1. Design and Communication Graphics
Axonometric Projection

2. Table of Contents Introduction Placing the Axonometric Plane
Positioning the Axonometric Plane
Isometric Projection
Introduction
Exploring the Axonometric Plane
Deriving Orthographic Views

3. 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

4. Parallel Projection onto a Plane

5. 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

6. Placing the Axonometric Plane

7. Exploring the Axonometric Plane
the trace triangle
the axonometric plane is infinite in size
the three planes of reference

8. 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 three traces form the sides of the trace triangle
The axonometric plane is represented by this trace triangle
another vertical trace
the vertical trace
the horizontal trace

9. Viewing the Axonometric Plane
The viewing direction is always at right angles to the axonometric plane
Edge view of Axonometric Plane
Axonometric Plane

10. Viewing the Axonometric Plane
the trace triangle is seen as a true shape
and
the traces appear as true lengths
true shape
true lengths

11. X, Y and Z axes Y
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 Z X

12. X, Y and Z axes The XY plane is the vertical plane
The YZ plane is the end vertical plane
The XZ plane is the horizontal plane Y X Z
The Y axis is always vertical X Z
The VP and EVP may be interchanged
The X and Z axes will be interchanged accordingly

13. X, Y and Z axes
In axonometric projection the X, Y and Z axes are projected onto the axonometric plane Y
The vertices of the trace triangle lie on the axes Z X

14. Positioning the Axonometric Plane
Changing distances D, D1 and D2 along the axes determines the type of projection Y X Z D2
There are 3 types of projection
Isometric
Dimetric
Trimetric D D1

15. Positioning the Axonometric PlaneY A° B° Z X C°
NOTE
Changing these angles will also determine different types of Axonometric Planes.

16. Further Exploring the Axonometric Plane

17. Further Exploring the Axonometric PlaneY
When the planes of reference are sectioned by the axonometric plane, 3 triangular lamina remain
End Vertical Plane
Vertical Plane
Vertical Plane Z X
Horizontal Plane
End Vertical Plane
Question:
What is known about these triangular planes on the reference planes?
Horizontal Plane

18. 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
the true angle at the origin is 90o
triangular plane on the Vertical Plane
Note:
This applies to all 3 triangular sections

19. Isometric Projection

20. Types of Axonometric Projection
Axonometric projections are classified according to how
the 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

21. Isometric Projection In Isometric Projection:Y
In Isometric Projection:
all 3 distances are equal
all 3 angles between the axes are equal
the trace triangle is equilateral D2
120° Z D D1 X

22. Isometric Projection
What is known about the triangular planes behind the reference planes?
the trace is a true length
Right-angled triangle
The triangle has 2 equal sides and is therefore isosceles

23. Deriving the Orthographic Views
If this triangular plane is contained on the vertical plane, an elevation can be projected onto it
Vertical Plane
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?
Elevation of a block

24. Deriving the Orthographic Views
The triangular planes could be rotated about the traces onto the axonometric plane.

25. 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

26. Deriving the Orthographic Views
If the planes are rotated (hinged) in the other direction a front view could obtained

27. Deriving the Orthographic Views
A true shape of each of the reference planes may be located
End Vertical Plane
Vertical Plane
The orthographic views may be drawn on them
Horizontal Plane

28. Setting up the Orthographic Views
What size is this Axonometric Plane?
Step 1: Draw the axes Y
In isometric projection the axes are inclined at 30° to the horizontal in order to produce the 120° angle between them
Step 2: Construct the axonometric plane O
The size of the axonometric plane does not matter
30°
30°
Size of Plane Z X

29. Setting up the Orthographic Views
Step 3: Rotate the triangular vertical plane to see true shape
The triangle is rotated about the vertical trace; therefore the lines of rabatment are perpendicular to this trace Y Y
A semi-circle is constructed to locate the 90° angle O O X Z X

30. Setting up the Orthographic Views
What is known about this triangle?
Section of vertical plane Y Y
90° angle
Isosceles triangle O
45° angle O X Z X

31. Worksheet 1 – Setting up Views
A 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.

32. Worksheet 1 – Setting up ViewsY Y Y
End Vertical Plane O O
Vertical Plane X Z O Z X O
Horizontal Plane Z x

33. Worksheet 2 – Child’s Playhouse
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.
120°
120°
120°
30°
30° 50 40 20 20 20 15 25 10 20 10
END ELEVATION
ELEVATION

34. Worksheet 2 – Child’s Playhouse

35. Worksheet 2 – Child’s Playhouse

36. Worksheet 2 – Child’s Playhouse

37. Worksheet 3 – Litter Bin
120° 10 25 10 70
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. 10
ELEVATION 60 65
PLAN

38. Worksheet 3 – Litter Bin

39. Worksheet 3 – Litter Bin

40. Dimetric Projection

41. Dimetric Projection
What if the viewing position is changed?

42. Dimetric Projection
The viewing position of the planes has been lowered
The apparent angles between the reference planes have changed Y
The Y axis has remained vertical
and
The apparent angles between the Y axis and the X and Z axes have reduced Z X
Two of the angles have remained equal-
This is Dimetric Projection

43. 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

44. Dimetric Projection Y Traces
As the plane rotates the traces of the axonometric plane change, producing an isosceles triangle
Equal
Equal
Two of the apparent angles between the axes remain equal at all times X Z

45. Dimetric Projection Observing the Traces of Axonometric Planes Y
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? X Z
Perpendicular

46. Dimetric Projection

47. Dimetric Projection Vertical Plane
The 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 Y
Perpendicular
Z axis X Z

48. 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.

49. Worksheet 4 C C Y C O O
110°
110° B B O A B X O Z A B

50. Worksheet 5 - Dimetric Projection
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. Y
105°
105° 25 40 Z X 15
150° 15
END-ELEVATION
ELEVATION 35 80 25
PLAN

51. Worksheet 5 - Dimetric Projection

52. Worksheet 5 - Dimetric Projection3 4 5 2 6 3 4 1 5 2 L2 7 6 L1 1 L 7 1 2 3 4 L2 5 L1 6 L 7
5mm

53. 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. 60 10 15 15 15 Y
R40
110°
110° X Z
140°
ELEVATION 20 35
PLAN

54. Worksheet 6 - Dimetric Projection

55. Worksheet 6 - Dimetric ProjectionY 4 5 3 6 2 7 4 5 1 8 3 6 12 9 2 7 11 10 1 8 12 9 X 11 10 Z 7
6,8
5,9
4,10
3,11
2,12 1

56. Trimetric Projection

57. Trimetric Projection
What if the viewing position is changed such that none of the apparent angles are equal?

58. Trimetric Projection

59. Trimetric Projection
There are numerous positions where the apparent angles between the reference planes appear unequal. Y
The Y axis has remained vertical
and
The apparent angles between the Y axis and the X and Z axes are unequal. Z X
In this case all three angle are unequal-
This is Trimetric Projection

60. Trimetric Projection
As the viewing position is changed, the position of the axonometric plane rotates perpendicular to the viewing position to produce a scalene trace triangle

61. Trimetric Projection
As the plane rotates the traces of the axonometric plane change, producing an scalene triangle Y
The apparent angles between the reference planes are all unequal. Z X

62. 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.

63. Worksheet 7 - Trimetric Projection
Edge view of End VP C Y C
Edge View of HP
Edge View of HP o o
115°
125° A o B A B Z X o
Trace is constructed perpendicular to Y-Axis
Edge view of VP A B

64. Worksheet 8 - Trimetric ProjectionY
R40
120°
135° 15
105° Z X 10 30
ELEVATION
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.
R50
PLAN

65. Worksheet 8 - Trimetric Projection

66. Worksheet 8 - Trimetric Projection
Centre of Sphere 7
6,8
5,9
4,10
Sphere is a sphere in all views
3,11 1
2,12 6 5 7 4 8 3 9 2 10 1 11 12

67. Worksheet 9 - Trimetric ProjectionY
130°
120°
110° 35 30 Z X 70
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.
ELEVATION 70 70
PLAN

68. Worksheet 9 - Trimetric Projection

69. Worksheet 9 - Trimetric Projection1 2 3 4 12 5 11 6 10 9 7 8