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Technical Drawing in Engineering Lecture 6. Axonometric projection system
Technical Drawing in Engineering
Lecture 6. Axonometric projection system
Lecture 6. Axonometric projection system
Basics I
The View point is very far away
Lecture 6. Axonometric projection system
Basics II
Plane : Plane of the paper.
The projection can be orthogonal or oblique.
Coordinate axes (XYZ): Origin in O and perpendicular between them.
Axonometric axes (X’Y’Z’).
O
Lecture 6. Axonometric projection system
Axonometric orthogonal projection
Trimetric system:
≠ ≠
Dimetric system:
= ≠ / ≠ = / = ≠
Isometric system:
= =
Lecture 6. Axonometric projection system
Representation of a point
To define the position of a point only 2 of its 4 projections are required. A’ Direct projection of the point.
A’1 Horizontal projection.
A’2 Vertical projection
A’3 Second vertical projection.
A2’ A3’
A1’
A’
z’
y’ x’
Lecture 6. Axonometric projection system
Representation of a line Line r’ is defined by 2 of its
projections, the other 2 can be obtained from these.
Data: r’ y r’1.
Find r’2 and r’3.
The traces are the intersections of the direct projection (r’) and the horizontal (H), vertical (V) and second vertical (W).
Hr’ intersection of lines r’ and r’1.
Vr’ intersection of r’ and r’2.
Wr’ intersection of r’ and r’3.
Lecture 6. Axonometric projection system
Representation of a plane It is represented by its traces.
The 3 traces cut in the axes in pairs.
These traces, when enlarged, form the Triangle of traces. Each of the vertex of the triangle are in the axes.
Triangle of traces
Lecture 6. Axonometric projection system
Membership: Line and plane
z’
r’
x’ y’
h’
w’
Vr’
Hr’
Wr’
v’
The traces of the line must be on the traces of the plane (and the other way round):
Vr’ over v’
Hr’ over h’
Wr’ over w’
Lecture 6. Axonometric projection system
Reduction coefficients I
xx
y
y
zz
ec
e
ec
e
ec
e
Lecture 6. Axonometric projection system
Reduction coefficients II
cos
cos
cos
xx
y
y
zz
ec
e
ec
e
ec
e
’
'sen
'sen
'sen
Lecture 6. Axonometric projection system
Reduction coefficients III
Isometric system:
2 2 2
22
3 2 0.816x y z
x x y z
x y z
c c cc c c c
c c c
2 2 2 2x y zc c c
’ ’
’ ' ' 'x y zc c c sen sen sen
2 2 2 2 2 2
2 2 2
' ' '
3 cos ' cos ' cos ' 2
x zyc c c sen sen sen
2 2 2cos ' cos ' cos ' 1
Lecture 6. Axonometric projection system
Parallelism and perpendicularity
Lecture 6. Axonometric projection system
Parallelism and perpendicularity
Lecture 6. Axonometric projection system
Construction of an isometric drawing I
X
Y
Z Draw in the axes direction
Lecture 6. Axonometric projection system
Construction of an isometric drawing II
X
Y
Z Non isometric lines
Lecture 6. Axonometric projection system
Construction of an isometric drawing II
X
Y
Z
Inclined surfaces Angles
X
Y
Z
Lecture 6. Axonometric projection system
Construction of an isometric drawing III
X
Y
Z
Irregular lines
Lecture 6. Axonometric projection system
Construction of an isometric drawing IV
