technical drawing in engineering · lecture 6. axonometric projection system representation of a...

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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

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