76. Types of axonometric projections

Axonometric projections, depending on the direction of projection, are divided into:

skew when the direction of projection is not perpendicular to the plane of axonometric projections;

rectangular, when the direction of projection is perpendicular to the plane of axonometric projections.

Depending on the relative magnitude of the distortion coefficients along the axes, there are three types of axonometry:

isometry - all three distortion coefficients are equal to each other (u = v = w);

Dimetry - two distortion coefficients are equal to each other and differ from the third (and not equal to v = w or and = v not equal to w);

trimetry - all three distortion factors are not equal to each other (u is not equal to v is not equal to w).

The main offer of axonometry was formulated by the German geometer K. Polka: three arbitrary lengths of a line segment lying in the same plane and emerging from a single point at arbitrary angles to each other, represent a parallel projection of three equal segments laid out on rectangular coordinate axes from the beginning.

According to this theorem, any three straight lines in a plane, outgoing from one point and not coinciding with each other, can be taken as axonometric axes. Any arbitrary length segments of these lines, pending from the point of their intersection, can be taken for axonometric scales.

This system of axonometric axes and scales is a parallel projection of some rectangular coordinate system

axes and natural scales, i.e., axonometric scales can be given out quite arbitrarily, and the distortion coefficients are related by the following relationship: u ² + v ² = w ² = 2 + ctg ² (p, where ф is the angle between the direction of projection and the plane of axonometric projections (Fig. 156). For a rectangular axonometry, when ф = 90 °, this ratio takes the form ² + v ² + w ² = 2 (1), that is, the sum of the squares of the distortion coefficient is two.

With a rectangular projection, only one isometric projection and an infinite number of dimetric and trimetric projections can be obtained. GOST 2.317-69 provides for the use in engineering graphics of two rectangular axonometries: rectangular isometry and rectangular dimetry with distortion coefficients and = w = 2v.