Nearly all isometric drawings are made with the 30-60 triangle, and most of them are done in angular "perspective" where the two sides make an angle of 120 degrees with each other and 30 degrees with the horizontal. In isometrics all sides that are parallel stay parallel and will not vanish to a vanishing point if prolonged. There are neither vanishing points nor foreshortening in isometric drawing. The difference between true perspective and isometric drawing is shown in the diagram, Figure 34, where A is the perspective of a block and B is the isometric drawing of it.

The three vertical edges a, b, and c of the block are called isometric axes, and all lines parallel to these edges are called isometric lines. Measurements can be made on the main isometric axis (b) only, for all other lines are inaccurate because they are not in true perspective. You can see why this is so if you consider the perspective drawings we have just been discussing. In the true perspective, we had the projection of all lines from a plan to a point S until they met the picture plane and were brought down parallel to the measuring line. This produced a definite foreshortening in the spacing on the lines which go off to the two vanishing points—equal divisions get closer together as they approach the vanishing point. In isometric drawing there are no vanishing points, and consequently there is no foreshortening. This is shown clearly in Figure 35 where C is the perspective and D the isometric drawing of the same thing.

While isometrics are ideal for objects whose lengths are not too great when compared with their widths, they are not as satisfactory for long objects which are very narrow. The main purpose of isometrics is to show, in the least possible time and with the least amount of effort, what three sides of an object look like. This they do very well. Nobody would ever think of going to the trouble of drawing a projected perspective of a machine part or a small object from which a working drawing is to be made. It would be totally unnecessary because an isometric drawing, properly dimensioned, will give the picture just as clearly in about one-tenth the time. If you examine the so-called perspectives shown in the working · drawing problems, you will see how simple they are and how well they show the three faces of the object without the necessity of picture planes, measuring lines and vanishing points. They are all isometric drawings.

Figure 36 shows the beginning of an isometric drawing. The 30-60 triangle is placed in the position 1, and a line drawn to the left. It is then turned around to the position 2, and another line is drawn to the right. These two lines meet at an angle of 120 degrees, and each is 30 degrees with the horizontal. They form the base of the isometric. Figure 37 shows the various steps in the completion of an isometric. After the base lines are drawn, the main isometric axis and the two vertical edges are penciled in as shown in number 3. The given distance is now measured on this main axis; two more sloping lines are drawn through the extremity of this distance, these lines being parallel to the two base lines as shown in number 4. The other two top lines are now drawn, as shown in 5, and the completed figure is shown in 6. The object in this figure is a cube; hence, the two outside vertical edges are equidistant from the main axis. If the object were a brick, one edge would be much further from the main axis than the other, either to the right or the left of the main axis as shown in Figure 38.

Pyramids, cylinders, prisms and odd-shaped articles may be drawn isometrically by enclosing them first in isometric "blocks" and erasing this block when the article is inked in. Note how the octagonal prism, the hexagonal pyramid and the cylinder are drawn isometrically from the working drawings shown on the opposite page. Note how the isometric block, drawn just the way you drew the first block, encloses these three solids; observe the result when these blocks are erased. Most machine parts may be drawn in this fashion.

A circle in isometric will always be an ellipse. Figure 39 shows the standard way of doing this. The rhombus ACBD is first drawn where AC and AD are the isometric base lines at 30 degrees with the horizontal, and 120 degrees with each other; BC and BD are parallel to AD and AC respectively. With your 60 degree angle of the 30-60 triangle, draw through the points A and B the lines AE, AF and BG and BH. These lines intersect at O and O', and these two points are the centers of the two circular arcs which form the left and right end of the ellipse. The points A and B are the centers of circular arcs which form the top and bottom of the ellipse. This type of ellipse has already been discussed, but this particular one should be used entirely for drawing tops and bottoms of cylinders in isometric. As all circular objects such as holes, shafts, axles, and cylinder ends become this ellipse in isometric drawing, it is important that you be thoroughly acquainted with it. Know how to draw the ellipse in any size. Practice drawing it over and over again, because you will meet it many times in mechanical drawing.

The ellipse which we just discussed has its major axis horizontal. There are two other ellipses in isometric drawing: one with its major axis inclined 60 degrees to the right side of the horizontal line, and the other with its major axis inclined 60 degrees to the left side of the horizontal line. These two are drawn in the same general way. A study of Figure 40 will enable you to see just how to construct them.

On the next page we show how to draw isometrics from a number of simple working drawings. Study these carefully and then try to draw them for yourself.

 

MAKING ISOMETRIC DRAWINGS

Since the main guide lines in all isometric drawings are either vertical, horizontal or at angles of 30 degrees with the horizontal, special isometric paper can be bought at any good instrument supply store. This paper is ruled vertically, horizontally and at 30-degree angles, and it is usually printed in light green ink because green will not reproduce. The draftsman can draw in the isometric, using the guide lines; when his drawing is reproduced the guide lines disappear. On page 86 we see a sample of this paper with two isometric drawings already inked in. Let us examine these drawings to see how useful the guide lines of the paper really are.

If you will refer to page 84, you will see six shop drawings from which you are to make isometrics. Drawing 1 is of an ordinary brick-like object and is shown laid out on the isometric paper. Note the dimensions of this brick—2 x 4 x 8 inches. Note that each sloping line is an inch on the isometric paper. You can also see how the simple brick is laid out with its front of 8 inches sloping to the left, its end of 2 inches sloping to the right and its height of 4 inches sloping vertically. You can readily see how simple this isometric paper makes the drawing of isometrics. The second shop drawing is of a gadget with all its dimensions given. This is also drawn for you on the isometric paper. Study it carefully and see how the guide lines help you in laying out the drawing. In every case, each space on the paper, whether vertical, horizontal or at the 30-degree angle, represents one inch. The ellipses may be drawn in by hand without the use of the compass.

Now, using the isometric paper, it is up to you to draw isometrics of the other four shop drawings. Sketch them in in pencil first and make sure that all the lines are correct before you ink them. After you have done these shop drawings, get yourself a dozen sheets of the isometric paper (you can order it from the Keuffel & Esser Co. in Hoboken, N. J., if you can't buy it in a local shop), and practice drawing isometrics of the shop drawings given elsewhere in this book.

Of course isometric paper is really made for the beginner. After you have become proficient in its use, you should learn to do without it because you may not always be able to obtain a supply when you most want it.

One final word: don't get discouraged if you find isometric drawing difficult at first. It is difficult until you "get the hang of it." Just keep on practicing and studying until you have convinced yourself that you understand it. It is very important to be able to make isometrics from shop drawings even if you can only do them free-hand. It is essential that you understand the general principle.

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