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[Illustration: THOMAS MUDGE
_The first Horologist who successfully applied the Detached Lever
Escapement to Watches._
_Born 1715--Died 1794._]
AN ANALYSIS
OF THE
LEVER ESCAPEMENT
BY H. R. PLAYTNER.
A LECTURE DELIVERED BEFORE THE CANADIAN WATCHMAKERS' AND RETAIL
JEWELERS' ASSOCIATION.
ILLUSTRATED.
CHICAGO:
HAZLITT & WALKER, PUBLISHERS.
1910.
PREFACE.
Before entering upon our subject proper, we think it advisable to
explain a few points, simple though they are, which might cause
confusion to some readers. Our experience has shown us that as soon as
we use the words "millimeter" and "degree," perplexity is the result.
"What is a millimeter?" is propounded to us very often in the course of
a year; nearly every new acquaintance is interested in having the metric
system of measurement, together with the fine gauges used, explained to
him.
The metric system of measurement originated at the time of the French
Revolution, in the latter part of the 18th century; its divisions are
decimal, just the same as the system of currency we use in this country.
A meter is the ten millionth part of an arc of the meridian of Paris,
drawn from the equator to the north pole; as compared with the English
inch there are 39+3708/10000 inches in a meter, and there are
25.4 millimeters in an inch.
The meter is sub-divided into decimeters, centimeters and millimeters;
1,000 millimeters equal one meter; the millimeter is again divided into
10ths and the 10ths into 100ths of a millimeter, which could be
continued indefinitely. The 1/100 millimeter is equal to the 1/2540 of
an inch. These are measurements with which the watchmaker is concerned.
1/100 millimeter, written .01 mm., is the side shake for a balance
pivot; multiply it by 2¼ and we obtain the thickness for the spring
detent of a pocket chronometer, which is about ⅓ the thickness of a
human hair.
The metric system of measurement is used in all the watch factories of
Switzerland, France, Germany, and the United States, and nearly all the
lathe makers number their chucks by it, and some of them cut the leading
screws on their slide rests to it.
In any modern work on horology of value, the metric system is used.
Skilled horologists use it on account of its _convenience_. The
millimeter is a unit which can be handled on the small parts of a watch,
whereas the inch must always be divided on anything smaller than the
plates.
Equally as fine gauges can be and are made for the inch as for the
metric system, and the inch is decimally divided, but we require another
decimal point to express our measurement.
Metric gauges can now be procured from the material shops; they consist
of tenth measures, verniers and micrometers; the finer ones of these
come from Glashutte, and are the ones mentioned by Grossmann in his
essay on the lever escapement. Any workman who has once used these
instruments could not be persuaded to do without them.
No one can comprehend the geometrical principles employed in escapements
without a knowledge of angles and their measurements, therefore we deem
it of sufficient importance to at least explain what a degree is, as we
know for a fact, that young workmen especially, often fail to see how to
apply it.
Every circle, no matter how large or small it may be, contains 360°; a
degree is therefore the 360th part of a circle; it is divided into
minutes, seconds, thirds, etc.
To measure the _value_ of a degree of any circle, we must multiply the
diameter of it by 3.1416, which gives us the circumference, and then
divide it by 360. It will be seen that it depends on the size of that
circle or its radius, as to the value of a degree in any _actual_
measurement. To illustrate; a degree on the earth's circumference
measures 60 geographical miles, while measured on the circumference of
an escape wheel 7.5 mm. in diameter, or as they would designate it in a
material shop, No. 7½, it would be 7.5 × 3.1416 ÷ 360 = .0655 mm., which
is equal to the breadth of an ordinary human hair; it is a degree in
both cases, but the difference is very great, therefore a degree cannot
be associated with any actual measurement until the radius of the
circle is known. Degrees are generated from the center of the circle,
and should be thought of as to ascension or direction and relative
value. Circles contain four right angles of 90° each. Degrees are
commonly measured by means of the protractor, although the ordinary
instruments of this kind leave very much to be desired. The lines can be
verified by means of the compass, which is a good practical method.
It may also be well to give an explanation of some of the terms used.
_Drop_ equals the amount of freedom which is allowed for the action of
pallets and wheel. See Z, Fig. 1.
_Primitive or Geometrical Diameter._--In the ratchet tooth or English
wheel, the primitive and real diameter are equal; in the club tooth
wheel it means across the locking corners of the teeth; in such a wheel,
therefore, the primitive is _less_ than the real diameter by the height
of two impulse planes.
_Lock_ equals the depth of locking, measured from the locking corner of
the pallet at the moment the drop has occurred.
_Run_ equals the amount of angular motion of pallets and fork to the
bankings _after_ the drop has taken place.
_Total Lock_ equals lock plus run.
A _Tangent_ is a line which _touches_ a curve, but does not intersect
it. AC and AD, Figs. 2 and 3, are tangents to the primitive circle GH at
the points of intersection of EB, AC, and GH and FB, AD and GH.
_Impulse Angle_ equals the angular connection of the impulse or ruby pin
with the lever fork; or in other words, of the balance with the
escapement.
_Impulse Radius._--From the face of the impulse jewel to the center of
motion, which is in the balance staff, most writers assume the impulse
angle and radius to be equal, and it is true that they must conform with
one another. We have made a radical change in the radius and one which
does not affect the angle. We shall prove this in due time, and also
that the wider the impulse pin the greater must the impulse radius be,
although the angle will remain unchanged.
Right here we wish to put in a word of advice to all young men, and that
is to learn to draw. No one can be a thorough watchmaker unless he can
draw, because he cannot comprehend his trade unless he can do so.
We know what it has done for us, and we have noticed the same results
with others, therefore we speak from personal experience. Attend night
schools and mechanic's institutes and improve yourselves.
The young workmen of Toronto have a great advantage in the Toronto
Technical School, but we are sorry to see that out of some 600 students,
only five watchmakers attended last year. We can account for the
majority of them, so it would seem as if the young men of the trade were
not much interested, or thought they could not apply the knowledge to be
gained there. This is a great mistake; we might almost say that
knowledge of any kind can be applied to horology. The young men who take
up these studies, will see the great advantage of them later on; one
workman will labor intelligently and the other do blind "guess" work.
We are now about to enter upon our subject and deem it well to say, we
have endeavored to make it as plain as possible. It is a deep subject
and is difficult to treat lightly; we will treat it in our own way,
paying special attention to all these points which bothered us during
the many years of painstaking study which we gave to the subject. We
especially endeavor to point out how theory can be applied to practice;
while we cannot expect that everyone will understand the subject without
study, we think we have made it comparatively easy of comprehension.
We will give our method of drafting the escapement, which happens in
some respects to differ from others. We believe in making a drawing
which we can reproduce in a watch.
AN ANALYSIS OF THE LEVER ESCAPEMENT.
The lever escapement is derived from Graham's dead-beat 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.
Our object will be to explain the whys and wherefores of this
escapement, and we will at once begin with the number of teeth in the
escape wheel. 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
16 × 2 = 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 9.375 × 8 = 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
(75 × 16 × 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°, which represents the angle of movement in modern watches. Some of
the finest ones only make 8 or 9° of a movement; the smaller the angle
the greater will the effects of defective workmanship be; 10° 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° leaving an interval of 24°
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°, which is equal to 2½ spaces of the wheel. Fig. 1
illustrates the lockings, spanning this arc. If the pallets embraced 4
teeth, the angle would be 84°; or in case of a 16 tooth wheel scaping
over three teeth, the angle would be 360 × 2.5/16 = 56¼°.
[Illustration: Fig. 1.]
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.
[Illustration: Fig. 2.]
AC and AD, Fig. 2, are tangents to the primitive circle GH. ABE and ABF
are angles of 30° each, together therefore forming the angle FBE of
60°. 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°, 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.
[Illustration: Fig. 3.]
The circular pallet is sometimes appropriately called "the pallet with
equal lifts," as the lever arms AMO and ANP, Fig. 3, are equal lengths.
It will be noticed by examining the diagram, that the pallets are
bisected by the 30° 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 finest
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. 2, 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. 4, 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.
[Illustration: Fig. 4.]
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 1½° drop
for the club and 2° 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 1½° by angular measurement?
7.5 × 3.1416 ÷ 360 × 1.5 = .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;
8.5 × 3.1416 ÷ 360 × 1.5 = .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.
[Illustration: Fig. 5.]
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° on the
engaging and 12° on the disengaging pallet; others again allow 12° on
each, which we deem sufficient. The draw is measured from the locking
edges M and N, Fig. 5. The locking planes _when locked_ are inclined 12°
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. 5, 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° draw for this pallet. As illustrated in the case of
the disengaging pallet, however, the motion is also towards 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 BNB are opposite and equal
angles of 12°. For practical reasons, from a manufacturing standpoint,
the angle on the tooth is made just twice the amount, namely 24°; we
could make it a little less or a little more. If we made it less than
20° 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°, 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; 1½° is the
angle generally allowed for the lock, but it is obvious that in a large
escapement it can be less.
[Illustration: Fig. 6.]
_The Run._--The run or, as it is sometimes called, "the slide," should
also be as light as possible; from ¼° to ½° is sufficient. It follows
then, the bankings 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 6 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° of run, while if placed at _b_ we would
only have ½° 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.
[Illustration: Fig. 7.]
_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°; if the lock is 1½° then the actual lift by means of the
inclined planes on teeth and pallets will be 8½°. 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. 7
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 8½° 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.
[Illustration: Fig. 8.]
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. 8, 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 G H, 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°, which is equal
to the entire lock; therefore if 8½° of work is to be accomplished
through this pallet, the lifting plane requires an angle of 10½° 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. 9 illustrates the engaging, and
Fig. 10 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. 11. 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.
[Illustration: Fig. 9.]
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 10½° 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 5¼° in width, and suppose we
have a lifting of 8½° to distribute between them, by allowing 4¼° on
each, the lift would take place as shown in Fig. 12, 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.
[Illustration: Fig. 10.]
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. 13. 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.
[Illustration: Fig. 11.]
[Illustration: Fig. 12.]
[Illustration: Fig. 13.]
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.
[Illustration: Fig. 2.]
_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. 2 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. 3, 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. 4) 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° 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 .1 mm. 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) × 2 = .4382 mm. It would not
be practicable to make anything smaller.
[Illustration: Fig. 3.]
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.
[Illustration: Fig. 4.]
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 10½°. Let us
divide it by 2, which would be the most natural thing to do, and examine
the problem. We will have 5¼° 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 5¼° 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° lift on the tooth is well
adapted for a width of 4½°, which would require a pallet 6° in width.
The tooth, therefore, would be ¾ 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.
_Equidistant vs. Circular._ At this stage we are able to weigh the
circular against the equidistant pallet. In beginning this essay 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. 14, 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. 14, 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.
[Illustration: Fig. 14.]
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 8½°, a locking angle of
1½°, and a run of ½°, we will have an angular movement of the fork of
8½ + 1½ + ½ = 10½°.
[Illustration: Fig. 15.]
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 10½° (JAW, Fig. 15), one-half, or 5¼°
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 31½°. The radius A′X Fig. 16, 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. 15. We will notice that the
intersection _k_ is much smaller in Fig. 15 than in Fig. 16. 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.
[Illustration: Fig. 16.]
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 1½ turns, which
is equal to 540° a fork angle of 10° and a proportion of 2.75 for the
impulse angle which would be equal to 10 × 2.75 = 27.5°. The _free_
vibration of the balance, or as this is called, "the supplemental arc,"
is equal to 540° - 27.5° = 512.50°, while with a proportion of 5 to 1,
making an impulse angle of 50°, it would be equal to 490°. 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. 14, 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. 14.
We will now consider the width of the ruby pin and to get a good insight
into the question, we will study Fig. 17. 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,
taking 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 equals 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 1¼°. 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 1½° and ½° run, we would have a total lock on the
pallets of 2°. By allowing 1¼° of freedom for the ruby pin at 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 ¾° 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?
4.5 × 2 × 3.1416 ÷ 360° = .0785 × 1.25 = .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 ¼° to ½°, 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. 20. 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. 17, we would require a _very_ narrow ruby pin. With 1°
of freedom at the edge, and ½° in the slot, we could only have a ruby
pin of a width of 1½°. Applying it to the preceding example it would
only have an actual width of .0785 × 1.5 = .1178 mm., or the size of an
ordinary balance pivot. At _n_, Fig. 17, 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 within 1° of half the total movement of the
fork from the line of centers; to illustrate, if the angular motion is
11° the ruby pin under discussion will begin action 4½° before the line
of centers, being an engaging, or "uphill" friction of considerable
magnitude.
[Illustration: Fig. 17.]
[Illustration: Fig. 18.]
[Illustration: Fig. 19.]
[Illustration: Fig. 20.]
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. 17; 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 the impulse
action.
Fig. 18 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.