p roced ur e.8.T hen r ed r e w 2nd Tv a s f inal Tv keeping a 1o1d1 tr ia ng ular face

pe r pendic ular to Vp I.e.xy. T hen a s us ual projec t f inal Fv.

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Lect 03 Points