_SCREW THREADS AND SPIRALS._
[Illustration: Fig. 202.]
[Illustration: 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 compasses 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 compasses 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 passing once around the bolt the thread advances
to the amount of the pitch as from _a_ to _b_; hence, in passing 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.
[Illustration: 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.
[Illustration: Fig. 205.]
[Illustration: 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 coarse pitch.
A double thread, such as in Figure 205, is drawn in the same way, except
that the slant of the thread is doubled, and the square is to be set for
the thread-pitch A, A, both for the tops and bottoms of the thread.
[Illustration: Fig 207.]
A round top and bottom thread, as the Whitworth thread, is drawn by
single lines, as in Figure 206. A left-hand thread, Figure 207, is
obviously drawn by the same process as a right-hand one, except that the
slant of the thread is given in the opposite direction.
For screw threads of a large diameter it is not uncommon to draw in the
thread curves as they appear to the eye, and the method of doing this is
shown in Figure 208. The thread is first marked on both sides of the
bolt, as explained, and instead of drawing, straight across the bolt,
lines to represent the tops and bottoms of the thread, a template to
draw the curves by is required. To get these curves, two half-circles,
one equal in diameter to the top, and one equal to the bottom of the
thread, are drawn, as in Figure 208.
[Illustration: Fig. 208.]
These half-circles are divided into any convenient number of equal
divisions: thus in Figure 208, each has eight divisions, as _a_, _b_,
_c_, etc., for the outer, and _i_, _j_, _k_, etc., for the inner one.
The pitch of the thread is then divided off by vertical lines into as
many equal divisions as the half-circles are divided into, as by the
lines _a_, _b_, _c_, etc., to _o_. Of these, the seven from _a_, to _h_,
correspond to the seven from _a'_ to _g'_, and are for the top of the
thread, and the seven from _i_ to _o_ correspond to the seven on the
inner half-circle, as _i_, _j_, _k_, etc. Horizontal lines are then
drawn from the points of the division to meet the vertical lines of
division; thus the horizontal dotted line from _a'_ meets the vertical
line _a_, and where they meet, as at A, a dot is made. Where the dotted
line from _b'_ meets vertical line _b_, another dot is made, as at B,
and so on until the point G is found. A curve drawn to pass from the top
of the thread on one side of the bolt to the top of the other side, and
passing through these points, as from A to G, will be the curve for the
top of the thread, and from this curve a template may be made to mark
all the other thread-tops from, because manifestly all the tops of the
thread on the bolt will be alike.
For the bottoms of the thread, lines are similarly drawn, as from _i'_
to meet _i_, where dot I is marked. J is got from _j'_ and _j_, while K
is got from the intersection of _k'_ with _k_, and so on, the dots from
I to O being those through which a curve is drawn for the bottom of the
thread, and from this curve a template also may be made to mark all the
thread bottoms. We have in our example used eight points of division in
each half-circle, but either more or less points maybe used, the only
requisite being that the pitch of the thread must be divided into as
many divisions as the two half-circles are. But it is not absolutely
necessary that both half-circles be divided into the same number of
equal divisions. Thus, suppose the large half-circle were divided into
ten divisions, then instead of the first half of the pitch being divided
into eight (as from _a_ to _h_) it would require to have ten lines. But
the inner half-circle may have eight only, as in our example. It is more
convenient, however, to use the same number of divisions for both
circles, so that they may both be divided together by lines radiating
from the centre. The more the points of division, the greater number of
points to draw the curves through; hence it is desirable to have as many
as possible, which is governed by the pitch of the thread, it being
obvious that the finer the pitch the less the number of distinct and
clear divisions it is practicable to divide it into. In our example the
angles of the thread are spread out to cause these lines to be thrown
further apart than they would be in a bolt of that diameter; hence it
will be seen that in threads of but two or three inches in diameter the
lines would fall very close together, and would require to be drawn
finely and with care to keep them distinct.
[Illustration: Fig. 208 _a_.]
[Illustration: Fig. 209.]
The curves for a United States standard form of thread are obtained in
the same manner as from the $V$ thread in Figure 208, but the thread
itself is more difficult to draw. The construction of this thread is
shown in Figure 208, it having a flat place at the top and at the bottom
of the thread. A common $V$ thread has its sides at an angle of 60
degrees, one to the other, the top and bottom meeting in a point. The
United States standard is obtained from drawing a common $V$ thread and
dividing its depth into eight equal divisions, as at _x_, in Figure 208
_a_, and cutting off one of these divisions at the top and filling in
one at the bottom to form flat places, as shown in the figure. But the
thread cannot be sketched on a bolt by this means unless temporary lines
are used to get the thread from, these temporary lines being drawn to
represent a bolt one-fourth the depth of the thread too large in
diameter. Thus, in Figure 208 _a_, it is seen that cutting off
one-eighth the depth of the thread reduces the diameter of the thread.
It is necessary, then, to draw the flat place on top of the thread
first, the order of procedure being shown in Figure 209. The lines for
the full diameter of the thread being drawn, the pitch is stepped off by
arcs, as 1, 2, 3, etc.; and from these, arcs, as 4, 5, 6, etc., are
marked for the width of the flat places at the tops of the threads.
Then one side of the thread is marked off by lines, as 7, which meet the
arcs 1, 2, 3, etc., as at _a_, _c_, etc. Similar lines, as 8 and 9, are
marked for the other side of the thread, these lines, 7, 8 and 9,
projecting until they cross each other. Line 10 is then drawn, making a
flat place at the bottom of the thread equal in width to that at the
top. Line 12 is then drawn square across the bolt, starting from the
bottom of the thread, and line 13 is drawn starting from the corner _f_
on one side of the thread and meeting line 12 on the other side of the
thread, which gives the angle for the tops of the thread. The depth of
the thread may then be marked on the other side of the bolt by the arcs
_d_ and _e_, and the line 14. The tops of all the threads may then be
drawn in, as by lines 15, 16, 17 and 18, and by lines, as 19, etc., the
thread sides may be drawn on the other side of the bolt. All that
remains is to join the bottoms of the threads by lines across the bolt,
and the pencil lines will be complete, ready to ink in. If the thread is
to be shown curved instead of drawn straight across, the curve may be
obtained by the construction in Figure 208, which is similar to that in
Figure 207, except that while the pitch is divided off into 16
divisions, the whole of these 16 divisions are not used to get the
curves, some of them being used twice over; thus for the bottom the
eight divisions from _b_ to _i_ are used, while for the tops the eight
from _g_ to _o_ are used. Hence _g_, _h_ and _i_ are used for getting
both curves, the divisions from _a_ to _b_ and from _o_ to _p_ being
taken up by the flat top and bottom of the thread. It will be noted that
in Figure 207, the top of the thread is drawn first, while in Figure
208 the bottom is drawn first, and that in the latter (for the U.S.
standard) the pitch is marked from centre to centre of the flats of the
thread.
[Illustration: Fig. 210.]
To draw a square thread the pencil lines are marked in the order shown
in Figure 210, in which 1 represents the centre line and 2, 3, 4 and 5,
the diameter and depth of the thread. The pitch of the thread is marked
off by arcs, as 6, 7, etc., or by laying a rule directly on the centre
line and marking with a lead pencil. To obtain the slant of the thread,
lines 8 and 9 are drawn, and from these line 10, touching 8 and 9 where
they meet lines 2 and 5; the threads may then be drawn in from the arcs
as 6, 7, etc. The side of the thread will show at the top and the bottom
as at A B, because of the coarse pitch and the thread on the other or
unseen side of the bolt slants, as denoted by the lines 12, 13; and
hence to draw the sides A B, the triangle must be set from one thread to
the next on the opposite side of the bolt, as denoted by the dotted
lines 12 and 13.
[Illustration: Fig. 211.]
If the curves of the thread are to be drawn in, they may be obtained as
in Figure 211, which is substantially the same as described for a V
thread. The curves _f_, representing the sides of the thread, terminate
at the centre line _g_, and the curves _e_ are equidistant with the
curves _c_ from the vertical lines _d_. As the curves _f_ above the
line are the same as _f_ below the line, the template for _f_ need not
be made to extend the whole distance across, but one-half only; as is
shown by the dotted curve _g_, in the construction for finding the curve
for square-threaded nuts in Figure 212.
[Illustration: Fig. 212.]
[Illustration: Fig. 213.]
A specimen of the form of template for drawing these curves is shown in
Figure 213; _g_ _g_, is the centre line parallel to the edges R, S;
lines _m_, _n_, represent the diameter of the thread at the top, and
_o_, _p_, that at the bottom or root; edge _a_ is formed to the points
(found by the constructions in the figures as already explained) for the
tops of the thread, and edge _f_ is so formed for the curve at the
thread bottoms. The edge, as S or R, is laid against the square-blade to
steady it while drawing in the curves. It may be noted, however, that
since the curve is the same below the centre line as it is above, the
template may be made to serve for one-half the thread diameter, as at
_f_, where it is made from _o_ to _g_, only being turned upside down to
draw the other half of the curve; the notches cut out at _x_, _x_, are
merely to let the pencil-lines in the drawing show plainly when setting
the template.
When the thread of a nut is shown in section, it slants in the opposite
direction to that which appears on the bolt-thread, because it shows the
thread that fits to the opposite side of the bolt, which, therefore,
slants in the opposite direction, as shown by the lines 12 and 13 in
Figure 210.
In a top or end view of a nut the thread depth is usually shown by a
simple circle, as in Figure 214.
[Illustration: Fig. 214.]
To draw a spiral spring, draw the centre line A, and lines B, C, Figure
215, distant apart the diameter the spring is to be less the diameter of
the wire of which it is to be made. On the centre line A mark two lines
_a b_, _c d_, representing the pitch of the spring. Divide the distance
between _a_ and _b_ into four equal divisions, as by lines 1, 2, 3,
letting line 3 meet line B. Line _e_ meeting the centre line at line
_a_, and the line B at its intersection with line 3, is the angle of the
coil on one side of the spring; hence it may be marked in at all the
locations, as at _e f_, etc. These lines give at their intersections
with the lines C and B the centres for the half circles _g_, which being
drawn, the sides _h_, _i_, _j_, _k_, etc., of the spring, may all be
marked in. By the lines _m_, _n_, _o_, _p_, the other sides of the
spring may be marked in.
[Illustration: Fig. 215.]
The end of the spring is usually marked straight across, as at L. If it
is required to draw the coils curved instead of straight across, a
template must be made, the curve being obtained as already described for
threads. It may be pointed out, however, that to obtain as accurate a
division as possible of the lines that divide the pitch, the pitch may
be divided upon a diagonal line, as F, Figure 216, which will greatly
facilitate the operation.
[Illustration: Fig. 216.]
Before going into projections it may be as well to give some examples
for practice.
[Illustration: Fig. 219. (Page 169.)]