436-105 Engineering Communications
GL11: Descriptive Geometry
• Elements
• Primary auxiliary views
• Rotations
Elements of DG
• Orthographic projection
– parallel projectors
Top (plane 1)
a1
b1
a1
b1
Fold line 1-2
1
b2
a2
Projection of line AB
on plane 1
B
A
2
Fold line 1-2
(or reference line)
b2
a2
Front (plane 2)
Projection of line AB
on plane 2
Elements of DG
• Geometric elements
– points
– lines
– planes
• Relationships
– angles
– distances
Point
Line
Plane
b1
C
B
c1
a1
1
2
A
2 3
c2
c3
b3
b2
a2
a3
Fundamental views
• Lines
–
–
–
–
seen in true length (TL) if parallel to projection plane
seen as a point if perpendicular to projection plane
an inclined line is seen in TL in one principal view
an oblique line is foreshortened in all principal views
TL
TL
Fundamental views
• Planes
– seen in true shape (TS) if parallel to projection plane
– seen as a line if perpendicular to projection plane
– an inclined plane is seen as a line (edge view) in one
standard view
– an oblique plane is ‘similar’ in all standard views
TS
edge
view
Summary of fundamental views
Geometry
Lines:
• Point View
• True Length (TL) view
Planes:
• Edge View
• Dihedral angle view
• True Shape (TS) view
Projection plane
• ⊥ to line
• // to line
• ⊥ to plane
• ⊥ to plane
• // to plane
Auxiliary views
• Often an object has significant features
inclined to the principal projection planes
• Primary auxiliary view
– projection on to an auxiliary plane which is
orthogonal to one of the principal projection
planes
• Secondary auxiliary view
– the auxiliary plane is inclined to all the
principal projection planes
Top
view
Primary
auxiliary
view
Front
view
Depth
1
True shape
view of sloping
surface
Top view
2
Reference line
= edge view of
auxiliary plane
4
2
Front view
th
p
De
ry
a
i
il
x
Au view
Review
•
Principal views
– projections onto principal planes of the orthographic box (top, front, left
side, right side, back, bottom)
– placed on one sheet of paper by unfolding top and sides about fold (or
hinge) lines
•
Primary auxiliary view
– projection onto an auxiliary plane which is orthogonal to a principal plane of
the orthographic box
– placed on drawing sheet by unfolding about fold (or hinge) line
•
Reference lines
– represent edge views of projection planes (fold lines, or hinge lines)
•
Adjacent views
– share a common reference line; hence are orthogonal to each other
•
Related views
– share a common adjacent view (e.g., top and side views are related
because they are both adjacent to the front view)
– points in related views are at the same distance from their respective
reference lines
Rotation of elements to
find true size
• To find true size we can:
– introduce an auxiliary projection plane
parallel to the element of interest (a line or
plane), or
– rotate the element until it is parallel to a
principal plane
a1
b1r
A
True length of a
line by rotation
b1
1
Axis of
rotation
2
a2
B
Br
TL
b2
b2r
Axis of
rotation
120º
Ø 11 m
15º
Exam question
Semester 1, 1998
120º
Find TL and angle of
guy wires to the ground
11 m
15º
120º
15º
1
3
a1
p1 O1
120º
Ø 11 m
b1
p3
1. PA by auxiliary
view
TL
1
2
TS of
triangle PAO
angle
a3
o3
p2
11 m
a2
o2
b2
15º
120º
15º
a1
b1r
p1
120º
Ø 11 m
b1
1
2
p2
2. PB by rotation
TS of
triangle PBO
11 m
TL
a2
angle
o2
b2
b2r
15º
A
r1
q1
s1
p1
c1
d1
b1
B
X
a1
Simple shadow problem:
Find true size and shape of
shadow cast by B on A
10º
Plan view
30º
A
r2s2
p2q2
d2c2
a2b2
A
B
Front elevation
p3
s3
r3
q3
View on X
Primary
aux. view
Another shadow problem:
What is true size of shaded
region of roof on A?
1. Find shadow limits
2. Edge view of roof plane
(primary aux. plane 4 _|_ ridge)
3. Secondary aux. plane 5
parallel to roof plane
1
4
TL
x4
y4
15º
x1
TL
4
5
y1
x5
TS
1
y5
2
Secondary
aux. view
35º
x2
y2
A
B
Follow up
• Read Bertoline:
– Ch 11: Auxiliary views
– Ch 12: Fundamentals of descriptive geometry
• Do problems from Bertoline:
– Probs 11.1(1)(6), 12.7-10