adapting their length to the process of cutting _spiral teeth on bevil
wheels_. But before entering on this subject, I would explain a kind of
inadvertency into which I fell at the close of my former description of
this Engine (see page 129). In my zeal to be candid in stating the
properties of my Machines, I have suffered it to _appear_ that I thought
this an “imperfect” one:--an expression which, although modified among
the errata, may still cause it to be looked upon as radically defective;
than which nothing could be further from the idea I wished to convey. I
intended merely to express the want of _absolute_ connection between the
two movements of the shaft--the rotatory and longitudinal motions. I
meant that the process by this Machine was not theoretically _certain_,
because dependent on the action of a weight (Plate 16, fig. 1 and 2) and
an _unforced obedience_ to the direction of the plates. But this small
remove from rigourous principle is in my opinion _much_ overballanced by
the facility of cutting _good wheels of all diameters_, by the sole
change of a morsel of tin, which leaves untouched every other part of
the Engine.
Entering then on this branch of the subject, I first observe that if we
chuse for the teeth an inclination of 15 degrees (in imitation of the
cylindrical wheels) it can only be for one point of such wheels--as
observed above. This point therefore I have placed at _r_ in the middle
of the face. And supposing now that at this point the wheel _O_ were 4
inches in diameter and the wheel _S_ two inches, these plates would be
found as before by these analogies:
(1) _wr_, or 2 inches : 11 inches (rad. of plate rim) ∷ 26.8 : 294.8/2 =
147.4 plate required.
(2) _vr_, or 1 inch : 11 inches (rad. of plate rim) ∷ 26.8 : 294.8/1 =
294.8 2d. plate required.
But it is plain that the conical face, _b C_, (common to both wheels) is
_broader_ than the supposed cylindrical ones _b e_ and _b d_: and
therefore that the above plates must be made longer (to furnish the said
obliquity) in the following proportions, namely: for the wheel _O_ in
the ratio of _b e_ to _b C_; and for the wheel _s_ in that of _b d_ to
_b C_: that is, these plates should be lengthened as the tabular
cosines of the angles _B A C_ and _D A C_ to radius (for _b e_ : _b C_ ∷
_A B_ : _A C_; and _b d_ : _b C_ ∷ _A D_ : _A C_.) Thus then,
(1) Cos. 63°27′ : radius ∷ 147.4 (present plate) : required plate _x_, =
147.4 r/Cos. 63°27′; and
(2) Cos. 26°33′ : radius ∷ 294.8 (present plate) : required plate _y_, =
294.8 r/Cos. 26°33′.
Now, by the tables, cosine 26°33′ = 894, and cosine 63°27′ (it’s
complement) = 447, when radius is 1000: whence dividing the two
equations by _r_, and substituting these values of cosines 63°27′ and
26°33′ we shall find the two quantities _x_ and _y_, _equal_. Whence it
appears that for every _pair_ of bevil wheels, whose shafts lie at right
angles, _the same plate serves for both wheels_: only turning it once to
the right, and once to the left hand on the plate rim.
And if now we _measure_ on a scale of _equal_ parts, the line _A r_ and
call it 100, we shall find the line _w r_ (near enough for practice) to
be 90, and the line _v r_ to be 45, and these numbers respectively, put
for rad. for cos. 26°33′, and for cos. 63°27′, will make the first
equation _x_ = 147.4 × 100/45 and _y_ = 294.8 × 100/90 or _x_ = 327.55
and _y_ = 327.55, &c. confirming the above deduction that the _same
plate_ serves for both wheels; and giving, withal, the length of the
plate required.
In performing this operation by actual measurement of the lines, I have
had in view to trace a path for those of my readers who may not have
the tables, or may be unaccustomed to use them. The process, generally,
is to take the diameter of any bevil wheel _O_ fig. 4, in the middle of
it’s face; and _supposing_ it a spur wheel, to find it’s plate by the
method above given: and then to multiply the length of that plate by the
line _A r_ and divide the product by the line _A w_, both measured on
the same scale of equal parts.
It may be well to observe, likewise, that the same method of finding the
plates, applies to bevil wheels of every description or angle: but that
it does not give equal plates for every _pair_, except in the above case
of wheels placed at right angles to each other.
I would just remark that by the figure near _B_, is shewn a _section_ of
the Machine on which I centre the wheels to be cut on this Engine. It is
an inverted cup _s t_, into which the _arbor_ is screwed in a _true_
position; and this cup is fixed on the top of the shaft _A B_, by the
_three_ pressure screws near _s t_, which enter a triangular neck made
round the shaft, against the _upper_ slope of which, the screws press so
as to draw the cup downward in the act of centering it. This I say is my
present method; but it is in a measure accidental, the shaft not having
been perforated to receive arbors of the usual kind. Mine, however, have
their utility in the ease with which they are varied in size, and
changed on the Machine: but on their _comparative_ usefulness I give no
opinion. The other is the most solid method.
In the description of my differential Steel-yard, (see page 163) I
stated that the load _P_ was wholly collected in the point _o_; and that
dividing the line _A C_ by the line _A o_, the power of the Machine was
known. But I should have shewn that this line (_A o_) is _equal to one
half the difference between the arms_ _A D_ _and_ _A E_. To do this,
here, (see Plate 23, fig. 4) I take the Machine in the state of infinite
power, before mentioned; and observe, that in moving the point of
suspension from _o_ towards _A_, I at once _lengthen_ the arm _A E_, and
_shorten_ the arm _A D_: by which process, (supposing each arm to have
been called _a_) that which I lengthen by any quantity _d_ becomes _a_ +
_d_, and that which I shorten by the same quantity becomes _a_ - _d_,
and the difference of these quantities, is 2_d_: so that the line _A o_
is in reality one half the difference between the two arms _A D_ and _A
E_ as was required to be shewn.
But we may go a step further: The two arms of the equibrachial lever _x
y_ may likewise be made _unequal_: and the line _s a_ be subdivided in
any ratio: which division will augment still more the power of this
Machine. If for example, we hang the load on the point _v_, halfway
between _a_ and _s_, that power will be doubled; for the line _c v_
(representing the space moved through by the load in this case) is only
one half of _that_ _w s_, or _o q_, and might be still less at pleasure.
Thus the whole power of the Machine is _now_ found by dividing the
length of the long arm, beyond _D_, by the line _a v_, instead of the
former line _A o_, or dividing the _motion_ of it’s extremity upward, by
the line _c v_, the motion downward, of the load _P_.
It has been further suggested, that the description of my excentric Bar
Press was not sufficiently explicit. I have therefore added the figure 2
of Plate 22, to assist in elucidating that description. I had, perhaps
made an undue use of the principle of virtual velocities by saying, too
concisely, (page 174) that “as the whole approaches toward _B C_, the
relative motion (of the cheeks _s_ and _B_) becomes insensible, the
circles parallel, and consequently, the power infinite.” It is however
_vulgarly_ said that _power_ cannot be gained without losing
_time_--which implies that if time _is_ lost, power will be gained: and
the principle of virtual velocities says the same thing, though in more
appropriate terms--that if a small movement be given to a system of
bodies actually counterpoising each other, the quantity of motion with
which one body ascends, and the other descends perpendicularly, will be
equal: so that, as remarked in page 50, by “whatever means a slow motion
is obtained, dependent on that of a moving force, the power is great in
the same proportion.” Now, in the eccentric Bar Press, (see fig. 2) this
is so in an eminent degree: for when the bars are in the position _A B_,
the distance of the cheeks is equal to _B s_; and they must move,
circularly, as far as _A f_, to bring them closer to each other by the
quantity _s a_: dividing therefore, the distance _B g_ by the line _s
a_, we find (near enough for practice) the power of the Machine within
the limits _A g B_. It is nearly as 10 to 1. In like manner this power
at _A e g_, is equal to the arc _e g_ divided by the line _f b_; and at
_A l n_ to the arc _l n_ divided by the line _d k_, namely by the
difference of the lines _k l_ and _m n_. From the above it appears that
the _nearing_ motion of the cheeks of the press, becomes slower and
slower as the bars _A_ and _C_ come nearer to the point _C_: insomuch
that the difference between the lines _m n_ and _o p_ is nearly
imperceptible, and _that_ between the lines _o p_ and _C q_ entirely so.
But according to the above process, the distance _p C_ should be divided
by this _imperceptible line_, to find the power of the press at the
point _C_; which therefore is _immense_. Another proof of this may be
drawn from the supposition (see fig. 3) that the small lever _a d_ is
turned round the centre _o_ by a bar _o C_ fixed to it, and of equal
length with the line _A C_ fig. 2. Fig. 3 shews that the lines or bars
_C d_, and _a C_ are moved endwise by the _circular_ action of the
points _a_ and _d_; and therefore (by statics) their motion is the same
as though caused by the perpendiculars _b o_ and _o c_ let down from the
centre _o_, on each of them. Hence the power of this Machine is found by
dividing the distance _o C_ by the sum of the lines _b o_ and _o c_;
which sum (when these lines _vanish_ by the union of the bars over the
centre) becomes infinitely small: the quotient of which division
therefore is infinitely great--as was to be shewn.
OF
A PUNCH MACHINE,
_For Engravers to Calico Printers_.
The usual method of making Punches for engraving Copper Cylinders,
(otherwise than by the _milling_ system) is to _cut_ the desired pattern
on _a die_, and then to transfer that pattern by blows or pressure to
the punch, from which it is again transferred to the cylinder. My
Machine in this operation, unites motion to the needful pressure; and
thus renders the result more easy and complete. This effect I could the
better ensure, because the surfaces of _my_ punches are essentially
convex, or rather cylindrical; as will appear when my engraving Machine
comes to be described. Their convexity however, can be diminished at
pleasure--whence this Machine is capable of offering useful assistance
to a maker of flat punches.
In Plate 23, _A B_ fig. 1 and 2, is the body of the Machine, with the
vibrating bar _C D_ laid upon it; reposing especially on the correct and
level parts of the body at _a b_; this bar contains the _die_ _c_, with
which it vibrates between the cheeks _B R_, as impelled by the screws _E
F_, it’s centre of motion being the pin _P_, duly supported by the
strong shoulder _A_. In a line with the bar _C D_, is placed a second
_vibrator_ _G_, containing the steel _d_, that is to become a punch,
already rounded into the cylindrical shape it must have when finished.
This vibrator has it’s centre of motion at _e_ fig. 1, and it need not
be added that the curvature of the punch depends on it’s distance _e d_
from that centre: for the centre of the long bar _C D_ is _so_ distant
as to have little influence on it’s formation. Further, the cap or
bridge _H I_, which furnishes a centre for the smaller vibrator _G_, can
be brought forward to any useful position by the nuts _K L_: that cap
sliding horizontally between the cheeks _M N_ as directed by the small
_arms_ _m n_. This motion, then, taken from the nuts _K L_, serves to
impress the _work_ of the die on the steel prepared for the punch; and
this being done to a _first_ degree, both the handles _O Q_, are laid
hold of: and by turning the screws the same way one of them goes forward
and the other recedes, until the punch and die have been in contact over
half their surface. At this moment both screws are turned backward, and
the motions of the two vibrators reversed: by the repetition of which
alternate motions accompanied by the needful pressure, the whole pattern
is transferred from the _die_ to the punch--when the latter is taken out
of the Machine, and _filed up_ in the usual method.
It should be observed, that the smaller vibrator _G_ can be displaced
with ease when the nuts _K L_ are withdrawn: and this should be
frequently done to examine the progress of the impression. Nor is there
any difficulty in re-entering the figures. In a word, the perfection of
this process depends more on _much_ motion than on violent pressure:
whence this facility of re-entering is a desirable property. This
Machine is usually laid on a bench or tressel, with a long mortice in
it, into which the feather _x_ of this Machine enters so as to be firmly
fixed.
OF
A DIFFERENTIAL PUNCH MACHINE
_For Engravers_.
I was the rather induced to attend a second time to the differential
Steel-yard, because I had it in contemplation to apply that principle to
the present purpose; since, to make flat punches, is to some engravers a
more desirable thing than to make cylindrical ones. I am not fully
persuaded that it is even possible to transfer a large pattern, from a
flat die to a flat punch, by _any_ pressure acting simultaneously on the
whole surface. In those cases, if there is much _work_, the whole
surface _goes_ _down_; and the parts that form the pattern do not
_rise_. But, all that can be done in this case, is, I believe, feasible
by the Machine now to be described.
Plate 23, gives in fig. 3 and 4, a representation of this Machine; _A B_
and _C D_, are two _slides_, having wedge-formed ends above _A_ and
below _D_, well made, well steeled, and well tempered. One of these
slides contains the _die_ and the other the steel prepared for the punch
(see _B C_). These wedge-ended slides are _embraced_ by two levers _E
F_, _G H_, which are themselves connected by two stirrups _I K_ and _L
M_, better shewn at fig. 3. These latter are supposed in fig. 4 to be
broken at _L M_, to leave the levers _E F_ and _G H_ more visible. They
are formed, at the turning below, into wedge-like edges _a b_; well
hardened, that clip the _nicks_ _c d_ of the lower lever: and at the top
of the Machine their arms _e f_, pass through the caps _m n_, above
which they are _nutted_ like a common bolt, and made to press strongly
on the main lever _E F_. The stirrup placed to the right hand, presses
in particular, by it’s cap _n_, on the moveable _step_ _o_, exactly in
the notch _q_: this step having a backward and forward motion
communicated by the regulating screw _p_. Before beginning to use this
Machine, I make all it’s arms _A E_, _A g_, _D e_, _D d_, equal, when
it’s power (see page 162) is infinite; and to put it in a working state,
I turn the screw _p_ backward, say one half round: which motion (if the
screw has 20 threads to the inch) makes a difference in the two arms _A
r_ and _A q_ of 1/40 of an inch, and the virtual centre of the Machine
is therefore 1/80 of an inch from the former point _A_, that is from the
_edge_ of the slide _A_ in this fig. 3. Supposing now, the whole working
lever _E F_ to be 3 feet, and the workman’s force to be 100lbs. in each
arm, then by displacing the lever to any proper distance from _F_
towards _f_, he will produce a pressure between the die and the punch of
200lbs. multiplied by 1440, the number of times that 1/80 of an inch is
contained in 18 inches.--That is, a pressure of two hundred and
eighty-eight thousand pounds!
I have been seduced, by the anticipated brilliancy of this result, from
the regular course of description,--and the plate _w x_, _y z_, which
forms the base or frame of this whole Machine has not yet been spoken
of. But that plate is supposed screwed down to a horizontal bench, at or
near the height of a man’s breast; the slides or cases are fastened to
it, and the man is supposed to _work_ the Machine nearly as he would a
die-stock in tapping a screw. This however is not indispensable; the
Machine might be placed vertically, and these motions given by any
proper mover; or a weight may be suspended to the arm _F_, so as to add
continuity to pressure. It is however important, that the position
should comport with the frequent extraction of the punch in order to
examine the progress of the work, or cut away any redundant metal. I
have before given it as my opinion that _much_ could not be expected
from mere pressure: but _this_ is a pressure of a peculiar kind,
consisting of immense powers with _very_ short motions. In this respect
it is _just_ what was wanted, as it can be renewed and repeated
frequently, without loss of time. And the more to facilitate this
delicate operation, the hollow slides or cases _B C_, are made slightly
pyramidical, to be furnished with _set-screws_ on the four sides, by
which to change the place of bearing; and thus to meet the case of a
flat punch with the advantage of impressing it by _portions_, so as to
have only to _finish_ it by brute pressure.
The foregoing application of the principle of the differential
Steel-yard, is, I think, important, and founded on unobjectionable
principles; for although by changing alone the place of the step _o_,
we disturb a _little_ the parallelism of the stirrups _I K_, and _L M_;
we do it not enough to produce, any material change in the theoretical
result. With respect then to the lesser properties of this Machine, I
leave them with confidence in the hands of those whom they most
concern--who doubtless, will treat them with greater practical utility
than I could myself hope to do.
OF
A MACHINE
_For Moulding Nails._
This Machine offers, I think, a valuable application of a well known
Instrument: or rather of the principle on which it is founded. I allude
to _that_ parallel ruler which, by means of an additional joint, keeps
it’s members not only parallel, but directly opposite each other. In my
Machine for moulding Nails, I wanted to give motions to the two plates
different, yet dependent on each other. Supposing then, (Plate 24 fig.
1, 2, 3, 4,) the upper plate _a b_, to be moved up and down by a lever,
a screw-press, or any other _first mover_, I connect the under plate _c
d_, with it by two (or four) _strong_ parallel rulers _e f_, in such a
manner, that when the plate _a b_ is drawn upward it shall extend the
arms of the ruler _almost_ to a straight line, as represented in fig. 4;
and then carry the under plate with it: and when it comes down again
(see fig. 3) it shall _not_ carry down the said under plate, until the
same arms are bent into the position _f g_; that is, till the two plates
touch each other: the use of which arrangement I will now explain.
The under side of the upper plate _a b_, is _ground_ perfectly flat, and
bored at proper distances with holes to receive and hold the punches
which represent the shanks of the nails that are to be moulded. The
lower plate _c d_ is ground _true_ both on it’s upper and under
surfaces; the first to fit the under surface of the upper plate, and the
under surface to impress a perfect plane on the sand below it. This
under surface, shewn in an inverted position at fig. 2, is moreover
covered with proper _prints_ 1, 2, 3, &c. to form the heads of the nails
in question, and with proper _gets_ (jets?) 3, 5, 6, &c. for conducting
the metal to every part of the surface. I mean models in relief of those
gets; and the under plate is further pierced with holes, placed exactly
like those in the upper plate, bored indeed from that (and through the
aforesaid _prints_ of the nail-heads) _after_ the parallel joints _e f_
have been affixed. Now on another level plate with proper ledges, the
sand boxes or flasks, fig. 5 and 6, have been prepared; and have
received an obtuse pyramidical form at one stroke from a competent
press, the construction of which is easily conceived: or this might be
done by hand, if preferred. These boxes, in-fine, are successively
brought under the before described mechanism while in the state
represented in fig. 3, in which all the nail models are protruded
through the under plate as at 1, 2, 3. The moulder now gives a stroke
under the following circumstances:--Both the plates drop together and
the nail models pierce the sand while the under plate makes it’s surface
perfectly level: but when _that_ motion is reversed, it is _not_ the
under plate which first rises, but the upper--by which the nail models
are drawn out of their holes _without disturbing the sand_, for this is
kept to it’s place by the under plate: and when, by the continued motion
upward of the upper plate, the parallel joints are duly extended, and
the nail models quite extracted; then, and not till then, the under
plate leaves the compressed sand, in which are moulded as many _scores_
of nails as the mould has been made for--and that, in a space of time
almost imperceptible.
I shall conclude the subject by observing, that the counter flask or box
for closing this mould is made in the same way, by a smooth plate
prepared in the same manner; and which _must_ fit the former, because
they are both perfectly level surfaces.
OF
A FIRE ENGINE
_Giving_ POWER, _while heating Rooms, Liquids, &c._
This Machine, though conceived many years ago, can hardly yet be called
an invention--if material existence is necessary to justify that
appellation: _for I have never seen it in action_. It _may_ possibly be
one of those fascinating conceptions of which my noble friend the late
Earl Stanhope used to say--“’tis a _beautiful_ invention--but ’twill not
do;” yet I give it with some confidence, because of the great utility it
_would_ present, if it’s chief properties should fulfil my expectations.
The principal idea on which it is founded, is this: _to use, as power,
the expansion of that air which feeds the fire_; and _again_ to employ
it’s heat heating liquids or rooms, or any similar purpose. The form I
have given to the Machine is by no means the only one it admits; nor
perhaps the best: but it was indispensable to give the idea (which I
hope is not an “airy nothing”) “a local habitation and a name.”
It consists, then, of two cylinders, lying horizontally, of nearly equal
length, but of unequal capacity:--one of which _A B_, (Plate 24, fig. 7)
is an air pump with a valve in it’s end _a_, and another in it’s piston,
both opening _to the left_. The second cylinder _C D_, is the working
cylinder, as much larger than the former, as may belong to the principle
of motion already announced. This cylinder receives the piston _E_,
which fits it nicely, but is not stuffed in the present case. (It may
perhaps be made tight by some of the methods, used to _close_ metallic
pistons.) At all events, this piston is connected with that _c_, by a
frame _F G H I_, which embraces the whole Machine, in a horizontal
position, though here shewn in a vertical. These two cylinders are cast
in one piece, together with an upright cylinder, not bored _K_; the use
of which is to receive the _earthen_ chafing dish _L M_, with it’s fire,
made (according to my present views) with _coak or charcoal_, and
lighted before it is introduced. It is needless to say, that this vessel
is let down into the cylinder _K_, by a kind of bucket handle entering
any _pair_ of holes in the dish. The top of this latter cylinder is
_ground_ to fit the flanch _A N_: It swings open on one of the bolts and
falls to again in a moment, to prevent loss of time in _firing_. The
_means_ of doing this I do not much insist on, from their extreme
facility. Nor do I make it a _condition_ to use this method at all. The
coak, (or perhaps the coal, or the wood) _might_ be introduced through
an upright tube furnished with two slides, one placed close above the
top _A N_, and the other at a proper distance above; so as for _one_ to
be always shut. This is nothing more than the System used for feeding
high pressure Steam Engines--only _this_ application is to dry
substances, which forms no insuperable obstacle.
When now the Machine is _fired_, the pistons _E_, and _c_, are pushed
towards _b_ and _B_ respectively; the valve _d_ having been previously
opened, and the valve _c_ opening by this very motion--which thus clears
the large cylinder of it’s included air, while the air in the pump _A
B_, is brought into contact with the fire; whence a _considerable
expansion_ ensues, and a _pressure_ is created tending at the same time
to drive the piston _c_ to the _right hand_, and that _E_ to the _left_:
but acting in the latter case on a larger area, the whole system moves
that way, and _all_ the air in the pump _A B_ is driven through the
fire: where, being much heated, it acquires great elasticity and
developes considerable _power_--which, by any of the known methods, may
be applied to any of the known purposes.