Part 18

Bloxam's escapement was modified in form by Lord Grimthorpe, his chief improvement being the addition of a fly vane, which, however, had previously been used for remontoires to steady the motion. He tried various modifications of construction, but finally adopted the "four-legged" and "double-three-legged" forms as being the most satisfactory, the former for regulators and the latter for large clocks. Fig. 19 is a back view of the escapement part of an astronomical clock with the four-legged wheel; seen from the front the wheel would turn the other way. The long locking teeth are made about 2 in. long from the centre, and the lifting pins, of which four point forwards while four other intermediate ones point backwards, are at not more than 1/30 of the distance between the centres EC, of the scape-wheel and pallets; or rather C is the top of the pendulum spring to which the pallets Cs, Cs' converge, though the resultant of their action is a little below C. It is not worth while to crank them as Bloxam did, in order to make them coincide exactly with the top of the pendulum, as the friction of the beat pins on the pendulum is insignificant, and even then would not be quite destroyed. The pallets are not in the same plane, but one is behind and the other in front of the wheel, with one stop pointing backwards and the other forwards to receive the teeth alternately--it does not matter which; in this figure the stop s is behind and the stop s' forward. The pendulum is now going to the right, and just beginning to lift the right pallet and free the stop s'; then the wheel will begin to turn and lift the other pallet by one of the pins which is now lowest, and which moves through 45° across the line of centres, and therefore lifts with very little friction. It goes on till the tooth now below s reaches s and is stopped there. Meanwhile the pallet Cs' goes on with the pendulum as far as it may go, to the end of the arc which we have called [alpha], starting from [gamma]; but it falls with the pendulum again, not only to [gamma] but to -[gamma] on the other side of 0, so that the impulse is due to the weight of each pallet alternately falling through 2[gamma]; and the magnitude of the impulse also depends on the obliqueness of the pallet on the whole, i.e. on the distance of its centre of gravity from the vertical through C. The fly KK' is set on with a friction spring like the common striking-part fly, and should be as long as there is room for, length being much more effective than width.

The double three-legged gravity escapement, which was first used in the Westminster clock, is shown in fig. 20. The principle of it is the same as of the four-legs; but instead of the pallets being one behind and the other in front of the wheel, with two sets of lifting pins, there are two wheels ABC, abc, with the three lifting pins and the two pallets between them like a lantern pinion. One stop B points forward and the other A backward. The two wheels have their teeth set intermediately or 60° apart, though that is not essential, and the angle of 120° may be divided between them in any other proportions, as 70° and 50°, and in that way the pallets may be still more oblique than 30° from the vertical, which, however, is found enough to prevent tripping even if the fly gets loose, which is more likely to happen from carelessness in large clocks than in astronomical ones.

Of course the fly for those escapements in large clocks, with weights heavy enough to drive the hands in all weather, must be much larger than in small ones. For average church clocks with 1¼ sec. pendulum the legs of the scape-wheels are generally made 4 in. long and the fly from 6 to 7 in. long in each vane by 1¼ or 1½ wide. For 1½ sec. pendulums the scape-wheels are generally made 4½ radius. At Westminster they are 6 in.

Lord Grimthorpe considered that these escapements act better, especially in regulators, if the pallets do not fall quite on the lifting pins, but on a banking, or stop at any convenient place, so as to leave the wheel free at the moment of starting; just as the striking of a common house clock will sometimes fail to start unless the wheel with the pins has a little run before a pin begins to lift the hammer. The best way to manage the banking is to make the beat-pins long enough to reach a little way behind the pendulum, and let the banking be a thin plate of any metal screwed adjustably to the back of the case. This plate cannot well be shown in the drawings together with the pendulum, which, it may be added, should take up one pallet just when it leaves the other.

Chronometer spring remontoire.

In chronometer spring remontoires the pendulum, as it goes by, flips a delicate spring and releases a small weight or spring which has been wound up in readiness by the action of the scape-wheel and which by leaping on to the pendulum gives it a push. One on this principle made about the middle of the 19th century by Robert Houdin is to be seen at the Conservatoire des Arts et Métiers. It is very complicated. The following is more simple. In fig. 21 a scape-wheel AB has 30 pins and 360 teeth. It is engaged with a fly vane EP mounted on a pinion of 12 teeth. Each pin as it passes raises an impulse arm CD which is hooked upon a detent K. A pall NM then engages the fly vane and prevents the scape-wheel from moving farther. The impulse arm being now set, as the plate F attached to the lower end of the pendulum flies past from left to right a pall G knocks aside the detent K, and allows a pin O projecting from the end of the impulse arm to fall upon an inclined pallet h, which is thus urged forward. As soon as the pallet has left the pin, the impulse arm in its further fall strikes N, which disengages the pall at P and allows the scape-wheel to move on and again wind up the impulse arm CD, which is then again locked by the detent K. On the return journey of the pendulum the light pall G, which acts the part of a chronometer spring, flips over the detent. The pallet is double sided, h and h', so that if by chance the clock runs down while the pendulum swings from left to right the impulse arm will be simply raised and not smashed. It has a flat apex, on which the pin falls before descending. The impulse given depends on the weight of the impulse arm and may be varied at pleasure. The work done in unlocking the detent is invariable, as it depends on the pressure of the fly vane at P and is independent of the clock-train. The duration of the impulse is very short--only about 1/10 of the arc of swing. It is given exactly at the centre of the swing, and when not under impulse the pendulum is detached.

_Clock Wheels._--Since, as we have seen, any increase in the arc of a pendulum is accompanied by a change in its going rate, it is very desirable to keep the force which acts on the pendulum uniform. This in fact is the great object of the best escapements. Inasmuch as the impulse on the pendulum, derived from the work done by a falling weight or an unwinding spring, is transmitted through a train of wheels, it is desirable that that transmission should be as free from friction and as regular as possible. This involves care in the shaping of the teeth. The object to be aimed at is that as the wheel turns round the ratio of the power of the driver to that of the driven wheel ("runner" or "follower") should never vary. That is to say, whether the back part of the tooth of the driver is acting on the tip of the tooth of the follower, or the tip of the driver is acting on the back part of the tooth of the follower, the leverage ratio shall always be uniform. For simplicity of manufacture the pinion wheels are always constructed with radial leaves, so that the surface of each tooth is a plane passing through the axis of the wheel. The semicircular rounding of the end of the tooth is merely ornamental. The question therefore is, suppose that it is desired by means of a tooth on a wheel to push a plane round an axis, what is the shape that must be given to that tooth in order that the leverage ratio may remain unaltered?

Epicycloidal teeth.

If a curved surface, known as a "cam," press upon a plane one, both being hinged or centred upon pivots A and B respectively (fig. 22), then the line of action and reaction at D, the point where they touch, will be perpendicular to their surfaces at the point of contact--that is perpendicular to BD, and the ratio of leverage will obviously be AE:BD, or AC:CB. Hence to cause the leverage ratio of the cam to the plane always to remain unaltered, the cam must be so shaped that in any position the ratio AC:CB will remain unchanged. In other words the shape of the cam must be such that, as it moves and pushes BD before it, the normal at the point of contact must always pass through the fixed point C.

If a circle PMB roll upon another circle SPT (fig. 23) any point M on it will generate an epicycloid MN. The radius of curvature of the curve at M will always be MP, for the part at M is being produced by rotation round the point P. It follows that a line from B to M will always be tangential to the epicycloid. If the epicycloid be a cam moving as a centre round the centre R (not shown in the figure) of the circle SPT, the leverage it will exert upon a plane surface BM moving round a parallel axis at B, will always be as BP to PR, that is, a constant; whence MN is the proper shape of a tooth to act on a pinion with radial arms and centred at B. In designing a pair of wheels to transmit motion, which is to be multiplied say 6 times in the transmission (about the usual ratio for clock wheels), if we take two circles (called the "pitch circles") touching one another with radii as 1:6, then the circumference of the smaller will roll 6 times round that of the larger. The smaller wheel will have a number of teeth, say 8 to 16, each of them being sectors of the circle (fig. 24). If there are 16 teeth, then on the surface of the driving wheel there will be 96 teeth. Each of these teeth will be shaped as the curve of an epicycloid formed by the rolling on the big circle of a circle whose diameter is the radius of the pitch circle of the pinion. Points of the teeth so formed are cut off, so as to allow of the pinion having a solid core to support it, and gaps are made into the pitch circle to admit the rounded ends of the leaves of the pinon wheel. Thus a cog-wheel is shaped out.

Clock wheels are made of hard hammered brass cut out by a wheel cutting machine. This machine consists of a vertical spindle on the top of which the wheel to be cut is fixed on a firmly resisting plate of metal of slightly smaller diameter, so as to allow the wheel to overlap. A cutter with the edges most delicately ground to the exact shape of the gap between two teeth is caused to rotate 3000 - 4000 times a minute, and brought down upon the edge of the wheel. The shavings that come off are like fine dust, but the cutter is pushed on so as to plunge right through the rim of the wheel in a direction parallel to the axis. In this way one gap is cut. The vertical spindle is now rotated one division, by means of a dividing plate, and another tooth is cut, and so the operation goes on round the wheel.

It is not desirable in clocks that the pinion wheels which are driven should have too few teeth, for this throws all the work on a pair of surfaces before the centres and is apt to produce a grinding motion. Theoretically the more leaves a pinion has the better. Pinions can be made with leaves of thin steel watch-spring. In this case quite small pinions can have 20 leaves or more. The teeth in the driving wheels then become mere notches for which great accuracy of shape is not necessary. Such wheels are easy to make and run well. Lantern pinions are also excellent and are much used in American clocks. They are easy to make in an ordinary lathe. The cog-wheels must, however, be specially shaped to fit them. They consist of a number of round pins arranged in a circle round the axis of the wheel and parallel to it. The ends are secured in flanges like the wires of a squirrel cage. The teeth of cog-wheels engage them and thus drive the wheel round. They were much used at one time but are now falling out of favour again.

Involute teeth.

It is possible to make toothed wheels that drive with perfect uniformity by using for the curve of the teeth involutes of circles. These involutes are traced out by a point on a string that is gradually unwound from a circle. They are in fact epicycloids traced by a rolling circle of infinite radius, i.e. a straight line. Involute teeth have the advantage that they roll on one another instead of sliding. When badly made they put considerable strain on the axes or shafts that carry them. Hence they have not been regarded with great favour by clockmakers.

Pitch.

By the pitch of a wheel is meant the number of teeth to the inch of circumference or diameter of the wheel; the former is called the circumferential pitch, the latter the diametral pitch. Thus if we say that a wheel has 40 diametral pitch we mean that it has 40 teeth to each inch of diameter. The circumferential pitch is of course got by dividing the diametral pitch by [pi]. Wheel-cutters are made for all sizes of pitches. If it were needed to make a pair of wheels the ratio of whose motion was say 6:1 and we determined to use a diametral pitch of 30 to the inch, that is teeth about 1/10 in. wide at the base, and if the smaller circle were to have 20 teeth, we should need a blank of a diameter of 20/30 + 2/30 = 22/30 in. for the smaller wheel, and one of 120/30 + 2/30 = 122/30 in. for the larger wheel which would have 120 teeth to the inch and be 4.06 in diameter to the tips of the teeth. The smaller toothed wheel would be .73 of an inch in diameter over all. The pitch circles of the wheels would be 2/3 and 4 in. respectively. For fine wheel work, where the driver is always much larger than the driven wheel, the epicycloidal tooth appears preferable, as it is generally considered to put less side strain on the pinion wheel. But the relative merits of the two systems have never been properly tested for clock work.

_Going Barrels._--A clock which is capable of going accurately must have some contrivance to keep it going while it is being wound up. In the old-fashioned house clocks, which were wound up by merely pulling one of the strings, and in which one such winding served for both the going and striking parts, this was done by what is called the endless chain of Huygens, which consists of a string or chain with the ends joined together, and passing over two pulleys on the arbors of the great wheels, with deep grooves and spikes in them, to prevent the chain from slipping. In one of the two loops or festoons which hang from the upper pulleys is a loose pulley without spikes, carrying the clock-weight, and in the other a small weight only heavy enough to keep the chain close to the upper pulleys. Now, suppose one of those pulleys to be on the arbor of the great wheel of the striking part, with a ratchet and click, and the other pulley fixed to the arbor of the great wheel of the going part; then (whenever the clock is not striking) the weight may be pulled up by pulling down that part of the string which hangs from the other side of the striking part; and yet the weight will be acting on the going part all the time. It would be just the same if the striking part and its pulley were wound up with a key, instead of the string being pulled, and also the same, if there were no striking part at all, but the second pulley were put on a blank arbor, except that in that case the weight would take twice as long to run down, supposing that the striking part generally requires the same weight x fall as the going part.

This kind of going barrel, however, is evidently not suited to the delicacy of an astronomical clock; and Harrison's going ratchet is now universally adopted in such clocks, and also in chronometers and watches for keeping the action of the train on the escapement during the winding. Fig. 25 (in which the same letters are used as in the corresponding parts of fig. 3) shows its construction. The click of the barrel-ratchet R is set upon another larger ratchet-wheel with its teeth pointing the opposite way, and its click rT is set in the clock frame. That ratchet is connected with the great wheel by a spring ss' pressing against the two pins s in the ratchet and s' in the wheel. When the weight is wound up (which is equivalent to taking it off), the click Tr prevents that ratchet from turning back or to the right; and as the spring ss' is kept by the weight in a state of tension equivalent to the weight itself it will drive the wheel to the left for a short distance, when its end s is held fast, with the same force as if that end was pulled forward by the weight; and as the great wheel has to move very little during the short time the clock is winding, the spring will keep the clock going long enough.

In the commoner kind of turret clocks a more simple apparatus is used, which goes by the name of the _bolt and shutter_, because it consists of a weighted lever with a broad end, which shuts up the winding-hole. When it is lifted a spring-bolt attached to the lever, or its arbor, runs into the teeth of one of the wheels, and the weight of the lever keeps the train going until the bolt has run itself out of gear. Clocks are not always driven by weights. When accuracy is not necessary, but portability is desirable, springs are used. The old form of spring became weaker as it was unwound and necessitated the use of a device called a fusee or spiral drum. This apparatus will be found described in the article WATCH.

_Striking Mechanism._--There are two kinds of striking work used in clocks. The older of them, the _locking-plate_ system, which is still used in most foreign clocks, and in turret clocks in England also, will not allow the striking of any hour to be either omitted or repeated, without making the next hour strike wrong; whereas in the _rack_ system, which is used in all English house clocks, the number of blows to be struck depends merely on the position of a wheel attached to the going part, and therefore the striking of any hour may be omitted or repeated without deranging the following ones. We shall only describe the second of these, which is the more usual in modern timepieces.

Fig. 26 is a front view of a common English house clock with the face taken off, showing the repeating or rack striking movement. Here, as in fig. 3, M is the hour-wheel, on the pipe of which the minute-hand is set, N the reversed hour-wheel, and n its pinion, driving the 12-hour wheel H, on whose socket is fixed what is called the snail Y, which belongs to the striking work exclusively. The hammer is raised by the eight pins in the rim of the second wheel in the striking train, in the manner which is obvious.

The hammer does not quite touch the bell, as it would jar in striking if it did, and prevent the full sound. The form of the hammer-shank at the arbor where the spring S acts upon it is such that the spring both drives the hammer against the bell when the tail T is raised, and also checks it just before it reaches the bell, the blow on the bell thus being given by the hammer having acquired momentum enough to go a little farther than its place of rest. Sometimes two springs are used, one for impelling the hammer, and the other for checking it. But nothing will check the chattering of a heavy hammer, except making it lean forward so as to act, partially at least, by its weight. The pinion of the striking-wheel generally has eight leaves, the same number as the pins; and as a clock strikes 78 blows in 12 hours, the great wheel will turn in that time if it has 78 teeth instead of 96, which the great wheel of the going part has for a centre pinion of eight. The striking-wheel drives the wheel above it once round for each blow, and that wheel drives a fourth (in which there is a single pin P), six, or any other integral number of turns, for one turn of its own, and that drives a fan-fly to moderate the velocity of the train by the resistance of the air, an expedient at least as old as De Vick's clock in 1379.

The wheel N is so adjusted that, within a few minutes of the hour, the pin in it raises the _lifting-piece_ LONF so far that that piece lifts the click C out of the teeth of the _rack_ BKRV, which immediately falls back (helped by a spring near the bottom) as far as its tail V can go by reason of the snail Y, against which it falls; and it is so arranged that the number of teeth which pass the click is proportionate to the depth of the snail; and as there is one step in the snail for each hour, and it goes round with the hour-hand, the rack always drops just as many teeth as the number of the hour to be struck. This drop makes the noise of "giving warning." But the clock is not yet ready to strike till the lifting piece has fallen again; for, as soon as the rack was let off, the tail of the _gathering pallet_ G, on the prolonged arbor of the third wheel, was enabled to pass the pin K of the rack on which it was pressing before, and the striking train began to move; but before the fourth wheel had got half round, its pin P was caught by the end of the lifting-piece, which is bent back and goes through a hole in the plate, and when raised stands in the way of the pin P, so that the train cannot go on till the lifting-piece drops, which it does exactly at the hour, by the pin N then slipping past it. Then the train is free; the striking wheel begins to lift the hammer, and the gathering pallet gathers up the rack, a tooth for each blow, until it has returned to the place at which the pallet is stopped by the pin K coming under it. In this figure the lifting-piece is prolonged to F, where there is a string hung to it, as this is the proper place for such a string when it is wanted for the purpose of learning the hour in the dark, and not (as it is generally put) on the click C; for if it is put there and the string is held a little too long, the clock will strike too many; and if the string accidentally sticks in the case, it will go on striking till it is run down--neither of which things can happen when the string is put on the lifting-piece.

The snail is sometimes set on a separate stud with the apparatus called a _star-wheel_ and _jumper_. On the left side of the frame we have placed a lever x, with the letters st below it, and si above. If it is pushed up to si, the other end will come against a pin in the rack, and prevent it from falling, and will thus make the clock silent; and this is much more simple than the old-fashioned "strike and silent" apparatus, which we shall therefore not describe, especially as it is seldom used now.