6. PROJECTION OF PLANES.ppt

8/20/2019 6. PROJECTION OF PLANES.ppt

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PROJECTIONS OF PLANES

In this topic various plane fgures are the objects.

What will be given in the problem?

1. Description of the plane figure.2. It’s position with HP and VP.

In which manner it’s position with HP & VP will be described?

1.Inclination o it’s SURFACE with one o the reerence planes will be

2. Inclination of one of it’s EDGES with other reference plane will be g

(Hence this will be a case of an object inclined to both reference Planes.)

To draw their projections means F!" T! #S!

What is usually asked in the proble!

Study the illustration showing

surfae ! side inlination gi"en on ne#t $age%

Upto16th

sheet

http://var/www/apps/conversion/tmp/scratch_5/


2/36

HP

a 1

b 1

c 1

d 1

VPVP

a ’

d ’ c ’

b ’

VP

a’ d’c’ b’

" o r " #

" o r $ #

F o r F .V .

F o r T . V .

F o r T . V .

F o r F .V .

HP

a

b c

d

a1’

d1’ c1’

b1’

HP

a1

b1 c1

d1

CASE OF A RECTAN&LE ' O(SER)E AN* NOTE ALL STEPS%

SURFAC PARALLEL !" HPPICTORIAL PRESENTATION

SURFAC INCLINE* !" HPPICTORIAL PRESENTATION

ONE S+ALL SI*E INCLINE* !" #PPICTORIAL PRESENTATION

ORT,O&RAP,IC!#$!r%e Shape

F#$ &ine '' to

ORT,O&RAP,ICF#$ *nclined to +,

!#$ Red%ced Shape

ORT,O&RAP,ICF#$ Apparent Shape!#$Pre-io%s Shape

A ( C



3/36

PROCEDURE OF SOLVING THE PROBLEM:

IN T,REE STEPS EAC, PRO(LE+ CAN (E SOL)E*- As Shown In Pre"ious Illustration .S!P 1. Ass%/e s%itable conditions 0 draw F- 0 !- of initial position.S!P . 2ow consider s%rface inclination 0 draw nd F- 0 !-.S!P 3. After this4consider side'ed5e inclination and draw 3rd ( final) F- 0 !-.

ASSU+PTIONS FOR INITIAL POSITION/(*nitial Position /eans ass%/in5 s%rface '' to HP or #P)1.*f in proble/ s%rface is inclined to HP ass%/e it '' HP "r *f s%rface is inclined to #P ass%/e it '' to #P

. 2ow if s%rface is ass%/ed '' to HP$ *t7s !# will show !r%e Shape. And *f s%rface is ass%/ed '' to #P *t7s F# will show !r%e Shape.3. Hence be5in with drawin5 !# or F# as !r%e Shape.8. 9hile drawin5 this !r%e Shape

:eep one side'ed5e ( which is /a:in5 inclination) perpendic%lar to line ( si/ilar to pair no. on pre-io%s pa5e ill%stration ).

A

(

Now Co0$lete STEP 1% (y 0a2ing surfae inlined to the res$ $lane ! $ro3et it4s other "iew%(Ref. 2 nd pair n pre!i"# pa$e i%%"#&ra&in )

C

Now Co0$lete STEP 5% (y 0a2ing side inlined to the res$ $lane ! $ro3et it4s other "iew%(Ref. 'nd pair n pre!i"# pa$e i%%"#&ra&in )

APPLY SAME STEPS TO SOLVE NEXT E EVEN PROBLEMS



4/36

6 7

891%:/ A regular $entagon of 1;00 side has one side on the ground% Its $lane is inlined at:;< to the ,P and $er$endiular to the )P% *raw its $ro3etions and show its traes

a

b

c

d

e

;

a7

e7

b7

d7c7 a

7

e 7

b 7

d 7

c 7

a1

b1

c1

d1

e1

,int/ As the $lane is inlined to ,P= it should >e 2e$t$arallel to ,P with one edge $er$endiular to )P

8;


5/36

8%91%;/*raw the $ro3etions of a irle of ; 0 dia0eter ha"ing its $lane "ertial and inlinedat 5?< to the )%P% Its entre is 50 a>o"e the ,%P% and 10 in front of the )%P% Show also itstraes

6 7

94

14

54:4

;4

@4

4

B4

49?4

994

914 3 =

=

1 41

3411

841=

;4>

64?

@

1

4 1 3 4

1 1 8 4 1 = ; 4

> 6 4 ? @

3=<

817

317 ;17

17617

117 @17

117 ?17

1117>17

1=17

;=


6/36

6 7

a’

b’

c’

d’

e’

f’

a

1’2’

%’

&’

'’

(’)’

*’

+’

1,’

11’

12’

e f a d b c

1, +

11

*

12

1

)

2

(

%

'

&

e f

a d

b c

1, +

11 *

12 1

) 2

( %

' &

30º

a1’

f 1’ b1’

e1’ c1’

d1’

11’121’ 21’

111’ %1’

1,1’ &1’

+1

’ '1’

*1’ (1’

)1’

Proble ' - draw a regular heagon of &, sides/ with its two sides #ertical. Draw a circle

of &, diaeter in its centre. $he figure represents a heagonal plate with a hole in it and

ha#ing its surfacre parallel to the VP. Draw its pro0ections when the surface is #ertical abd

inclined at %, to the VP.


7/36


8/36

+ ,

45º

7 5

a’

c’

b’

a b c

1’2’

%’

&’

'’

(’)’

*’

+’

1,’

11’

12’

1, +

11

*

12

1

)

2

(

%

'

&

30º

a

b

c

1 , +

1 1 * 1 2 1

) 2

( % '

&

a’

b’

c’

11’

121’ 21’

111’

1,1’

+1’

*1’ (1’

)1’

%1’

&1’

'1’

Proble 1 - Draw an euilateral triangle of )' sides and inscribe a circle in it. Draw the

pro0ections of the figure/ when its plane is #ertical and inclined at %, to the VP and one of the

sides of the triangle is inclined at &' to the HP.


9/36

891%/ *raw the $ro3etions of a regular he#agon of 1;00 sides= ha"ing one of itsside in the ,%P% and inlined at @? to the )%P% and its surfae 0a2ing an angle of :;<with the ,%P%

+ ,

a

b

c

d

e

f

f7 e7d7c7b7a7

f 7

e 7

d 7

c 7

b 7 a 7

a1

b1

c1

d1

e1

f 1f 1

a 1

c 1

b 1

d 1

e 1

8;<

6=<

a17b17

c17

d17e17f 17

Plane parallel to HP

Plane inclined to HPat 8;Band to #P

Side on the H.P. /a:in5 6=Bwith the #P.


10/36

891%@/ A sDuare A(C* of ;? 00 side has its orner A in the ,%P%= its diagonal AC inlined at5?< to the ,%P% and the diagonal (* inlined at :;< to the )%P% and $arallel to the ,%P% *raw its$ro3etions%

6 7

a

b

c

d

8;<

; =

a7 b7d7 c7 a7

b7

d7

c7

3=<

a1 c1

b1

d1

8;<

a1

c1

b1

d1

b17

c17

d17

ee$ AC $arallel to the ,%P%

! (* $er$endiular to )%P%-onsidering inlination ofAC as inlination of the$lane.

Inline AC at 5?< to the ,%P%

i%e% inline the edge "iew-F). at 5?< to the ,P

Inline (* at :;< to the )%P%

a17


11/36

!" #raw a rhomb$s o% 00 mm and 0 mm lon' dia'onals with lon'er dia'onal hori(ontal. )he %i'$re

is the top *iew o% a s+$are ha*in' 00 mm lon' dia'onals. #raw its %ront *iew.

6 7

1,,

1 , , a

b

c

d

a’ b’ c’d’

(,

a’

b’

c’

d’

a1

b1

c1

d1

a1

c1

d1 b1

1,,

( ,

a1

c1

d1 b1


12/36

8:/ *raw $ro3etions of a rho0>us ha"ing diagonals 91; 00 and ;? 00 long= the s0allerdiagonal of whih is $arallel to >oth the $rini$al $lanes= while the other is inlined at 5?< tothe ,%P%

6 7

a

b

c

d

1;

a7

b7d7 c7

ee$ AC $arallel to the ,%P% !(* $er$endiular to )%P%-onsidering inlination of ACas inlination of the $lane andinlination of (* as inlinationof edge.

Inline AC at 5?< to the ,%P% +a2e (* $arallel to 67

a7

b7d7

c7

3=<

a1

b1

c1

d1

a 1

b 1

c 1

d 1

a17

b17

c17

d17

; =


13/36

a

b c

d

ef

a7b7f7

c7e7 d7

a 7

b 7 f 7

c 7

e 7

d 7

8;B

a1

f 1 e1

d1

b1 c1

6=B

a1

b1

c1d1

e1

f 1

a17

b17

c17

d17

e17

f 17

8 1/A regular he#agon of :?00 side has a orner in the ,P% Its surfae inlined at:; tothe ,P and the to$ "iew of the diagonal through the orner whih is in the ,P 0a2es anangle of @? with the )P% *raw its $ro3etions%

Plane parallel to HPPlane inclined to HPat 8;Band to #P

!op -iew of the dia5onal/a:in5 6=B with the #P.

,+


14/36

8/A se0iirular $late of B?00 dia0eter has its straight edge in the )P and inlined at :;to ,P%The surfae of the $late 0a2es an angle of 5? with the )P% *raw its $ro3etions%

6 7

177

37

87

;7

67@7

1@

6

3;

8 3=


15/36

Proble 12.* - Draw the pro0ections of a circle of ', diaeter resting on the HP on point 3

on the circuference. Its plane inclined at &' to the HP and 4a5 $he top #iew of the diaeter 36

aking %, angle with the VP 4b5 $he the diaeter 36 aking %, angle with the VP

9

1

5:

;

@

B

9?

99

91

1 41

3411

841=

;4>

64?

@

1

41

3411

841=

;4>

64?

@

+ ,&'

11

891 9? A thi t l l t f id @? 6 5? h it h t id i th ) P d


16/36

891%9?/ A thin retangular $late of sides @? 00 6 5? 00 has its shorter side in the )%P% andinlined at 5?< to the ,%P% Pro3et its to$ "iew if its front "iew is a sDuare of 5? 00 long sides

6 7

a

b

3 =

a7

b7 c7

A retangle an >e seen as asDuare in the F%)% only when itssurfae is inlined to )P% So forthe first "iew 2ee$ the $lane HHto )P ! shorter edge G to ,P

F%)% -sDuare. is drawn first Inline a94>94 at 5?< to the

,%P%

d7

6=

c

d

a

b

cd

a17

b17 c17

d17 3=<a17

b17

c17

d17

a1b1

c1 d1

6 =

891 99 A i l l t f li i>l thi 2 d ;? di t lli i


17/36

891%99/ A irular $late of negligi>le thi2ness and ;? 00 dia0eter a$$ears as an elli$se inthe front "iew= ha"ing its 0a3or a#is ;? 00 long and 0inor a#is 5? 00 long% *raw its to$"iew when the 0a3or a#is of the elli$se is horiontal%

A irle an >e seen as aelli$se in the F%)% only when its

surfae is inlined to )P% So forthe first "iew 2ee$ the $lane HHto )P%

6 7

94

14

54:4

;4

@4

4

B4

49?4994

914

1 41

3411

841=

;4>

64?

@

1

4 1

3 4 1

1

8 4 1

=

;

4 > 6 4 ?

@

;=

Inline the T%)% till the

distane >etween the end$ro3etors is 5? 00

3=

117

17

317817

;17

617

@17

?17

>17

1=17

1117

117

1 1

7

1

7

3 1

7 8

1 7

; 1

7

6 1

7

@ 1

7

? 1

7

> 1 7

1 = 1

7 1 1 1 7

1 1

7

Inline the F%)% till the 0a3or

a#is >eo0es horiontal

117 17

317

817

;17

6177

?17>17

1=17

1117

117

P bl > A l t h i h f i l t i l h b ;= l d


18/36

a7

b7

c7

a.b c

; =

@= a.b

c

a17

b17

c17

a17

b17

c17

a1 b1

c1

8;<

Proble/ > A plate ha-in5 shape of an isosceles trian5le has base ;= // lon5 andaltit%de @= //. *t is so placed that in the front -iew it is seen as an eD%ilateral trian5le of;= // sides an done side inclined at 8; to . Eraw its top -iew



19/36

7 8

a

b c

d

a’ b’

c’d’

a1

b1 c1

d1

a 1

b 1

c 1

d 1

a’b’

d’c’ c’1 d’1

b’1 a’1&',

%,,

Problem "

9ectangle %, and ',

sides is resting on HP on one

sall side which is %,, inclined

to VP/while the surface of the plane akes &', inclination with

HP. Draw it’s pro0ections.

,ead problem and answer %ollowin' +$estions

1. :urface inclined to which plane! ;;;;;;; HP

2. 3ssuption for initial position! ;;;;;;


20/36

6

94

14

54:4

;4

@4

4

B4

49?4

994

914

8

>11

1=

?1

@1

6

;38

>11

?1

@1

6;3

6=< 7

69

79

594

994

194

:94 ;94

@94

94

B94

949?94

9994

9194

8131 ;11 6111 @1

11 ?1111 >11=1


21/36

94

14

54:4

;4

@4

4

B4

49?4

994

914

8

>111=

?1

@1

6

;38

>11

?1

@1

6

;3

6=<

6 7

69

79

8131 ;11 61

11 @1

11 ?1111 >1

1=1

594

994

194

:94;94

@94

94

B94

94

9?94

9994

9194

$h t i f l t th f f hi h i i li d t (, t th HP i i l f (,


22/36

+ ,

$he top #iew of a plate/ the surface of which is inclined at (, to the HP is a circle of (,

diaeter. Draw its three #iews.

1

2

% & '

(

)

*

+1,11

12

(,,

1’

2’

%’

&’

'’

(’ )’

*’

+’

1,’

11’

12’

+1

,1

1>

2>

%>

&>

'>

(>

)>

*>

+>

1,>

11>

12>

(,



23/36

Pro>le0 91%/ A 3== 6== set sD%are of lon5est side1== // lon54 is in #P and 3== inclinedto HP while it7s s%rface is 8;= inclinedto #P.Eraw it7s projections

-Surfae ! Side inlinations diretlygi"en.

Read proble/ and answer followin5 D%estions1 .S%rface inclined to which planeG $$$$$$$ #P. Ass%/ption for initial positionG $$$$$$'' to #P3. So which -iew will show !r%e shapeG $$$ F#8. 9hich side will be -erticalG $$$$$$lon5est side.

c1

7 8%,,

&',

a’1

b’1

c’1

a

c

a’

a b1

b’

b

a1 b

c

a’1

b’1

c’1

c’

Hene )e$in *i&+ FV, dra* &rian$%e a)!e -/

0eepin$ %n$e#& #ide !er&ia% .

Surfae HH to )$ Surfae inlined to )$

side inlined to ,$

P >l 5 Read proble/ and answer followin5 D%estions



24/36

cc1

7 8&',

a’1

b’1

c’1

a

c

a’

a b1

b’

b

a1 b

a’1

b’1

c’1

c’

3;

1=

Pro>le0 5/ A 3== 6== set sD%are of lon5est side1== // lon5 is in #P and it7s s%rface8;= inclined to #P. "ne end of lon5estside is 1= // and other end is 3; //abo-e HP. Eraw it7s projections

-Surfae inlination diretly gi"en%Side inlination indiretly gi"en)

Read proble/ and answer followin5 D%estions1 .S%rface inclined to which planeG $$$$$$$ #P. Ass%/ption for initial positionG $$$$$$'' to #P3. So which -iew will show !r%e shapeG $$$ F#8. 9hich side will be -erticalG $$$$$$lon5est side.

Hene )e$in *i&+ FV, dra* &rian$%e a)!e -/0eepin$ %n$e#& #ide !er&ia% .

First TO ste$s are si0ilar to $re"ious $ro>le0%Note the 0anner in whih side inlination is gi"en%End A 5; 00 a>o"e ,$ ! End ( is 9? 00 a>o"e ,$%

So redraw 1nd

F" as final F" $laing these ends as said%



25/36

,ead problem and answer %ollowin' +$estions1. :urface inclined to which plane! ;;;;;;; HP

2. 3ssuption for initial position! ;;;;;; // to HP

%. :o which #iew will show $rue shape! ;;; TV

&. Which side will be #ertical! ;;;;;;;; any side.

Hence begin with TV,draw pentagon below

X-Y line, taking one side vertical .

Problem 4"1 re'$lar penta'on o% 30 mm sides is

restin' on HP on one o% it’s sides with it’s

s$r%ace 450 inclined to HP.

#raw it’s pro2ections when the side in HP

maes 300 an'le with VP

a’ b’ d’

b1

d

c1

a

c’e’

b

c

d1

b’1

a1

e’1 c’1

d’1

a1

b1

c1d1

d’

a’ b’

c’e’

e1

e1

a’17 8&',

%,,e

SURF1CE 1ND SIDE INCLIN1TIONS

1RE DIRECTL/ GIVEN.

http://var/www/apps/conversion/tmp/scratch_5/http://var/www/apps/conversion/tmp/scratch_5/


26/36

Problem 5"3 regular pentagon of %, sides is resting

on HP on one of it’s sides while it’s opposite

#erte 4corner5 is %, abo#e HP.

Draw pro0ections when side in HP is %,,

inclined to VP.

9ead proble and answer following uestions




&. Which side will be #ertical! ;;;;;;;;any side.

Hence begin with TV,draw pentagon below X-Y line, taking one side vertical .

b’

d’

a’

c’e’

a1

b1

c1d1

e1

b1

c1

d1

a1

e1

b’1

e’1 c’1

d’1

a’17 8a’ b’ d’c’e’

3=

a

b

c

d

e%,,

SURF1CE INCLIN1TION INDIRECTL/ GIVEN

SIDE INCLIN1TION DIRECTL/ GIVEN:

"2&, CHA2 isthe /anner in which s%rface inclination is described

"ne side on Hp 0 it7s opposite corner 3= // abo-e Hp.

Hence redraw 1st F- as a nd F- /a:in5 abo-e arran5e/ent.Ieep a7b7 on 0 d7 3= // abo-e .

c 7 c71



27/36

T L

a

d

c

b

a7 b7 d7 c7

+ , a 7

b 7 d 7

c

a1

b1

d1

c1

a 1

b 1

d 1

c 1

8;=3== a71

b71c 1

d71

a1

b1

d1

c1a

d

c

b

a7 b7 d7 c7 a 7 b 7

d 7 c 7

a 1

b 1

d 1

c 1

3==

a71

b71c71

d71

Pro>le0 B A circle of ;= // dia/eter isrestin5 on Hp on end A of it7s dia/eter ACwhich is 3== inclined to Hp while it7s !-is 8;= inclined to #p.Eraw it7s projections.

Pro>le0 A circle of ;= // dia/eter isrestin5 on Hp on end A of it7s dia/eter ACwhich is 3== inclined to Hp while it /a:es8;= inclined to #p. Eraw it7s projections.





&. Which diaeter hori?ontal! ;;;;;;;;;; A

Hence begin with TV,draw rho!b"s below X-Y line, taking longer diagonal // to X-Y

The differene in these two $ro>le0s is in ste$ 5 only%In $ro>le0 no%B inlination of T" of that AC is

gi"en=It ould >e drawn diretly as shown in 5rd

ste$%+i%e in n.3 an$%e f 1C ie%f i.e. i&4# TL, i#$i!en. Hene +ere an$%e f TL i# &a0en,%"# f 5I# dra*n and &+en LTV I.e. a5 5 i# 6ar0ed and

fina% TV *a# 6p%e&ed.S&"d7 i%%"#&ra&in aref"%%7.

Note the differene inonstrution of 5rd ste$

in >oth solutions%


28/36



29/36

As 5rd ste$redraw 1nd T" 2ee$ing

side *E on #y line%(eause it is in )P

as said in $ro>le0%

+ ,

a

b

c

d

e

f

Pro>le0 99/ A hea5onal la/ina has its one side in HP and*ts apposite parallel side is ;// abo-e Hp and*n #p. Eraw it7s projections.!a:e side of hea5on 3= // lon5.

"2&, CHA2 is the /anner in which s%rface inclinationis described"ne side on Hp 0 it7s opposite side ; // abo-e Hp.Hence redraw 1st F- as a nd F- /a:in5 abo-e arran5e/ent.Ieep a7b7 on 0 d7e7 ; // abo-e .

1;

f7 e7d7c7b7a7

f 7

e 7 d 7

c 7

b 7 a 7

a1

b1

c1

d1

e1

f 1

c17

b71a71

f71

d71e71

f 1

a1

c1

b1

d1e1





&. Which diaeter hori?ontal! ;;;;;;;;;; A

Hence begin with TV,draw rho!b"s below X-Y line, taking longer diagonal // to X-Y



30/36

A J

C

H

H'3

+ ,

a7

b7

c7

g4

b a45 c

b

a 4 5

c

8;=

a71

c71

b71571

FREELY SUSE!"E" #$SES.

1.In this case the plane of the figure always reains perpendic"lar to Hp .

2.It ay reain parallel or inclined to Vp.

%.Hence TV in this case will be always a &$)' view.

&.3ssuing surface le0of Se0iKirle

First draw a gi"en triangleith gi"en di0ensions=

Loate it4s entroid $ositionAnd

3oin it with $oint of sus$ension%

I%&R'$!' &I!'S



31/36

= . 8

1 8

R

A

P

= //

C

+ ,

e7

c7

d7

b7

a7

p7

57

b c a p45 d e

b c

a p 4 5

d

e

Pro>le0 95/ A se/icircle of 1== // dia/eter is s%spended fro/ a point on its strai5ht ed5e 3= // fro/ the /idpointof that ed5e so that the s%rface /a:es an an5le of 8;= with #P.Eraw its projections.

First draw a gi"en se0iirleith gi"en dia0eter=

Loate it4s entroid $ositionAnd

3oin it with $oint of sus$ension%

1.In this case the plane of the figure always reains perpendic"lar to Hp .

2.It ay reain parallel or inclined to Vp.

%.Hence TV in this case will be always a &$)' view.

&.3ssuing surface


32/36

To deter0ine true sha$e of $lane figure when it4s $ro3etions are gi"en%(7 USIN& AU6ILIAR7 PLANE +ET,O*

9HA! 9*&& J !H PR"J&KGEescription of final F- 0 !- will be 5i-en.

,o% are s%pposed to deter/ine tr%e shape of that plane fi5%re.F%%* &+e )e%* $i!en #&ep#1. Eraw the 5i-en F- 0 !- as per the 5i-en infor/ation in proble/.. !hen a/on5 all lines of F- 0 !- select a line showin5 !r%e &en5th

(!.&.) (*t7s other -iew /%st be '' to )3. Eraw 1$1 perpendic%lar to this line showin5 !.&.8. Project -iew on 1$1 ( it /%st be a line -iew);. Eraw $ '' to this line -iew 0 project new -iew on it.

It will >e the reDuired answer i%e% True Sha$e%!he facts o% /%st :now$

*f o% caref%ll st%d and obser-e the sol%tions of all pre-io%s proble/s4,o% will find

*F "2 #*9 *S A &*2 #*9 0 !HA! !"" PARA&&& !" +, &*24!H2 A2E !H2 *!7S "!HR #*9 9*&& SH"9 !RU SHAP

2"9 F*2A& #*9S AR A&9A,S S"K SHAP4 2"! &*2 #*9SS" APP&,*2 AJ"# K!H"E

9 F*RS! C"2#R! "2 #*9 *2 *2C&*2E &*2 #*9 .(J %sin5 11 a%.plane)

!H2 J, KAI*2 *! '' !" +$, 9 ! !RU SHAP.

Study Ne#t Four Cases



33/36

+ ,

a

c

b

C7

b7

a7

1=

1;

1; ! &

69

79

C1

b1a1

a71

b71

c71 !RU SH AP

C??

+

,

Pro>le0 9: T" is a triangle a>% A> is ;? 00 long= angle a> is 5?? and angle >a is @;?%a4>44 is a F"% a4 is 1; 00= >4 is :? 00 and 4 is 9? 00 a>o"e ,$ res$eti"ely% *raw $ro3etionsof that figure and find it4s true sha$e%

3== 6;=

;= //

As $er the $roedure$9%First draw F" ! T" as $er the data%1%In T" line a> is HH to #y hene it4s other "iew a4>4 is TL% So draw #

9y

9 $er$endiular to it%

5%Pro3et "iew on #9y9% a. First draw $ro3etors fro0 a4>4 ! 4 on #9y9% >. fro0 #y ta2e distanes of a=> ! - T". 0ar2 on these $ro3etors fro0 #9y9% Na0e $oints a9>9 ! 9% . This line "iew is an Au#%T"% *raw #1y1 HH to this line "iew and $ro3et Au#% F" on it% for that fro0 #9y9 ta2e distanes of a4>4 ! 4 and 0ar2 fro0 #1y on new $ro3etors%:%Na0e $oints a49 >49 ! 49 and 3oin the0% This will >e the reDuired true sha$e.

ALA7S FOR NE F) TAE*ISTANCES OF PRE)IOUS F)AN* FOR NE T)= *ISTANCES

OF PRE)IOUS T)

REMEMBER88



34/36

1

1

c71

b71

a71

b1

c1

d1! R U S H AP

> = =

c7

! &

+ ,

a7

b7

b

ca

1=

=

1;

1;

17

18=

;=;

Pro>le0 9;/ F- 0 !- of a trian5%lar plate are shown.Eeter/ine it7s tr%e shape.

US SAK PR"CEUR S!PS"F PR#*"US PR"J&K

BUT THERE IS ONE DIFFICULT/

2" &*2 *S '' !" +, *2 A2, #*9.KA2S 2" !& *S A#A*&AJ&.

*2 SUCH CASS ERA9 "2 &*2'' !" +, *2 A2, #*9 0 *!7S "!HR#*9 CA2 J C"2S*ERE AS !&

F"R !H PURP"S.

HR a7 17 line in F- is drawn '' to .H2C it7s !- a$1 beco/es !&.

!H2 F"&&"9 SAK S!PS A2EE!RK*2 !RU SHAP.

(S!UE, !H *&&US!RA!*"2)

ALA7S FOR NE F) TAE*ISTANCES OF PRE)IOUS F)AN* FOR NE T)= *ISTANCES

OF PRE)IOUS T)

REMEMBER88



35/36

1

+

+1

a1c1

d1

b1

c71

d71

b71

a71

!RU SHAPa

b

c

d ,+

a7

d7

c7

b7

;= E.

;=E

!&

PRO(LE+ 9@/ F" ! T" >oth are irles of ;? 00 dia0eter% *eter0ine true sha$e of an elli$tial $late%

A*OPT SA+E PROCE*URE.a is onsidered as line HH to #y%Then a44 >eo0es TL for the $ur$ose%Using ste$s $ro$erly true sha$e an >eEasily deter0ined%

Study the illustration%

ALA7S= FOR NE F)TAE *ISTANCES OF

PRE)IOUS F) AN*FOR NE T)= *ISTANCES

OF PRE)IOUS T)

REMEMBER88



36/36

a

bc

d

e

a7

b7

e7

c7d7

a1

b1

e1 d1

c1

3==+ ,

+1

,1

8;=

! R U S H A P

Pro>le0 9 / Eraw a re5%lar penta5on of3= // sides with one side 3== inclined to .!his fi5%re is !- of so/e plane whose F- is A line 8;= inclined to .Eeter/ine it7s tr%e shape.

*2 !H*S CAS A&S" !RU &2!H*S 2"! A#A*&AJ& *2 A2, #*9.

JU! AC!UA&&, 9 E"2"! RLU*R!& !" F*2E *!7S !RU SHAP4 AS "2#*9 (F#) *S A&RAE, A &*2 #*9.S" MUS! J, ERA9*2 +1,1 '' !" !H*S#*9 9 CA2 PR"MC! #*9 "2 *! A2E ! !RU SHAP

S!UE, !H *&&US!RA!*"2..

ALA7S FOR NE F)TAE *ISTANCES OF

PRE)IOUS F) AN* FORNE T)= *ISTANCES OF

PRE)IOUS T)

REMEMBER88

6. PROJECTION OF PLANES.ppt

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