DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.25888#0064
48
ENGINEER AND MACHINIST’S DRAWING-BOOK.
drawn. Describe, in like manner, the corresponding semi-
circle A' G'B', Fig. 4, in the reverse position from the former,
to indicate that, as the cutting plane bisects the nut, the
part to be represented by this figure is that which fits the
more remote half of the screw. Now draw, Figs. 1 and 3,
the perpendiculars A' N, B B3, which will represent the
vertical projections of the exterior cylinders. The interior
cylinders are now to be projected horizontally and verti-
cally by drawing from the centre C' the semicircle H T M',
with a radius equal to half the distance 3J- inches, marked
as the diameter of this part. Then divide the semicircles
first described into any number of equal parts, and through
each point draw radii, which will, of course, divide the
interior semicircles similarly.
To avoid fraying the paper at the part where the draw-
ing is to be executed, let the straight line X X be laid
down, parallel to the axis, and set off upon it the length
of the pitch (1^ inches), as many times as may be re-
quired ; and through the points of division, draw straight
lines A2 M2, A3 M3, &c., parallel to the ground line. Then
divide each distance A A3, A A3, &c\, into twice the num-
ber of equal parts that the semicircles have been divided
into, and following instructions already laid down, con-
struct the helix A B A2. Construct, in like manner, the
corresponding helical curve in Fig. 3, only observing that
the part which has been supposed to be removed must not
be drawn either in full or in dotted lines.
Having obtained the point H by the intersection of
the horizontal line passing through the middle division of
A A2 with the perpendicular H' H2, we must now, in like
manner, cause it to describe the helix H M2 H2, which
will represent the bottom of the groove. The apparent
outlines of the screw and its nut will then be completed
by drawing the tangents A H, A2 H, &c., to the curves
of the helices ; these tangents are not, strictly speaking,
straight lines, but their deviation from the straight line
is, in most instances, so small as to be imperceptible, and
accordingly, we have deemed it unnecessary to complicate
the drawing by introducing the method of determining
them with rigorous exactness.
When a long series of threads have to be delineated,
they should be drawn mechanically, by means of a mould
or templet, Fig. 5, constructed in the following manner:
-—Take a small slip of thin wood or pasteboard, and draw
upon it the straight line a b' equal to A' B' ; then set off,
on each side of the central point c, the distance c k, Fig. 1,
at the points 1c and l, as also the distance c i, at i' and m,
&lc. Through all these points, raise perpendiculars to
a b'; set off upon each of these, the distances c G, k F, i E,
&c., respectively, and through the points thus obtained;
draw a curve line a g 6, and pare the slip carefully and
accurately to this line. If now we apply this templet
upon Fig. 1, so that the points a and b shall coincide with
A and B, we shall be enabled to draw the curve A G B
mechanically, and so on for the remaining curves of the
outer helix. The same mould may be employed to draw
the corresponding curves in Fig. 3, by simply inverting
it; but for the interior helix a separate mould must be
cut, its outlines being laid off in the manner above de-
scribed, as shown at Fig. 6.
Projections of a Square-threaded Screw.—Plate X.
The depth of the thread is equal to its thickness, and
this latter to the breadth of the groove.
Screws may have two, three, or even a greater number
of threads, according to the velocity which their action
may be required to produce. A double-threaded screw is
one in which the pitch of any individual helix includes
two threads; a three-threaded screw, one in which it
embraces three threads, and so on.
Having laid down, as before, Figs. 2 and 4, the hori-
zontal projections of the exterior and interior cylinders of
the screw, by describing semicircles with radii equal to
half the dimensions marked; let them be divided into
equal parts, and setting out upon X Y, drawn parallel to
the axis, the length (3 A inches) of the pitch, divide it
also into the same number of parts, and construct, upon.
Figs. 1 and 3. the vertical projection of the helix de-
scribed upon the exterior cylinder. Then draw, in
like manner, another helix of the same pitch upon the
surface of the interior cylinder, and dividing the pitch,
3tV inches into six equal parts, draw through the points
a, b, c, d, and e, other helical curves parallel to the
first, so as to form three ridges and three grooves. The
bottom of each groove will now be represented by the
helical curves, similarly drawn, upon the interior cylinder,
the outlines of which will terminate at the points of con-
tact /, h, &c.; and the points of the threads, as well as
the bottoms of the grooves in the nut, will be expressed
by the lines A a, b c, d e, &c., forming portions of the out-
line of the exterior cylinder. And, to complete the repre-
sentation of this object, we have only to determine by
inspection, those parts of each curve which are visible,
and those which are concealed. Thus for example, the
helix G F G2, Fig. 1, will obviously be represented by a
full line only so far as the point F; the remaining portion
F G2 being concealed by the thread, and therefore dotted.
When the screw to be represented is of no great dimen-
sions, it will be unnecessary to go through the tedious
operation of drawing the helical curves with rigid ac-
curacy; and various simple approximations to the curve
may be resorted to, which the ingenuity and taste of the
learner will easily enable him to supply. If a portion of
the circumference of the outer cylinder equal to about
one-sixth of the whole be projected vertically at an equal
distance on each side of the centre line, the part of the
curve comprised between these lines will be found to
approach very nearly to a straight line, at an inclination
to the axis proportioned to the magnitude of the pitch.
Therefore by setting out the divisions of the pitch, and of
the thickness of the thread, upon the centre line, and
drawing through these points a series of parallel straight
lines at the proper inclination (determined beforehand),
we shall have a near approximation to the outline of the
central portion of the curve of the threads within the
limits above indicated; and the remaining parts, on either
ENGINEER AND MACHINIST’S DRAWING-BOOK.
drawn. Describe, in like manner, the corresponding semi-
circle A' G'B', Fig. 4, in the reverse position from the former,
to indicate that, as the cutting plane bisects the nut, the
part to be represented by this figure is that which fits the
more remote half of the screw. Now draw, Figs. 1 and 3,
the perpendiculars A' N, B B3, which will represent the
vertical projections of the exterior cylinders. The interior
cylinders are now to be projected horizontally and verti-
cally by drawing from the centre C' the semicircle H T M',
with a radius equal to half the distance 3J- inches, marked
as the diameter of this part. Then divide the semicircles
first described into any number of equal parts, and through
each point draw radii, which will, of course, divide the
interior semicircles similarly.
To avoid fraying the paper at the part where the draw-
ing is to be executed, let the straight line X X be laid
down, parallel to the axis, and set off upon it the length
of the pitch (1^ inches), as many times as may be re-
quired ; and through the points of division, draw straight
lines A2 M2, A3 M3, &c., parallel to the ground line. Then
divide each distance A A3, A A3, &c\, into twice the num-
ber of equal parts that the semicircles have been divided
into, and following instructions already laid down, con-
struct the helix A B A2. Construct, in like manner, the
corresponding helical curve in Fig. 3, only observing that
the part which has been supposed to be removed must not
be drawn either in full or in dotted lines.
Having obtained the point H by the intersection of
the horizontal line passing through the middle division of
A A2 with the perpendicular H' H2, we must now, in like
manner, cause it to describe the helix H M2 H2, which
will represent the bottom of the groove. The apparent
outlines of the screw and its nut will then be completed
by drawing the tangents A H, A2 H, &c., to the curves
of the helices ; these tangents are not, strictly speaking,
straight lines, but their deviation from the straight line
is, in most instances, so small as to be imperceptible, and
accordingly, we have deemed it unnecessary to complicate
the drawing by introducing the method of determining
them with rigorous exactness.
When a long series of threads have to be delineated,
they should be drawn mechanically, by means of a mould
or templet, Fig. 5, constructed in the following manner:
-—Take a small slip of thin wood or pasteboard, and draw
upon it the straight line a b' equal to A' B' ; then set off,
on each side of the central point c, the distance c k, Fig. 1,
at the points 1c and l, as also the distance c i, at i' and m,
&lc. Through all these points, raise perpendiculars to
a b'; set off upon each of these, the distances c G, k F, i E,
&c., respectively, and through the points thus obtained;
draw a curve line a g 6, and pare the slip carefully and
accurately to this line. If now we apply this templet
upon Fig. 1, so that the points a and b shall coincide with
A and B, we shall be enabled to draw the curve A G B
mechanically, and so on for the remaining curves of the
outer helix. The same mould may be employed to draw
the corresponding curves in Fig. 3, by simply inverting
it; but for the interior helix a separate mould must be
cut, its outlines being laid off in the manner above de-
scribed, as shown at Fig. 6.
Projections of a Square-threaded Screw.—Plate X.
The depth of the thread is equal to its thickness, and
this latter to the breadth of the groove.
Screws may have two, three, or even a greater number
of threads, according to the velocity which their action
may be required to produce. A double-threaded screw is
one in which the pitch of any individual helix includes
two threads; a three-threaded screw, one in which it
embraces three threads, and so on.
Having laid down, as before, Figs. 2 and 4, the hori-
zontal projections of the exterior and interior cylinders of
the screw, by describing semicircles with radii equal to
half the dimensions marked; let them be divided into
equal parts, and setting out upon X Y, drawn parallel to
the axis, the length (3 A inches) of the pitch, divide it
also into the same number of parts, and construct, upon.
Figs. 1 and 3. the vertical projection of the helix de-
scribed upon the exterior cylinder. Then draw, in
like manner, another helix of the same pitch upon the
surface of the interior cylinder, and dividing the pitch,
3tV inches into six equal parts, draw through the points
a, b, c, d, and e, other helical curves parallel to the
first, so as to form three ridges and three grooves. The
bottom of each groove will now be represented by the
helical curves, similarly drawn, upon the interior cylinder,
the outlines of which will terminate at the points of con-
tact /, h, &c.; and the points of the threads, as well as
the bottoms of the grooves in the nut, will be expressed
by the lines A a, b c, d e, &c., forming portions of the out-
line of the exterior cylinder. And, to complete the repre-
sentation of this object, we have only to determine by
inspection, those parts of each curve which are visible,
and those which are concealed. Thus for example, the
helix G F G2, Fig. 1, will obviously be represented by a
full line only so far as the point F; the remaining portion
F G2 being concealed by the thread, and therefore dotted.
When the screw to be represented is of no great dimen-
sions, it will be unnecessary to go through the tedious
operation of drawing the helical curves with rigid ac-
curacy; and various simple approximations to the curve
may be resorted to, which the ingenuity and taste of the
learner will easily enable him to supply. If a portion of
the circumference of the outer cylinder equal to about
one-sixth of the whole be projected vertically at an equal
distance on each side of the centre line, the part of the
curve comprised between these lines will be found to
approach very nearly to a straight line, at an inclination
to the axis proportioned to the magnitude of the pitch.
Therefore by setting out the divisions of the pitch, and of
the thickness of the thread, upon the centre line, and
drawing through these points a series of parallel straight
lines at the proper inclination (determined beforehand),
we shall have a near approximation to the outline of the
central portion of the curve of the threads within the
limits above indicated; and the remaining parts, on either