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0
projection. . Thus the plane П, which an object is designed on, is called axonometric, and
projections on it axes of 0х, 0у, 0z is called axonometric axes. The size of corner between them
0
depends on the direction of planning and the position of a plane П according to the axes of х, y, z .
The main positions of parallel projections are also used for axonometric projections : the
axonometric projections of parallel lines are parallel between themselves; even segments which
belong to the parallel lines are designed in even segments; if a point divides a segment in a certain
correlation, its an axonometric projection divides the axonometric projection of cutting-off in that
correlation. Segments on the axes of coordinates of х, y, z are designed generally with distortion.
The sizes of projected objects are also distorted. The coefficients (indexes) of the distortion on axes
equal the attitude of axonometric co-ordinates (on a drawing) toward natural (on an object).
Depending on the direction of projected rays axonometric projections are divided into rectangular
and oblique-angled. Axonometric projections are called rectangular, if a corner between projected

0
rays and a plane of П is equal 90. Axonometric projections are called oblique-angled, if a corner
0
between projected rays and plane of П less than from a direct corner. Depending on the distortion
of linear sizes of an object along axes axonometric projections are divided into isometry and
dimetry. State standard 2.317-69 recommends to use two types of rectangular axonometric
projections – isometry (figure 3.3) and dimetry (figure 3.4) and three types of oblique-angled
axonometric projections – frontal isometry (figure 3.5), horizontal isometry (figure 3.6) and frontal
dimetry (figure 3.7).

3.2 TYPES OF AXONOMETRY
3.2.1 RECTANGULAR ISOMETRIC PROJECTION

Izometry is a axonometric projection with the equal indexes of distortion for all three axes.
Figure 3.3,а shows a sphere in a rectangular isometric projection the diameter of which equals a
metage. A corner between axes is 120. Place this sphere into a cube ribs of which, also equal to the
direction of axonometric axes (see fig. 3.3,b). Project a sphere on the verge of cube. Such type of
planning is called American. The projections of the sphere on the verge of a cube are smaller in size
(disfigured). That segment of coordinate ax long 1 mm in rectangular izometry will be represented
the segment of axonometric ax long 0,82 mm. Correlation 1 / 0,82=1,22 times determines a
coefficient down-scaling on which we increase the sphere (see figure 3.3,c). Now the projections of
the sphere as ellipses are inscribed in the verge of a cube (see figure 3.3,d). The major ax of ellipse
makes 1,22 diameter – D of a projection circle of the sphere (equator, frontal meridian, type
meridian), and minor axis – 0,71 diameter. Place a sphere in the usual (europian) first angle
projection method. Figure 3.3,e shows the correlation for determination of length of cuttings-off of
major [AB] and minor [CD] axes of ellipses. Sizes of cuttings-off [1, 2] and [3, 4] equal the
diameter of projected circle of a sphere, and in general case the diameter of a cylinder or a hole on a
figure. While making of quaternary cuts in rectangular izometry follow to the rules resulted of
hatching as shown in fig.3.3,f. Stroke lines are drawn parallell to the axonometric axes.

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