Lever Escapement
(The student will do well to read: The Detached Lever Escapement, by Moritz Grossman; Modern Horology in Theory and Practice, by Claudius Saunier, and Watch and Clock Making, by David Glasgow.) The lever escapement is derived from Graham's deadbeat escapement for clocks. Thomas Mudge was the first horologist who successfully applied it to watches in the detached form, about 1750. The locking faces of the pallets were arcs of circles struck from the pallet centers. Many improvements were made upon it until to-day it is the best form of escapement for a general purpose watch, and when made on mechanical principles is capable of producing first rate results.
It is not obligatory in the lever, as in the verge, to have an uneven number of teeth in the wheel. While nearly all have 15 teeth, we might make them of 14 or 16; occasionally we find some in complicated watches of 12 teeth, and in old English watches of 30, which is a clumsy arrangement, and if the pallets embrace only three teeth in the latter, the pallet center cannot be pitched on a tangent.
Although advisable from a timing standpoint that the teeth in the escape wheel should divide evenly into the number of beats made per minute in a watch with seconds hand, it is not, strictly speaking, necessary that it should do so, as an example will show. We will take an ordinary watch, beating 300 times per minute; we will fit an escape wheel of 16 teeth; multiply this by 2, as there is a forward and then a return motion of the balance and consequently two beats for each tooth, making 16X2=32 beats for each revolution of the escape wheel. 300 beats are made per minute; divide this by the beats made on each revolution, and we have the number of times in which the escape wheel revolves per minute, namely, 300/32=9.375. This number then is the proportion existing for the teeth and pitch diameters of the 4th wheel and escape pinion. We must now find a suitable number of teeth for this wheel and pinion. Of available pinions for a watch, the only one which would answer would be one of 8 leaves, as any other number would give a fractional number of teeth for the 4th wheel, therefore 9.375X8=75 teeth in 4th wheel. Now as to the proof: as is well known, if we multiply the number of teeth contained in 4th and escape wheels also by 2, for the reason previously given, and divide by the leaves in the escape pinion, we get the number of beats made per minute; therefore 75X16 2/8<??>=300 beats per minute.
Pallets can be made to embrace more than three teeth, but would be much heavier and therefore the mechanical action would suffer. They can also be made to embrace fewer teeth, but the necessary side shake in the pivot holes would prove very detrimental to a total lifting angle of 10 deg. which represents the angle of movement in modern watches. Some of the finest ones only make 8 or 9 deg. of a movement: the smaller the angle the greater will the effects of defective workmanship be; 10 deg. is a common-sense angle and gives a safe escapement capable of fine results. Theoretically, if a timepiece could be produced in which the balance would vibrate without being connected with an escapement, we would have reached a step nearer the goal. Practice has shown this to be the proper theory to work on. Hence, the smaller the pallet and impulse angles the less will the balance and escapement be connected. The chronometer is still more highly detached than the lever. The pallet embracing three teeth is sound and practical, and when applied to a 15-tooth wheel, this arrangement offers certain geometrical and mechanical advantages in its construction, which we will notice in due time. 15 teeth divide evenly into 360 deg. leaving an interval of 24 degrees from tooth to tooth, which is also the angle at which the locking faces of the teeth are inclined from the center, which fact will be found convenient when we come to cut our wheel.
From locking to locking on the pallet scaping over three teeth, the angle is 60 deg. which is equal to 2 1/2 spaces of the wheel. Fig. 196 illustrates the lockings, spanning this arc. If the pallets embraced 4 teeth, the angle would be 84 deg.; or in case of a 16-tooth wheel scaping over 3 teeth, the angle would be 360x25/16=56 1/4 deg.
Pallets may be divided into two kinds, namely: equidistant and circular. The equidistant pallet is so-called because the lockings are an equal distance from the center; sometimes it is also called the tangential escapement, on account of the unlocking taking place on the intersection of tangent AC with EB, and FB with AD, the tangents, which is the valuable feature of this form of escapement.
AC and AD, Fig. 197, are tangents to the primitive circle GH. ABE and ABF are angles of 30 deg. each, together therefore forming the angle FBE of 60 deg. The locking circle MN is struck from the pallet center A; the interangles being equal, consequently the pallets must be equidistant. The weak point of this pallet is that the lifting is not performed so favorably; by examining the lifting planes MO and NP, we see that the discharging edge O, is closer to the center, A, than the discharging edge, P; consequently the lifting on the engaging pallet is performed on a shorter lever arm than on the disengaging pallet, also any inequality in workmanship would prove more detrimental on the engaging than on the disengaging pallet. The equidistant pallet requires fine workmanship throughout. We have purposely shown it of a width of 10 deg. which is the widest we can employ in a 15-tooth wheel, and shows the defects of this escapement more readily than if we had used a narrow pallet. A narrower pallet is advisable, as the difference in the discharging edges will be less, and the lifting arms would, therefore, not show so much difference in leverage.
The circular pallet is sometimes appropriately called "the pallet with equal lifts," as the lever arms AMO and ANP, Fig. 198, are equal lengths. It will be noticed by examining the diagram, that the pallets are bisected by the 30 deg. lines EB and FB, one half their width being placed on each side of these lines. In this pallet we have two locking circles, MP, for the engaging pallet, and NO for the disengaging pallet. The weak points in this escapement are that the unlocking resistance is greater on the engaging than on the disengaging pallet, and that neither of them lock on the tangents AC and AD, at the points of intersection with EB and FB. The narrower the circular pallet is made, the nearer to the tangent will the unlocking be performed. In neither the equidistant or circular pallets can the unlocking resistance be exactly the same on each pallet, as in the engaging pallet the friction takes place before AB, the line of centers, which is more severe than when this line has been passed, as is the case with the disengaging pallet; this fact proportionately increases the existing defects of the circular over the equidistant pallet, and vice versa, but for the same reason, the lifting in the equidistant is proportionately accompanied by more friction than in the circular.
Both equidistant and circular pallets have their adherents; the finer Swiss, French and German watches are made with equidistant escapements, while the majority of English and American watches contain the circular. In our opinion the English are wise in adhering to the circular form. We think a ratchet wheel should not be employed with equidistant pallets. By examining Fig. 197, we see an English pallet of this form. We have shown its defects in such a wide pallet as the English (as we have before stated), because they are more readily perceived; also, on account of the shape of the teeth, there is danger of the discharging edge, P, dipping so deep into the wheel, as to make considerable drop necessary, or the pallets would touch on the backs of the teeth. In the case of the club tooth, the latter is hollowed out, therefore less drop is required. We have noticed that, theoretically, it is advantageous to make the pallets narrower than the English, both for the equidistant and circular escapements. There is an escapement, Fig. 199, which is just the opposite to the English. The entire lift is performed by the wheel, while in the case of the ratchet wheel, the entire lifting angle is on the pallets; also, the pallets being as narrow as they can be made, consistent with strength, it has the good points of both the equidistant and circular pallets, as the unlocking can be performed on the tangent and the lifting arms are of equal length. The wheel, however, is so much heavier as to considerably increase the inertia; also, we have a metal surface of quite an extent sliding over a thin jewel. For practical reasons, therefore, it has been slightly altered in form and is only used in cheap work, being easily made. We will now consider the drop, which is a clear loss of power, and, if excessive, is the cause of much irregularity. It should be as small as possible consistent with perfect freedom of action.
In so far as angular measurements are concerned, no hard and fast rule can be applied to it, the larger the escape wheel the smaller should be the angle allowed for drop. Authorities on the subject allow 1 1/2 deg. drop for the club and 2 deg. for the ratchet tooth. It is a fact that escape wheels are not cut perfectly true; the teeth are apt to bend slightly from the action of the cutters. The truest wheel can be made of steel, as each tooth can be successively ground after being hardened and tempered. Such a wheel would require less drop than one of any other metal. Supposing we have a wheel with a primitive diameter of 7.5 mm., what is the amount of drop, allowing 1 1/2 deg. by angular measurement? 7.5 X 3.1416<??>360X1.5 = .0983 mm., which is sufficient; a hair could get between the pallet and tooth, and would not stop the watch. Even after allowing for imperfectly divided teeth, we require no greater freedom, even if the wheel is larger. Now suppose we take a wheel with a primitive diameter of 8.5 mm. and find the amount of drop; 8.5X3.1416<??>360X1.5=.1413 mm., or .1413-.0983=.043 mm., more drop than the smaller wheel, if we take the same angle. This is a waste of force. The angular drop should, therefore be proportioned according to the size of the wheel. We wish it to be understood that common sense must always be our guide. When the horological student once arrives at this standpoint, he can intelligently apply himself to his calling.
THE DRAW.
The draw or draft angle was added to the pallets in order to draw the fork back against the bankings and the guard point from the roller whenever the safety action had performed its function.
Pallets with draw are more difficult to unlock than those without it, this is in the nature of a fault, but whenever there are two faults we must choose the less. The rate of the watch will suffer less on account of the recoil introduced than it would were the locking faces arcs of circles struck from the pallet center, in which case the guard point would often remain against the roller. The draw should be as light as possible consistent with safety of action; some writers allow 15 deg. on the engaging and 12 deg. on the disengaging pallet; others again allow 12 deg. on each, which we deem sufficient. The draw is measured from the locking edges M and N, Fig. 200. The locking planes when locked are inclined 12 deg. from EB, and FB. In the case of the engaging pallet it inclines toward the center A. The draw is produced on account of MA being longer than RA, consequently, when power is applied to the scape tooth S, the pallet is drawn into the wheel. The disengaging pallet inclines in the same direction, but away from the center A; the reason is obvious from the former explanation. Some people imagine that the greater the incline on the locking edge of the escape teeth, the stronger the draw would be. This is not the case but it is certainly necessary that the point of the tooth alone should touch the pallet. From this it follows that the angle on the teeth must be greater than on the pallets; examine the disengaging pallet in Fig. 200, as it is from this pallet that the inclination of the teeth must be determined, as in the case of the engaging pallet the motion is toward the line of centers AB, and therefore away from the tooth which partially explains why some people advocate 15 deg. draw for this pallet. As illustrated in the case of the disengaging pallet, however the motion is also toward the line of centers AB, and towards the tooth as well, all of which will be seen by the dotted circles MM2 and NN2, representing the paths of the pallets. It will be noticed that UNF and TNB are opposite and equal angles of 12 deg. For practical reasons, from a manufacturing standpoint, the angle on the tooth is made just twice the amount, namely 24 deg.; we could make it a little less or a little more. If we made it less than 20 deg. too great a surface would be in contact with the jewel, involving greater friction in unlocking and an inefficient draw, but in the case of an English lever with such an arrangement we could do with less drop, which advantage would be too dearly bought; or if the angle is made over 28 deg. the point or locking edge of the tooth would rapidly become worn in case of a brass wheel. Also in an English lever more drop would be required.
THE LOCK.
What we have said in regard to drop also applies to the lock, which should be as small as possible, consistent with perfect safety. The greater the drop the deeper must be the lock; 1 1/2 deg. is the angle generally allowed for the lock, but it is obvious that in a large escapement it can be less. THE RUN.
The run or, as it is sometimes called, "the slide," should also be as light as possible: from 1/4 deg. to 1/2 deg. is sufficient. It follows, then, the banking should be as close together as possible, consistent with requisite freedom for escaping. Anything more than this increases the angular connection of the balance with the escapement, which directly violates the theory under which it is constructed; also, a greater amount of work will be imposed upon the balance to meet the increased unlocking resistance, resulting in a poor motion. and accurate time will be out of the question. It will be seen that those workmen who make a practice of opening the banks, "to give the escapement more freedom," simply jump from the frying pan into the fire. The bankings should be as far removed from the pallet center as possible, as the further away they are pitched the less run we require, according to angular measurement. Figure 201 illustrates this fact; the tooth S has just dropped on the engaging pallet, but the fork has not yet reached the bankings. At a we have 1 deg. of run, while if placed at b we would only have 1/2 deg. of run, but still the same freedom for escaping, and less unlocking resistance. The bankings should be placed towards the acting end of the fork as illustrated, as in case the watch "rebanks" there would be more strain on the lever pivots if they were placed at the other end of the fork. THE LIFT.
The lift is composed of the actual lift on the teeth and pallets and the lock and run. We will suppose that from drop to drop we allow 10 deg.; if the lock is 1 1/2 deg. then the actual lift by means of the inclined planes on teeth and pallets will be 8 1/2 deg. We have seen that a small lifting angle is advisable, so that the vibrations of the balance will be as free as possible. There are other reasons as well. Fig. 202 shows two inclined planes; we desire to lift the weight 2 a distance equal to the angle at which the planes are inclined; it will be seen at a glance that we will have less friction by employing the smaller incline, whereas with the larger one the motive power is employed through a greater distance on the object to be moved. The smaller the angle the more energetic will the movement be; the grinding of the angles and fit of the pivots, etc., also increases in importance. An actual lift of 8 1/2 deg. satisfies the conditions imposed very well. We have before seen that both on account of the unlocking and the lifting leverage of the pallet arms, it would be advisable to make them narrow both in the equidistant and circular escapement. We will now study the question from the standpoint of the lift, in so far as the wheel is concerned.
It is self-evident that a narrow pallet requires a wide tooth, and a wide pallet a narrow or thin tooth wheel; in the ratchet wheel we have a metal point passing over a jeweled plane. The friction is at its minimum, because there is less adhesion than with the club tooth, but we must emphasize the fact that we require a greater angle in proportion on the pallets in this escapement than with the narrow pallets and wider tooth. This seems to be a point which many do not thoroughly comprehend, and we would advise a close study of Fig. 203, which will make it perfectly clear, as we show both a wide and a narrow pallet. GH represents the primitive, which, in this figure is also the real diameter of the escape wheel. In measuring the lifting angles for the pallets, our starting point is always from the tangents AC and AD. The tangents are straight lines, but the wheel describes the circle GH, therefore they must deviate from one another, and the closer to the center A the discharging edge of the engaging pallet reaches, the greater does this difference become; and in the same manner the further the discharging edge of the disengaging pallet is from the center A the greater it is. This shows that the loss is greater in the equidistant than in the circular escapement. After this we will designate this difference as the "loss". In order to illustrate it more plainly we show the widest pallet--the English--in equidistant form. This gives another reason why the English lever should only be made with circular pallets, as we have seen that the wider the pallet the greater the loss. The loss is measured at the intersection of the path of the discharging edge OO, with the circle GH, and is shown through AC2, which intersects these circles at that point. In the case of the disengaging pallet, PP illustrates the path of the discharging edge; the loss is measured as in the preceding case where GH is intersected as shown by AD2. It amounts to a different value on each pallet. Notice the loss between C and C2, on the engaging, and D and D2 on the disengaging pallet; it is greater on the engaging pallet, so much so that it amounts to 2 deg. which is equal to the entire lock; therefore if 8 1/2 deg. of work is to be accomplished through this pallet, the lifting plane requires an angle of 10 1/2 deg. struck from AC.
Let us now consider the lifting action of the club tooth wheel. This is decidedly a complicated action, and requires some study to comprehend. In action with the engaging pallet the wheel moves up, or in the direction of the motion of the pallets, but on the disengaging pallet it moves down, and in a direction opposite to the pallets, and the heel of the tooth moves with greater velocity than the locking edge; also in the case of the engaging pallet, the locking edge moves with greater velocity than the discharging edge; in the disengaging pallet the opposite is the case, as the discharging edge moves with greater velocity than the locking. These points involve factors which must be considered, and the drafting of a correct action is of paramount importance; we therefore show the lift as it is accomplished in four different stages in a good action. Fig. 204 illustrates the engaging, and Fig. 205 the disengaging pallet; by comparing the figures it will be noticed that the lift takes place on the point of the tooth similar to the English, until the discharging edge of the pallet has been passed, when the heel gradually comes into play on the engaging, but more quickly on the disengaging pallet. We will also notice that during the first part of the lift the tooth moves faster along the engaging lifting plane than on the disengaging; on pallets 2 and 3 this difference is quite large; towards the latter part of the lift the action becomes quicker on the disengaging pallet and slower on the engaging. To obviate this difficulty some fine watches, notably those of A. Lange & Sons, have convex lifting planes on the engaging and concave on the disengaging pallets; the lifting planes on the teeth are also curved. See Fig. 206. This is decidedly an ingenious arrangement, and is in strict accordance with scientific investigation. We should see many fine watches made with such escapements if the means for producing them could fully satisfy the requirements of the scientific principles involved.
The distribution of the lift on tooth and pallet is a very important matter; the lifting angle on the tooth must be less in proportion to its width than it is on the pallet. For the sake of making it perfectly plain, we illustrate what should not be made; if we have 10 1/2 deg. for width of tooth and pallet, and take half of it for a tooth, and the other half for the pallet, making each of them 5 1/4 deg. in width, and supposing we have a lifting of 8 1/2 deg. to distribute between them, by allowing 4 1/4 deg. on each, the lift would take place as shown in Fig. 207, which is a very unfavorable action. The edge of the engaging pallet scrapes on the lifting plane of the tooth, yet it is astonishing to find some otherwise very fine watches being manufactured right along which contain this fault; such watches can be stopped with the ruby pin in the fork and the engaging pallet in action, nor would they start when run down as soon as the crown is touched, no matter how well they were finished and fitted.
The lever lengths of the club tooth are variable, while with the ratchet they are constant, which is in its favor; in the latter it would always be as SB, Fig. 208. This is a shorter lever than QB, consequently more powerful, although the greater velocity is at Q, which only comes into action after the inertia of wheel and pallets has been overcome, and when the greatest momentum during contact is reached. SB is the primitive radius of the club tooth wheel, but both primitive and real radius of the ratchet wheel. The distance of centers of wheel and pallet will be alike in both cases; also the lockings will be the same distance apart on both pallets; therefore, when horologists, even if they have worldwide reputations, claim that the club tooth has an advantage over the ratchet because it begins the lift with a shorter lever than the latter, it does not make it so. We are treating the subject from a purely horological standpoint, and neither patriotism or prejudice has anything to do with it. We wish to sift the matter thoroughly and arrive at a just conception of the merits and defects of each form of escapement, and show reasons for our conclusions.
Anyone who has closely followed our deductions must see that in so far as the wheel is concerned the ratchet or English wheel has several points in its favor. Such a wheel is inseparable from a wide pallet; but we have seen that a narrower pallet is advisable; also as little drop and lock as possible; clearly, we must effect a compromise. In other words, so far the balance of our reasoning is in favor of the club tooth escapement and to effect an intelligent division of angles for tooth, pallet and lift is one of the great questions which confronts the intelligent horologist. Anyone who has ever taken the pains to draw pallet and tooth with different angles, through every stage of the lift, with both wide and narrow pallets and teeth, in circular and equidistant escapements, will have received an eye-opener. We strongly advise all our readers who are practical workmen to try it after studying what we have said. We are certain it will repay them. THE CENTER DISTANCE OF WHEEL AND PALLETS.
The direction of pressure of the wheel teeth should be through the pallet center by drawing the tangents AC and AD, Fig. 197, to the primitive circle GH, at the intersection of the angle FBE. This condition is realized in the equidistant pallet. In the circular pallet, Fig. 198, this condition cannot exist, as in order to lock on a tangent the center distance should be greater for the engaging and less for the disengaging pallet, therefore watchmakers aim to go between the two and plant them as before specified at A. When planted on the tangents the unlocking resistance will be less and the impulse transmitted under favorable conditions, especially so in the circular, as the direction of pressure coincides (close to the center of the lift) with the law of the parallelogram of forces.
It is impossible to plant pallets on the tangents in very small escapements, as there would not be enough room for a pallet arbor of proper strength, nor will they be found planted on the tangents in the medium size escapement with a long pallet arbor, nor in such a one with a very wide tooth (see Fig.199) as the heel would come so close to the center A, that the solidity of pallets and arbor would suffer. We will give an actual example. For a medium sized escape wheel with a primitive diameter of 7.5 mm., the center distance AB is 4.33 mm. By using 3 deg. of a lifting angle on the teeth, the distance from the heel of the tooth to the pallet center will be .4691 mm.; by allowing. 1mm. between wheel and pallet and .15 mm. for stock on the pallets we find we will have a pallet arbor as follows: .4691-(.1+.15)X2=.4382mm. It would not be practicable to make anything smaller.
It behooves us now to see that while a narrow pallet is advisable a very wide tooth is not; yet these two are inseparable. Here is another case for a compromise, as, unquestionably the pallets ought to be planted on the tangents. There is no difficulty about it in the English lever, and we have shown in our example that a judiciously planned club tooth escapement of medium size can be made with the center distance properly planted. When considering the center distance we must of necessity consider the widths of teeth and pallets and their lifting angles. We are now at a point in which no watchmaker of intelligence would indicate one certain division for these parts and claim it to be "the best." It is always those who do not thoroughly understand a subject who are the first to make such claims. We will, however, give our opinion within certain limits. The angle to be divided for tooth and pallet is 10 1/2 deg. Let us divide it by 2, which would be the most natural thing to do, and examine the problem. We will have 5 1/4 deg. each for width of tooth and pallet. We must have a smaller lifting angle on the tooth than on the pallet, but the wider the tooth the greater should its lifting angle be. It would not be mechanical to make the tooth wide and the lifting angle small, as the lifting plane on the pallets would be too steep on account of being narrow. A lifting angle on the tooth which would be exactly suitable for a given circular, would be too great for a given equidistant pallet. It follows, therefore, taking 5 1/4 deg. as a width for the tooth, that while we could employ it in a fair sized escapement with equidistant pallets, we could not do so with circular pallets and still have the latter pitched on the tangents. We see the majority of escapements made with narrower teeth than pallets, and for a very good reason.
In the example previously given, the 3 deg. lift on the tooth is well adapted for a width of 4 1/2 deg. which would require a pallet 6 deg. in width. The tooth, therefore, would be 3/4 the width of pallets, which is very good indeed.
From what we have said it follows that a large number of pallets are not planted on the tangents at all. We have never noticed this question in print before. Writers generally seem to, in fact do, assume that no matter how large or small the escapement may be, or how the pallets and teeth are divided for width and lifting angle no difficulty will be found in locating the pallets on the tangents. Theoretically there is no difficulty, but in practice we find there is.