0.5

1 cm

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