Design and Communication Graphics Axonometric Projection

Table of Contents Introduction 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 trace triangle the axonometric plane is infinite in size the three planes of reference

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

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

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

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

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

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

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

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

Further Exploring the Axonometric Plane

Further Exploring the Axonometric Plane Y 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

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

Isometric Projection

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

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

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

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

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

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 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

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

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

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

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.

Worksheet 1 – Setting up Views Y Y Y End Vertical Plane O O Vertical Plane X Z O Z X O Horizontal Plane Z x

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

Worksheet 2 – Child’s Playhouse

Worksheet 2 – Child’s Playhouse

Worksheet 2 – Child’s Playhouse

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

Worksheet 3 – Litter Bin

Worksheet 3 – Litter Bin

Dimetric Projection

Dimetric Projection What if the viewing position is changed?

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

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 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

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

Dimetric Projection

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

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 C C Y C O O 110° 110° B B O A B X O Z A B

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

Worksheet 5 - Dimetric Projection

Worksheet 5 - Dimetric Projection 3 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

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

Worksheet 6 - Dimetric Projection

Worksheet 6 - Dimetric Projection Y 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

Trimetric Projection

Trimetric Projection What 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. 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

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

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

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 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

Worksheet 8 - Trimetric Projection Y 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

Worksheet 8 - Trimetric Projection

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

Worksheet 9 - Trimetric Projection Y 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

Worksheet 9 - Trimetric Projection

Worksheet 9 - Trimetric Projection 1 2 3 4 12 5 11 6 10 9 7 8