Mechanical Drawing Self-Taught Part 10

The dotted line 2-1/2 shows the length of the side of a nine-sided polygon, having a radius across corners of 2-1/2 inches. The dotted line 1 shows the diameter, across corners, of a square whose sides measure an inch, and so on.

[Ill.u.s.tration: Fig. 184.]

This scale lacks, however, one element, in that the diameter across the flats of a regular polygon being given, it will not give the diameter across the corners. This, however, we may obtain by a somewhat similar construction. Thus, in Figure 184, draw the line O B, and divide it into inches and parts of an inch. From these points of division draw horizontal lines; from the point O draw the following lines and at the following angles from the horizontal line O P.

[Ill.u.s.tration: Fig. 185.]

A line at 75 for polygons having 12 sides.

" 72 " " 10 "

" 67-1/2 " " 8 "

" 60 " " 6 "

From the point O to the numerals denoting the radius of the polygon is the radius across the flats, while from point O to the horizontal line drawn from those numerals is the radius across corners of the polygon.

[Ill.u.s.tration: Fig. 186.]

A hexagon measures two inches across the flats: what is its diameter measured across the corners? Now from point O to the horizontal line marked 1 inch, measured along the line of 60 degrees, is 1 5-32nds inches: hence the hexagon measures twice that, or 2 5-16ths inches across corners. The proof of the construction is shown in the figure, the hexagon and other polygons being marked simply for clearness of ill.u.s.tration.

[Ill.u.s.tration: Fig. 187.]

[Ill.u.s.tration: Fig. 188.]

Let it be required to draw the stud shown in Figure 185, and the construction would be, for the pencil lines, as shown in Figure 186; line 1 is the centre line, arcs, 2 and 3 give the large, and arcs 4 and 5 the small diameter, to touch which lines 6, 7, 8, and 9 may be drawn.

Lines 10, 11, and 12 are then drawn for the lengths, and it remains to draw the curves in. In drawing these curves great exact.i.tude is required to properly find their centres; nothing looks worse in a drawing than an unfair or uneven junction between curves and straight lines. To find the location for these centres, set the compa.s.ses to the required radius for the curve, and from the point or corner A draw the arcs _b_ and _c_, from _c_ mark the arc _e_, and from _b_ the arc _d_, and where _d_ and _e_ cross is the centre for the curve _f_.

[Ill.u.s.tration: Fig. 189.]

Similarly for the curve _h_, set the compa.s.ses on _i_ and mark the arc _g_, and from the point where it crosses line 6, draw the curve _h_. In inking in it is best to draw in all curves or arcs of circles first, and the straight lines that join them afterward, because, if the straight lines are drawn first, it is a difficult matter to alter the centres of the curves to make them fall true, whereas, after the curves are drawn it is an easy matter, if it should be necessary, to vary the line a trifle, so as to make it join the curves correctly and fair. In inking in these curves also, care must be taken not to draw them too short or too long, as this would impair the appearance very much, as is shown in Figure 187.

[Ill.u.s.tration: Fig. 190.]

[Ill.u.s.tration: Fig. 191.]

To draw the piece shown in Figure 188, the lines are drawn in the order indicated by the letters in Figure 189, the example being given for practice. It is well for the beginner to draw examples of common objects, such as the hand hammer in Figure 190, or the chuck plate in Figure 191, which afford good examples in the drawing of arcs and circles.

In Figure 191 _a_ is a cap nut, and the order in which the same would be pencilled in is indicated by the respective numerals. The circles 3 and 4 represent the thread.

[Ill.u.s.tration: Fig. 191 _a_.]

In Figure 192 is shown the pencilling for a link having the hubs on one side only, so that a centre line is unnecessary on the edge view, as all the lengths are derived from the top view, while the thickness of the stem and height of the hubs may be measured from the line A. In Figure 193 there are hubs (on both sides of the link) of unequal height, hence a centre line is necessary in both views, and from this line all measurements should be marked.

[Ill.u.s.tration: Fig. 192.]

[Ill.u.s.tration: Fig. 193.]

In Figure 194 are represented the pencil lines for a double eye or knuckle joint, as it is sometimes termed, an example that it is desirable for the student to draw in various sizes, as it is representative of a large cla.s.s of work.

These eyes often have an offset, and an example of this is given in Figure 195, in which A is the centre line for the stem distant from the centre line B of the eyes to the amount of offset required.

[Ill.u.s.tration: Fig. 194.]

[Ill.u.s.tration: Fig. 195.]

[Ill.u.s.tration: Fig. 196.]

[Ill.u.s.tration: Fig. 197.]

In Figure 196 is an example of a connecting rod end. From a point, as A, we draw arcs, as B C for the width, and E D for the length of the block, and through A we draw the centre line. It is obvious, however, that we may draw the centre line first, and apply the measuring rule direct to the paper, and mark lines in place of the arcs B, C, D, E, and F, G, which are for the stem. As the block joins the stem in a straight line, the latter is evidently rectangular, as will be seen by referring to Figure 197, which represents a rod end with a round stem, the fact that the stem is round being clearly shown by the curves A B. The radius of these curves is obtained as follows: It is obvious that they will join the rod stem at the same point as the shoulder curves do, as denoted by the dotted vertical line. So likewise they join the curves E F at the same point in the rod length as the shoulder curves, both curves in fact being formed by the same round corner or shoulder. The centre of the radius of A or B must therefore be the same distance from the centre of the rod as is the centre from which the shoulder curve is struck, and at the same time at such a distance from the corner (as E or F) that the curve will meet the centre line of the rod at the same point in its length as the shoulder curves do.

[Ill.u.s.tration: Fig. 198.]

Figure 198 gives an example, in which the similar curved lines show that a part is square. The figure represents a bolt with a square under the head. As but one view is given, that fact alone tells us that it must be round or square. Now we might mark a cross on the square part, to denote that it is square; but this is unnecessary, because the curves F G show such to be the case. These curves are marked as follows: With the compa.s.ses set to the radius E, one point is rested at A, and arc B is drawn; then one point of the compa.s.s is rested at C, and arc D is drawn; giving the centre for the curve F by a similar process on the other side of the figure, curve G is drawn. Point C is obtained by drawing the dotted line across where the outline curve meets the stem. Suppose that the corner where the round stem meets the square under the head was a sharp one instead of a curve, then the traditional cross would require to be put on the square, as in Figure 199; or the cross will be necessary if the corner be a round one, if the stem is reduced in diameter, as in Figure 200.

[Ill.u.s.tration: Fig. 199.]

[Ill.u.s.tration: Fig. 200.]

[Ill.u.s.tration: Fig. 201.]

Figure 201 represents a centre punch, giving an example, in which the flat sides gradually run out upon a circle, the edges forming curves, as at A, B, etc. The length of these curves is determined as follows: They must begin where the taper of the punch joins the parallel, or at C, C, and they must end on that part of the taper stem where the diameter is equal to the diameter across the flats of the octagon. All that is to be done then is to find the diameter across the flats on the end view, and mark it on the taper stem, as at D, D, which will show where the flats terminate on the taper stem. And the curved lines, as A, B, may be drawn in by a curve that must meet at the line C, and also in a rounded point at line D.

CHAPTER VIII.

_SCREW THREADS AND SPIRALS._

[Ill.u.s.tration: Fig. 202.]

[Ill.u.s.tration: Fig. 203.]

The screw thread for small bolts is represented by thick and thin lines, such as was shown in Figure 152, but in larger sizes; the angles of the thread also are drawn in, as in Figure 202, and the method of doing this is shown in Figure 203. The centre line 1 and lines 2 and 3 for the full diameter of the thread being drawn, set the compa.s.ses to the required pitch of the thread, and stepping along line 2, mark the arcs 4, 5, 6, etc., for the full length the thread is to be marked. With the triangle resting against the $T$-square, the lines 7, 8, 9, etc. (for the full length of the thread), are drawn from the points 4, 5, 6, on line 2.

These give one side of the thread. Reversing the drawing triangle, angles 10, 11, etc., are then drawn, which will complete the outline of the thread at the top of the bolt. We may now mark the depth of the thread by drawing line 12, and with the compa.s.ses set on the centre line transfer this depth to the other side of the bolt, as denoted by the arcs 13 and 14. Touching arc 14 we mark line 15 for the thread depth on that side. We have now to get the slant of the thread across the bolt.

It is obvious that in pa.s.sing once around the bolt the thread advances to the amount of the pitch as from _a_ to _b_; hence, in pa.s.sing half way around, it will advance from _a_ to _c_; we therefore draw line 16 at a right-angle to the centre line, and a line that touches the top of the threads at _a_, where it meets line 2, and also meets line 16, where it touches line 3, is the angle or slope for the tops of the threads, which may be drawn across by lines, as 18, 19, 20, etc. From these lines the sides of the thread may be drawn at the bottom of the bolt, marking first the angle on one side, as by lines 21, 22, 23, etc., and then the angles on the other, as by lines 24, 25, etc.

[Ill.u.s.tration: Fig. 204.]

There now remain the bottoms of the thread to draw, and this is done by drawing lines from the bottom of the thread on one side of the bolt to the bottom on the other, as shown in the cut by a dotted line; hence, we may set a square blade to that angle, and mark in these lines, as 26, 27, 28, etc., and the thread is pencilled in complete.

If the student will follow out this example upon paper, it will appear to him that after the thread had been marked out on one side of the bolt, the angle of the thread might be obtained, as shown by lines 16 and 17, and that the bottoms of the thread as well as the tops might be carried across the bolt to the other side. Figure 204 represents a case in which this has been done, and it will be observed that the lines denoting the bottom of the thread do not meet the bottoms of the thread, which occurs for the reason that the angle for the bottom is not the same as that for the top of the thread.

[Ill.u.s.tration: Fig. 205.]

[Ill.u.s.tration: Fig. 206.]

In inking in the thread, it enhances the appearance to give the bottom of the thread and the right-hand side of the same, heavy shade lines, as in Figure 202, a plan that is usually adopted for threads of large diameter and coa.r.s.e pitch.