Chapter II: Appendix: A 99 (1)

APPENDIX B 102
INDEX 113

AN INTRODUCTION

TO

MACHINE DRAWING AND DESIGN.

I. INTRODUCTION.

_Drawing Instruments._--For working the exercises in this book the student should be provided with the following:--A well-seasoned yellow pine _drawing-board_, 24 inches long, 17 inches wide, and 3/8 inch or 1/2 inch thick, provided with cross-bars on the back to give it strength and to prevent warping. A =T= _square_, with a blade 24 inches long attached permanently to the stock, _but not sunk into it_. One 45 deg. and one 60 deg. _set square_. The short edges of the former may be about 6 inches and the short edge of the latter about 5 inches long. A _pair of compasses_ with pen and pencil attachments, and having legs from 5 inches to 6 inches long. A _pair of dividers_, with screw adjustment if possible. A _pair of small steel spring pencil bows_ for drawing small circles, and a _pair of small steel spring pen bows_ for inking in the same. A _drawing pen_ for inking in straight lines. All compasses should have _round points_, and if possible _needle_ points. A piece of india-rubber will also be required, besides two pencils, one marked H or HH and one marked HB or F; the latter to be used for lining in a drawing which is not to be inked in, or for freehand work.

Pencils for mechanical drawing should be sharpened with a _chisel point_, and those for freehand work with a _round point_. _Do not wet the pencil_, as the lines afterwards made with it are very difficult to rub out.

Drawing-paper for working drawings may be secured to the board by _drawing-pins_, but the paper for finished drawings or drawings upon which there is to be a large amount of colouring should be _stretched_ upon the board.

The student should get the best instruments he can afford to buy, and he should rather have a few good instruments than a large box of inferior ones.

_Drawing-paper._--The names and sizes of the sheets of drawing paper are given in the following table:--

Inches
Demy 20 x 15
Medium 22 x 17
Royal 24 x 19
Imperial 30 x 22
Atlas 34 x 26
Double Elephant 40 x 27
Antiquarian 52 x 31

The above sizes must not be taken as exact. In practice they will be found to vary in some cases as much as an inch.

Cartridge-paper is made in sheets of various sizes, and also in rolls.

Hand-made paper is the best, but it is expensive. Good cartridge-paper is quite suitable for ordinary drawings.

_Centre Lines._--Drawings of most parts of machines will be found to be symmetrical about certain lines called _centre lines_. These lines should be drawn first with great care. On a pencil drawing centre lines should be thin continuous lines; in this book they are shown thus -- - -- - --.

After drawing the centre line of any part the dimensions of that part must be marked off from the centre line, so as to insure that it really is the centre line of that part: thus in making a drawing of a rivet, such as is shown at (_a_) fig. 1, after drawing the centre line, half the diameter of the rivet would be marked off on each side of that line, in order to determine the lines for the sides of the rivet.

_Inking._--For inking in drawings the best Indian ink should be used, and not common writing ink. Common ink does not dry quick enough, and rapidly corrodes the drawing pens. The pen should be filled by means of a brush or a narrow strip of paper, and not by dipping the pen into the ink.

In cases where there are straight lines and arcs of circles touching one another _ink in the arcs first_, then the straight lines; in this way it is easier to hide the joints.

_Colouring._--Camel's-hair or sable brushes should be used; the latter are the best, but are much more expensive than the former. The colour should be rubbed down in a dish, and the tint should be light. The mistake which a beginner invariably makes is in having the colour of too dark a tint.

First go over the part to be coloured with the brush and _clean_ water for the purpose of damping it. Next dry with clean blotting-paper to take off any superfluous water. Then take another brush with the colour, and beginning at the top, work from left to right and downwards. If it is necessary to recolour any part let the first coating dry before beginning.

Engineers have adopted certain colours to represent particular materials; these are given in the following table:--

_Table showing Colours used to represent Different Materials._

MATERIAL COLOUR

Cast iron Payne's grey or neutral tint.
Wrought iron Prussian blue.
Steel Purple (mixture of Prussian blue and crimson lake).
Brass Gamboge with a little sienna or a very little red
added.
Copper A mixture of crimson lake and gamboge, the former
colour predominating.
Lead Light Indian ink with a very little indigo added.
Brickwork Crimson lake and burnt sienna.
Firebrick Yellow and Vandyke brown.
Greystones Light sepia or pale Indian ink, with a little
Prussian blue added.
Brown freestone Mixture of pale Indian ink, burnt sienna, and
carmine.
Soft woods For ground work, pale tint of sienna.
Hard woods For ground work, pale tint of sienna with a little
red added.
For graining woods use darker tint with a greater
proportion of red.

_Printing._--A good drawing should have its title printed, a plain style of letter being used for this purpose, such as the following:--

The following letters look well _if they are well made_, but they are much more difficult to draw.

For remarks on a drawing the following style is most suitable:--

All printing should be done by freehand.

_Border lines_ are seldom put on engineering drawings.

_Working Drawings._--A good working drawing should be prepared in the following manner. It must first be carefully outlined in pencil and then inked in. After this all parts cut by planes of section should be coloured, the colours used indicating the materials of which the parts are made. Parts which are round may also be lightly shaded with the brush and colours to suit the materials. The centre lines are now inked in with _red_ or _blue ink_. The red ink may be prepared by rubbing down the cake of crimson lake, and the blue ink in like manner from the cake of Prussian blue. Next come the _distance_ or _dimension_ lines, which should be put in with _blue_ or _red ink_, depending on which colour was used for the centre lines. Dimension lines and centre lines are best put in of different colour. The arrow-heads at the ends of the dimension lines are now put in with _black ink_, and so are the figures for the dimensions. The arrow-heads and the figures should be made with a common writing pen. The dimensions should be put on neatly. Many a good drawing has its appearance spoiled through being slovenly dimensioned.

We may here point out the importance of putting the dimensions on a working drawing. If the drawing is not dimensioned, the workman must get his sizes from the drawing by applying his rule or a suitable scale. Now this operation takes time, and is very liable to result in error. Time is therefore saved, and the chance of error reduced, by marking the sizes in figures.

In practice it is not usual to send original drawings from the drawing office to the workshop, but copies only. The copies may be produced by various 'processes,' or they may be tracings drawn by hand. Many engineers do not ink in their original drawings, but leave them in pencil; especially is this the case if the drawings are not likely to be much used.

_Scales._--The best scales are made of ivory, and are twelve inches long. Boxwood scales are much cheaper, although not so durable as those made of ivory. If the student does not care to go to the expense of ivory or boxwood scales, he can get paper ones very cheap, which will be quite sufficient for his purpose. The divisions of the scale should be marked down to its edge, so that measurements may be made by applying the scale directly to the drawing. For working such exercises as are in this book the student should be provided with the following scales:--

A scale of 1, or 12 inches to a foot.
" 1/2 " 6 "
" 1/3 " 4 "
" 1/4 " 3 "
" 1/6 " 2 "

A scale of 1 is spoken of as 'full size,' and a scale of 1/2 as 'half size.'

Engineers in this country state dimensions of machines in feet, inches, and fractions of an inch, the latter being the 1/2, 1/4, 1/8, 1/16, &c. In making calculations it is generally more convenient to use decimal fractions, and then substitute for the results the equivalent fractions in eighths, sixteenths, &c. The following table will be found useful for this purpose:--

_Decimal Equivalents of Fractions of an Inch._

+----------+--------------------+
| Fraction | Decimal Equivalent |
+----------+--------------------+
| 1/32 | .03125 |
| 1/16 | .0625 |
| 3/32 | .09375 |
| 1/8 | .125 |
| 5/32 | .15625 |
| 3/16 | .1875 |
| 7/32 | .21875 |
| 1/4 | .25 |
| 9/32 | .28125 |
| 5/16 | .3125 |
| 11/32 | .34375 |
| 3/8 | .375 |
| 13/32 | .40625 |
| 7/16 | .4375 |
| 15/32 | .46875 |
| 1/2 | .5 |
| 17/32 | .53125 |
| 9/16 | .5625 |
| 19/32 | .59375 |
| 5/8 | .625 |
| 21/32 | .65625 |
| 11/16 | .6875 |
| 23/32 | .71875 |
| 3/4 | .75 |
| 25/32 | .78125 |
| 13/16 | .8125 |
| 27/32 | .84375 |
| 7/8 | .875 |
| 29/32 | .90625 |
| 15/16 | .9375 |
| 31/32 | .96875 |
| 1 | 1.0 |
+----------+--------------------+

Engineers use a single accent (') to denote _feet_, and a double accent (") to denote _inches_. Thus 2' 9" reads two feet nine inches.

II. RIVETED JOINTS.

Two plates or pieces to be riveted together have holes punched or drilled in them in such a manner that one may be made to overlap the other so that the holes in the one may be opposite the holes in the other. The rivets, which are round bars of iron, or steel, or other metal, are heated to redness and inserted in the holes; the head already formed on the rivet, and called the tail, is then held up, and the point is hammered or pressed so as to form another head. This process of forming the second head on the rivet is known as riveting, and may be done by hand-hammering or by a machine.

_Forms of Rivet Heads._--In fig. 1 are shown four different forms of rivet heads: (_a_) is a _snap head_, (_b_) a _conical head_ (_c_) a _pan head_, and (_d_) _a countersunk head_.

_Proportions of Rivet Heads._--The diameter of the snap head is about 1.7 times the diameter of the rivet, and its height about .6 of the diameter of the rivet. The conical head has a diameter twice and a height three quarters of the rivet diameter. The greatest diameter of the pan head is about 1.6, and its height .7 of the rivet diameter. The greatest diameter of the countersunk head may be one and a half, and its depth a half of the diameter of the rivet.

In fig. 1 at (_a_) and (_b_) are shown geometrical constructions devised by the author for drawing the snap and conical head for any size of rivet, the proportions being nearly the same as those given above.

_Geometrical Construction for Proportioning Snap Heads._--With centre A, and radius equal to half diameter of rivet, describe a circle cutting the centre line of the rivet at B and C. With centre B and radius BC describe the arc CD. Make BE equal to AD. With centre E and radius ED describe the arc DFH.

_Construction for Conical Head._--With centre K, and radius equal to diameter of rivet, describe the semicircle LMN, cutting the side of the rivet at M. With centre M and radius MN describe the arc NP to cut the centre line of rivet at P. Join PL and PN.

When a number of rivets of the same diameter have to be shown on the same drawing the above constructions need only be performed on one rivet. After the point E has been discovered the distance AE may be measured off on all the other rivets, and the arcs corresponding to DFH drawn with radii equal to ED. In like manner the height KP of the conical head may be marked off on all rivets of the same diameter with conical heads.

_Caulking._--In order to make riveted joints steam- or water-tight the edges of the plates and the edges of the heads of the rivets are burred down by a blunt chisel or caulking tool as shown at Q and R.

EXERCISE 1: _Forms of Rivets._--Draw, full size, the rivets and
rivet heads shown in fig. 1. The diameter of the rivet in each
case to be 1-1/8 inches, and the thickness of the plates 7/8 inch.

EXERCISE 2: _Single Riveted Lap Joint._--Draw, full size, the
plan and sectional elevation of the _single riveted lap joint_
shown in fig. 2.

_Table showing the Proportions of Single Riveted Lap Joints for various Thicknesses of Plates._ (_Plates and Rivets Wrought Iron._)

+--------------+-------------+----------+--------------+
| Thickness of | Diameter of | Pitch of | Width of lap |
| plates | rivets | rivets | |
+--------------+-------------+----------+--------------+
| 1/4 | 9/16 | 1-5/8 | 1-3/4 |
| 5/16 | 5/8 | 1-3/4 | 2 |
| 3/8 | 11/16 | 1-7/8 | 2-1/4 |
| 7/16 | 3/4 | 2 | 2-1/2 |
| 1/2 | 13/16 | 2-1/8 | 2-3/4 |
| 9/16 | 7/8 | 2-1/4 | 2-7/8 |
| 5/8 | 15/16 | 2-5/16 | 3 |
| 11/16 | 1 | 2-3/8 | 3-1/8 |
| 3/4 | 1-1/16 | 2-1/2 | 3-1/4 |
+------------------------------------------------------+

All the dimensions are in inches.

EXERCISE 3.--Draw, half size, a plan and section of a single
riveted lap joint for plates 3/4" thick to the dimensions given in
the above table.

EXERCISE 4: _Double Riveted Lap Joint._--Draw, full size, the two
views of the _double riveted lap joint_ shown in fig. 3.

_Table showing the Proportions of Double Riveted Lap Joints for various Thicknesses of Plates._ (_Plates and Rivets Wrought Iron._)

+-----------+-------------+----------+------------------+----------+
| Thickness | Diameter of | Pitch of | Distance between | Width of |
| of plates | rivets | rivets | rows of rivets | lap |
+-----------+-------------+----------+------------------+----------+
| 3/8 | 11/16 | 2-1/2 | 1-1/8 | 3-1/2 |
| 7/16 | 3/4 | 2-5/8 | 1-1/4 | 3-3/4 |
| 1/2 | 13/16 | 2-3/4 | 1-3/8 | 4 |
| 9/16 | 7/8 | 2-7/8 | 1-7/16 | 4-1/4 |
| 5/8 | 15/16 | 3 | 1-9/16 | 4-1/2 |
| 11/16 | 1 | 3-1/8 | 1-3/4 | 4-3/4 |
| 3/4 | 1-1/16 | 3-1/4 | 1-7/8 | 5 |
| 13/16 | 1-1/16 | 3-3/8 | 1-7/8 | 5 |
| 7/8 | 1-1/8 | 3-1/2 | 1-15/16 | 5-1/4 |
| 15/16 | 1-1/8 | 3-5/8 | 1-15/16 | 5-1/4 |
| 1 | 1-3/16 | 3-3/4 | 2 | 5-1/2 |
+-----------+-------------+----------+------------------+----------+

EXERCISE 5.--Draw, half size, a plan and section of a double
riveted lap joint for plates 7/8 inch thick to the dimensions
given in the above table.

EXERCISE 6: _Single Riveted Butt Joints._--In fig. 4 are shown
_single riveted butt joints_. One of the sectional views shows a
butt joint with one _cover plate_ or _butt strap_; the other
sectional view shows the same joint with two cover plates; the
third view is a plan of both arrangements. Draw all these views
full size.

EXERCISE 7.--Fig. 5 shows a plan and sectional elevation of the
connection of three plates together, which are in the same plane,
by means of single riveted butt joints and single cover plates.
The butt straps where they overlap are forged so as to fit one
another as shown, and thus form a close joint. Draw these views to
the scale of 6 inches to a foot.

The plates are 1/2 inch thick and the butt straps 9/16 inch thick.
All other dimensions must be deduced from the table for single
riveted lap joints.

EXERCISE 8.--The connection of three plates by single riveted lap
joints is shown in fig. 6. To make the joint close one plate has a
portion of its edge thinned out, and the plate above it is set up
at this part so as to lie close to the former.

Draw the three views shown in fig. 6 to the same scale as the last
exercise.

The plates are 7/16 inch thick. All other dimensions to be
obtained from table for single riveted lap joints.

EXERCISE 9: _Corner of Wrought-iron Tank._--This exercise is to
illustrate the connection of plates which are at right angles to
one another by means of _angle irons_. Fig. 7 is a plan and
elevation of the corner of a wrought-iron tank. The sides of the
tank are riveted to a vertical angle iron, the cross section of
which is clearly shown in the plan. Another angle iron of the same
dimensions is used in the same way to connect the sides with the
bottom. The sides do not come quite up to the corner of the
vertical angle iron, excepting at the bottom where the horizontal
angle iron comes in. At this point the vertical plates meet one
another, and the edge formed is rounded over to fit the interior
of the bend of the horizontal angle iron so as to make the joint
tight. Draw half size.

The dimensions are as follows: angle irons 2-1/2 inches x 2-1/2
inches x 3/8 inch; plates 3/8 inch thick; rivets 11/16 inch
diameter and 2 inches pitch.

EXERCISE 10: _Gusset Stay._--In order that the flat ends of a
steam boiler may not be bulged out by the pressure of the steam
they are strengthened by means of stays. One form of boiler stay,
called a 'gusset stay,' is shown in fig. 8. This stay consists of
a strip of wrought-iron plate which passes in a diagonal direction
from the flat end of the boiler to the cylindrical shell. One end
of this plate is placed between and riveted to two angle irons
which are riveted to the shell of the boiler. A similar
arrangement connects the other end of the stay plate to the flat
end of the boiler. In this example the stay or gusset plate is 3/4
of an inch thick; the angle irons are 4 inches broad and 1/2 inch
thick. The rivets are 1 inch in diameter. The same figure also
illustrates the most common method of connecting the ends of a
boiler to the shell. The end plates are _flanged_ or bent over at
right angles and riveted to the shell as shown. The radius of the
inside curve at the angle of the flange is 1-1/4 inches. Draw this
example to a scale of 3 inches to 1 foot.

III. SCREWS, BOLTS, AND NUTS.

_Screw Threads._--The various forms of screw threads used in machine construction are shown in fig. 9. The _Whitworth_ =V= thread is shown at (_a_). This is the standard form of triangular thread used in this country. The angle between the sides of the =V= is 55 deg., and one-sixth of the total depth is rounded off both at the top and bottom. At (_b_) is shown the _Sellers_ =V= thread, which is the standard triangular thread used by engineers in America. In this form of thread the angle between the sides of the =V= is 60 deg., and one-eighth of the total depth is cut square off at the top and bottom. The _Square_ thread is shown at (_c_). This form is principally used for transmitting motion.

Comparing the triangular and square threads, the former is the stronger of the two; but owing to the normal pressure on the =V= thread being inclined to the axis of the screw, that pressure must be greater than the pressure which is being transmitted by the screw; and therefore, seeing that the normal pressure on the square thread is parallel, and therefore equal to the pressure transmitted in the direction of the axis of the screw, the friction of the =V= thread must be greater than the friction of the square thread. In the case of the triangular thread there is also a tendency of the pressure to burst the nut. The _Buttress_ thread shown at (_e_) is designed to combine the advantages of the =V= and square threads, but it only has these advantages when the pressure is transmitted in one direction; if the direction of the pressure be reversed, the friction and bursting action on the nut are even greater than with the =V= thread, because of the greater inclination of the slant side of the buttress thread. The angles of the square thread are frequently rounded to a greater or less extent to render them less easily damaged. If this rounding is carried to excess we get the _Knuckle_ thread shown at (_d_). The rounding of the angles increases both the strength and the friction.

EXERCISE 11: _Forms of Screw Threads._--Draw to a scale of three
times full size the sections of screw threads as shown in fig. 9.
The pitch for the Whitworth, Sellers, and buttress threads to be
3/8 inch, and the pitch of the square and knuckle threads to be 1/2
inch.

_Dimensions of Whitworth Screws._

+-----------------------------------+
| Diameter | Number | Diameter |
| of screw | of threads | at bottom |
| | per inch | of thread |
+----------+------------+-----------+
| 1/8 | 40 | .093 |
| 3/16 | 24 | .134 |
| 1/4 | 20 | .186 |
| 5/16 | 18 | .241 |
| 3/8 | 16 | .295 |
| 7/16 | 14 | .346 |
| 1/2 | 12 | .393 |
| 5/8 | 11 | .508 |
| 3/4 | 10 | .622 |
| 7/8 | 9 | .733 |
| 1 | 8 | .840 |
| 1-1/8 | 7 | .942 |
| 1-1/4 | 7 | 1.067 |
| 1-3/8 | 6 | 1.162 |
| 1-1/2 | 6 | 1.286 |
| 1-5/8 | 5 | 1.369 |
| 1-3/4 | 5 | 1.494 |
| 1-7/8 | 4-1/2 | 1.590 |
| 2 | 4-1/2 | 1.715 |
| 2-1/4 | 4 | 1.930 |
| 2-1/2 | 4 | 2.180 |
| 2-3/4 | 3-1/2 | 2.384 |
| 3 | 3-1/2 | 2.634 |
| 3-1/4 | 3-1/4 | 2.856 |
| 3-1/2 | 3-1/4 | 3.106 |
| 3-3/4 | 3 | 3.323 |
| 4 | 3 | 3.573 |
| 4-1/4 | 2-7/8 | 3.805 |
| 4-1/2 | 2-7/8 | 4.055 |
| 4-3/4 | 2-3/4 | 4.284 |
| 5 | 2-3/4 | 4.534 |
| 5-1/4 | 2-5/8 | 4.762 |
| 5-1/2 | 2-5/8 | 5.012 |
| 5-3/4 | 2-1/2 | 5.238 |
| 6 | 2-1/2 | 5.488 |
+-----------------------------------+

_Gas Threads_[1] (_Whitworth Standard_).

[1] Used for wrought-iron and brass tubes.

+-------------------------------------------------------------+
| Diameter of Screw | 1/8 | 1/4 | 3/8 | 1/2 | 5/8 | 3/4 | 1 |
+-------------------+-----+-----+-----+-----+-----+-----+------
| Number of threads | | | | | | | |
| per inch | 28 | 19 | 19 | 14 | 14 | 14 | 11 |
+-------------------------------------------------------------+

+-------------------------------------------------+
| Diameter of Screw | 1-1/4 | 1-1/2 | 1-3/4 | 2 |
+-------------------+-------+-------+-------+-----+
| Number of threads | | | | |
| per inch | 11 | 11 | 11 | 11 |
+-------------------------------------------------+

_Representation of Screws._--The correct method of representing screw threads involves considerable trouble, and is seldom adopted by engineers for working drawings. For an explanation of the method see the author's Text-book on Practical Solid Geometry, Part II., problem 134. A method very often adopted on working drawings is shown in fig. 15; here the thin lines represent the points, and the thick lines the roots of the threads. At fig. 16 is shown a more complete method. The simplest method is illustrated by figs. 10, 11, 13, and 14.

Here dotted lines are drawn parallel to the axis of the screw as far as it extends, and at a distance from one another equal to the diameter of the screw at the bottom of the thread.

_Forms of Nuts._--The most common form of nut is the hexagonal shown in figs. 10, 13, 14, 15, and 16; next to this comes the square nut shown in fig. 11. The method of drawing these nuts will be understood by reference to the figures; the small circles indicate the centres, and the inclined lines passing through them the radii of the curves which represent the chamfered or bevelled edge of the nut. In all the figures but the first the chamfer is just sufficient to touch the middle points of the sides, and in these cases the drawing of the nut is simpler.

_Forms of Bolts._--At (_a_), fig. 12, is shown a bolt with a square head and a square neck. If this form of bolt is passed through a square hole the square neck prevents the bolt from turning when the nut is being screwed up. Instead of a square neck a snug may be used for the same purpose, as shown on the cup-headed bolt at (_b_). The snug fits into a short groove cut in the side of the hole through which the bolt passes. At (_a_) the diagonal lines are used to distinguish the flat side of the neck from the round part of the bolt above it. At (_c_) is shown a tee-headed bolt, and at (_d_) an eye-bolt. Fig. 13 represents a hook bolt. A bolt with a countersunk head is shown in fig. 11. If the countersunk head be lengthened so as to take up the whole of the unscrewed part of the bolt, we get the taper bolt shown in fig. 14, which is often used in the couplings of the screw shafts of steamships. The taper bolt has the advantage of having no projecting head, and it may also be made a tight fit in the hole with less trouble than a parallel bolt. Bolts may also have hexagonal heads.

_Studs_, or _stud bolts_, are shown in figs. 15 and 16; that in fig. 15 is a _plain stud_, while that in fig. 16 has an intermediate collar forged upon it, and is therefore called a _collared stud_.

_Proportions of Nuts and Bolt-heads._--In the hexagonal nut the diameter D across the flats is 1-1/2_d_ + 1/8, where _d_ is the diameter of the bolt. The same rule gives the width of a square nut across the flats. A rule very commonly used in making drawings of hexagonal nuts is to make the diameter D, across the angles equal to 2_d_. H, the height of the nut, is equal to the diameter of the bolt. In square and hexagonal headed bolts the height of the head varies from _d_ to 2/3_d_; the other dimensions are the same as for the corresponding nuts.

_Washers_ are flat, circular, wrought-iron plates, having holes in their centres of the same diameter as the bolts on which they are used. The object of the washer is to give a smooth bearing surface for the nut to turn upon, and it is used when the surfaces of the pieces to be connected are rough, or when the bolt passes through a hole larger than itself, as shown in fig. 10. The diameter of the washer is a little more than the diameter of the nut across the angles, and its thickness about 1/8 of the diameter of the bolt.

EXERCISE 12.--Draw, full size, the views shown in fig. 10 of an
hexagonal nut and washer for a bolt 1-1/4 inches in diameter. The
bolt passes through a hole 1-3/4 x 1-1/4. All the dimensions are
to be calculated from the rules which have just been given.

EXERCISE 13.--Draw, full size, the plan and elevation of the
square nut and bolt with countersunk head shown in fig. 11, to the
dimensions given.

EXERCISE 14.--Draw, full size, the elevation of the hook bolt with
hexagonal nut shown in fig. 13 to the dimensions given, and show
also a plan.

EXERCISE 15.--Draw, to a scale of 4 inches to a foot, the conical
bolt for a marine shaft coupling shown in fig. 14. All the parts
are of wrought iron.

EXERCISE 16.--Fig. 15 is a section of the mouth of a small
steam-engine cylinder, showing how the cover is attached; draw
this full size.

EXERCISE 17.--Fig. 16 shows the central portion of the
india-rubber disc valve which is described on page 68. A is the
central boss of the grating, into which is screwed the stud B,
upon which is forged the collar C. The upper part of the stud is
screwed, and carries the guard D and an hexagonal nut E. F is the
india-rubber. The grating and guard are of brass. The stud and nut
are of wrought iron. Draw full size the view shown.

_Lock Nuts._--In order that a nut may turn freely upon a bolt, there is always a very small clearance space between the threads of the nut and those of the bolt. This clearance is shown exaggerated at (_a_), fig. 17, where A is a portion of a bolt within a nut B. Suppose that the bolt is stretched by a force W. When the nut B is screwed up, the upper surfaces of the projecting threads of the nut will press on the under surfaces of the threads of the bolt with a force P equal and opposite to W, as shown at (_b_), fig. 17. When in this condition the nut has no tendency to slacken back, because of the friction due to the pressure on the nut. Now suppose that the tension W on the bolt is momentarily diminished, then the friction which opposes the turning of the nut may be so much diminished that a vibration may cause it to slacken back through a small angle. If this is repeated a great many times the nut may slacken back so far as to become useless.

A very common arrangement for locking a nut is shown at (_a_), fig. 18. C is an ordinary nut, and B one having half the thickness of C. B is first screwed up tight so as to act on the bolt, as shown at (_b_), fig. 17. C is then screwed on top of B. When C is almost as tight as it can be made, it is held by one spanner, while B is turned back through a small angle with another. The action of the nuts upon the bolt and upon one another is now as shown at (_b_), fig. 18. It will be seen that the nuts are wedged tight on to the bolt, and that this action is independent of the tension W in the bolt. The nuts will, therefore, remain tight after the tension in the bolt is removed.

It is evident that if the nuts are screwed up in the manner explained, the outer nut C will carry the whole load on the bolt; hence C should be the thicker of the two nuts. In practice, the thin nut, called the lock nut, is often placed on the outside, for the reason that ordinary spanners are too thick to act on the thin nut when placed under the other.

Another very common arrangement for locking a nut is shown in fig. 19. A is the bolt and B the nut, the lower part of which is turned circular. A groove C is also turned on the nut at this part. The circular part of the nut fits into a circular recess in one of the parts connected by the bolt. Through this part passes a set screw D, the point of which can be made to press on the nut at the bottom of the groove C. D is turned back when the nut B is being moved, and when B is tightened up, the set screw is screwed up so as to press hard on the bottom of the groove C. The nut B is thus prevented from slackening back. The screw thread is turned off the set screw at the point where it enters the groove on the nut.

The use of the groove for receiving the point of the set screw is this: The point of the set screw indents the nut and raises a bur which would interfere with the free turning of the nut in the recess if the bur was not at the bottom of a groove. Additional security is obtained by drilling a hole through the point of the bolt, and fitting it with a split pin E.

Locking arrangements for nuts are exceedingly numerous, and many of them are very ingenious, but want of space prevents us describing them. We may point out, however, that many very good locking arrangements have the defect of only locking the nut at certain points of a revolution, say at every 30 deg.. It will be noticed that the two arrangements which we have described are not open to this objection.

EXERCISE 18.--Draw, full size, a plan, front elevation, and side
elevation of the arrangement of nuts shown in fig. 18, for a bolt
7/8 inch diameter.

EXERCISE 19.--Draw the plan and elevation of the nut and locking
arrangement shown in fig. 19. Make also an elevation looking in
the direction of the arrow. Scale 6 inches to a foot.

IV. KEYS.

_Keys_ are wedges, generally rectangular in section, but sometimes circular; they are made of wrought iron or steel, and are used for securing wheels, pulleys, cranks, &c., to shafts.

Various sections of keys are shown in fig. 20. At (_a_) is the _hollow_ or _saddle key_. With this form of key it is not necessary to cut the shaft in any way, but its holding power is small, and it is therefore only used for light work. At (_b_) is the _key on a flat_, sometimes called a _flat key_. The holding power of this key is much greater than that of the saddle key. At (_c_) is the _sunk key_, a very secure and very common form.

The part of the shaft upon which a key rests is called the _key bed_ or _key way_, and the recess in the boss of the wheel or pulley into which the key fits is called the _key way_; both are also called _key seats_. With saddle, flat, and sunk keys the key bed is parallel to the axis of the shaft; but the key way is deeper at one end than the other to accommodate the taper of the key. The sides of the key are parallel.

The _round key_ or taper pin shown at (_d_) is in general only used for wheels or cranks which have been previously shrunk on to their shafts or forced on by great pressure. After the wheel or crank has been shrunk on, a hole is drilled, half into the shaft and half into the wheel or crank, to receive the pin.

When the point of a key is inaccessible the other end is provided with a _gib head_ as shown at (_e_), to enable the key to be withdrawn.

A _sliding_ or _feather key_ secures a piece to a shaft so far as to prevent the one from rotating without the other, but allows of relative motion in the direction of the axis of the shaft. This form of key has no taper, and it is secured to the piece carried by the shaft, but is made a _sliding fit_ in the key way of the shaft. In one form of feather key the part within the piece carried by the shaft is dovetailed as shown at (_f_). In another form the key has a round projecting pin forged upon it, which enters a corresponding hole as shown at (_g_). The feather key may also be secured to the piece carried by the shaft by means of one or more screws as shown at (_h_). The key way in the shaft is made long enough to permit of the necessary sliding motion.

_Cone Keys._--These are sometimes fitted to pulleys, and are shown in fig. 32, page 38. In this case the eye of the pulley is tapered and is larger than the shaft. The space between the shaft and the boss of the pulley is filled with three _saddle_ or _cone keys_. These keys are made of cast iron and are all cast together, and before being divided the casting is bored to fit the shaft and turned to fit the eye of the pulley. By this arrangement of keys the same pulley may be fixed on shafts of different diameters by using keys of different thicknesses; also the pulley may be bored out large enough to pass over any boss which may be forged on the shaft.

_Proportions of Keys._--The following rules are taken from Unwin's 'Machine Design,' pp. 142-43.

Diameter of eye of wheel, or boss of shaft = _d_.
Width of key = 3/4_d_ + 1/8.
Mean thickness of sunk key = 1/8_d_ + 1/8.
" key on flat = 1/16_d_ + 1/16.

The following table gives dimensions agreeing with average practice.

_Dimensions of Keys._

D = diameter of shaft.
B = breadth of key.
T = thickness of sunk key.
T_{1} = thickness of flat key, also = thickness of saddle key. Taper
of key 1/8 inch per foot of length, _i.e._ 1 in 96.

+---------------------------------------------------------------+
| D | 3/4 | 1 | 1-1/4 | 1-1/2 | 1-3/4 | 2 | 2-1/4 | 2-1/2 |
+-----+-----+-----+-------+-------+-------+-----+-------+-------+
| B | 5/16| 3/8 | 7/16 | 1/2 | 9/16 | 5/8 | 11/16 | 11/16 |
| T | 1/4 | 1/4 | 1/4 | 5/16 | 5/16 | 5/16| 3/8 | 3/8 |
|T_{1}| 3/16| 3/16| 3/16 | 3/16 | 1/4 | 1/4 | 1/4 | 5/16 |
+---------------------------------------------------------------+

+-------------------------------------------------------------------+
| D | 2-3/4 | 3 | 3-1/2 | 4 | 4-1/2 | 5 | 5-1/2 | 6 |
+-----+-------+-----+-------+-------+-------+-------+-------+-------+
| B | 3/4 | 7/8 | 1 | 1-1/8 | 1-1/4 | 1-3/8 | 1-1/2 | 1-5/8 |
| T | 3/8 | 7/16| 1/2 | 1/2 | 9/16 | 5/8 | 11/16 | 3/4 |
|T_{1}| 5/16 | 5/16| 3/8 | 7/16 | 1/2 | 1/2 | 9/16 | 5/8 |
+-------------------------------------------------------------------+

+-------------------------------------------------------+
| D | 7 | 8 | 9 | 10 | 11 | 12 |
+-----+-------+-------+-------+--------+--------+-------+
| B | 1-7/8 | 2-1/8 | 2-3/8 | 2-5/8 | 2-7/8 | 3-1/8 |
| T | 13/16 | 15/16 | 1 | 1-1/16 | 1-3/16 | 1-1/4 |
|T_{1}| 11/16 | 3/4 | 7/8 | 15/16 | 1-1/16 | 1-1/8 |
+-------------------------------------------------------+

V. SHAFTING.

Shafting is nearly always cylindrical and made of wrought iron or steel. Cast iron is rarely used for shafting.

_Axles_ are shafts which are subjected to bending without twisting.

The parts of a shaft or axle which rest upon the bearings or supports are called _journals_, _pivots_, or _collars_.

In journals the supporting pressure is at right angles to the axis of the shaft, while in pivots and collars the pressure is parallel to that axis.

Shafts may be solid or hollow. Hollow shafts are stronger than solid shafts for the same weight of material. Thus a hollow shaft having an external diameter of 10-1/4 inches and an internal diameter of 7 inches would have about the same weight as a solid shaft of the same material 7-1/2 inches in diameter, but the former would have about double the strength of the latter. Hollow shafts are also stiffer and yield less to bending action than solid shafts, which in some cases, as in propeller shafts, is an objection.

VI. SHAFT COUPLINGS.

For convenience of making and handling, shafts used for transmitting power are generally made in lengths not exceeding 30 feet. These lengths are connected by couplings, of which we give several examples.

_Solid_, _Box_, or _Muff Couplings._--One form of box coupling is shown in fig. 21. Here the ends of the shafts to be connected butt against one another, meeting at the centre of the box, which is made of cast iron. The shafts are made to rotate as one by being secured to the box by two wrought-iron or steel keys, both driven from the same end of the box. A clearance space is left between the head of the forward key and the point of the hind one, to facilitate the driving of them out, as then only one key needs to be started at a time. Sometimes a single key the whole length of the box is used, in which case it is necessary that the key ways in the shafts be of exactly the same depth.

The half-lap coupling, introduced by Sir William Fairbairn, is shown in fig. 22. In this form of box coupling the ends of the shafts overlap within the box. It is evident that one shaft cannot rotate without the other as long as the box remains over the lap. To keep the box in its place it is fitted with a saddle key.

It will be noticed that the lap joint is sloped in such a way as to prevent the two lengths of shaft from being pulled asunder by forces acting in the direction of their length.

Half-lap couplings are not used for shafts above 5 inches in diameter.

It may here be pointed out that the half-lap coupling is expensive to make, and is now not much used.

As shafts are weakened by cutting key ways in them, very often the ends which carry couplings are enlarged in diameter, as shown in fig. 21, by an amount equal to the thickness of the key. An objection to this enlargement is that wheels and pulleys require either that their bosses be bored out large enough to pass over it, or that they be split into halves, which are bolted together after being placed on the shaft.

_Dimensions of Box Couplings._

D = diameter of shaft.
T = thickness of metal in box.
L = length of box for butt coupling.
L_{1} = length of box for lap coupling.
_l_ = length of lap.
D_{1} = diameter of shaft at lap.

+---------------------------------------------------------------+
| D | 1-1/2 | 2 | 2-1/2 | 3 | 3-1/2 | 4 |
+-------+--------+--------+---------+-------+----------+--------+
| T | 1-1/8 | 1-5/16 | 1-1/2 | 1-3/4 | 1-15/16 | 2-1/8 |
| L | 5-3/4 | 7 | 8-1/4 | 9-1/2 | 10-3/4 | 12 |
| L_{1} | 4-1/8 | 5-1/4 | 6-3/8 | 7-1/2 | 8-5/8 | 9-3/4 |
| _l_ | 1-7/16 | 1-7/8 | 2-5/16 | 2-3/4 | 3-3/16 | 3-5/8 |
| D_{2} | 2-5/16 | 3 | 3-11/16 | 4-3/8 | 5-1/16 | 5-3/4 |
+---------------------------------------------------------------+

+----------------------------------------------+
| D | 4-1/2 | 5 | 5-1/2 | 6 |
+-------+---------+--------+--------+----------+
| T | 2-5/16 | 2-1/2 | 2-3/4 | 2-15/16 |
| L | 13-1/4 | 14-1/2 | 15-3/4 | 17 |
| L_{1} | 10-7/8 | 12 | -- | -- |
| _l_ | 4-1/16 | 4-1/2 | -- | -- |
| D_{2} | 6-7/16 | 7-1/8 | -- | -- |
+----------------------------------------------+

Slope of lap 1 in 12.

EXERCISE 20: _Solid Butt Coupling._--From the above table of
dimensions make a longitudinal and a transverse section of a solid
butt coupling for a shaft 2-1/2 inches in diameter. Scale 6 inches
to a foot.

EXERCISE 21: _Fairbairn's Half-Lap Coupling._--Make the same views
as in the last exercise of a half-lap coupling for a 3-inch shaft
to the dimensions in the above table. Scale 6 inches to a foot.

_Flange Couplings._--The form of coupling used for the shafts of marine engines is shown in fig. 23. The ends of the different lengths of shaft have flanges forged on them, which are turned along with the shaft. These flanges butt against one another, and are connected by bolts. These bolts may be parallel or tapered; generally they are tapered. A parallel bolt must have a head, but a tapered bolt will act without one. In fig. 23 the bolts are tapered, and also provided with heads. In fig. 14, page 17, is shown a tapered bolt without a head. The variation of diameter in tapered bolts is 3/8 of an inch per foot of length.

Sometimes a projection is formed on the centre of one flange which fits into a corresponding recess in the centre of the other, for the purpose of ensuring the shafts being in line.

Occasionally a cross-key is fitted in between the flanges, being sunk half into each, for the purpose of diminishing the shearing action on the bolts.

EXERCISE 22: _Marine Coupling._--Draw the elevation and section of
the coupling shown in fig. 23; also an elevation looking in the
direction of the arrow. Scale 3 inches to a foot.

The following table gives the dimensions of a few marine couplings taken from actual practice.

_Examples of Marine Couplings._

+--------------------------------------------------------------------+
| Diameter of shaft |2-3/8 | 9-3/4 | 12-7/8 |16-1/2 | 22-1/2 | 23 |
+--------------------+------+-------+--------+-------+--------+------+
|Diameter of flange | 6 | 19 | 24 | 32 | 35 | 38 |
|Thickness of flange | 1 | 2-3/4 | 3-1/8 | 4-1/4 | 6 | 5 |
|Diameter of bolts | 3/4 | 2-3/4 | 2-11/16| 3-1/2 | 4-1/4 | 4-1/4|
|Number of bolts | 3 | 6 | 6 | 8 | 9 | 8 |
|Diameter of bolt | | | | | | |
| circle |4-1/8 | 14-1/8|18-13/16| 25 | 28-3/4 |30-3/8|
+--------------------------------------------------------------------+

All the above dimensions are in inches.

EXERCISE 23.--Select one of the couplings from the above table, and
make the necessary working drawings for it to a suitable scale.

The cast-iron flange coupling is shown in fig. 24. In this kind of coupling a cast-iron centre or boss provided with a flange is secured to the end of each shaft by a sunk key driven from the face of the flange. These flanges are then connected by bolts and nuts as in the marine coupling.

To ensure the shafts being in line the end of one projects into the flange of the other.

In order that the face of each flange may be exactly perpendicular to the axis of the shaft they should be 'faced' in the lathe, after being keyed on to the shaft.

If the coupling is in an exposed position, where the nuts and bolt-heads would be liable to catch the clothes of workmen or an idle driving band which might come in the way, the flanges should be made thicker, and be provided with recesses for the nuts and bolt-heads.

_Dimensions of Cast-iron Flange Couplings._

+--------------------------------------------------------------------+
| |Diameter| | |Depth | |Diameter|Diameter|
|Diameter| of |Thickness|Diameter| at |Number| of | of bolt|
|of shaft| flange |of flange| of boss| boss | of | bolts | circle |
| D | F | T | B | L | bolts| d | C |
+--------|--------|---------|--------|------|------|--------|--------+
| 1-1/2 | 7-1/4 | 7/8 | 3-1/2 |2-5/8 | 3 |5/8 | 5-1/2 |
| 2 | 8-7/8 | 1-1/16 | 4-3/8 |3-3/16| 4 | 3/4| 6-3/4 |
| 2-1/2 | 10-5/8 | 1-1/4 | 5-5/16 |3-3/4 | 4 |7/8 | 8-1/8 |
| 3 | 12-3/8 | 1-7/16 | 6-1/4 |4-5/16| 4 | 1 | 9-1/2 |
| 3-1/2 | 13-1/8 | 1-5/8 | 7-1/8 |4-7/8 | 4 | 1 |10-5/16 |
| 4 | 14 | 1-3/4 | 8 |5-7/16| 6 | 1 |11-1/4 |
| 4-1/2 | 15-5/8 | 2 | 8-7/8 |6 | 6 |1-1/8 |12-1/2 |
| 5 | 17-3/8 | 2-1/8 | 9-13/16|6-5/8 | 6 | 1-1/4|13-13/16|
| 5-1/2 | 18-1/4 | 2-5/16 |10-3/4 |7-1/4 | 6 |1-1/4 |14-3/4 |
| 6 | 19-7/8 | 2-1/2 |11-5/8 |7-3/4 | 6 | 1-3/8| 16 |
+--------------------------------------------------------------------+

The projection of the shaft _p_ varies from 1/4 inch in the small shafts to 1/2 inch in the large ones.

EXERCISE 24: _Cast-iron Flange Coupling._--Draw the views shown in
fig. 24 of a cast-iron flange coupling, for a shaft 4-1/2 inches in
diameter, to the dimensions given in the above table. Scale 4 inches
to a foot.

VII. BEARINGS FOR SHAFTS.

An example of a very simple form of bearing is shown in fig. 25, which represents a brake shaft carrier of a locomotive tender. The bearing in this example is made of cast iron and in one piece. Through the oval-shaped flange two bolts pass for attaching the bearing to the wrought-iron framing of the tender. With this form of bearing there is no adjustment for wear, so that when it becomes worn it must be renewed.

EXERCISE 25: _Brake Shaft Carrier._--Draw the elevation and
sectional plan of the bearing shown in fig. 25. Draw also a
vertical section through the axis. The latter view to be projected
from the first elevation. Scale 6 inches to a foot.

_Pillow Block_, _Plummer Block_, or _Pedestal_.--The ordinary form of plummer block is represented in fig. 26. A is the block proper, B the sole through which pass the holding-down bolts. C is the cap. Between the block and the cap is the brass bush, which is in halves, called _brasses_ or _steps_. The bed for the steps in this example is cylindrical, and is prepared by the easy process of boring. The steps are not supported throughout their whole length, but at their ends only where fitting strips are provided as shown. As the wear on a step is generally greatest at the bottom, it is made thicker there than at the sides, except where the fitting strips come in. To prevent the steps turning within the block they are generally furnished with lugs, which enter corresponding recesses in the block and cover.

In the block illustrated the journal is lubricated by a _needle lubricator_; this consists of an inverted glass bottle fitted with a wood stopper, through a hole in which passes a piece of wire, which has one end in the oil within the bottle, and the other resting on the journal of the shaft. The wire or needle does not fill the hole in the stopper, but if the needle is kept from vibrating the oil does not escape owing to capillary attraction. When, however, the shaft rotates, the needle begins to vibrate, and the oil runs down slowly on to the journal; oil is therefore only used when the shaft is running.

EXERCISE 26: _Pillow Block for a Four-inch Shaft._--Draw the views
shown of this block in fig. 26. Make also separate drawings, full
size, of one of the steps. Scale 6 inches to a foot.

_Proportions of Pillow Blocks._--The following rules may be used for proportioning pillow blocks for shafts up to 8 inches diameter. It should be remembered that the proportions used by different makers vary considerably, but the following rules represent average practice.

Diameter of journal = _d_.
Length of journal = _l_.
Height to centre = 1.05_d_ + .5.
Length of base = 3.6_d_ + 5.
Width of base = .8_l_.
" block = .7_l_.
Thickness of base = .3_d_ + .3.
" cap = .3_d_ + .4.
Diameter of bolts = .25_d_ + .25.
Distance between centres of cap bolts = 1.6_d_ + 1.5.
" " base bolts = 2.7_d_ + 4.2.
Thickness of step at bottom = _t_ = .09_d_ + .15.
" " sides = 3/4 _t_.

The length of the journal varies very much in different cases, and depends upon the speed of the shaft, the load which it carries, the workmanship of the journal and bearing, and the method of lubrication. For ordinary shafting one rule is to make _l_ = _d_ + 1. Some makers use the rule _l_ = 1.5_d_; others make _l_ = 2_d_.

EXERCISE 27: _Design for Pillow Block._--Make the necessary
working drawings for a pillow block for a shaft 5 inches in
diameter, and having a journal 7 inches long.

_Brackets._--When a pillow block has to be fixed to a wall or column a bracket such as that shown in figs. 27 and 28 may be used. The pillow block rests between the _joggles_ A A, and is bolted down to the bracket and secured in addition with keys at the ends of the base of the block, in the same manner as is shown, for the attachment of the bracket to the column.

EXERCISE 28: _Pillar Bracket._--Fig. 27 shows a side elevation and
part horizontal section, and fig. 28 shows an end elevation of a
pillar bracket for carrying a pillow block for a 3-inch shaft.
Draw these views _properly projected from one another_, showing
the pillow block, which is to be proportioned by the rules given
on page 32. Draw also a plan of the whole. Scale 4 inches to a
foot.