Figure 6.1 shows three views of a cube in orthographic
projection; the phantom line indicates the original
position of the cube, and the full line indicates the
position after rotation about the diagonal AB. The cube
has been rotated so that the angle of 45° between side
AC1 and diagonal AB now appears to be 30° in the
front elevation, C1 having been rotated to position C.
It can clearly be seen in the end view that to obtain
this result the angle of rotation is greater than 30°.
Also, note that, although DF in the front elevation
appears to be vertical, a cross check with the end
elevation will confirm that the line slopes, and that
point F lies to the rear of point D. However, the front
elevation now shows a three dimensional view, and
when taken in isolation it is known as an isometric
projection.
This type of view is commonly used in pictorial
presentations, for example in car and motor-cycle service
manuals and model kits, where an assembly has been
‘exploded’ to indicate the correct order and position of
the component parts.
It will be noted that, in the isometric cube, line AC1
is drawn as line AC, and the length of the line is reduced.
Figure 6.2 shows an isometric scale which in principle
is obtained from lines at 45° and 30° to a horizontal
axis. The 45° line XY is calibrated in millimetres
commencing from point X, and the dimensions are
projected vertically on to the line XZ. By similar
triangles, all dimensions are reduced by the same
amount, and isometric lengths can be measured from
point X when required. The reduction in length is in
the ratio
isometric length
true length
= cos 45
cos 30
= 0.7071
0.8660
= 0.8165 °°
Now, to reduce the length of each line by the use of an
isometric scale is an interesting academic exercise,
but commercially an isometric projection would be
drawn using the true dimensions and would then be
enlarged or reduced to the size required.
Note that, in the isometric projection, lines AE and
DB are equal in length to line AD; hence an equal
reduction in length takes place along the apparent
vertical and the two axes at 30° to the horizontal. Note
also that the length of the diagonal AB does not change
from orthographic to isometric, but that of diagonal
C1D1 clearly does. When setting out an isometric
projection, therefore, measurements must be made only
along the isometric axes EF, DF, and GF.
Figure 6.3 shows a wedge which has been produced
from a solid cylinder, and dimensions A, B, and C
indicate typical measurements to be taken along the
principal axes when setting out the isometric projection.
Any curve can be produced by plotting a succession of
points in space after taking ordinates from the X, Y,
and Z axes.
Figure 6.4(a) shows a cross-section through an extruded
alloy bar: the views (b), (c), and (d) give alternative
isometric presentations drawn in the three principal
planes of projection. In every case, the lengths of
ordinates OP, OQ, P1, and Q2, etc. are the same, but
are positioned either vertically or inclined at 30° to
the horizontal.
Figure 6.5 shows an approximate method for the
construction of isometric circles in each of the three
major planes. Note the position of the points of
intersection of radii RA and RB.
The construction shown in Fig. 6.5 can be used
partly for producing corner radii. Fig. 6.6 shows a
small block with radiused corners together with
isometric projection which emphasises the construction
to find the centres for the corner radii; this should be
the first part of the drawing to be attempted. The
thickness of the block is obtained from projecting back
these radii a distance equal to the block thickness and
at 30°. Line in those parts of the corners visible behind
the front face, and complete the pictorial view by adding
the connecting straight lines for the outside of the profile.
In the approximate construction shown, a small
inaccuracy occurs along the major axis of the ellipse,
and Fig. 6.7 shows the extent of the error in conjunction
with a plotted circle. In the vast majority of applications
where complete but small circles are used, for example
spindles, pins, parts of nuts, bolts, and fixing holes,
this error is of little importance and can be neglected.
Manual of
Engineering Drawing
Second edition
Colin H Simmons
I.Eng, FIED, Mem ASME.
Engineering Standards Consultant
Member of BS. & ISO Committees dealing with
Technical Product Documentation specifications
Formerly Standards Engineer, Lucas CAV.
Dennis E Maguire
CEng. MIMechE, Mem ASME, R.Eng.Des, MIED
Design Consultant
Formerly Senior Lecturer, Mechanical and
Production Engineering Department, Southall College
of Technology
City & Guilds International Chief Examiner in
Engineering Drawing
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