design and communication graphics

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

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Worksheet 2 – Child’s Playhouse

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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

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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

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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

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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

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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

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Worksheet 9 - Trimetric Projection

1 2 34

5

6

78910

11

12