PECULIARITIES OF ANGULAR MEASUREMENT—HOW TO READ DRAWINGS.
We now come to a point at which, if we are to keep our pendulum
vibrating, we must apply power to it, evenly, accurately and in small
doses. In order to do this conveniently we must store up energy by
raising a weight or winding a spring and allow the weight to fall or
the spring to unwind very slowly, say in thirty hours or in eight
days. This brings about the necessity of changing rotary motion to
reciprocating motion, and the several devices for doing this are called
“escapements” in horology, each being further designated by the names
of their inventors, or by some peculiarity of the devices themselves;
thus, the Graham is also called the dead beat escapement; Le Paute’s is
the pin wheel; Dennison’s in its various forms is called the gravity;
Hooke’s is known as the recoil; Brocot’s as the visible escapement, etc.
THE MECHANICAL ELEMENTS.—We shall understand this subject more clearly,
perhaps, if we first separate these mechanical devices into their
component parts and consider them, not as parts of clocks, but as
various forms of levers, which they really are. This is perhaps the
best place to consider the levers we are using to transmit the energy
to the pendulum, as at this point we shall find a greater variety of
forms of the lever than in any other place in the clock, and we shall
have less difficulty in understanding the methods of calculating for
time and power by a thorough preliminary understanding of leverage and
the peculiarities of angular or circular motion.
If we take a bar, A, Fig. 21, and place under it a fulcrum, B, then by
applying at C a given force, we shall be able to lift at D a weight
whose amount will be governed by the relative distances of C and D from
the fulcrum B. If the distance CB is four times that of BD, then a
force of 10 pounds at C will lift 40 pounds at D, for one-fourth of the
distance through which C moves, minus the power lost by friction. The
reverse of this is also true; that is, it will take 40 pounds at D to
exert a force of 10 pounds at C and the 10 pounds would be lifted four
times as far as the 40 pound weight was depressed.
[Illustration: Fig. 21.]
[Illustration: Fig. 22.]
If instead of a weight we substitute other levers, Fig. 22, the result
would be the same, except that we should move the other levers until
the ends which were in contact slipped apart.
[Illustration: Fig. 23.]
If we divide our lever and attach the long end to one portion of an
axle, as at A, Fig. 23, and the short end to another part of it at B,
the result will be the same as long as the proportions of the lever are
not changed. It will still transmit power or impart motion according
to the relative lengths of the two parts of the lever. The capacity of
our levers, Fig. 22, will be limited by that point at which the ends
of the levers will separate, because they are held at the points of
the fulcrums and constrained to move in circles by the fulcrums. If
we put more levers on the same axles, so spaced that another set will
come into action as the first pair are disengaged, we can continue
our transmission of power, Fig. 24; and if we follow this with still
others until we can add no more for want of room we shall have wheels
and pinions, the collection of short levers forming the pinion and
the group of long levers forming the wheel, Fig. 25. Thus every wheel
and pinion mounted together on an arbor are simply a collection of
levers, each wheel tooth and its corresponding pinion leaf forming one
lever. This explains why the force decreases and the motion increases
in proportion to the relative lengths of the radii of the wheels and
pinions, so that eight or ten turns of the barrel of a clock will run
the escape wheel all day.
[Illustration: Fig. 24.]
We now come to the verge or anchor, and here we have the same sort
of lever in a different form; the verge wire, which presses on the
pendulum rod and keeps it going is the long arm of our lever, but
instead of many there is only one. The short arm of our lever is the
pallet, and there are two of these. Therefore we have a form of lever
in which there is one long arm and two short ones; but as the two are
never acting at the same time they do not interfere with each other.
[Illustration: Fig. 25.]
These systems of levers have another advantage, which is that one arm
need not be on the opposite side of the fulcrum from the other. It
may be on the same side as in the verge or at any other convenient
point. This enables us to save space in arranging our trains, as such
a collection of wheels and pinions is called, by placing them in any
position which, on account of other facts, may seem desirable.
PECULIARITIES OF ANGULAR MOTION.—Now our collections of levers must
move in certain directions in order to be serviceable and in order to
describe these things properly, we must have names for these movements
so that we can convey our thoughts to each other. Let us see how they
move. They will not move vertically (up or down) or horizontally
(sidewise), because we have taken great pains to prevent them from
doing so by confining the central bars of our levers in a fixed
position by making pivots on their ends and fitting them carefully into
pivot holes in the plates, so that they can move only in one plane, and
that movement must be in a circular direction in that predetermined
plane. Consequently we must designate any movement in terms of the
portions of a circle, _because that is the only way they can move_.
These portions of a circle are called angles, which is a general term
meaning always a portion of a circle, measured from its center; this
will perhaps be plainer if we consider that whenever we want to be
specific in mentioning any particular size of angle we must speak of it
in degrees, minutes and seconds, which are the names of the standard
parts into which a circle is divided. Now in every circle, large or
small, there are 360 degrees, because a degree is ¹/₃₆₀th part of a
circle, and this measurement is always _from its center_. Consequently
a degree, or any angle composed of a number of degrees, is always the
same, because, being _measured from its center_, such measurements
of any two circles will coincide as far as they go. If we draw two
circles having their centers over each other at A, Fig. 26, and take
a tenth part of each, we shall have 360° ÷ 10 = 36°, which we shall
mark out by drawing radial lines to the circumference of each circle,
and we shall find this to be true; the radii of the smaller circle AB
and AC will coincide with the radii AD and AE as far as they go. This
is because each is the tenth part of its circle, _measured from its
center_. Now that portion of the circumference of the circle BC will be
smaller than the same portion DE of the larger circle, but each will be
a _tenth part of its own circle_, although they are not the same size
when measured by a rule on the circumference. This is a point which has
bothered so many people when taking up the study of angular measurement
that we have tried to make it absurdly clear. An angle _never_ means
so many feet, inches or millimeters; it _always_ means a _portion of a
circle, measured from the center_.
[Illustration: Fig. 26.]
There is one feature about these angular (or circular) measurements
that is of great convenience, which is that as no definite size is
mentioned, but only proportionate sizes, the description of the machine
described need not be changed for any size desired, as it will fit all
sizes. It thus becomes a flexible term, like the fraction “one-half,”
changing its size to suit the occasion. Thus, one-half of 300,000
bushels of wheat is 150,000 bushels; one-half of 10 bushels is 5
bushels; one-half of one bushel is two pecks; yet each is _one-half_.
It is so with our angles.
There are some other terms which we shall do well to investigate
before we leave the subject of angular measurements, which are the
relations between the straight and curved lines we shall need to study
in our drawings of the various escapements. A radius (plural radii) is
a straight line drawn from the center of a circle to its circumference.
A tangent is a straight line drawn outside the circumference, touching
(but not cutting) it _at right angles_ (90 degrees) to a radius drawn
to the point of tangency (point where it touches the circumference).
A general misunderstanding of this term (tangent) has done much to
hinder a proper comprehension of the writers who have attempted to make
clear the mysteries of the escapements. Its importance will be seen
when we recollect that about the first thing we do in laying out an
escapement is to draw tangents to the pitch circle of the escape wheel
and plant our pallet center where these tangents intersect on the line
of centers. They should always be drawn at _right angles_ to the radii
which mark the angles we choose for the working portion of our escape
wheel. If properly drawn we shall find that the pallet arbor will then
_locate itself_ at the correct distance from the escape wheel center
for any desired angle of escapement. We shall also discover that it
will take a different center distance for every different angle and yet
each different position will be the correct one for its angle, Fig. 27.
Because an angle is always the same, no matter how far from the center
the radii defining it are carried, we are able to work conveniently
with large drawing instruments on small drawings. Thus we can use an
eight or ten inch protractor in laying off our angles, so as to get
the degrees large enough to measure accurately, mark the degrees with
dots on our paper and then draw our lines with a straight edge from the
center towards the dots, as far as we wish to go. Thus we can lay off
the angles on a one-inch escape wheel with a ten inch protractor more
easily and correctly than if we were using a smaller instrument.
[Illustration: Fig. 27.]
Another thing which will help us in understanding these drawings is
that the _effective_ length of a lever is its distance from the center
to the working point, _measured in a straight line_. Thus in a pallet
of a clock the distance of the pallets from the center of the pallet
arbor is the _effective length_ of that arm of the lever, no matter how
it may be curved for ornament or for other reasons.
The lines and circles drawn to enable us to take the necessary
measurements of angles and center distances are called “construction
lines” and are generally dotted on the paper to enable us to
distinguish them as lines for measurement only, while the lines which
are intended to define the actual shapes of the pieces thus drawn are
solid lines. By observing this distinction we are enabled to show the
actual shapes of the objects and all their angular measurements clearly
on the one drawing.
With these explanations the student should be able to read clearly
and correctly the many drawings which follow, and we will now turn
our attention to the escapements. In doing this we shall meet with a
constant use of certain terms which have a peculiar and special meaning
when applied to escapements.
THE LIFT is the amount of angular motion imparted to the verge or
anchor by the teeth of the escape wheel pressing against the pallets
and pushing first one and then the other out of the way, so that the
escape wheel teeth may pass. According as the angular motion is more
or less the “lift” is said to be greater or less; as this motion is
circular, it must be expressed in degrees. The lifting planes are
those surfaces which produce this motion; in clocks with pendulums
the lifting planes are generally on the pallets, being those hard and
smoothly polished surfaces over which the points of the escape wheel
teeth slide in escaping. In lever escapements the lifting planes are
frequently on the escape wheel, the pallets being merely round pins.
Such an escape wheel is said to have club teeth, as distinguished from
the pointed teeth used when the lifting planes are on the pallets. In
the cylinder escapement the lifting planes are on the escape wheel;
they are curved instead of being straight; and there is but one pallet,
which is on the lip of the cylinder. In the forms of lever escapement
used in watches and some clocks the lift is divided, part of the
lifting planes being also on the pallets; in this case both sets of
planes are shorter than if they were entirely on one or the other,
but they must be long enough so that combined they will produce the
requisite amount of angular motion of the pallets, so as to give the
requisite impulse to the pendulum or balance.
THE DROP is the amount of circular motion, measured in degrees, which
the escape wheel has from the instant the tooth escapes from one pallet
to that point at which it is stopped by the other pallet catching
another tooth. During this period the train is running down without
imparting any power to the pendulum or balance, hence the drop is
entirely lost motion. We must have it, however, as it requires some
time for the other pallet to move far enough within the pitch circle
of the escape wheel to safely catch and stop the next tooth under all
circumstances. It is the freedom and safety of the working plan of
our escapement, but it is advisable to keep the drop as small as is
possible with safe locking.
THE LOCK is also angular motion and is measured in degrees from the
center of the pallet arbor. It is the distance which the pallet has
moved inside of the pitch circle of the escape wheel before being
struck by the escape wheel tooth. It is measured from the edge of the
lifting plane to the point of the tooth where it rests on the locking
face of the pallet. A safe lock is necessary in order to prevent the
points of the escape wheel teeth butting against the lifting planes,
stopping the clock and injuring the teeth. We want to point out that
from the instant of escaping to the instant of locking we have the two
parts of our escapement propelled by different and entirely separate
forces and moving at different speeds. The pallets, after having given
impulse to the pendulum, are controlled by the pendulum and moved by
it; in the case of a heavy pendulum ball at the end of a 40-inch lever,
this control is very steady, powerful and quite slow. The escape wheel,
the lightest and fastest in the train, is driven by the weight or
spring and moves independently of the pallets during the drop, so that
safe locking is important. It should never be too deep, as it would
increase the swing of the pendulum too much; this is especially true
with short and light pendulums and strong mainsprings.
THE RUN.—After locking the pallet continues to move inward towards
the escape wheel center as the pendulum continues its course, and the
amount of this motion, measured in degrees from the center of the
pallet arbor, is called the run.
When the escapement is properly adjusted the lifting planes are of
the same length on both pallets, when they are measured in degrees
of motion given to the pallet arbor. They may or may not be equal in
_length_ when measured by a rule on the faces of the pallets. There
should also be an equal and safe lock on each pallet, as measured in
degrees of movement of the pallet arbor. The run should also be equal.
The reason why one lifting plane may be longer than the other and still
give the same amount of lift is that some escapements are constructed
with unequal lockings, so that one radius is longer than the other, and
this, as we explained at length in treating of angles, Fig. 26, would
make a difference in the length of arc traversed by the longer arm for
the same angle of motion.