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Engineering GraphicsProjection of Lines
Submitted By:Akabari Nirali(130130116002)Bhut Vidhi(130120116013)Bavasar Mausam(130120116012)
Projection of straight linesDefinition :
A straight line is the shortest distance between two points. •Top views of two end points of a straight line, when joined, give the top view of the straight line.
•Front views of the two end points of a straight line, when joined, give the front view of the straight line.
•Both the above projections are straight lines.
Orientation of Straight Line in Space• A line in space may be parallel, perpendicular or
inclined to either the H.P. or V.P. or both.
• It may be in one or both the reference Planes.
• Line ends may be in different Quadrants.
• Position of Straight Line in space can be fixed by various combinations of data like distance of its end points from reference planes, inclinations of the line with the reference planes, distance between end projectors of the line etc.
Notations used for Straight Line True length of the line:
Denoted by Capital letters. e.g. AB=100 mm, means that true length of the line is 100 mm.
Front View Length:
Denoted by small letters. e.g. a’b’=70 mm, means that Front View Length is 70 mm.
Top View Length:
Denoted by small letters. e.g. ab=80 mm, means that Top View Length is 80 mm.
Inclination of True Length of Line with H.P.: It is denoted by θ. e.g. Inclination of the line with H.P. (or Ground) is given as 30º means that θ = 30º.
Inclination of Front View Length with XY :
It is denoted by α. e.g. Inclination of the Front View of the line with XY is given as 50º means that α = 50º.
Inclination of Top View Length with XY :
It is denoted by β. e.g. Inclination of the Top View of the line with XY is given as 30º means that β = 30º.
End Projector Distance: It is the distance between two projectors passing through end points of F.V. & T.V. measured parallel to XY line.
Inclination of True Length of Line with V.P.: It is denoted by Φ. e.g. Inclination of the line with V.P. is given as 40º means that Φ = 40º.
Line in Different Positions with respect to H.P. & V.P.
CLASS A: Line perpendicular to (or in) one reference plane & hence parallel to both the other
planes
(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.
Line in Different Positions with respect to H.P. & V.P.
CLASS B: Line parallel to (or in) one reference plane & inclined to other two
planes
(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 .
Line in Different Positions with respect to H.P. & V.P.
CLASS C: Line inclined to all three reference planes ( Oblique lines )
Line inclined to H.P. by , to V.P. by and also inclined to profile plane.
P.P..
H.P.
V.P.
Y
X
BA
a’b’
ba
b”a”
z x
Y
Class A(1) : Line perpendicular to P.P. & hence parallel to both the other planes
X
Y
a’
b’
H.P.
V.P.
a
b
Class A(1) : Line perpendicular to P.P. & hence parallel to both the other planes
V.P.
H.P.
Y
X
A
B
b
a
a’, b’.
Y
XClass A(2):Line perpendicular to V.P. & (hence) parallel to both the other Planes(i.e. H.P. & P.P.)
a’, b’
X
Y
V.P.
H.P.
a
b
.
Class A(2):Line perpendicular to V.P. & (hence) parallel to both the other Planes
H.P.
a,b.
V.P.
A
B
a’
b’
X
Y
Class A(3):Line perpendicular to H.P. & (hence) parallel to both the other Planes
Y
X
a,b.H.P.
Class A(3):Line perpendicular to H.P. & (hence) parallel to both the other Planes V.P.
a’
b’
Y
X
H.P.
V.P.
a’
b’
X
Y
a
b
X
Y
A
B
Class B(1): Line contained by ( or parallel to) V.P. & inclined to H.P. by Ө
θθ
Y
X
V.P.
b’
a’a
bθθ
H.P.
Class B(1): Line contained by ( or parallel to) V.P. & inclined to H.P. by Ө
V.P.
H.P.
A Ba’
H.P.
V.P.
β=φa b
b’ a’ b’
a
b
X
Y
ø
YXβ
X
Y
Class B(2) : Line parallel to (or contained by) H.P. & inclined to V.P. by
H.P.
V.P.
P.P.
Class B(3): Line parallel to (or contained by) P.P.,
inclined to H.P. by Ө & to V.P. by
Y
X
A
B
a”
b”
Y
XZb
a
b’
a’
V.P.
H.P.
P.P.
Class B(3): Line parallel to (or contained by) P.P.,
inclined to H.P. by Ө & to V.P. by
XY
a’
b’
a
b
b”
a”
H.P.
V.P.
X
Y
a b
a’
b’
Y
X
B
A
Class C:Line inclined to H.P. by θ & V.P. by ( i.e. Line inclined to both the planes)
a
b
H.P.
X
Y
V.P.
a’
b’
Class C:Line inclined to H.P. by Ө & V.P. by ( i.e. Line inclined to both the planes)
TRACES OF A LINE
Definition: When a line is inclined to a plane, it will meet that plane, produced if necessary. The point where the line or line produced meets the plane is called trace.
Horizontal Trace: The point of intersection of the inclined line with the H.P. is called Horizontal Trace or simply H.T.
Vertical Trace: The point of intersection of the inclined line with the V.P. is called Vertical Trace or simply V.T.
V.P.
V.P.
H.P..
.
a b
b’
a’B
A
Y
X
Example to illustrate the concept of traces
F.V.
T.V.
H.T.
h
v
V.T.
IMPORTANT POINTS REGARDING TRACES OF A LINE
• If a line is inclined to both H.P. & V.P. then its Front view, h’ and V.T. must be on the same straight line.
e.g. if front view of a line AB is a’b’, then h,a’,b’ and V.T. must be on a same straight line.
• If a line is inclined to both H.P. & V.P. then its Top view, v and H.T. must be on the same straight line.
e.g. if Top View of a line AB is ab, then v, a, b and H.T. must be on a same straight line.
IMPORTANT POINTS REGARDING TRACES OF A LINE
(1) If a line is parallel to any of the plane, it has no trace upon that plane.
e.g. If the line is parallel to horizontal plane then that line will not meet H.P and hence there will be no H.T. and only V.T.
V.P.
H.P.
A
B
b
a
a’, b’.
V.T.
Y
IMPORTANT POINTS REGARDING TRACES OF A LINE
e.g. If the line is parallel to Vertical Plane then that line will not meet V.P and hence there will be no V.T. and only H.T. Y
X H.P.
a,b.
V.P.
A
B
a’
b’
H.T.
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