**
**

**Axonometric
Projection**

**Versus**

**Axonometric
Drawing**

The distinguishing feature between projections and drawings is the unit of measurement used. In projections a scale is constructed and this scale is used to step off measurements. These measurements are not standard units of measurement, e.g. mm, cm, m, etc. In drawings however, standard units of measurement are always used. The scales constructed for isometric, dimetric and trimetric are always smaller than standard units of measurements from which they are derived. This means that axonometric projections are always smaller than axonometric drawings. However, using standard units of measurement rather than scales, a satisfactory axonometric representation of an object can be obtained. An axonometric drawing of an object is slightly distorted but is visually as satisfactory as an axonometric projection of it. No time is wasted constructing scales and then using them in generating an axonometric drawing. Thus, axonometric drawings are generally preferred to axonometric projections. Below is shown an isometric projection and an isometric drawing of a cube. As you can see the drawing is bigger but the same information is available in both.

**Axonometric
Projection Methods**

Axonometric projections can be obtained by a number of methods,

- By auxiliary views.
- By auxiliary scales.
- By two methods of rotation and tilt.
- Method of Intersections.

In general the method most widely used is the **Method
of Intersections**. This is a very simple method of
producing axonometric projections and was introduced by Rudolf
Schuessler in 1905. It was published by Theodor Schmid in 1922
and L. Eckhart in 1937. This method is applicable to isometric,
dimetric and trimetric projections. It is particularly useful
when orthographic views of an object are available. The question
of scale on the various axes is automatically determined. So, if
two or more orthographic views of an object are available then
this method can be used to obtain an axonometric projection of
it.

The simplest way of
explaining this method is to work backwards i.e. from the
axonometric projection back to the orthographic views. Position
the object as shown. Now position the axonometric plane to
intersect the 'X','Y' and 'Z' axis at 'A','B' and 'C'
respectively. If a view is taken along 'OY' the true shape of the
triangle 'AOC' is obtained. This view and the plan and end-view
are shown animated in the introduction.
It is on this triangle, 'AOC', that the true elevation of the
object is projected. Actually it is onto the plane on which the
triangle 'AOC' lies that the true shape of the elevation is
projected.

The elevation is obtained by projecting
lines from the edges of the object onto the triangle 'AOC'
parallel to 'OY'. So, if the true shape of 'AOC' can be obtained
then the true elevation can be drawn by projecting lines parallel
to 'OY'. The true shape of 'AOC' is found using the method for
obtaining axonometric scales discussed in "Alternate
Isometric Scale" in isometric
projection. The triangle 'AOC' is hinged or rotated about
line segment 'AC' until it is perpendicular to the line of vision
i.e. when the angle 'AOC' equals 90 degrees. If 'AOC' is rotated
rebatted about 'AC' in its present position then its true shape
will overlap onto other lines in the drawing. To prevent this and
maintain a neat legible drawing the line 'AC' is moved a
satisfactory distance away from the rest of the drawing so that
the true shape of 'AOC' will not interfere with the rest of the
drawing. Using the "Angle in a semi-circle theorem", a
semi-circle is drawn and the point of intersection of the 'Z' and
'Y' axes is projection onto the semicircle parallel to the line
segment 'OY'. The true shape of the triangle 'AOC' is then drawn
i.e.'A_{1}O_{1}C_{1}'.

The elevation of the object
can now be drawn in this triangle, aligning its edges with the
axes 'O_{1}A_{1}' and 'O_{1}C_{1}'.
Edges from the axonometric view are projected onto 'A1O1C1'
perpendicular to line 'AC'.

If the triangles 'AOB' and 'BOC' were
hinged in their present positions to obtain their true shapes 'A_{3}O_{3}B_{3}'
and 'B_{2}O_{2}C_{2}' respectively, then
they would overlap with other lines on the drawing. For this
reason the hinge lines, 'AB' and 'BC', are positioned, 'A_{3}B_{3}'
and 'B_{2}C_{2}' so that when the true shape of
all three triangles are obtained no over lapping takes place. The
true shape of the end-view and plan view are obtained following
the same procedure outlined above for the elevation. The
illustration on the left shows the axonometric projection and its
three orthographic views. The same procedure follows when given
the orthographic views of an object to find its axonometric
projection except that it is reversed. Lines are projected from
the orthographic views perpendicular to the axonometric traces
e.g. 'AB', 'AC' and 'BC'. Where corresponding projection lines
intersect gives points on the axonometric projection of the
object. Indexing corresponding points in the orthographic views
greatly simplifies this operation. Notice that only two
orthographic views are required to obtain an axonometric
projection of an object.

Here is the above example
animated, see if you can follow it.

**Axes
Projections **

**and**

**Axonometric
Traces**

Given the angles between the projection of the axes, determine the axonometric traces?

This is often the first step in obtaining an axonometric
representation of an object. The projection of the axes are shown
here.
The 'ZX' plane and the 'XY'
plane intersect to give the trace known as the 'X' axis. The 'ZX'
plane and the 'ZY' plane intersect to give the 'Z' axis. Finally,
the 'XY' and 'ZY' planes intersect to give the 'Y' axis. The
planes are perpendicular to each other i.e. 90 degrees though
they do not **appear** so in an axonometric
projection. The angle between the projection of the axes in an
isometric projection is 120 degrees. However, if a view, showing
any one of the axes as a true length, is taken, the other axes
will always appear perpendicular to it. To appreciate this more
fully observe closely the animated plan, elevation and end-view
of an object shown in the introduction.
If a view is taken looking along the 'X' axis, the 'Z' and 'Y'
axes will appear as true lengths. In this view it is important to
appreciate that the 'X' axis is perpendicular to the 'Z' and 'Y'
axis and perpendicular to the plane on which they lie i.e. the
'ZY' plane.

In orthographic projection
the end-view of an object is projected onto the 'ZY' plane
parallel to the 'X' axis. The 'X' axis is perpendicular to the
plane on which the elevation lies but not perpendicular to the
lines in the elevation.

The axonometric trace 'CB'
lies on the 'ZY' plane. This line is used to rebate the triangle
'BOC' to get its true shape. Once the true shape of this triangle
is established the true end-view is drawn. Lines are drawn from
the axonometric view perpendicular to line 'CB' onto this
triangle. These lines are drawn perpendicular to 'CB' because it
is also on the plane 'ZY' onto which the outline of the end-view
is projected.

How does this help position the traces of the axonometric plane?

Well, the axonometric plane intersects the 'ZX', 'ZY' and 'XY'
planes. When two planes intersect a line is generated known as a
"trace". In an axonometric projection the axonometric
plane intersects the 'ZX' plane leaving a trace which runs from a
point on the 'Z' axis to a point on the 'X' axis e.g. 'AC'. The
'Y' axis will **appear** perpendicular to this line.
The axonometric plane can be positioned anywhere as long as it is
perpendicular to the viewers line of vision. So a line drawn from
any point on the 'Z' axis to some point on the 'X' axis which is
perpendicular to the 'Y' axis is an axonometric trace.
Axonometric trace lines intersect so drawing a line from the
point of intersection on the 'X' axis to some point on the 'Y'
axis and perpendicular to the 'Z' axis gives the second trace of
the axonometric plane in question. The final trace line can now
be obtained following the same procedure as before or by simply
joining the points where the other trace lines intersect the 'Z'
and 'Y' axes. In isometric projection the traces of the
axonometric projection form an equilateral triangle. In dimetric
they form an isosceles triangle and in trimetric they form a
scalene triangle. This information is very useful when
determining what type of axonometric projection has been employed
to generate a drawing.