ON THE ADVANTAGES OF THE ARRANGEMENT OF PROJECTIONS IN DRAWINGS ADOPTED IN THE USSR

L. S. SKRIPOV

(Presented by the scientific seminar of the departments of descriptive geometry of Tomsk higher educational institutions)

The question of how it is more convenient to arrange projections in drawings—according to the European method or the American method—still interests everyone dealing with drawings, and a number of articles on this subject appear both in our journals and in foreign ones.

When representing an object in orthogonal projections, it may be placed either in the first angle of space, or in the seventh angle (or in the third, in the American direction of the axes of projection) (Fig. 1).

In one of the journals [1] there appeared an article by Dr. N. Abbott devoted to the same question, showing that abroad as well the question of the arrangement of projections has not been definitively resolved.

The usual method of arranging projections, adopted in European countries, assumes the placement of the object being projected in the first angle of space (Fig. 1), in which the planes of projection are located behind the object under consideration. In England this system was put forward by the British Standards Institution only in 1927. However, not so long ago the same institute also recommended as standard another system of arrangement, obtained by placing the object under consideration in the third angle of space (according to the English arrangement) or in the seventh—according to the European arrangement of angles.

Fig. 1.

The system of the “third angle of space” is adopted in the USA, and in this case the planes of projection are situated between the object and the observer.

It is useful to consider the merits of these two systems not only from the point of view of the execution of drawings, but also from the point of view of their educational significance, especially in the study of descriptive geometry.

The method of projection onto mutually perpendicular planes of projection (with the planes unfolded) was proposed by Gaspard Monge [2] in 1795, and in practice he used only the first angle of space (Fig. 2).

Figure 3 shows the arrangements of the views of an object with the planes unfolded.

Fig. 2.            Fig. 3.

It follows from Fig. 3 that the “view from the left” (side view) may have two positions, one of which is shown by solid lines and the other by dashed lines, when the profile plane is rotated about the axis \(OY\).

If the object is placed in the VII angle of space (Fig. 4), then, in the unfolded position of the planes, the views are arranged as shown in Fig. 5.

Fig. 4.            Fig. 5.

Figure 5 also shows two cases of the arrangement of the “view from the left”—by dashed lines—when the profile plane is rotated about the axis \(OY\).

When one of the projection planes is replaced (for example, the “horizontal” plane in Fig. 6), the arrangement of the views on the unfolded projection planes is shown in Fig. 7 in the I angle of space.

Fig. 6.            Fig. 7.

In the case of using the VII angle of space, the arrangement of views is shown in Figs. 8 and 9.

The process of finding the “new” third view is carried out automatically according to the rules of descriptive geometry set forth in the section “Methods of Replacing Projection Planes.”

Fig. 8.          Fig. 9.

When projecting simple bodies, the dispute as to which of the systems of arranging the object—in the I or in the VII angles of space—is preferable is useless, since both cases are possible and natural, and both have their advantages and disadvantages. Those persons who find that preference should be given to the method of arranging the object behind transparent planes must agree that it would be more natural to mark the arrangement of furnishings in rooms or of equipment in workshops on the floor, as on the projection plane, and not on the ceiling (in the VII angle of space).

Those who consider the method of projection in the I angle of space the most convenient must likewise acknowledge the inconvenience of this system in the case where the object is very long and its view (for example, from the front) may be very far removed from the side that is being projected (the front side).

For those persons who cannot easily read drawings, training in the spatial representation of an object is required, no matter by what method it has been projected in the drawings.

However, when two systems of projection are in use (the I and VII angles of space), there is always the danger of an erroneous spatial representation of the object when only two views are given without indicating in which system they are depicted.

Such a case is presented in Fig. 10a, from which one may imagine a construction such as that shown in Fig. 10b, or one such as in Fig. 10c.

Fig. 10.

Thus, the unified system of projection in our country, approved by the GOST standard, is undoubtedly free of any erroneous interpretations, as may occur in England or the USA.

In application to the study of projections in the course of descriptive geometry, the contradictions between the two systems of projection are accommodated less satisfactorily. Questions arise: should both systems be expounded in descriptive geometry when solving its problems, or should the exposition of the laws-

of projections in descriptive geometry to conduct only in one system (for example, in the first angle of space), while in mechanical-engineering drawing to use another as well.

For a correct resolution of the question, one should examine the use of both systems on examples from descriptive geometry, at least those concerning points, lines, and planes.

In courses of analytic geometry in space, such problems are customarily solved in the first angle of space, assigning to the coordinate axes a positive direction in it. This tradition was also adopted by Monge in his theory of descriptive geometry.

Usually the solution of problems in descriptive geometry is first carried out on pictorial drawings, and only then repeated on the orthogonal épure, which is generally understood with greater difficulty.

If the seventh angle of space is used for such a method, then the pictorial quality and clarity are already considerably reduced, as may be seen from the following examples.

Example. Given a segment of the straight line \(AB\) (Fig. 11) by its projections \(ab\), \(a'b'\), it is required to determine:

1) the true length of the segment \(L\),
2) the angles of inclination \(\theta\) and \(\varphi\) of the straight line to the projection planes,
3) the traces of the straight line \(AB\) on the projection planes.

The spatial solution of the problem is presented in Fig. 11 in the first angle of space, and the planar one—on the épure (Fig. 12). The solution is entirely clear and requires no explanation. The solution of the same problem in the seventh angle of space is shown in Figs. 13 and 14.

Fig. 11.

Fig. 12.

Fig. 13.

Fig. 14.

A comparison of drawings 11 and 13, 12 and 14 cannot fully convince the reader that solving the problem in the first angle is preferable to solving it in the seventh angle.

The results will be clearer in the case of a more complex problem.

If we consider more complex problems—for example, finding the shortest distance between two given skew lines—then the spatial pictorial view in the seventh angle of projection becomes extremely confused. It should be noted that American textbooks on descriptive geometry, which set forth the laws of descriptive geometry in the seventh angle of space, avoid the use of pictorial “spatial” solutions, thereby acknowledging the inconvenience of the adopted system. Thus, the following conclusions may be drawn:

1. Technical drawings must always be clearly readable and unambiguous.

2. Both projection systems (in the first or seventh angles of space) will satisfy this requirement, provided that the drawings are supplied with the necessary explanations in cases of ambiguity.

3. In orthogonal plane drawings, neither system has any particular advantages over the other.

4. When pictorial representations are used in courses of descriptive geometry to solve its problems together with orthogonal plane drawings, the undoubted advantage lies with the system of the first angle of space.

5. The unified projection system adopted in the USSR (the first angle of space) is free from all the above-mentioned shortcomings and necessary reservations in comparison with the American projection system, and possesses an unquestionable advantage over the American one.

REFERENCES

1. The journal Engineering, No. 4358, 5.08.1949.
2. G. Monge, Descriptive Geometry. Publishing House of the Academy of Sciences of the USSR, 1947.