Design and Communication Graphics
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Design and Communication Graphics
Axonometric Projection
Table of Contents
Placing the Axonometric Plane
Positioning the Axonometric Plane
Isometric Projection
Introduction
Exploring the Axonometric Plane
Deriving Orthographic Views
What is Axonometric Projection?
• Axonometric Projection is a parallel projection technique used to create a pictorial drawing of an object by projecting that object onto a plane
• The plane of projection is called the axonometric plane
• When the projectors are drawn perpendicular to the axonometric plane, axonometric projection becomes a form of orthographic projection
• In axonometric projection, the spectator is located at an infinite distance from the axonometric plane
Parallel Projection onto a Plane
Placing the Axonometric Plane
• The axonometric plane is an oblique plane which is inclined to the horizontal, vertical and end vertical planes
• It extends to infinity• It intersects the three planes of
reference to form a triangle • This triangle is called the trace
triangle
Placing the Axonometric Plane
Exploring the Axonometric Plane
the axonometric plane is infinite in size
the three planes of reference
the trace triangle
The Trace Triangle
The lines of intersection between the axonometric plane and the planes of reference give the three traces of the axonometric plane
the vertical trace
the horizontal trace
another vertical trace
The three traces form the sides of the trace triangleThe axonometric plane is represented by this trace triangle
Viewing the Axonometric Plane
Axonometric Plane
Edge view of Axonometric Plane
The viewing direction is always at right angles to the axonometric plane
Viewing the Axonometric Plane
the trace triangle is seen as a true shape
and
the traces appear as true lengths
true lengths
true shape
X, Y and Z axes
The X axis is the line of intersection between the vertical plane and the horizontal plane
The Y axis is the line of intersection between the vertical plane and the end vertical plane
The Z axis is the line of intersection between the end vertical plane and the horizontal plane
The origin is the point of intersection of the 3 planes
Y
XZ
X, Y and Z axesThe XY plane is the vertical plane
The YZ plane is the end vertical plane
The XZ plane is the horizontal plane
Y
XZ
The Y axis is always vertical
ZX
The VP and EVP may be interchanged
The X and Z axes will be interchanged accordingly
X, Y and Z axes
Y
XZ
The vertices of the trace triangle lie on the axes
In axonometric projection the X, Y and Z axes are projected onto the axonometric plane
Y
XZ
Positioning the Axonometric Plane
Changing distances D, D1 and D2 along the axes determines the type of projection
D1
D2
D
There are 3 types of projection
Isometric
Dimetric
Trimetric
Positioning the Axonometric Plane
A° B
°
C°
Y
XZ
NOTE
Changing these angles will also determine different types of Axonometric Planes.
Further Exploring the Axonometric Plane
Further Exploring the Axonometric Plane
When the planes of reference are sectioned by the axonometric plane, 3 triangular lamina remain
Vertical Plane
Horizontal Plane
End Vertical Plane
•Vertical Plane
•Horizontal Plane
•End Vertical Plane
Question:
What is known about these triangular planes on the reference planes?
Y
XZ
Further Exploring the Axonometric Plane
What is known about the remaining triangular sections of the planes of reference?
the trace is seen as a true length
triangular plane on the Vertical Plane
the true angle at the origin is 90o
Note:
This applies to all 3 triangular sections
Isometric Projection
Types of Axonometric Projection
Axonometric projections are classified according to howthe 3 principal axes are inclined to the axonometric plane
There are 3 types of projection:
– Isometric Projection
– Dimetric Projection
– Trimetric Projection
In isometric projection, the 3 principal axes are equally inclined to the axonometric plane
In dimetric projection, two of the axes are equally inclined to the axonometric plane
In trimetric projection, all three axes are inclined at different angles to the axonometric plane
D1
D2
D
Isometric Projection
In Isometric Projection:
• all 3 distances are equal
• all 3 angles between the axes are equal
• the trace triangle is equilateral
Y
XZ12
0°
120°
120°
Isometric Projection
What is known about the triangular planes behind the reference planes?
Right-angled triangle
The triangle has 2 equal sides and is therefore isosceles
the trace is a true length
Deriving the Orthographic Views
If this triangular plane is contained on the vertical plane, an elevation can be projected onto it
Vertical Plane
Elevation of a block
This triangular vertical plane is inclined behind the axonometric plane and a true shape of the triangle and elevation cannot be seen
Question:
How can a True Shape of the Triangle be located?
The triangular planes could be rotated about the traces onto the axonometric plane.
Deriving the Orthographic Views
Deriving the Orthographic Views
What would the problem be with projecting this view onto the Axonometric Plane?
Viewed
If the block is projected back onto the axonometric plane in this position it will be drawn upside-down
The position of the developed planes will need to change to view the block from the front
Deriving the Orthographic Views
If the planes are rotated (hinged) in the other direction a front view could obtained
Deriving the Orthographic Views
End
Vertical
Plane
Vertical Plane
Horizontal Plane
A true shape of each of the reference planes may be located
The orthographic views may be drawn on them
Setting up the Orthographic Views
What size is this Axonometric Plane?
Z
Y
O
X
30°30°
Step 1: Draw the axes
Step 2: Construct the axonometric plane
In isometric projection the axes are inclined at 30° to the horizontal in order to produce the 120° angle between them
The size of the axonometric plane does not matter
Size of Plane
Setting up the Orthographic Views
Step 3: Rotate the triangular vertical plane to see true shape
Z
Y
O
X
Y
X
O
The triangle is rotated about the vertical trace; therefore the lines of rabatment are perpendicular to this trace
A semi-circle is constructed to locate the 90° angle
Setting up the Orthographic Views
Z
Y
O
X
Y
X
O
What is known about this triangle?
Section of vertical plane
90° angle
Isosceles triangle
45° angle
Worksheet 1 – Setting up ViewsA set of isometric axes is given. The horizontal trace AB of the axonometric plane ABC is also shown.(i) Determine the traces of the axonometric plane ABC.(ii) Develop each of the reference planes.(iii) Index all views.
Z
YY
Y
X
O
O
O
O
xZ
X
Z
Horizontal Plane
Vertical PlaneEnd Vertical Plane
Worksheet 1 – Setting up Views
Worksheet 2 – Child’s Playhouse
120°
120°
120°
50
15 25 10 20 10
40
30° 30°
20 20 20
A child’s playhouse is shown in the photograph across. The elevation and end elevation of the house is also included.
Draw the isometric projection of the house having axes inclined as shown.
ELEVATIONEND ELEVATION
Worksheet 2 – Child’s Playhouse
eDrawings Control
Worksheet 2 – Child’s Playhouse
eDrawings Control
Worksheet 2 – Child’s Playhouse
Worksheet 3 – Litter Bin
Shown in the photograph is a litter bin, also included is the Elevation and Plan of the litter bin.
Draw the isometric projection of the bin having axes inclined as shown.
120° 120°
120°
65
6010
7010
25
10
PLAN
ELEVATION
Worksheet 3 – Litter Bin
eDrawings Control
Worksheet 3 – Litter Bin
Dimetric Projection
Dimetric ProjectionWhat if the viewing position is changed?
Dimetric Projection
The apparent angles between the reference planes have changed
Y
XZ
The viewing position of the planes has been lowered
The Y axis has remained vertical
and
The apparent angles between the Y axis and the X and Z axes have reduced
Two of the angles have remained equal-
This is Dimetric Projection
Dimetric Projection
The viewing position may be lowered or raised. The position of the axonometric plane will rotate so that it remains perpendicular to the viewing direction
Dimetric Projection
As the plane rotates the traces of the axonometric plane change, producing an isosceles triangle
EqualEqual
X Z
Y
Two of the apparent angles between the axes remain equal at all times
Traces
Dimetric Projection
X Z
YObserving the Traces of Axonometric Planes
Perpendicular
If the Y axis is extended to intersect the trace, the angle formed is 90°
In turn, if the X and Z axes are extended the angle formed is also 90°
Perpendicular
Why is this so?
Dimetric Projection
Dimetric Projection
X Z
YThe Z axis is the line of intersection between two reference planes
The Z axis is perpendicular to the Vertical Plane
The Vertical Plane contains the vertical trace of the axonometric plane, therefore the Z axis must be perpendicular to this trace
Z axis
Vertical Plane
Perpendicular
Worksheet 4 - Dimetric Projection
As set of dimetric axes is given as well as the horizontal trace AB of the axonometric plane ABC.(i) Determine the traces of the axonometric plane ABC(ii) Develop each of the reference planes.(iii) Index all views.
Worksheet 4
Z
Y
X
A B
BA
C
CC
O
O
O
O
BB
110°
110°
Worksheet 5 - Dimetric Projection
80
35
15
40
25
15
25
PLAN
ELEVATIONEND-ELEVATION
A photograph of a measuring tape is shown. The elevation, plan and end elevation are also given.
Draw the dimetric projection of the measuring tape having axes inclined as shown.
105°
150°
105°
Y
XZ
Worksheet 5 - Dimetric Projection
eDrawings Control
Worksheet 5 - Dimetric Projection
1
2
3 4
5
6
7
1
6
2
3
4
5
7
1
2
3 4
5
6
7
L
L1
L2
L
L1
L2
5mm
Worksheet 6 - Dimetric Projection
A photograph of an apartment intercom is shown with the elevation, plan and end elevation given.
Draw the dimetric projection of the intercom having axes inclined as shown.
ELEVATION
PLAN
R40
20
35
60
1015
15
15
110°
110°
140°
Y
X Z
Worksheet 6 - Dimetric Projection
eDrawings Control
Worksheet 6 - Dimetric Projection
1
2
34 5
6
7
8
9
1011
12
12,12
3,11
4,10
5,9
6,87
1
2
3
4 5
6
7
8
9
1011
12
X
Y
Z
Trimetric Projection
Trimetric ProjectionWhat if the viewing position is changed such that none of the apparent angles are equal?
Trimetric Projection
Trimetric Projection
There are numerous positions where the apparent angles between the reference planes appear unequal.
The Y axis has remained vertical
and
The apparent angles between the Y axis and the X and Z axes are unequal.
In this case all three angle are unequal-
This is Trimetric Projection
Y
X
Z
Trimetric ProjectionAs the viewing position is changed, the position of the axonometric plane rotates perpendicular to the viewing position to produce a scalene trace triangle
Trimetric Projection
As the plane rotates the traces of the axonometric plane change, producing an scalene triangle
X
Y
Z
The apparent angles between the reference planes are all unequal.
Worksheet 7 - Trimetric Projection
As set of Trimetric Axes are given.(i) Determine the traces of the Axonometric Plane ABC(ii) Develop each of the Reference Planes.(iii) Index all views.
Worksheet 7 - Trimetric Projection
X
Y
ZA B
C
C
B
o
o
o
C
A
A B
o
115°
125°
Trace is constructed perpendicular to Y-Axis
Edge View of HP
Edge view of End VP
Edge view of VP
Edge View of HP
Worksheet 8 - Trimetric Projection
A photograph of a Disco Ball is shown with the Elevation and Plan over.
Draw the trimetric projection of the Disco Ball having axes inclined as shown.
R40
R50
30
15
10
ELEVATION
PLAN
135°
120°
105°
Y
XZ
Worksheet 8 - Trimetric Projection
eDrawings Control
Worksheet 8 - Trimetric Projection
1
2
3
4
56
7
8
9
10
1112
1 2,123,11
4,10
5,96,8
7 Centre of Sphere
Sphere is a sphere in all views
Worksheet 9 - Trimetric Projection
130°120°
110°
Y
XZ
70
70
7035
R30
30
ELEVATION
PLAN
Shown is photograph of news reporters microphone. The Elevation and Plan of the microphone is shown over.
Draw the trimetric projection of the Microphone having axes inclined as shown.
Worksheet 9 - Trimetric Projection
eDrawings Control
Worksheet 9 - Trimetric Projection
1 2 34
5
6
78910
11
12
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