Part 13 (1/2)

In describing thethe cylinder escapement we shall make a radical departure from the systems usually laid down in text-books, and seek to siiven for such delineations In considering the cylinder escapement we shall pursue an analytical course and strive to build up fros for this purpose we shall co an escape wheel of 10” radius, and our first effort will be the pri 129 Here we establish the point _A_ for the center of our escape wheel, and from this center sweep the short arc _a a_ with a 10” radius, to represent the circumference of our escape wheel From _A_ we draw the vertical line _A B_, and from the intersection of said line with the arc _a a_ we lay off twelve degree spaces on each side of the line _A B_ on said arc _a_ and establish the points _b c_ Froh the points _b c_ the radial lines _b' c'_

To define the face of the incline to the teeth we set our dividers to the radius of any of the convenient arcs of sixty degrees which we have provided, and sweep the arc _t t_ From the intersection of said arc with the line _A b'_ we lay off on said arc sixty-four degrees and establish the point _g_ and draw the line _b g_ Why we take sixty-four degrees for the angle _A b g_ will be explained later on, e are discussing the angular ree fro two of them, we establish the point _y_ and draw the radial line _A y'_ Where this line _A y'_ intersects the line _b g_ we name the point _n_, and in it is located the point of the escape-wheel tooth That portion of the line _b g_ which lies between the points _b_ and _n_ represents the measure of the inner diath of the chord of the arc which rounds the impulse face of the tooth We divide the space _b n_ into two equal portions and establish the point _e_, which locates the position of the center of the cylinder Froh the point _e_ eep the arc _e' e'_, and it is on this line that the points establishi+ng the center of the cylinder will in every instance be located Froh the point _n_ eep the arc _k_, and on this line we locate the points of the escape-wheel teeth For delineating the curved impulse faces of the escape-wheel teeth we draw fro_ the line _e o_ We next take in our dividers the radius of the arc _k_, and setting one leg at either of the points _b_ or _n_, establish with the other leg the point _p'_ on the line _e o_, and from the point _p'_ as a center eep the arc _b v n_, which defines the curve of the ih the point _p'_ eep the arc _p_, and in all instances where we desire to delineate the curved face of a tooth we locate either the position of the point or the heel of such tooth, and setting one leg of our dividers at such point, the other leg resting on the arc _p_, we establish the center fro the face of said tooth

ADVANTAGES GAINED IN SHAPING

The reason for giving a curved form to the impulse face of the teeth of cylinder escape wheels are somewhat intricate, and the problees in so shaping the incline or impulse face is conceded, we believe, by all recent manufacturers The chief benefit derived from such curved iht and study of the situation and relation of parts as shown in Fig 129 It will be seen on inspection that the angular motion imparted to the cylinder by the ireater during the first half of the twelve degrees of escape-wheel action than during the last half, thus giving the escape wheel the advantage at the tie of the escape-wheel tooth across the lip of the cylinder Or, in other words, as the ratio of resistance of the balance spring increases, in a like ratio the curved forreater power to the escape-wheel action in proportion to the angular motion of the escape wheel Hence, in actual service it is found that cylinder watches with curved impulse planes to the escape-wheel teeth are less liable to set in the pocket than the teeth having straight impulse faces

THE OUTER DIAMETER OF THE CYLINDER

[Illustration: Fig 129]

To define the remainder of the form of our escape-wheel tooth ill next delineate the heel To do this we first define the outer diameter of our cylinder, which is the extent fro the line _n c_ we halve the space and establish the point _x_, from which point as a center eep the circle _hich defines the outer circumference of our cylinder With our dividers set to embrace the extent fro at the point _b_, and with the other leg establish on the arc _k_ the point _h_ We next draw the line _b h_, and frole to the line _b h_ Our object for drawing these lines is to define the heel of our escape-wheel tooth by a right angle line tangent to the circle _w_, from the point _b_; which circle _w_ represents the curve of the outer circumference of the cylinder We shape the point of the tooth as shown to give it the proper stability, and draw the full line _j_ to a curve from the center _A_ We have now defined the form of the upper face of the tooth How to delineate the U arms will be taken up later on, as, in the present case, the necessary lines would confuse our drawing

We would here take the opportunity to say that there is a great latitude taken by iven to the cylinder, or, as it is terreat extent the angle _A b g_, which we gave as sixty-four degrees in our drawing It is well to understand that the use of sixty-four degrees is based on no hard-and-fast rules, but varies back and forth, according as a greater or lesser angle of ie the ile is probably more easily estimated by the ratio between the diameter of the cylinder and the ht of the impulse plane Or, to be more explicit, we measure the radial extent from the center _A_ between the arcs _a k_ on the line _A b_, and use this for comparison with the outer diameter of the cylinder

We can readily see that as we increase the height of the heel of the ile of ies of accurate ical student it is an easy ular extent of the real lift of any cylinder The advantage of suchwhen the proper proportion of the cylinder is cut away for the half shell

[Illustration: Fig 130]

In the olderit was a very coht of the incline of the tooth be one-seventh of the outer diameter of the cylinder, and at the same time the trade was furnished with no tools except a clue; but with micrometer calipers which read to one-thousandths of an inch such rules can be definitely carried into effect and not left to guess work Let us compare the old method with the new: Suppose we have a new cylinder to put in; we have the old escape wheel, but the forone

The old-style workman would take a round broach and calculate the size of the cylinder by finding a place where the broach would just go between the teeth, and the size of the broach at this point was supposed to be the outer diameter of the cylinder By our method we measure the diameter of the escape wheel in thousandths of an inch, and from this size calculate exactly what the diameter of the new cylinder should be in thousandths of an inch Suppose, to further carry out our comparison, the escape wheel which is in the watch has teeth which have been stoned off to permit the use of a cylinder which was too small inside, or, in fact, of a cylinder too small for the watch: in this case the broach systeive us a cylinder which would permit too much inside drop

DRAWING A CYLINDER

We have already instructed the pupil how to delineate a cylinder escape wheel tooth and ill next describe how to draw a cylinder As already stated, the center of the cylinder is placed to coincide with the center of the chord of the arc which defines the in a cylinder escape wheel tooth as previously described, and setting one leg of our compasses at the point _e_ which is situated at the center of the chord of the arc which defines the ih the points _d_ and _b_ we define the inside of our cylinder We next divide the chord _d b_ into eight parts and set our dividers to five of these parts, and from _e_ as a center sweep the circle _h_ and define the outside of our cylinder Froles to the line _A e'_ and through the point _e_ we draw the line from _e_ as a center, and with our dividers set to the radius of any of the convenient arcs which we have divided into sixty degrees, eep the arc _i_

Where this arc intersects the line _f_ we term the point _k_, and frorees, and draw the line _l e l'_, which we see coincides with the chord of the impulse face of the tooth We set our dividers to the sa at the point _b_ for a center and sweep the arc _j'_ If we measure this arc from the point _j'_ to intersection of said arc _j'_ with the line _l_ ill find it to be sixty-four degrees, which accounts for our taking this nurees e defined the face of our escape-wheel tooth, Fig 129

There is no reason e should take twenty-degrees for the angle _k e l_ except that the practical construction of the larger sizes of cylinder watches has established the fact that this is about the right angle to eh as twenty-five Although the cylinder is seely a very simple escapement, it is really a very abstruce one to follow out so as to become familiar with all of its actions

THE CYLINDER PROPER CONSIDERED

[Illustration: Fig 131]

We will now proceed and consider the cylinder proper, and to aid us in understanding the position and relation of the parts we refer to Fig

131, where we repeat the circles _d_ and _h_, shown in Fig 130, which represents the inside and outside of the cylinder We have here also repeated the line _f_ of Fig 130 as it cuts the cylinder in half, that is, divides it into two segrees each If we conceive of a cylinder in which just one-half is cut away, that is, the lips are bounded by straight radial lines, we can also conceive of the relation and position of the parts shown in Fig 130 The first position of which we should take cognizance is, the tooth _D_ is moved back to the left so as to rest on the outside of our cylinder The cylinder is also supposed to stand so that the lips correspond to the line _f_ On pressing the tooth _D_ forward the incline of the tooth would attack the entrance lip of the cylinder at just about the center of the curved iular motion, but the point of the tooth at _d_ would exactly encounter the inner angle of the exit lip, and of course the cylinder would afford no rest for the tooth; hence, we see the i away too much of the half shell of the cylinder

But before we further consider the action of the tooth _D_ in its action as it passes the exit lip of the cylinder we must finish with the action of the tooth on the entrance lip A very little thought and study of Fig 130 will convince us that the incline of the tooth as it enters the cylinder will co 130, but at the close of the action the tooth parts frole Now it is evident that it would require greater force to propel the cylinder by its inner angle than by the outer one To coe of the entrance lip so that the action of the tooth instead of coe of the entrance lip and also ends its action on the center of the entrance lip To give angular extent enough to the shell of the cylinder to allow for rounding and also to afford a secure rest for the tooth inside the cylinder, we add six degrees to the angular extent of the entrance lip of the cylinder shell, as indicated on the arc _o'_, Fig 131, three of these degrees being absorbed for rounding and three to insure a dead rest for the tooth when it enters the cylinder

WHY THE ANGULAR EXTENT IS INCREASED

Without rounding the exit lip the action of the tooth on its exit would be entirely on the inner angle of the shell To obviate this it is the usual practice to increase the angular extent of the cylinder ten degrees, as shown on the arc _o'_ between the lines _f_ and _p_, Fig

131 Why we should allow ten degrees on the exit lip and but six degrees on the entrance lip will be understood by observing Fig 130, where the radial lines _s_ and _r_ show the extent of angular motion of the cylinder, which would be lost if the tooth cole of the exit lip This arc is a little over six degrees, and if we add a trifle over three degrees for rounding ould account for the ten degrees between the lines _f_ and _p_, Fig