The fundamental theory is rooted in the principles of solid geometry and need not concern us. The basic idea, so far as drawing is concerned, is that there are three planes mutually at right angles, like the sides of a box. The views are projected onto these planes which are then developed or opened out into a flat sheet - the paper we draw on.
In first angle projection, Fig. 89, the object with faces A, B and C visible, is imagined to be suspended inside such a box. Three of the sides are shown, one on each of the three planes OX, OY and OZ. The object is viewed in three directions at right angles -1 have shown a sketched eye and an arrow to indicate these directions of view. The image behind the object is then drawn on the plane behind it; the projection lines from object to plane run in the same direction as the lines of sight. Once all the views have been drawn on the inside of the imaginary box this is cut open and laid flat, as shown at (b). The relative positions of the three views is thus fixed by the projection convention used. The plan lies below the main elevation, and the eye follows the projection lines in that direction. Similarly for all other views. You will see that view of B seen in (b) is exactly what you would see if the object at A had been
turned through 90 degrees - the first right angle. For a complete orthographic projection we should use all six sides of the box, producing six views in all. In third angle projection, Fig. 90, the object is imagined to be suspended within a transparent box, as shown at (a). The three planes OX, OY and OZ are the same, but the relationship between OY and OZ has changed. Look at the little diagram (c). ZOY forms one right angle - the first, and YOZ' forms another -the second. The third right angle is formed by Z'OY'. The imaginary box is formed round these last two planes, hence the term third angle.
I have again shown sketches of eyes and arrows to show the direction of sight, but this time the image is drawn on the face of the transparent plane, between the eye and the object. The line of projection runs opposite to the line of sight. Hence you see the face D on Z'OY' - compare with Fig. 89.
When the box is opened out we find the views disposed as shown at (b). The plan is now above the main elevation and you can see that to get the face C into that position from the elevation the object must be rotated through three right angles. Again, a complete projection would form six views.
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