Axonometric projections THEME 9 Introduction Axonometric projecting

Axonometric projections THEME 9

Introduction Axonometric projecting is the method when an object with respective orthogonal planes is projected on the new plane that is termed as perspective plane. When the direction of projecting is perpendicular to the perspective plane, the obtained projections termed as “orthogonal axonometric projections”. In the other cases, the obtained projections termed as “oblique axonometric projections”.

Introduction The position of the perspective plane may be oriented respective to the coordinate system when measures of axonometric axes will be equal to each other or two of them will be equal. When distortion coefficients of all axes will be equal to each other, the axonometric projection called “isometric projection”. When two distortion coefficients of axes are equal the axonometric projection called “diametric projection”, and when all coefficients are different – “trimetric projection”.

Isometric projection All axes are produced the same angles are equal to 120°, and OZ axis is vertically oriented. Distortion coefficients of the axes are equal to 0, 82 but isometric projections are drawn without any distortion and distortion coefficients are established as 1. The image of an object obtained by isometric projection is large than real object in 1, 22 times.

Isometric projection of the circle is an ellipse, but for simplification of the drawing oval is used instead of ellipse.

Diametric projection The angle of OX axis (7° 10ʹ) may be obtained by right-angle triangle drawing with ratio of cathetus length as 1: 8 units, and the angle OY (41° 25ʹ) – by right-angle triangle drawing with ratio of cathetus length as 7: 8 units. Distortion coefficient of Y-axis is equal to 0, 47 and the similar coefficients for X and Z axes are equal to 0, 94. Diametrical projecting usually drawn without distortion on X and Z axes (Kx=Kz=1), and using of coefficient KY=0, 5 for Y axis.

Diametric projections of the circle are ellipses, but for simplification of the drawing ovals are used instead of ellipses.

Oblique frontal diametric projection It is allowed to use the oblique frontal diametric projections with inclination angle of OY-axis like 30° and 60°. Distortion coefficient of OY-axis is equal to 0, 5 and these coefficients for X and Z axes are equal to 1.

Hatching of the isometric projections Lines of hatching on sections or section views that are represented on axonometric plane must be parallel to one of the square diagonals which are placed on the respective coordinate planes. Sides of that square must be parallel to the coordinate axes.

Hatching of the diametric projection

Hatching of the oblique frontal projection