projection of straight line engineering108.com

5/19/2018 Projection of Straight Line Engineering108.Com

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R O J E C T I O N S

O F

R A I G H T L I N


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PROJECTIONS OF STRAIGHT LINES

Definition of Straight line:

A straight line is the shortest distancebetween two points.

-Top views of two end points of a straight

line, when joined, give the top view ofthe straight line.

-Front views of the two end points of a

straight line, when joined, give the frontview of the straight line.

Both the above projections are straight

lines.


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Orientation of Straight LineinSpaceA line in space may be parallel,perpendicular or inclined to either the H..

or !.. or both.

"t may be in one or both the referencelanes.

#ine ends may be in different $uadrants.

osition of %traight #ine in space can be

fi&ed by various combinations of data li'edistance of its end points from referenceplanes, inclinations of the line with thereference planes, distance between end

projectors of the line etc.


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Notatioans used for StraightLineTrue length of the

line(

Denoted by )apital letters. e.g. AB*+ mm,

means thattrue lengthof the line is + mm.

Front View Length(

Denoted by small letters. e.g. a-b-* mm,

means thatFront View Lengthis mm.

Top View Length(

Denoted by small letters. e.g. ab*/ mm,

means thatTop View Lengthis / mm.

Inclination of True Length of Line with H.P.(

"t is denoted by 0. e.g. "nclination of the line

with H.. 1or 2round3 is given as 45 meansthat0 * 45.


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Inclination of Front View Length with XY (

"t is denoted by 6. e.g. "nclination of the Front

!iew of the line with 78 is given as 95 means

that 6 * 95.Inclination of Top View Length with XY (

"t is denoted by :. e.g. "nclination of the Top

!iew of the line with 78 is given as 45 meansthat : * 45.

End Projector i!tance:"t is the distance between two projectorspassing through end points of F.!. ; T.!.measured parallel to 78 line.

Inclination of True Length of Line with V.P.(

"t is denoted by


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Line in Dierent Positions withrespect to H.P. & V.P.

)#A%% A(#ine perpendicular to 1or in3 one

reference plane ; hence parallel to boththe other planes

1+3 #ine perpendicular to ..; 1hence3 parallel

to both H.. ; !..

1>3 #ine perpendicular to !..; 1hence3 parallel

to both H.. ; ..

143 #ine perpendicular to H..; 1hence3 parallel to both !.. ; ..


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)#A%% B( #ine parallel to 1or in3 one

reference plane ; inclined to other twoplanes

1+3 #ine parallel to 1 or in3 !..; inclined to H.. by .

1>3 #ine parallel to 1 or in3 H..; inclined to !.

by

.

143 #ine parallel to 1 or in3 ..; inclined to H.. by ; !.. by .


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)#A%% )(#ine inclined to all three reference

planes 1 ?bli@ue lines 3

#ine inclined to H.. by , to !.. by and alsoinclined to profile plane.


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P.P..

H.P.

V.P.

Y

X

B

A

a

b

b

a

ba

z x

Y

Class A(1 !L"#$ %$&%$#'")la& *+ P.P. , -$#$

%a&all$l *+ b+*- *-$ +*-$& %la#$s


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X

Y

a

b

H.P.

V.P.

a

b

Class A(1 ! L"#$ %$&%$#'")la& *+ P.P. , -$#$

%a&all$l *+ b+*- *-$ +*-$& %la#$s


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P.P.

a. b

Y1

.

H.P.

V.P.

a

b

a

bX

Y

Class A(1 ! L"#$ %$&%$#'")la& *+ P.P. , -$#$

%a&all$l *+ b+*- *-$ +*-$& %la#$s


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a b

a b

a b

X Y1

.F.V. L.H.S.V.

T.V.

Y

Class A(1 ! L"#$ %$&%$#'")la& *+ P.P. , -$#$

%a&all$l *+ b+*- *-$ +*-$& %la#$s


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X Y

Profile

Plane

a

/0

b

aT.V.T.L.

F.V.T.L.

20

10

Y1

Y1

50

Data given:-

(1T.L. 3044

(2P+"#* A20 b$l+5 H.P.

/044 B$-"#'

V.P.

(/L"#$ "s %$&%$#'")la&*+ P.P.

(6L"#$ "s 1044 l$7* +7P.P.

Sal$ !8 1!1

Exercise 1!8 A L"#$ AB 3044 l+#9 "s %$&%$#'")la& *+ *-$%&+7"l$ %la#$. T-$ $#' A "s 2044 b$l+5 H.P. /044b$-"#' V.P. , 1044 *+ *-$ l$7* +7 P.P. :&a5 *-$%&+;$*"+#s +7 s*&a"9-* l"#$ AB (".$. F&+#* V"$5 , T+%V"$5.

.

..b

.


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V.P.

H.P.

Y

X

A

B

b

a

a b.

Y

XClass A(2!L"#$ %$&%$#'")la& *+ V.P. , (-$#$

%a&all$l *+ b+*- *-$ +*-$& Pla#$s

(".$. H.P. , P.P.


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a b

X

Y

V.P.

H.P.

a

b

.

Class A(2!L"#$ %$&%$#'")la& *+ V.P. , (-$#$

%a&all$l *+ b+*- *-$ +*-$& Pla#$s

Cl A(2 L" '" l * V P , (-


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V.P.

H.P.

a b

X Ya

b

T.V.

F.V..

Class A(2!L"#$ %$&%$#'")la& *+ V.P. , (-$#$%a&all$l *+ b+*- *-$ +*-$& Pla#$s

E i 2 A L" ABC =0 l " '" l


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.

30 a

b

ab

20

)al (AB AC

Answer :-

8 T-$ &$al a#9l$ b$*5$$# *5+

)#$>)al l$9s BAC123@

Bb Aa

ab

Y

L+)s +7 Sal$ !8 1!1

/

L+)s +7

2

/

T.L.

T.L.

T.L.

Exercise 11 :- T5+ a#9+$s +# a *&$$ %la#*$' #$a& *-$


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0.34

14

1.234

0.34>2

F.V.

T.V.

>

>

%

%

Y

L

9 %+4%+)#' 5all +7 a b)#9l+5 a&$ 14 a#' 1.234 ab+$ *-$

9&+)#' a#' 0.34 , 0.34 7&+4 a 134 *-" +4%+)#' 5all

b)* +# *-$ +%%+s"*$ s"'$s +7 "*. T-$ '"s*a#$ b$*5$$# a#9+$s

4$as)&$' al+#9 *-$ 9&+)#' a#' %a&all$l *+ *-$ 5all "s 14.:$*$&4"#$ *-$ &$al '"s*a#$ b$*5$$# $#*&$s +7 *5+ 4a#9+$s.

Data Given :-(1 E.P.:. 14

Answer :-8 *-$ &$al '"s*a#$ b$*5$$#

$#*&$s +7 *5+ 4a#9+$s %>2 1.

Sal$ !8 1!20

(2 P+"#* P 14 ab+$ 9&+)#0.3 b$-"#' 5all

(/ P+"#* 1.234 ab+$ 9&+)#

0.34 "# 7&+#* +7

5all

134

(6 all *-"#$ss 134

L+)s +7 >

>2

Exercise 12 : T-$ F.V. +7 a l"#$ N 0 44 l+#9 4$as)&$s


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Exercise 12 :T-$ F.V. +7 a l"#$ N 0 44 l+#9 4$as)&$s


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TRACS O! A L"N

efinition:hen a line is inclined to a plane, it

will meet that plane, produced ifnecessary. The point where the line orline produced meets the plane is calledtrace.

Hori"ontal Trace: The point of intersection ofthe inclined line with the H.. is calledHori"ontal Traceor simplyH.T.

Vertical Trace:The point of intersection of theinclined line with the !.. is calledVertical Traceor simplyV.T.

Exa4%l$ *+ "ll)s*&a*$


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V.P.

V.P.

H.P..

.

ab

b

a

B

A

Y

X

Exa4%l$ *+ "ll)s*&a*$

*-$ +#$%* +7 *&a$s

F.V.

T.V.

H.T.

-

V.T.

"#PORTANT PO"NTS R$ARD"N$


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"#PORTANT PO"NTS R$ARD"N$TRACS O! A L"N

"f a line is inclined to both H.. ; !.. thenits Front view, h- and !.T. must be on thesame straight line.

e.g. if front view of a line AB is a#$#, then

h,a-,b- and !.T. must be on a same straightline.

"f a line is inclined to both H.. ; !.. thenits Top view, v and H.T. must be on the samestraight line.

e.g. if Top !iew of a line AB is a$, then v, a, b

and H.T. must be on a same straight line.

IPORTANT POINTS REGAR:ING


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TRACES OF A LINE

(1 I7 a l"#$ "s %a&all$l *+ a#? +7 *-$ %la#$ "* -as #+*&a$ )%+# *-a* %la#$.

$.9. I7 *-$ l"#$ "s %a&all$l *+

-+&"z+#*al %la#$ *-$#*-a* l"#$ 5"ll #+* 4$$*

H.P a#' -$#$ *-$&$

5"ll b$ #+ H.T. a#'

+#l? V.T.

A

B

b

a

a b.

V.T.

Y



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TRACES OF A LINE

(1 I7 a l"#$ "s %a&all$l *+ a#? +7 *-$ %la#$ "* -as #+*&a$ )%+# *-a* %la#$.

$.9. I7 *-$ l"#$ "s %a&all$l *+

-+&"z+#*al %la#$ *-$#*-a* l"#$ 5"ll #+* 4$$*

H.P a#' -$#$ *-$&$

5"ll b$ #+ H.T. a#'

+#l? V.T.

V.T.

A Ba

a b

b

D

.



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TRACES OF A LINE

$.9. I7 *-$ l"#$ "s %a&all$l *+

V$&*"al Pla#$ *-$#

*-a* l"#$ 5"ll #+* 4$$*V.P a#' -$#$ *-$&$

5"ll b$ #+ V.T. a#' +#l?

H.T.

Y

X H.P.ab.

V.P.

A

B

a

b

H.T.



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TRACES OF A LINE

$.9. I7 *-$ l"#$ "s %a&all$l *+ V$&*"al Pla#$*-$# *-a* l"#$ 5"ll #+* 4$$* V.P a#' -$#$

*-$&$ 5"ll b$ #+ V.T. a#' +#l? H.T.

20

/0@

b

a

ba

F.V.1T

.L.

T.V.

-

H.T.


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Exercise 13 :A line AB 80 !! l"ng is seen as

a straig#t line "$ lengt# 55!! in its $r"nt

view an% "$ lengt# 65 !! in its t"& view'

(ts en% A is 10 !! a)"ve *'+' , is in $irst.a%rant w#ere as en% B is 25 !! )e#in%

/'+' an% is in ec"n% .a%rant' Draw its

&r"ecti"ns an% $in% ".t its inclinati"nswit# *'+' , /'+' an% als" l"cate its traces'

Data Given:


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1 ''80 !! 2 '/' 55!! 3 '/' 65!!

4 En% A10 !! a)"ve *'+'

('' /'+'

5 En% B a)"ve *'+'

25!! )e#in% /'+'

X Y

b

b

L+)s +7 b

L+)s +7 b

b1

23

b1


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Exercise 14 : #e en% &r"ect"rs %istance "$ a

line er"' (ts en% < is 25!! )el"w*'+' , 40!! )e#in% /'+' w#ere as en% = is

10 a)"ve *'+' , 55!! in $r"nt "$ /'+'

Draw its &r"ecti"ns an% $in% ".t itsinclinati"ns wit# *'+' , /'+' an% als"

l"cate its traces'

Data Given:


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.

10

60

23

4

.

.

.

.

.

Y

4

#

#

#

4

V.T. H.T.

-33

. .

1 En%


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%

-a"#9 *5+ $>)al a&4s AB , BC -"#9$' a* B "s $%*

"# H.P. +# "*s #$$'l$ %+"#* A , C 5"*- *-$ l"#$ ;+"#"#9

A , C "s %$&%$#'")la& *+ V.P. I* "s s$$# "# 7&+#* "$5as a s*&a"9-* l"#$ 10044 l+#9 "#l"#$' a* /0K *+ H.P.

5-"l$ "* "s s$$# "# *+% "$5 as a# a#9l$ a)c wit# @a)c

60K. :&a5 "*s 7&+#* "$5 a#' *+% "$5 a#' 7"#'Q

(1 T-$ -$"9-* +7 %+"#* B ab+$ H.P.

(2 T-$ a%a&* '"s*a#$ b$*5$$# *-$ #$$'l$ %+"#*s

A , C

(/T-$ l$#9*-s +7 a&4s AB , BC 5"*- &$al

b$*5$$# *-$4

Data Given: "c.s "$ )


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Data Given:

1 '/'100 !!f

2

30;3 @a)c 2 60;

4 ac is &er&en%ic.lar

t" /'+' aA

a

C

b1

b1B

b

X Y

HF.V.

60;

"c.s "$ )

"c.s "$ )

b2AB'

"s*.

Answers:

1 AB 112!!

2 2 53;

3 A 100 !!


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Exercise 16 :#e en% A "$ a straig#t line AB

120!! l"ng is 50 !! )e#in% /'+' , 35 !!

)el"w *'+' #e line is incline% t" *'+' )C 30; ,#as a &"int "n it in )"t# t#e re$erence

&lanes' Draw t#e &r"ecti"ns "$ t#e line an%

$in% ".t its inclinati"ns wit# /'+' Als" l"cate itstraces'

Data Given:


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2 ''120 !!3

30;

1 En% A35 )el"w *'+'

50 )e#in% /'+'

4 "n AB in

)"t# re$' +lanes

Answers:

1 45;

2 *'' in/'+', *'+'

3 /'' in /'+'

, *'+'

/3

a

a

b

b

C

1

30

b2

X 1

b1

b1

b2.

.

L+)s +7 b

L+)s +7 b

F.V. +7 AC

T.V. +7 AC

H.T. , V.T..


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PRO%CT"ONS O!STRA"$HT L"NS

projection of straight line engineering108.com

Documents

view ofthe straight

ine parallel

end points of astraight

ine perpendicular

ine ends

s5192018 projection

view lengthdenoted

end projector i