Introduction
The term axonometric projection
includes four types of pictorial drawing.
These are as follows:
(a) Isometric Projection
*
(b) Dimetric Projection
**
(c) Trimetric Projection
***
(d)Oblique Axonometric
Projection
The first three of the above,
namely Isometric, Dimetric and Trimetric Projections are categorised as
Orthogonal Axonometric Projections because the projectors from the object
are perpendicular to the plane of projection.
Orthogonal Axonometric
Projection is in fact classified as Orthographic Projection.
The following definition establishes this relationship:
Definition: "Orthographic projection is a system of views of an object formed by projectors from the object perpendicular to the desired planes of projection".
Elevations and Plan views
are the "regular" orthographic projections, whereas Isometric, Dimetric
and Trimetric projections are pictorial projections.
Pictorial projections show
several faces of an object at once, approximately as they appear to the
observer.
Figure 2 below shows the
following:
1. Draw projections of coordinate
axes as shown in Figure 3. (120° between each)
2. Draw trace triangle ABC (equilateral) as shown in Figure 4. BC at right angles to Xaxis AC at right angles to Yaxis AB at right angles to Zaxis
3. Draw development of planes
of reference. (Note application of the angle in a semicircle).
4. Draw any two of the orthographic views. In the case of the elevation, the view should be drawn with the edges respectively parallel to the lines o¹a¹ and o¹c¹. In the case of the end elevation, the view should be drawn with the edges respectively parallel to the lines o¹b¹ and o¹c¹. In the case of the plan,
the view should be drawn with the edges respectively parallel to the lines
o¹a¹ and o¹b¹.
6. The intersections of these projectors will yield points on the axonometric (isometric) projection.


Stages involved in constructing
a dimetric projection**
1. Draw projections of
coordinate axes. (two angles between axes equal and over 90°)
2. Draw trace triangle
ABC. (isosceles)
36. As before.
Stages involved in constructing
a trimetric projection***
1. Draw projections of
coordinate axes. (all three angles unequal and not less than 90°)
2. Draw trace triangle
ABC. (scalene)
36. As before.
Definitions:
* "An isometric projection
is an axonometric projection of an object so placed that all three of its
axes make equal angles with the plane of projection. Hence, the three axes
are foreshortened equally". (isometric means "of equal measure")
** "A dimetric projection is an axonometric projection of an object so placed that two of its axes make equal angles with the plane of projection and the third axis makes either a smaller or a greater angle. Hence, the two axes making equal angles with the plane of projection are foreshortened equally, while the third axis is foreshortened in a different ratio".
*** "A trimetric projection is an axonometric projection of an object so placed that no two axes make equal angles with the plane of projection. In other words, each of the three axes and the lines parallel to them, respectively, have different ratios of foreshortening when projected to the plane of projection".
References:
Engineering Graphics
Graphics for Engineers
Giesecke & Others
O'Bryant & Dobrovolny
Macmillan Publishers
Stipes Publishing Co.
ISBN 0129463262
ISBN 0875633617