Projection of straight line engineering drawing

Description of basic engineering drawing

2. PROJECTIONS OF STRAIGHT LINES
DefinitionofStraightline:
Astraightlineistheshortestdistance
betweentwopoints.
-Topviewsoftwoendpointsofastraight
line,whenjoined,givethetopviewof
thestraightline.
-Frontviewsofthetwoendpointsofa
straightline,whenjoined,givethefront
viewofthestraightline.
-Boththeaboveprojectionsarestraight
lines.

3. Orientation of Straight Linein Space
-Alineinspace may beparallel,
perpendicularorinclinedtoeithertheH.P.
orV.P.orboth.
-Itmaybeinoneorboththereference
Planes.
-LineendsmaybeindifferentQuadrants.
-PositionofStraightLineinspacecanbe
fixedbyvariouscombinations ofdatalike
distanceofitsendpointsfromreference
planes,inclinationsofthelinewiththe
referenceplanes,distancebetween end
projectorsofthelineetc.

4. Notatioans used for Straight Line
Truelengthoftheline:
DenotedbyCapitalletters.e.g.AB=100mm,
meansthattruelengthofthelineis100mm.
FrontViewLength:
Denoted bysmallletters.e.g.a’b’=70mm,
meansthatFrontViewLengthis70mm.
TopViewLength:
Denoted bysmallletters.e.g.ab=80mm,
meansthatTopViewLengthis80mm.
InclinationofTrueLengthofLinewithH.P.:
Itisdenotedbyθ.e.g.Inclinationoftheline
withH.P.(orGround)isgivenas30ºmeans
thatθ=30º.

5. InclinationofFrontViewLengthwithXY:
Itisdenotedbyα.e.g.InclinationoftheFront
ViewofthelinewithXYisgivenas50ºmeans
thatα=50º.
InclinationofTopViewLengthwithXY:
Itisdenotedbyβ.e.g.InclinationoftheTop
ViewofthelinewithXYisgivenas30ºmeans
thatβ=30º.
EndProjectorDistance:
Itisthedistancebetween twoprojectors
passingthroughendpointsofF.V.&T.V.
measuredparalleltoXYline.
InclinationofTrueLengthofLinewithV.P.:
ItisdenotedbyΦ.e.g.Inclinationoftheline
withV.P.isgivenas40ºmeansthatΦ=40º.

6. Line in Different Positions with respect to H.P. & V.P.
CLASSA:Lineperpendicularto(orin)one
referenceplane&henceparallelto
boththeotherplanes
(1)Line perpendicular to P.P.& (hence) parallel
to both H.P. & V.P.
(2) Line perpendicular to V.P.& (hence) parallel
to both H.P. & P.P.
(3) Line perpendicular to H.P.& (hence) parallel
to both V.P. & P.P.

7. Line in Different Positions with respect to H.P. & V.P.
CLASSB:Lineparallelto(orin)one
referenceplane&inclinedtoother
twoplanes
(1)Line parallel to ( or in) V.P.& inclined to H.P.
by .
(2) Line parallel to ( or in) H.P.& inclined to V.P.
by .
(3) Line parallel to ( or in) P.P.& inclined to H.P.
by & V.P. by .

8. Line in Different Positions with respect to H.P. & V.P.
CLASSC:Lineinclinedtoallthreereference
planes(Obliquelines)
Line inclined to H.P. by , to V.P. by and also
inclined to profile plane.

9. .
ClassA(1):LineperpendiculartoP.P.&hence
paralleltoboththeotherplanes

10. a’
b’
ClassA(1):LineperpendiculartoP.P.&hence
paralleltoboththeotherplanes

11. Y
1
.
a’
b’
a
b
X
Y
ClassA(1):LineperpendiculartoP.P.&hence
paralleltoboththeotherplanes

12. a’ b’
a b
a”, b”
X Y
1
.
F.V.
L.H.S.V.
T.V.
Y
ClassA(1):LineperpendiculartoP.P.&hence
paralleltoboththeotherplanes

13. X Y
Profile
Plane
a’
b’
a
T.V.=T.L.
F.V.=T.L.
10
Y
1
Y
1
50
Data given:-
(1)T.L. = 50mm
(2)Point A
20 below H.P.
30mm Behind
V.P.
(3)Line is perpendicular
to P.P.
(4)Line is 10mm left of
P.P.
Scale :-1:1
Exercise1:-ALineAB,50mmlongisperpendiculartothe
profileplane.TheendAis20mmbelowH.P.,30mm
behindV.P.&10mmtotheleftofP.P.Drawthe
projectionsofstraightlineAB(i.e.FrontView&Top
View).
.
..
b
.

14. A
B
b
a
a’, b’
.
Y
X
ClassA(2):LineperpendiculartoV.P.&(hence)
paralleltoboththeotherPlanes
(i.e.H.P.&P.P.)

15. a’, b’
X
Y
a
b
.
ClassA(2):LineperpendiculartoV.P.&(hence)
paralleltoboththeotherPlanes

16. V.P.
H.P.
a’, b’
X Y
a
b
T.V.
F.V.
.
ClassA(2):LineperpendiculartoV.P.&(hence)
paralleltoboththeotherPlanes

17. .
50
a
b
c
a’,b’,c’
20
60
YX
Exercise2:-ALineABC,80mmlongisperpendicular
toV.P&50mmbelowH.P.PointB,20mmfromAison
V.P.Aisin4
th
quadrant.Drawtheprojectionsofline
ABC.
Data given :-
(1)T.L. = 80mm
(3)Point B is in V.P.
-Line is perpendicular to V.P.
(4)Line is 50mm below H.P.
Scale :-1:1
(2)AB = 20, BC = 60
-Point A is in 4
th
quadrant
.
.
.

18. a,b
.
A
B
a’
b’
X
Y
ClassA(3):LineperpendiculartoH.P.&(hence)
paralleltoboththeotherPlanes

19. a,b
.
ClassA(3):LineperpendiculartoH.P.&(hence)
paralleltoboththeotherPlanes
a’
b’

20. X Y
a’
b’
a, b
.
H.P.
V.P.
ClassA(3):LineperpendiculartoH.P.&(hence)
paralleltoboththeotherPlanes

21. Exercise3:-ALineAB,50mmlongisperpendicularto
H.P.&itisbelowH.P.PointAisonH.P.&30mm
behindV.P.DrawtheprojectionsofthelineAB.
a’
a,b
X Y
b’
F.V.=T.L.
Data given:-
(1)T.L. = 50mm
(2) Point A
On H.P.
30mm Behind
V.P.
(3) Line is perpendicular
to H.P.
Scale :-1:1
.
.

22. a’
b’
X
Y
a
b
X
Y
A
B
ClassB(1):Linecontainedby(orparallelto)
V.P.&inclinedtoH.P.by
θ

23. Y
X
b’
a’
a
b
θ
ClassB(1):Linecontainedby(orparallelto)V.P.
&inclinedtoH.P.by

24. V.P.
b’
a’
ba
V.P.
X Y
ClassB(1):Linecontainedby(orparallelto)V.P.
&inclinedtoH.P.by

25. ==30º
b’
a’
ba
T.V.
X Y
Exercise4:-ALineAB,75mmlong,isinV.P.It
makesanangleof30ºwiththeH.P.PointAis
20mmaboveH.P.DrawtheprojectionsoflineAB.
Data given:-
(1)T.L. = 75mm
Scale :-1:1
(2)= 30º
(3)Point A = 20mm
above H.P.
-Line AB is in V.P.
.
.

26. A B
a’
H.P.
V.P.
=
a b
b’ a’ b’
a
b
ø
YX

X
Y
Class B(2) : Line parallel to (or contained by) H.P. &
inclined to V.P. by 

27. X Y
a
b
b’a’
=
F.V.
Data given:-
(1)T.L. = 120mm
(3)Point B
10 above H.P.
40mm in Front of
V.P.
-Line is parallel to H.P.
-Point A is behind V.P.
Scale :-1:1
(2)= 50º
Exercise5:-ALineAB,120mmlong,isparalleltoH.P.
andinclinedtoV.P.by50º.PointBis10mmaboveH.P.
and40mmoninfrontofV.P.PointAisbehindV.P.Draw
theprojectionoflineAB.
.
.
..

28. ClassB(3):Lineparallelto(orcontainedby)P.P.,
inclinedtoH.P.by&toV.P.by
Y
X
A
B
a”
b”


Y
X
Z
b
a
b’
a’



29. V.P.
H.P.
P.P.

ClassB(3):Lineparallelto(orcontainedby)P.P.,
inclinedtoH.P.by&toV.P.by

X
Y
a’
b’
a
b
b”
a”

30. Exercise6:-Thedistancebetweentheendprojectorsof
lineMNiszero.PointMis40mmbelowH.P.&25mm
behindV.P.PointNis15mmbelowH.P.&65mmbehind
V.P.Drawitsprojectionsandfindtheangleofthelinewith
H.P.andV.P.Alsofindthetruelengthoftheline.
Data given:-
(1)Point M
40 below H.P.
25 mm behind V.P.
(2)Point N
15 below H.P.
65 mm behind V.P.
(3) End projector dist. = 0
.
.
.
.
.
.
Y
X
25
65
15
40
n’
m’
m
n

n”
m”

45
T.L.
F.V.
T.V.

31. a b
a’
b’
Y
X
B
A
Class C:Line inclined to H.P. by & V.P. by 
( i.e. Line inclined to both the planes)

32. a
b
a’
b’
Class C:Line inclined to H.P. by & V.P. by (
i.e. Line inclined to both the planes)

33. X Y
a

b
b’
H.P.
V.P.
a’
Class C:Line inclined to H.P. by & V.P. by (
i.e. Line inclined to both the planes)

34. 25
15
Φ
α
β
Exercise7:-ALineAB,90mmlong,isinclinedtoH.P.
by30°andinclinedtoV.P.by45º.Thelineisinfirst
quadrantwithPointA15mmaboveH.P.and25mmin
frontofV.P.DrawtheprojectionoflineAB.
a’
a
b’b
1’
Y
X
b b
2
θ
Locus of b’
Locus of b
Data Given :-
(1) T.L.=90 mm
(2) Θ =30°
(3) Φ =45°
(4)Point A
15 above H.P.
25 mm in Front of
V.P.
Answers :-
(1) F.V.= 64 mm
(2) T.V= 78 mm
(3) = 45°(4) = 55°
b
2’
b
1.
.

35. Exercise8:-Thedistancebetweentheendprojectorsofa
straightlineABis80mm.PointAis10mmaboveH.P.and
30mminfrontofV.P.PointBis40mmaboveH.P.and50mm
behindV.P.Drawtheprojectionsandfindtheinclinationof
straightlineABwithH.P&V.P.andthetruelengthofthe
line. Data given:-
(1)E.P.D. = 80mm
(3)Point B 40 above H.P.
50mm behind
V.P.
X Y
(2)Point A
10 above H.P.
30mm in front of
V.P.
80
30
10
a
a’
b
1
b
40
50
b’
Locus of b
b
2’

 Answers:-
(1)=
(2)=
(3)T.L. =
15º
43º
117mm
.
.
.
Locus of b’
.
b
2
b
1’

36. YX
b
2’
B
b’
a’
a
b
L
Data Given :-
(1) Length of the room=L=5m
(2) Breadth of the room=B=4.5m
(3) Height of the room=H=4m
Answer :-
(1)Diagonal distance between
opposite corners of the
room
Exersice9:Aroomis5mX4.5mX4mhigh.Determine
bymethodofprojectionsofstraightlines,distance
betweendiagonally(solid)oppositecornersoftheroom.
a’b
2’= 7.826m
Scale :-1:100
b
2
Locus of b’
θ

37. C
c
2’
Exercise10:-TwounequallegsABandAC,hingedatA
makeanangleof135ºbetweenthemintheirelevationand
plan.LegABisperpendiculartotheProfilePlane.
Determinetherealanglebetweenthem.
Data Given :-
(1) = 135º
(2) = 135º
-AB is perpendicular to P.P.
-Legs are unequal (AB > AC)
Answer :-
-The real angle between two
unequal legs = BAC=125º
B,b’ A,a’
a
b
c
c’
YX
Locus of c
Scale :-1:1


c
3’
Locus of c’
c
2
c
3
T.L.

38. 0.5m
1m 1.25m
0.75m
q
2’
q
q’
p’
p
YX
G L
Exercise11:-TwoMangoesonatree,plantednearthe
compoundwallofabunglow,are1mand1.25mabovethe
groundand0.5m&0.75mfroma15cmthickcompoundwall
butontheoppositesidesofit.ThedistancebetweenMangoes
measuredalongthegroundandparalleltothewallis1m.
Determinetherealdistancebetweencentresoftwomangoes.
Data Given :-
(1) E.P.D. = 1m
Answer :-
-the real distance between
centres of two mangoes =
p’q
2’= 1.63m1m
Locus of q
Scale :-1:20
(2)Point P
1m above ground
0.5 behind wall
(3)Point Q
1.25m above ground
0.75m in front of
wall
15cm
(4) Wall thickness = 15cm
Locus of q’
q
2

39. Exercise 12 :The F.V. of a line MN, 90 mm long, measures
65 mm. Point M is in V.P. and 20 mm below H.P. Point N is
in the first quadrant. Draw the projections and find
inclinations of line with H.P. and V.P.Data Given:
(1)Point M
20mm below H.P.
In V.P.
(2)T.L.= 90 mm
(3)F.V.= 65 mm
(4)α =45°
(5)Point N is in
first Quadrant
X Y
m’
m
20
n’ n
1’
n
1
n
2
n
2’
n
θ
Answers:
(1)Θ = 31°
(2)Φ = 44°
T.V.
F.V.
.
.
α
Locus of n’
Locus of n
Φ
Scale:-1:1

40. TRACES OF A LINE
Definition:Whenalineisinclinedtoaplane,it
willmeet thatplane,produced if
necessary.Thepointwherethelineor
lineproducedmeetstheplaneiscalled
trace.
HorizontalTrace:Thepointofintersectionof
theinclinedlinewiththeH.P.iscalled
HorizontalTraceorsimplyH.T.
VerticalTrace:Thepointofintersectionofthe
inclinedlinewiththeV.P.iscalledVertical
TraceorsimplyV.T.

41. .
.
a
b
b’
a’
B
A
Y
X
Example to illustrate
the concept of traces


H.T.
h
v
V.T.

42. IMPORTANT POINTS REGARDING TRACES OF A LINE
-IfalineisinclinedtobothH.P.&V.P.then
itsFrontview,h’andV.T.mustbeonthe
samestraightline.
e.g.iffrontviewofalineABisa’b’,then
h,a’,b’andV.T.mustbeonasamestraight
line.
-IfalineisinclinedtobothH.P.&V.P.then
itsTopview,vandH.T.mustbeonthesame
straightline.
e.g.ifTopViewofalineABisab,thenv,a,b
andH.T.mustbeonasamestraightline.

43. IMPORTANT POINTS REGARDING
TRACES OF A LINE
(1)Ifalineisparalleltoanyoftheplane,ithasno
traceuponthatplane.
e.g.Ifthelineisparallelto
horizontalplanethen
thatlinewillnotmeet
H.Pandhencethere
willbenoH.T.and
onlyV.T.
A
B
b
a
a’, b’
.
V.T.

44. IMPORTANT POINTS REGARDING
TRACES OF A LINE
(1)Ifalineisparalleltoanyoftheplane,ithasno
traceuponthatplane.
e.g.Ifthelineisparallelto
horizontalplanethen
thatlinewillnotmeet
H.Pandhencethere
willbenoH.T.and
onlyV.T.
V.T.
A B
a’
a b
b’
ø

.

45. IMPORTANT POINTS REGARDING
TRACES OF A LINE
e.g.Ifthelineisparallelto
VerticalPlanethen
thatlinewillnotmeet
V.Pandhencethere
willbenoV.T.andonly
H.T.
a,b
.
A
B
a’
b’
H.T.

46. IMPORTANT POINTS REGARDING
TRACES OF A LINE
e.g.IfthelineisparalleltoVerticalPlane
thenthatlinewillnotmeetV.Pandhence
therewillbenoV.T.andonlyH.T.
= 
=30º
b’
a’
ba
T.V.
h’
H.T.

47. Exercise13:AlineAB,80mmlongisseenas
astraightlineoflength55mminitsfront
viewandoflength65mminitstopview.
ItsendAis10mmaboveH.P.&isinfirst
quadrantwhereasendBis25mmbehind
V.P.andisinSecondQuadrant.Drawits
projectionsandfindoutitsinclinations
withH.P.&V.P.andalsolocateitstraces.

48. Data Given:
(1) T.L.=80 mm(2) F.V. = 55mm(3) T.V. = 65mm
(4) End A
10 mm above H.P.
??? I.F.O V.P.
(5) End B
??? above H.P.
25mm behind V.P.
X Y
b’
b
Locus of b’
Locus of b
b
1’
25
b
1
65
H.T.
a
F.V.
V.T.
v
T.V.
10
a’
.
.
b
2’
b
2
h
Answers:
(1) = 36°
(2) = 46°
(3) H.T.=46mm
I.F.O. V.P.
(4) V.T.=36mm
above H.P.



49. Exercise14:Theendprojectorsdistanceofa
lineMNiszero.ItsendMis25mmbelow
H.P.&40mmbehindV.P.whereasendNis
10aboveH.P.&55mminfrontofV.P.
Drawitsprojectionsandfindoutits
inclinationswithH.P.&V.P.andalso
locateitstraces.

50. .
v
m’
.
.
.
.
.
X Y
m
n’
n
n”
m”
Z
Z
V.T. H.T.
h
.
.
Data Given:
(1) End M
25 below H.P.
40 behind V.P.
(2) End N
10 above H.P.
55mm I.F.O.V.P.
(3) E.P.D. = 0
Answers:
(1) = 20°
(2) = 70°
(4) H.T.=27mm
I.F.O. V.P.
(5) V.T.=12mm
below H.P.
..

(6) + = 90°
(3) T.L.= 101mm

51. Exercise15:Adividerinstrumentofacompassbox
havingtwoequalarmsAB&BChingedatBiskept
inH.P.onitsneedlepointA&Cwiththelinejoining
A&CisperpendiculartoV.P.Itisseeninfrontview
asastraightline100mmlonginclinedat30°toH.P.
whileitisseenintopviewasanangleabcwith<abc
=60°.Drawitsfrontviewandtopviewandfind;
(1)TheheightofpointBaboveH.P.
(2)Theapartdistancebetweentheneedlepoints
A&C
(3)ThelengthsofarmsAB&BCwithreal
betweenthem

52. Data Given:
(1) F.V.=100 mm
f
(2) = 30°
(3) <abc =2= 60°
(4) ac is perpendicular
to V.P. a,A
a’,c’
c,C
b
1’
b
1,B
b’
X Y
H
F.V.

60°
Locus of b’
Locus of b’
b
2
AB dist.
Answers:
(1) AB = 112mm
(2) 2= 53°
(3) AC = 100 mm

53. Exercise16:TheendAofastraightlineAB,
120mmlong,is50mmbehindV.P.&35mm
belowH.P.ThelineisinclinedtoH.P.by30°&
hasapointConitinboththereference
planes.Drawtheprojectionsofthelineand
findoutitsinclinationswithV.P.Alsolocateits
traces.

54. Data Given:
(2) T.L.=120 mm
(3) = 30°
(1) End A
35 below H.P.
50 behind V.P.
(4) C on AB in
both ref. Planes
Answers:
(1) = 45°
(2) H.T.= in
V.P.& H.P.
(3) V.T.= in V.P.
& H.P.
35
a’
a
b
b’
C,c’,c

c
1
50
b
2
X Y
c
1’
b
1’
b
1
b
2’

.
.
Locus of b’
Locus of b’
F.V. of AC
T.V. of AC
H.T. & V.T.
.

55. PROJECTIONS OF
STRAIGHT LINES