Equidistant Vs
CIRCULAR.
At this stage we are able to weigh the circular against the equidistant pallet. In the beginning we had to explain the difference between them, so the reader could follow our discussion, and not until now, are we able to sum up our conclusions.
The reader will have noticed that for such an important action as the lift, which supplies power to the balance, the circular pallet is favored from every point of view. This is a very strong point in its favor. On the other hand, the unlocking resistance being less, and as nearly alike as possible on both pallets in the equidistant, it is a question if the total vibration of the balance will be greater with the one than the other, although it will receive the impulse under better conditions from the circular pallet; but it expends more force in unlocking it. Escapement friction plays an important role in the position and isochronal adjustments; the greater the friction encountered the slower the vibration of the balance. The friction should be constant. In unlocking, the equidistant comes nearer to fulfilling this condition, while during the lift it is more nearly so in the circular. The friction in unlocking, from a timing standpoint, overshadows that of the impulse, and the tooth can be a little wider in the equidistant than the circular escapement with the pallet properly planted. Therefore for the finest watches the equidistant escapement is well adapted, but for anything less than that the circular should be our choice.
THE FORK AND ROLLER ACTION.
While the lifting action of the lever escapement corresponds to that of the cylinder, the fork and roller action corresponds to the impulse action in the chronometer and duplex escapements.
Our experience leads us to believe that the action now under consideration is but imperfectly understood by many workmen. It is a complicated action, and when out of order is the cause of many annoying stoppages, often characterized by the watch starting when taken from the pocket.
The action is very important, and is generally divided into impulse and safety action, although we think we ought to divide it into three, namely, by adding that of the unlocking action. We will first of all consider the impulse and unlocking actions, because we cannot intelligently consider the one without the other, as the ruby pin and the slot in the fork are utilized in each. The ruby pin, or strictly speaking, the "impulse radius," is a lever arm, whose length is measured from the center of the balance staff to the face of the ruby pin, and is used, firstly, as a power or transmitting lever on the acting or geometrical length of the fork (i.e., from the pallet center to the beginning of the horn), and which at the moment is a resistance lever, to be utilized in unlocking the pallets. After the pallets are unlocked the conditions are reversed, and we now find the lever fork, through the pallets, transmitting power to the balance by means of the impulse radius. In the first part of the action we have a short lever engaging a longer one, which is an advantage. See Fig. 209, where we have purposely somewhat exaggerated the conditions. A' X represents the impulse radius at present under discussion, and AW the acting length of the fork. It will be seen that the shorter the impulse radius, or in other words, the closer the ruby pin is to the balance staff and the longer the fork, the easier will the unlocking of the pallets be performed, but this entails a great impulse angle, for the law applicable to the case is, that the angles are in the inverse ratio to the radii. In other words, the shorter the radius, the greater is the angle, and the smaller the angle the greater is the radius. We know, though, that we must have as small an impulse angle as possible in order that the balance should be highly detached. Here is one point in favor of a short impulse radius, and one against it. Now, let us turn to the impulse action. Here we have the long lever, AW, acting on a short one, A' X, which is a disadvantage. Here, then, we ought to try and have a short lever acting on a long one, which would point to a short fork and a great impulse radius. Suppose AP, Fig. 209, is the length of fork, and A' P is the impulse radius; here, then, we favor the impulse, and it is directly in accordance with the theory of the free vibration of the balance, for, as before stated, the longer the radius the smaller the angle. The action at P is also closer to the line of centers than it is at W, which is another advantage.
We will notice that by employing a large impulse angle, and consequently a short radius, the intersection m of the two circles ii and cc is very safe, whereas, with the conditions reversed in favor of the impulse action, the intersection at k is more delicate. We have now seen enough to appreciate the fact that we favor one action at the expense of another. By having a lifting angle on pallet and tooth of 8 1/2 deg., a locking angle of 1 1/2 deg.; and a run of 1/2 deg., we will have an angular movement of the fork of 8 1/2 + 1 1/2 + 1/2=10 1/2 deg.
Writers generally only consider the movement of the fork from drop to drop on the pallets, but we will be thoroughly practical in the matter. With a total motion of the fork of 10 1/2 deg. (JAW, Fig. 210), one-half of 5 1/4 deg. will be performed on each side of the line of centers. We are at liberty to choose any impulse angle which we may prefer; 3 to 1 is a good proportion for an ordinary well-made watch. By employing it the angle XA'Y would be equal to 31 1/2 deg. The radius A'X, Fig. 211, is also of the same proportion, but the angle AA'X is greater because the fork angle WAA' is greater than the same angle in Fig. 210. We will notice that the intersection k is much smaller in Fig. 210 than in Fig. 211. The action in the latter begins much further from the line of centers than in the former and outlines an action which should not be made.
To come back to the impulse angle, some might use a proportion of 3.5, 4 or even 5 to 1, while others for the finest of watches would only use 2.75 to 1. By having a total vibration of the balance of 1 1/2 turns, which is equal to 540 deg., a fork angle of 10 deg. and a proportion of 2.75 for the impulse angle which would be equal to 10X2.75=27.5 deg. The free vibration of the balance, or as this is called, "the supplemental arc," is equal to 540 deg.-27.5 deg.=512.5 deg., while with a proportion of 5 to 1, making an impulse angle of 50 deg., it would be equal to 490 deg. To sum up, the finer the watch the lower the proportion, the closer the action to the line of centers, the smaller the friction. On account of leverage the more difficult the unlocking, but the more energetic the impulse when it does occur. The velocity of the ruby pin at P, Fig. 209, is much greater than at W, consequently it will not be overtaken as soon by the fork as at W. The velocity of the fork at the latter point is greater than at P; the intersection of ii and cc is also not as great; therefore the lower the proportion the finer and more exact must the workmanship be. We will notice that the unlocking action has been overruled by the impulse. The only point so far in which the former has been favored is in the diminished action before the line of centers, as previously pointed out at P, Fig. 209.
We will now consider the width of the ruby pin, and to get a good insight into the question, we will study Fig. 212. A is the pallet center, A' the balance center, the line AA' being the line of centers; the angle WAA' equals half the total motion of the fork, the other half, of course, takes place on the opposite side of the center line. WA is the center of the fork when it rests against the bank. The angle AA'X represents half the impulse angle; the other half, the same as with the fork, is struck on the other side of the center line. At the point of intersection of these angles we will draw cc from the pallet center A, which equals the acting length of the fork, and from the balance center we will draw ii, which equal the theoretical impulse radius; some writers use it as the real radius. The wider the ruby pin the greater will the latter be, which we will explain presently. The ruby pin in entering the fork must have a certain amount of freedom for action, from 1 to 1 1/4 deg. Should the watch receive a jar at the moment the guard point enters the crescent or passing hollow in the roller, the fork would fly against the ruby pin. It is important that the angular freedom between the fork and ruby pin at the moment it enters into the slot be less than the total locking angle on the pallets. If we employ a locking angle of 1 1/2 deg. and 1/2 deg. run, we would have a total lock on the pallet of 2 deg. By allowing 1 1/4 deg. of freedom for the ruby pin the moment the guard point enters the crescent, in case the fork should strike the face of the ruby pin, the pallets will still be locked 3/4 deg. and the fork drawn back against the bankings through the draft angle.
We will see what this shake amounts to for a given acting length of fork, which describes an arc of a circle, therefore the acting length is only the radius of that circle and must be multiplied by two in order to get the diameter. The acting length of fork =4.5 mm., what is the amount of shake when the ruby pin passes the acting corner? 4.5X2X3.1416<??>360 deg.=.0785X1.25=.0992 mm. The shake of the ruby pin in the slot of the fork must be as slight as possible, consistent with perfect freedom of action. It varies from 1/4 deg. to 1/2 deg., according to length of fork and shape of ruby pin. A square ruby pin requires more shake than any other kind; it enters the fork and receives the impulse in a diagonal direction on the jewel, in which position it is illustrated at Z, Fig. 215. This ruby pin acts on a knife edge, but for all that the engaging friction during the unlocking action is considerable.
Our reasoning tells us it matters not if a ruby pin be wide or narrow, it must have the same freedom in passing the acting edge of the fork, therefore, to have the impulse radius on the point of intersection of A'X with AW, Fig. 212, we would require a very narrow ruby pin. With 1 deg. of freedom at the edge, and 1/2 deg. in the slot, we could only have a ruby pin of a width of 1 1/2 deg. Applying it to the preceding example it would only have an actual width of .0785X1.5=.1178 mm., or the size of an ordinary balance pivot. At n, Fig. 212, we illustrate such a ruby pin; the theoretical and real impulse radius coincide with one another. The intersection of the circle ii and cc is very slight, while the friction in unlocking begins with 1 deg. of half the total movement of the fork from the line of centers; to illustrate, if the angular motion is 11 deg. the ruby pin under discussion will begin action 4 1/2 deg. before the line of centers, being an engaging, or "uphill" friction of considerable magnitude.
The intersection with the fork is also much less than with the wider ruby pin, making the impulse action very delicate. On the other hand the widest ruby pin for which there is any occasion is one beginning the unlocking action on the line of centers, Fig. 212; this entails a width of slot equal to the angular motion of the fork. We see here the advantage of a wide ruby pin over a narrow one in the unlocking action. Let us now examine the question from the standpoint of impulse action.
Fig. 213 illustrates the moment the impulse is transmitted; the fork has been moved in the direction of the arrow by the ruby pin; the escapement has been unlocked and the opposite side of the slot has just struck the ruby pin. The exact position in which the impulse is transmitted varies with the locking angle, the width of ruby pin, its shake in the slot, the length of fork, its weight, and the velocity of the ruby pin, which is determined by the vibrations of the balance and the impulse radius.
In an escapement with a total lock of 1 3/4 deg. and 1 1/4 of shake in the slot, theoretically, the impulse would be transmitted 2 deg. from the bankings. The narrow ruby pin n receives the impulse on the line v, which is closer to the line of centers than the line u, on which the large ruby pin receives the impulse. Here then we have an advantage of the narrow ruby pin over a wide one; with a wider ruby pin the balance is also more liable to rebank when it takes a long vibration. Also on account of the greater angle at which the ruby pin stands to the slot when the impulse takes place, the drop of the fork against the jewel will amount to more than its shake in the slot (which is measured when standing on the line of centers). On this account some watches have slots dovetailed in form, being wider at the bottom, others have ruby pins of this form. They require very exact execution; we think we can do without them by judiciously selecting a width of ruby pin between the two extremes. We would choose a ruby pin of a width equal to half the angular motion of the fork. There is an ingenious arrangement of fork and roller which aims to, and partially does, overcome the difficulty of choosing between a wide and narrow ruby pin; it is known as the Savage pin roller escapement. We intend to describe it later.
If the face of the ruby pin were planted on the theoretical impulse radius ii, Fig. 214, the impulse would end in a butting action as shown; hence the great importance of distinguishing between the theoretical and real impulse radius and establishing a reliable data from which to work. We feel that these actions have never been properly and thoroughly treated in simple language; we have tried to make them plain so that anyone can comprehend them with a little study.
Three good forms of ruby pins are the triangular, the oval and the flat faced; for ordinary work the latter is as good as any, but for fine work the triangular pin with the corners slightly rounded off is preferable. English watches are met with having a cylindrical or round ruby pin. Such a pin should never be put into a watch. The law of the parallelogram of forces is completely ignored by using such a pin; the friction during the unlocking and impulse action is too severe, as it is, without the addition of so unmechanical an arrangement. Fig. 216 illustrates the action of a round ruby pin; ii is the path of the ruby pin; cc that of the acting length of the fork. It is shown at the moment the impulse is transmitted. It will be seen that the impact takes place below the center of the ruby pin, whereas it should take place at the center, as the motion of the fork is upwards and that of the ruby pin downwards until the line of the centers has been reached. The same rule applies to the flat-faced pin, and it is important that the right quantity be ground off. We find that 3/7 is approximately the amount which should be ground away. Fig. 217 illustrates the fork standing against the bank. The ruby pin touches the side of the slot but has not as yet begun to act; ri is the real impulse circle for which we allow 1 1/4 deg. of freedom at the acting edge of the fork; the face of the ruby pin is therefore on this line. The next thing to do is to find the center of the pin. From the side n of the slot we construct the right angle o n t; from n we transmit 1/2 the width of the pin, and plant the center x on the line n t. We can have the center of the pin slightly below this line, but in no case above it; but if we put it below, the pin will be thinner and therefore more easily broken. THE SAFETY ACTION.
Although this action is separate from the impulse and unlocking actions, it is still very closely connected with them, much more so in the single than in the double roller escapement. If we were to place the ruby pin at X, Fig. 209, we could have a much smaller roller than by placing it at P. With the small roller the safety action is more secure, as the intersection at m is greater than at k. It is not as liable to "butt" and the friction is less when the guard point is thrown against the small roller. Suppose we take two rollers, one with a diameter of 2.5 mm., the other just twice this amount, or 5 mm. By having the guard radius and pressure the same in each case, if the guard point touched the larger roller it would not only have twice, but four times more effect than on the smaller one. We will notice that the smaller the impulse angle the larger the roller, because the ruby pin is necessarily placed farther from the center. The position of the ruby pin should, therefore, govern the size of the roller, which should be as small as possible. There should only be enough metal left between the circumference of the roller and the face of the jewel to allow for a crescent or passing hollow of sufficient depth and an efficient setting for the jewel. For this reason, as well as securing the correct impulse radius and therefore angle, when replacing the ruby pin, and having it set securely and mechanically in the roller, it is necessary that the pin and the hole in the roller be of the same form and a good fit. Fig. 218 illustrates the difference in size of rollers. In the smaller one the conditions imposed are satisfied, while in the larger one they are not. In the single roller the safety action is at the mercy of the impulse and pallet angles. We have noticed that in order to favor the impulse we require a large roller, and for the safety action a small one, therefore escapements made on fine principles are supplied with two rollers, one for each action.
It may be well to say that in our opinion a proportion between the fork and impulse angles in 10 deg. pallets of 3 or 3 1/2 to 1, depending upon the size of the escapement, is the lowest which should be made in single roller. We have seen them in proportions of 2 to 1 in single roller--a scientific principle foolishly applied--resulting in an action entirely unsatisfactory. When the guard point is pressed against the roller the escape tooth must still rest on the locking face of the pallet; if the total lock is 2 deg., by allowing 1 1/4 deg. freedom for the guard point between the bank and the roller the escapement will still be locked 3/4 deg. How much this shake actually amounts to depends upon the guard radius. Suppose this to be 4 mm., then the freedom would equal 4X2X3.1416<??>360X1.25=.0873 mm. THE CRESCENT The crescent in the roller must be large and deep enough so it will be impossible for the guard point to touch in or on the corners of it; at the same time it must not be too large, as it would necessitate a longer horn on the fork than is necessary.
Fig. 219 shows the slot n of the fork standing at the bank. The ruby pin o touches it, but has not as yet acted on it; s s illustrates a single roller, while S2 illustrates the safety roller for a double roller escapement. In order to find the dimensions of the crescent in the single roller we must proceed as follows: WA is in the center of the fork when it rests against the bank, and is, therefore, one of the sides of the fork angle, and is drawn from the pallet center; V A W is an angle of 1 1/4 deg., which equals the freedom between the guard point and the roller; g g represents the path of the guard pin u for the single roller, and is drawn at the intersection of VA with the roller. A' A2 is a line drawn from the balance center through that of the ruby pin, and therefore also passes through the center of the crescent. By planting a compass on this line, where it cuts the periphery of the roller, and locating the point of intersection of VA with the roller, will give us one-half the crescent, the remaining half being transferred to the opposite side of the line A' A2. We will notice that the guard point has entered the crescent 1 1/4 deg. before the fork begins to move.
The angle of opening for the crescent in the double roller escapement is greater than in the single, because it is placed closer to the balance center, and the guard point or dart further from the pallet center, causing a greater intersection; also the velocity of the guard point has increased, while that of the safety roller has decreased. Fig. 219, at ff, shows the path of the dart h, which also has 1 1/4 deg. freedom between bank and roller. From the balance center we draw A' d touching the center or point of the dart; from this point we construct at 5 deg. angle b A'd. This is to insure sufficient freedom for the dart when entering the crescent. We plant a compass on the point of intersection of A' A2 with the safety roller, S2, and locating the point where A' b intersects it, have found one half the opening for the crescent, the remaining half being constructed on the opposite side of the line A' A2.
THE HORN.
The horn on the fork belongs to the safety action; more horn is required with the double than with the single roller, on account of the greater angle of opening for the crescent. The horn should be of such a length that when the crescent has passed the guard point, the end of the horn should point to at least the center of the ruby pin.
The dotted circle, s s, Fig. 220, represents a single roller. It will be noticed that the corner of the crescent has passed the guard pin u by a considerable angle, and although this is so, in case of an accident the acting edge of the fork would come in contact with the ruby pin: this proves that a well made single roller escapement really requires but little horn, only enough to ensure the safe entry of the ruby pin in case the guard point at that moment be thrown against the roller. We will now examine the question from the standpoint of the double roller; S2, Fig. 220, is the safety roller; the corner of the crescent has safety passed the dart h; the centers of the ruby pin 0 and of the crescent being on the line A' A2, we plant the compass on the pallet center and the center of the face of the ruby pin and draw k k, which will be the path described by the horn. The end of the horn is therefore planted upon it from 1 1/2 deg. to 1 3/4 deg. from the ruby pin; this freedom at the end of the horn is therefore from 1/4 deg. to 1/2 deg. more than we allow for the guard point; it depends upon the size of the escapement and locking angles which we would choose. It must in any case be less than the lock on the pallets, so that the fork will be drawn back against the bank in case the horn be thrown against the ruby pin.
When treating on the width of the ruby pin, we mentioned the Savage pin roller escapement, which we illustrate in Figs. 221 and 222. This ingenious arrangement was designed with the view of combining the advantages of both wide and narrow pins and at the same time without any of their disadvantages.