Part 11

OF A DYNAMOMETER, _Or a second Machine to measure power & resistance in motion_.

In Plate 21 fig. 4, there is a representation of this Instrument. It is composed of a frame _A B_, containing a strong shaft _C D_, on which are placed the three following objects. First, a fixed pulley _E_, working by a strap, the Machine whose resistance is to be measured. 2ndly, a loose pulley _F_, receiving the power from the _mover_ whatever it be. And 3rdly, a barrel _G_, which is the acting pulley, when the strap is put on it from _F_ in the common method. But this barrel _G_ acts by means of a barrel-spring within it, which is hooked by one end to the boss of the shaft, and the other to the rim of the barrel, as is usual for barrel-springs in general. Now the power produces the desired motion by coiling this spring to the necessary degree: and to make that degree _visible_, there is fixed to this barrel _G_ a spiral _s_, which as the spring bends, drives _outward_ the stud _t_, and with it the _finger_ _v_, which, pointing to the graduated scale, shews at once the number of pounds with which the spring acts on the shaft _C D_ to turn it. By these means the stress on the straps and on the Machine turned is known; of which also the velocity is easily determined by counting the number of revolutions performed by either of the pulleys _E F G_, which are alike in diameter.

* * * * *

In ending the first part of this work, I gave my readers room to expect _this part_ “within three months,” and am happy now to fulfil that engagement. Although these pages contain fewer errors than the former--an apology is due for those that have crept in: to which I add the promise that every thing shall be done to lessen them further in the future parts, and wholly to correct them before the work closes.

Page 100, line 2, for “:”, read ∷; „ 126, „ 4, „ “on its surface” read at its pitch line. „ 126, „ 17, „ “its height _f g_,” read the length required. „ 129, „ 16, „ “2,” read 4, „ „ „ 20, „ “imperfect,” read homely. „ 144, „ 7, take away “_alone_.” „ „ „ 8, for “usually” read chiefly. „ 146, „ 23, for “the friction,” read it. „ 147, „ 1, for “nothing,” read little or nothing. In fig. 7 of Plate 19, slope the groove of both _faces_ the same way.

* * * * *

A few words seem wanting to complete the description of the Cutting Engine above given. They relate principally to the cutter-frame and cutters. Although, with a view to celerity, I have shewn the cutter _out_ of the frame (fig. 4) yet a common frame, carrying the arbor on points, may be used with propriety; and would often be an eligible substitute for the frame above described. In cutting bevel wheels however, either on this Machine or that to be described, there is a form of the cutter frame which leaves less freedom of choice, as the cutter itself _must_ have a peculiar form and position. To return to the cutter for spur wheels, their form (or section) depends on the degree of _finish_ which the wheels require. For _rough_ work they may be cylindrical on the face, the sides being _under cut_, so as to leave them thickest at the circumference--whence a certain coarseness of cut ensues, but without _any injury_ to the spiral form. But, generally speaking, the cutters are best, when made a little tapering towards the edge, and toothed on both sides as well as on the circumference. The teeth should be tolerably fine, but not very so, unless great _smoothness_ of surface were required: and we have seen above that, in this System, great smoothness is very seldom necessary, _provided the obliquities be correct_. I may add, that those cutters used on common engines, whose great rapidity compensates for the small number of their teeth, would not answer here, on account of the twisting motion in the wheel. But nothing prevents using cutters, so formed on the sides, as to round off the teeth in the act of cutting--only the cutter must be so thin as that its thickness, added to the aforesaid twist, may not make the _spaces_ too wide. A little observation will render these things familiar to an attentive observer: nor shall this work conclude before all that I have gathered from long observation on this subject, be fully known to my readers.

J. W.

_5, Bedford-street, Chorlton Row,_

_20th. November, 1822._

PART THIRD. A NEW CENTURY OF Inventions.

It has been observed and regretted by a well-known writer, that “a periodical work resembles a public carriage--which _must_ depart at the usual hour, whether full or empty;”--and having undertaken to deliver _this_ work at stated periods, I have found myself in a situation not unsimilar: the consequence of which has been a too cursory view of some of the subjects. I feel however, that _this_ is not a sufficient apology for any essential defect: nor would it be more so to say that, although verging to old age, I am still a young author. Yet I may claim the privilege of supplying, in the latter parts of the work, what is most deficient in the former; and thus of proving that I do not intentionally neglect any thing that might make it practically useful.

With these views I commence this third _part_: intending first to continue the description of the Cutting Engine given at page 121, _and here applied to Bevil Wheels_; and then to re-consider, shortly, one or two other objects, that were too rapidly passed over in their proper places.

Plate 22, repeats at fig. 1, the first figure of Plate 15; by way of shewing the additions required to extend this method of cutting teeth, to Bevil Wheels. These additions are _first_, a disk _n n_, concentrically fixed to the main axis _A B_ of the engine. And, _second_, an inclined plane _o_, of _variable_ obliquity, connected by a joint with the _forked_ sliding bar _p q_, by which the plane _o_ is put in contact with the disk, at whatever distance the cutter-stand _e f_ may be from the common centre, _which distance_ depends, of course, on the diameter of the wheel to be cut; and to secure which is the office of the fixing screw _r_, in the figure.

It is now evident that for the disk _n n_, and the shaft _A B_ to rise, the slide _p q_ and the cutter-stand _e f_ must recede: and _this_ more or less according to the degree of obliquity of the inclined plane _o_, that is according to the slope of the _bottom_ of the teeth in the wheel _w_: see the dotted line _w p_.

A circumstance presents itself, that should be here explained: when the bevil of the wheel _w_, or the cone of which the wheel is a part, is very obtuse, the cutter-stand _e f_, can not be driven back by the action of the disk _n n_ on the plane _o_, without too great a stress being applied from below, to the axis _A B_. (See the apparatus _I M O N_, Plate 16, fig. 2.) In this case therefore, the handle _R_ is not used: but a weight is suspended to the end _N_ of the lever _M N_, sufficient to give the whole System _A B_, a tendency _to rise_; and the operator now acts on the screw _g_, so as to draw back the plane _o_; by which motion the disk _m n_ with it’s axis _A B_ is _suffered_ to move upward, and the wheel is cut, as desired. But on the other hand when the wheels are portions of _acute_ cones, they are cut by means of the aforesaid handle; by which the plane _o_ and the cutter-stand are _forced_ backward as before intimated.

We proceed now to describe the perpendicular part of the cutter stand _e f_; which is made double, as shewn at _i k_ in fig. 4 of Plate 15; and is also perforated at various heights to receive the bolt which forms the centre of motion of the arm _m u_, the latter having a cylindrical boss _u_, fitted into the _fork_ of the stand _e f_, and so graduated as to determine the angle of it’s obliquity to the horizon, or it’s parallelism to the dotted line _w p_, which indicates the slope of the bottom of the teeth on the wheel. Finally, the cutter-frame _x_ is fastened to this arm at right angles to it, and thus forms a right angle (or nearly so) with the surface of the wheel: and is, moreover, directed to the centre, produced, of the shaft _A B_. This latter fact is strictly true, only when the teeth required are of so common a kind as _not_ to require greater exactness: for in theory the sides of the cutter (supposed cylindrical) must alternately direct to that centre--namely, _that_ side which is actually cutting: so that a provision must be made to shift the cutter spindle sideways, a distance equal to it’s diameter; this being no more than what is necessary in every system of wheel cutting.

We may also consider here, the form of the cutter itself, _v_, fig. 1. It is slightly conical, (more or less so according to it’s use) and of no greater diameter than the smallest width of the _spaces_ between the teeth of the wheel. A common disk-like cutter would not produce perfect, nor even tolerable teeth on a bevil wheel. The reason of this will appear by considering that a spiral line, either on a cone or it’s base, _turns_ more the further it is from the centre, and less the nearer it comes to it. So that a _flat_ cutter placed at _any_ angle, is parallel to the curve at _one_ place only; whence the propriety of using a cutter of the kind represented in this figure. It is however true, that the first opening of the spaces may be made with a common cutter; but it should be very thin comparatively with the spaces required: and it’s cut would serve only as a _sketch_ of such space, serving principally to permit the metal to escape while finishing the teeth with the cutter just described.

I proceed now to the examination of _the plates_, and the manner of 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.