DETAILS OF THE WILLIS APPARATUS USED IN ILLUSTRATING THE FOREGOING
LECTURES.
The ultimate parts of the various contrivances figured in this volume
are mainly those invented by the late Professor Willis of Cambridge.
They are minutely described and illustrated in a work written by him
for the purpose under the title _System of Apparatus for the use
of Lecturers and Experimenters in Mechanical Philosophy_, London,
Weale & Co., 1851. This work has long been out of print. It may
therefore be convenient if I give here a brief account of those parts
of this admirable apparatus that I have found especially useful The
illustrations have been copied from the plates in Professor Willis’
book.[2]
[2] I ought to acknowledge the kindness with which Mr. J. Willis Clark,
of Cambridge, the literary executor of Professor Willis, has responded
to my queries, while I am also under obligations to the courtesy of
Messrs. Crosby, Lockwood, & Co.
The Willis system provides the means for putting versatile framework
together with or without revolving gear for the purpose of mechanical
illustration. Many parts which enter into the construction of the
machine used at the lecture to-day will reappear to-morrow as essential
parts of some totally different contrivance. The parts are sufficiently
substantial to work thoroughly well. The scantlings and dimensions
generally have been so chosen as to produce models readily visible to a
large class.
It will of course be understood that every model contains some one
or more _special_ parts such as the punch and die in Fig. 73, or the
spring balance in Fig. 17, or the pulley-block in Fig. 33. But for
the due exhibition of the operation of the machine a further quantity
of ordinary framework and of moving mechanism is usually necessary.
This material, which may be regarded as of a _general_ type, it is the
function of the Willis system to provide.
THE BOLTS.—The system mainly owes its versatility and its steadiness
to the use of the iron screw bolt for all attachments. The bolts used
are ⅜ diameter; the shape of the head is hemispherical and the shank
must be square for a short distance from the head so that the bolt
cannot turn round when passed through the slits of the _brackets_
or _rectangles_. When the head of the bolt bears on a slit in one
of the wooden pieces a circular iron washer 2" in diameter, or a
square washer 2" on each side, is necessary to protect the wood from
crushing. There is to be a square hole, in the washer to receive the
square shank of the bolt and the thickness of the washers should be
⅛". The nut is square or hexagonal, and should _always_ have a washer
underneath when screwed home with a spanner or screw-wrench. The most
useful lengths are 2", 4", 6". The proper kind are known commercially
as _coach-bolts_, and they should be chosen with easy screws, for
facility in erecting or modifying apparatus. At least two dozen of the
intermediate size and a dozen of each of the others are required. For
elaborate contrivances many more will be necessary.
[Illustration: THE BED. FIG. 104.]
THE BEDS.—The simplest as well as the longest parts of the framework
are called “beds” (Fig. 104). Each bed is made of two wooden bars.
These bars are united by strong screws passing through small blocks of
hard wood so as to keep the bars full ⅜" asunder, and thus allow the
shanks of the bolts to pass freely through the slit The scantling of
each bar is 2½" × 1½", and the beds are of various lengths from 1' to
10' or even longer. The beds can be attached together in any required
position by bolts 6" long. The rectangles and the brackets are attached
to the beds by 4" bolts. In one conjunction or another the beds will be
found represented in almost every figure in the book. We may specially
refer to Figs. 20, 44, 48, 49, 50, 65, 83.
[Illustration: THE STOOL. FIG. 105.]
THE STOOL.—Most of the larger pieces of apparatus have the _stool_ as
their foundation (see Figs. 11, 39, 102). It is often convenient as
in Fig. 65 to employ a pair of stools, while one stool superposed on
another gives the convenient stand in Fig. 80. The stool is a stout
wooden frame, providing a choice of slits to which beds or other
pieces may be attached by bolts. The structure of the frame is shown
in Fig. 105. It is 2' 6" high and its extreme horizontal dimensions
are 2' 6" × 1' 9" of which the greater is A E. In other words, the
longer sides of the stool are those open at the top. Each top corner
is strengthened by an iron plate of which a separate sketch is shown.
The scantlings of the parts of the stool are as follows:—The legs
and horizontal top rails are 3" × 2⅛". Two of these rails with the
intervening ⅜" slit make the top and legs to be 4⅝" wide. The bottom
front rail I is 3" wide and 4" deep. The double side rails D, H are 1¾"
wide and 2½" deep, being made thinner than the legs into which they
are mortised in order to allow the washers of the bolts to pass behind
them. The slits are to be full ⅜" wide throughout. Beech or birch are
very suitable materials, but softer woods will answer if large washers
are invariably used.
[Illustration: THE RECTANGLE. FIG. 106.]
THE RECTANGLE.—The useful element of the Willis system known by this
name is of iron cast in one piece (Fig. 106). The rectangles are used
in the attachment of beds to each other under special conditions, or
they are often attached to the stools or to brackets. Indeed their
uses are multifarious, see for examples Figs. 12, 58, 62, 89, 97, 102
and many others. The faces of the rectangle are 2½" broad. The outside
dimensions are 6" and 9", and the thickness of metal is ⅝". Each side
of the rectangle has the usual bolt slit ⅜" clear. Rectangles of a
larger size are often found useful, their weight makes them effective
stands (see Figs. 35, 43, 52, 65).
THE TOOTHED WHEEL.—The most convenient type of toothed wheel for our
present purpose is that known as the cast iron _ten-pitch_. In all
such wheels the number of teeth is simply ten times the number of
inches in the diameter. For example a wheel with 120 teeth is 12 inches
in diameter. A number of ten-pitch wheels large and small must be
provided. The actual assortment that will be necessary depends upon
circumstances. For most purposes it will be sufficient to have the
multiples of 5 from 25 upwards to 120, and then a few larger sizes such
as 150, 180, 200. Duplicates of the constantly recurring numbers such
as 30, 60, 120 are convenient. _Arm_ wheels are always preferable to
_plate_ wheels in lightness and appearance as well as in price. All
wheels are to be 1" thick at the boss which is faced in the latter
at each side, and bored with a hole full 1" diameter, in which a key
groove is cut. A pair of mitre wheels such as are used in Fig. 80 are
sometimes useful.
[Illustration: THE STUD SOCKET. FIG. 107.]
THE PULLEY.—We have frequent occasion to use the pulley for conveying
a cord, and a somewhat varied stock is convenient Thus light brass
pulleys are used in the apparatus shown in Fig. 3, and a stout pulley
in Fig. 71. A cast iron pulley about 10" in diameter is seen in Figs.
32 and 34. It is bored 1" in diameter with a key groove, and the boss
is 1" thick. Some small pulley-blocks similar to those used on yachts
are often very useful.
THE STUD SOCKET.—For mounting toothed wheels on the larger pulleys or
for almost any rotating or oscillating pieces the stud socket is used
(see Fig. 107). The socket A B may be made of brass or of cast iron. It
is 1" in diameter so as to pass through the bosses of the wheels that
have been bored to 1" with this object:—The socket is provided with a
shoulder at one end (A) which is 1½" diameter, and with a strong screw
B and octagonal nut at the other end. The extreme length of the socket
is 3½", and the plain part of the 1" cylinder is 1¾" long. When two
wheels are placed on the socket each of which has a boss 1" thick, the
tightening of the nut will secure the wheels against the shoulder. A
feather is screwed on the plain part which enters the key grooves in
the wheels, and thus ensures that the wheels shall turn together. This
feather should be small enough to slip _easily_ into the key groove.
If only a single wheel or if any peculiar piece such as a wooden cam
or a disk of sheet iron has to be mounted, then collars or large thick
washers must be placed on the socket so as permit the screw to bind the
whole together. The socket revolves upon a stout iron stud C D, which
is ⅝" in diameter. It bears a shoulder or flange C at the back of the
same diameter as the base of the socket The stud bears on the other
side of the shoulder a strong screw and nut which project 1⅝" so as to
allow the stud to be secured in a hole 1" deep in one of the brackets
(to be presently described). The plain part of this screw near the
shoulder must be ⅝" diameter. The front end of the stud is pierced with
a hole to receive a spring pin to keep the socket from sliding off the
stud. Among the many applications of the stud socket we may mention
those shown in Figs. 30, 73, 74.
[Illustration: BRACKET NO. I. FIG. 108.]
[Illustration: BRACKET NO. II. FIG. 109.]
[Illustration: BRACKET NO. III. FIG. 110.]
THE BRACKET.—There are six different forms of cast iron brackets
represented in the adjoining figures (Figs. 108-113).
The brackets are primarily intended as the supports of the
stud sockets. For this purpose each has a head 1" thick bored with
a hole ⅝" diameter, and thus fitted to receive the screw on any of
the studs. Each bracket stands on a base or _sole_ with a slit full
⅝" wide for the bolts. The thickness of the sole is ⅝". The larger
of the brackets I., II., and IV. have also slits in their vertical
faces. Brackets can be fastened either to the stool or to the beds
or rectangles, and the variety of their forms enables the wheel-work
carried on the stud sockets to be disposed in any desired fashion.
Brackets avail for many other purposes besides those of supporting
rotating mechanism. (Look at Figs. 11, 12, 17, 20, 33, 38, 39, 73 and
many others.)
[Illustration: BRACKET NO. IV. FIG. 111.]
[Illustration: BRACKET NO. V. FIG. 112.]
[Illustration: BRACKET NO. VI. FIG. 113.]
[Illustration: THE TUBE FITTING. FIG. 114.]
THE SHAFTS AND TUBE-FITTINGS.—The stud sockets will not provide for
every case in which wheels have to be mounted and driven. We must
often employ shafts (see for instance Figs. 30, 47, 101). The shafts
we use are turned iron rods ¾" in diameter, and of various lengths
from 6" up to 4'. To support the shafts we use for bearings the _tube
fitting_ (Fig. 114). This is a brass casting which consists of a tube
M N 2" long, and 1¼" in external diameter, bored ¾" so as to fit the
shaft. The back of this tube is a flat surface parallel to the bore,
and from it projects a screw ⅝" diameter, and 1⅝" long with a nut which
is however omitted in the drawing. This screw may be of the same size
as that of the studs, and it is intended for the same purpose, namely
to attach the bearing to the hole in a bracket. The tube may of course
be fixed at any desired angle in the plane parallel to the face of the
bracket. To prevent the endlong motion of the shaft cast iron or brass
rings are employed (Fig. 115). These are bored ¾", and furnished with
a binding screw by which they may be tightened on the shaft in any
position. To avoid injury to the shaft it is well to have a narrow flat
surface filed along it to receive the end of the binding screw. The use
of the rings is shown in Fig. 47. If as often happens (see for example
Fig. 102) a barrel has to be set in motion by a shaft the required
attachment can be made by simply slipping on the barrel, and then
putting at each end of it two of the pinned rings (Fig. 115). The pins
enter holes bored into the barrel for their reception so that when the
rings are bound to the shaft by their screws the barrel must revolve
with the shaft.
[Illustration: THE PINNED RING. FIG. 115.]
[Illustration: THE ADAPTER. FIG. 116.]
THE ADAPTER.—For the attachment of wheels or other rotating pieces to
the shaft an adapter is employed (Fig. 116). It is bored with a ¾" hole
to fit the shaft, and the external diameter is 1". At one end is a
shoulder through which the binding screw is tapped, and there is a nut
and screw at the opposite end. A feather will prevent the wheel from
turning round on the adapter which is itself made to revolve with the
shaft by screwing the binding screw down on the shaft. Some adapters
are only large enough for a single wheel 1" thick in the boss, but it
is useful to have others that will take two wheels. Adapters are shown
in use in Figs. 46 and 101.
[Illustration: THE LEVER ARM. Fig. 117.]
THE LEVER ARM.—To give motion to the mechanism a lever arm with a
handle is frequently required (Fig. 117). It is bored 1" and has a
key groove, and the hole is 1" long, so that the lever arm can be
fixed on a stud socket like a wheel. By the aid of an adapter the
lever arm is attached to a shaft. For the use of the handle see Figs.
30 and 101. There are however many other uses to which the lever
arm is occasionally put. It can be used as a crank, and in linkage
arrangements a pair of lever arms are very convenient. Studs A or C can
replace the handle when necessary.
Such are the parts of the Willis apparatus which are adapted for our
present purpose. It remains to add that the fits should be very easy,
and the parts should be readily interchangeable.