Using parallel projection, which was discussed in Ch. 1, one of the types of visual images of objects is obtained - axonometric projections.
Axonometric projections are obtained if the imaged object, together with the coordinate axes to which it is assigned, is projected by means of parallel beams onto a single plane, called axonometric (Figure 3.3).
The word & quot; axonometry & quot; - Greek. It consists of two words: & quot; ahsop & quot; - axis and & quot; metro & quot; - I measure. The translation of this word means measuring along the axes, or measuring parallel to the axes, since the dimensions of the represented object in the drawing are laid only parallel to the axes x, y, z, called the axonometric coordinate axes.
Axonometric projections are used to explain the drawings of machines, mechanisms and their parts. This can be seen from a comparison of a drawing containing three types of parallelepiped with slices (Figure 3.1, a ), with its axonometric projection (Fig. 3.1, 6 ). Without axonometric projection, it is more difficult to represent the shape of the depicted object.
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Fig. 3.1. Comparison of the drawing in three views and the axonometric projection
On the basis of axonometric projections, technical drawings are performed.
Depending on the inclination of the axes of coordinates to which the depicted object is related, to the axonometric plane and the angle made up by the projecting rays with this plane, different axonometric projections are formed. If the projecting rays are perpendicular to the picture plane, then the projection is called rectangular. If the projecting rays are inclined to it, then the projection is called oblique. We will consider the following types of axonometric projections recommended by GOST 2.317-2011: from oblique - the frontal dimetric (Figure 3.2, a ), from rectangular - isometric (Figure 3.2, 6 ) and the dimetric one (Figure 3.2, c).
Fig. 3.2. Different types of axonometric projections
Frontal Dimensional Projection
Formation of frontal dimetric projection
In Fig. 3.3 shows the formation of frontal dimetric projection. A cube with coordinate axes x0, y 0, z0 is located in front of the plane so that its front and back faces are parallel to it. Projecting the cube with parallel rays directed at an acute angle to the axonometric plane P, we obtain on it the image of the cube and the axes x, y, z in the frontal dimetric projection.
Fig. 3.3. Formation of the frontal dimetric projection
The construction of the frontal dimetric projection begins with the tracing of the axonometric axes x, y, z, which are located, as shown in Fig. 3.4, at certain angles and proceed from one point O - the origin of the axonometric coordinates. One of the axes is located horizontally and is denoted by the Latin letter x, the second is directed vertically upwards and is denoted by the letter z, the third passes at an angle of 45 ° to the horizontal axis and is denoted by the letter y . To draw an axis at an angle of 45 °, it is enough to divide the square cell of the school notebook diagonally, if the axonometric projection is performed on paper, lined in a cage. This axis can be drawn by dividing the angle 90 ° in half by a compass and a ruler, or by using an isosceles triangle with angles of 45 °.
Fig. 3.4. Location of the axes in the frontal dimetric projection
In the direction of the axes x and z postpone the true dimensions of the object. Dimensions along the y axis and directions parallel to it are cut by half. This corresponds to an apparent shortening of the length beyond the items of objects that are from us.
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