Descriptive Geometry

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DESCRIPTIVE GEOMETRY

• Dr. Tarun Kanti Naskar
• Prof. Mechanical Engineering Department
• Jadavpur University
• Kolkata, India

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Projections on 3 Principal Planes
P
Rays of light
V
H
3
Projection of a Solid
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3 Principal Planes Convention of Rotation
V
P
P
V
H
H
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1st Angle Projection Solid
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Projection of a solid
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3 views of a solid 1st angle
PP
GL
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Projection of a solid
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Views in 4 Quadrants
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Views in 4 Quadrants
No to lt2
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Views in 4 Quadrants
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Views in 4 Quadrants
No to lt4
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3rd Angle Projection Solid
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3rd Angle Projection
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Multi-view Projections
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Projection of a Point
A
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Projection of a Point
P
A
V
H
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3 views of a point
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Projection of a Line
A
B
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Types of Lines

• Oblique Line
• Horizontal Line
• Frontal Line
• Profile Line
• Horizontal-Frontal Line
• Horizontal-Profile Line
• Frontal-Profile Line or Vertical Line

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Projection of an Oblique Line 3 Views
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Projections of a Horizontal Line
A
B
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Projection of a Frontal Line
AB is parallel to Front plane, called Frontal
Line. Other similar lines are Horizontal
Profile lines.
True lengths are obtained.
True lengths are obtained for these lines.
B
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3 Views of a line Frontal Line
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Horizontal-Frontal Line
TL
TL
TL
PROJECTION OF DIFFERENT SPECIAL LINES
Profile Line
Vertical Line
TL
TL
Horizontal-Profile Line
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True Length of a Line Revolution Method
A2
OA is an oblique line.
It is revolved about O keeping at a fixed
distance from H-plane.
A
A1
Two positions are obtained, OA1 OA2, when the
line is parallel to V-plane.
True lengths will be obtained on V-plane for
these positions.
O
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TL and True Angle a of a Line Revolution Method
TL
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True Length of a Line Revolution Method
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TL and True Angle b of a Line Revolution Method
TL
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True Length of a Line Auxiliary View Method
Auxiliary Plane A parallel to oblique line PQ
perpendicular to H
A
Q
V
TL
a
P
H
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True Lengths Angles by Auxiliary View Method
TL
g
TL
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True Shape of a Plane
H
TS
V
EV
TL
B
Projections of an oblique plane
A
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Traces of a Line
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Traces of a Line
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Traces of a Plane
Q is an oblique plane in space
V
The plane is extended to intersect V H planes
VQ HQ are the respective traces
The traces intersect at a point on GL Traces of
any line on the plane Q will lie on VQ HQ.
VQ
H
Q
HQ
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Traces of a Plane Normal to HP Angle with VP
Q
VQ
VQ
PQ
HQ
HQ
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Finding Dihedral Angle
If two planes in space are intersecting, there
must be a plane which is normal to both the
planes.
Q
A
R
P Q are two planes in space with line of
intersection AB.
P
RQ
Plane R is normal to the line of intersection AB
of the planes P Q. RP RQ are the traces of
the planes on R.
B
RP
Included angle between traces RP RQ is the
dihedral angle.
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Point of Intersection of Line Plane
Point of intersection of line plane
H
Angle between line plane
TL of Line EV of Plane
Projections of point of intersection
C
B
True Shape (TS) of Plane
V
Edge View (EV) of Plane
A
True Length Line on plane
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Line of Intersection of two Planes 1 2 and
Dihedral Angle between them
Line of intersection
2
1
2
H
A
V
EV
1
2
Points of intersection
TL
1
Line of intersection