Ward L. Goodrich

Before going further with the mechanism of our clocks we will now consider the means by which the various members are held in their positions, namely, the plates. Like most other parts of the clock these have undergone various changes. They have been made of wood, iron and brass and have varied in shapes and sizes so much that a great deal may be told concerning the age of a clock by examining the plates.

Most of the wooden clocks had wooden plates. The English and American movements were simply boards of oak, maple or pear with the holes drilled and bushed with brass tubes—full plates. The Schwarzwald movements were generally made with top and bottom boards and stanchions, mortised in between them to carry the trains, which were always straight-line trains. The rear stanchions were glued in position and the front ones fitted friction-tight, so that they could be removed in taking down the clock. This gave a certain convenience in repairing, as, for instance, the center (time) train could be taken down without disturbing the hour or quarter trains, or vice versa. Various attempts have been made since to retain their convenience with brass plates, but it has always added so much to the cost of manufacture that it had to be abandoned.

The older plates were cast, smoothed and then hammered to compact the metal. The modern plate is rolled much harder and stiffer and it may consequently be much thinner than was formerly necessary. The proper thickness of a plate depends entirely upon its use. Where the movement rests upon a seat board in the case and carries the weight of a heavy pendulum attached to one of the plates they must be made stiff enough to furnish a rigid support for the pendulum, and we find them thick, heavy and with large pillars, well supported at the corners, so as to be very stiff and solid. An example of this may be seen in that class of regulators which carry the pendulum on the movement. Where the pendulum is light the plates may therefore be thin, as the only other reason necessary for thickness is that they may provide a proper length of bearing for the pivots, plus the necessary countersinking to retain the oil.

In heavy machinery it is unusual to provide a length of box or journal bearing of more than three times the diameter of the journal. In most cases a length of twice the diameter is more than sufficient; in clock and other light work a “square” bearing is enough; that is one in which the length is equal to the diameter. In clocks the pivots are of various sizes and so an average must be found. This is accomplished by using a plate thick enough to furnish a proper bearing for the larger pivots and countersinking the pivot holes for the smaller pivots until a square bearing is obtained. This countersinking is shaped in such a manner as to retain the oil and as more of it is done on the smaller and faster moving pivots, where there is the greatest need of lubrication, the arrangement works out very nicely, and it will be seen that with all the lighter clocks very thin plates may be employed while still retaining a proper length of bearing in the pivot holes.

The side shake for pivots should be from .002 to .004 of an inch; the latter figure is seldom exceeded except in cuckoos and other clocks having exposed weights and pendulums. Here much greater freedom is necessary as the movement is exposed to dust which enters freely at the holes for pendulum and weight chains, so that such a clock would stop if given the ordinary amount of side shake.

We are afraid that many manufacturers of the ordinary American clock aim to use as thin brass as possible for plates without paying too much attention to the length of bearing. If a hole is countersunk it will retain the oil when a flat surface will not. The idea of countersinking to obtain a shorter bearing will apply better to the fine clocks than to the ordinary. In ordinary clocks the pivots must be longer than the thickness of the plates for the reason that freight is handled so roughly that short pivots will pop out of the plates and cause a lot of damage, provided the springs are wound when the rough handling occurs.

It will be seen by reference to Chapter VII (the mechanical elements of gearing), Figs. 21 to 25, that a wheel and pinion are merely a collection of levers adapted to continuous work, that the teeth may be regarded as separate levers coming into contact with each other in succession; this brings up two points. The first is necessarily the relative proportions of those levers, as upon these will depend the power and speed of the motion produced by their action. The second is the shapes and sizes of the ends of our levers so that they shall perform their work with as little friction and loss of power as possible.

To Get Center Distances.—As the radii and circumferences of circles are proportional, it follows that the lengths of our radii are merely the lengths of our levers (See Fig. 24), and that the two combined (the radius of the wheel, plus that of the pinion) will be the distance at which we must pivot our levers (our staffs or arbors of our wheels) in order to maintain the desired proportions of their revolution. Consequently we can work this rule backwards or forwards.

For instance if we have a wheel and pinion which must work together in the proportion of 7½ to 1; then 7½+1=8½ and if we divide the space between centers into 8½ spaces we will have one of these spaces for the radius of the pitch circle of the pinion and 7½ for the pitch circle of the wheel, Fig. 65. This is independent of the number of teeth so long as the proportions be observed; thus our pinion may have eight teeth and the wheel sixty, 60÷8=7.5, or 75÷10=7.5, or 90÷12=7.5, or any other combination of teeth which will make the correct proportion between them and the center distances. The reason is that the teeth are added to the wheel to prevent slipping, and if they did not agree with each other and also with the proportionate distance between centers there would be trouble, because the desired proportion could not be maintained.

Now we can also work this rule backwards. Say we have a wheel of 80 teeth and the pinion has 10 leaves but they do not work together well in the clock. Tried in the depthing tool they work smoothly. 80÷10=8, consequently our center distance must be as 8 and 1. 8+1=9; the wheel must have 8 parts and the pinion 1 part of the radius of the pitch circle of the wheel. Measure carefully the diameter of the pitch circle of the wheel; half of that is the pitch radius, and nine-eighths of the pitch radius is the proper center distance for that wheel and pinion.

Say we have lost a wheel; the pinion has 12 teeth and we know the arbor should go seven and one-half times to one of the missing wheel; we have our center distances established by the pivot holes which are not worn; what size should the wheel be and how many teeth should it have? 12×7.5=90, the number of teeth necessary to contain the teeth of the pinion 7.5 times. 7.5+1=8.5, the sum of the center distances; the pitch radius of the pinion can be closely measured; then 7.5 times that is the pitch radius of the missing wheel of 90 teeth. Other illustrations with other proportions could be added indefinitely but we have, we think, said enough to make this point clear.

Fig. 65. Spacing off center distances; c, center of wheel;
e, pitch circle; d, dedendum; b, addendum; a, center of pinion.

Conversion of Numbers.—There is one other point which sometimes troubles the student who attempts to follow the expositions of this subject by learned writers and that is the fact that a mathematician will take a totally different set of numbers for his examples, without explaining why. If you don’t know why you get confused and fail to follow him. It is done to avoid the use of cumbersome fractions. To use a homely illustration: Say we have one foot, six inches for our wheel radius and 4.5 inches for our pinion radius. If we turn the foot into inches we have 18 inches. 18÷4.5=4, which is simpler to work with. Now the same thing can be done with fractions. In the above instance we got rid of our larger unit (the foot) by turning it into smaller units (inches) so that we had only one kind of units to work with. The same thing can be done with fractions; for instance, in the previous example we can get rid of our mixed numbers by turning everything into fractions. Eighteen inches equals 36 halves and 4.5 equals 9 halves; then 36÷9=4. This is called the conversion of numbers and is done to simplify operations. For instance in watch work we may find it convenient to turn all our figures into thousands of a millimeter, if we are using a millimeter gauge. Say we have the proportions of 7.5 to 1 to maintain, then turning all into halves, 7½×2=15 and 1×2=2. 15+2=17 parts for our center distance, of which the pitch radius of the pinion takes 2 parts and that of the wheel 15.

The Shapes of the Teeth.—The second part of our problem, as stated above, is the shapes of the ends of our levers or the teeth of our wheels, and here the first consideration which strikes us is that the teeth of the wheels approach each other until they meet; roll or slide upon each other until they pass the line of centers and then are drawn apart. A moment’s consideration will show that as the teeth are longer than the distance between centers and are securely held from slipping at their centers, the outer ends must either roll or slide after they come in contact and that this action will be much more severe while they are being driven towards each other than when they are being drawn apart after passing the line of centers. This is why the engaging friction is more damaging than the disengaging friction and it is this butting action which uses up the power if our teeth are not properly shaped or the center distances not right. Generally speaking this butting causes serious loss of power and cutting of the teeth when the pivot holes are worn or the pivots cut, so that there is a side shake of half the diameter of the pivots, and bushing or closing the holes, or new and larger pivots are then necessary. This is for common work. For fine work the center distances should be restored long before the wear has reached this point.

If we take two circular pieces of any material of different diameters and arrange them so that each can revolve around its center with their edges in contact, then apply power to the larger of the two, we find that as it revolves its motion is imparted to the other, which revolves in the opposite direction, and, if there is no slipping between the two surfaces, with a velocity as much greater than that of the larger disc as its diameter is exceeded by that of the larger one. We have, then, an illustration of the action of a wheel and pinion as used in timepieces and other mechanisms. It would be impossible, however, to prevent slipping of these smooth surfaces on each other so that power (or motion) would be transmitted by them very irregularly. They simply represent the “pitch” circles or circles of contact of these two mobiles. If now we divide these two discs into teeth so spaced that the teeth of one will pass freely into the spaces of the other and add such an amount to the diameter of the larger that the points of its teeth extend inside the pitch circle of the smaller, a distance equal to about 1? times the width of one of its teeth, and to the smaller so that its teeth extend inside the larger one-half the width of a tooth, the ends of the teeth being rounded so as not to catch on each other and the centers of revolution being kept the same distance apart, on applying power to the larger of the two it will be set in motion and this motion will be imparted to the smaller one. Both will continue to move with the same relative velocity as long as sufficient power is applied. Other pairs of mobiles may be added to these to infinity, each addition requiring the application of increased power to keep it in motion.

These pairs of mobiles as applied to the construction of timepieces are usually very unequal in size and the larger is designated as a “wheel” while the smaller, if having less than 20 teeth, is called a “pinion” and its teeth “leaves.” Now while we have established the principle of a train of wheels as used in various mechanisms, our gearing is very defective, for while continuous motion may be transmitted through such a train, we will find that to do so requires the application of an impelling force far in excess of what should be required to overcome the inertia of the mobiles, and the amount of friction unavoidable in a mechanism where some of the parts move in contact with others.

This excess of power is used in overcoming a friction caused by improperly shaped teeth, or when formed thus the teeth of the wheel come in contact with those of the pinion and begin driving at a point in front of what is known as the “line of centers,” i. e., a line drawn through the centers of revolution of both mobiles, and as their motion continues the driven tooth slides on the one impelling it toward the center of the wheel. When this line is reached the action is reversed and the point of the driving tooth begins sliding on the pinion leaf in a direction away from the center of the pinion, which action is continued until a point is reached where the straight face of the leaf is on a line tangential to the circumference of the wheel at the point of the tooth. It then slips off the tooth, and the driving is taken up on another leaf by the next succeeding tooth. The sliding action which takes place in front of the line of centers is called “engaging,” that after this line has been passed “disengaging” friction.

Now we know that in the construction of timepieces, friction and excessive motive power are two of the most potent factors in producing disturbances in the rate, and that, while some friction is unavoidable in any mechanism, that which we have just described may be almost entirely done away with. Let us examine carefully the action of a wheel and pinion, and we will see that only that part of the wheel tooth is used, which is outside the pitch circle, while the portion of the pinion leaf on which it acts is the straight face lying inside this circle, therefore it is to giving a correct shape to these parts we must devote our attention. If we form our pinion leaves so that the portion of the leaf inside the pitch circle is a straight line pointing to the center, and give that portion of the wheel tooth lying outside the pitch circle (called the addenda, or ogive of the tooth) such a degree of curvature that during its entire action the straight face of the leaf will form a tangent to that point of the curve which it touches, no sliding action whatever will take place after the line of centers is passed, and if our pinion has ten or more leaves, the “addenda” of the wheel is of proper height, and the leaves of the pinion are not too thick, there will be no contact in front of the line of centers. With such a depth the only friction would be from a slight adhesion of the surfaces in contact, a factor too small to be taken into consideration.

Showing that a hypocycloid of half the pitch circle is a straight line.

Generating an epicycloid curve for a cut pinion. D, generating circle.
Dotted line epicycloid curve. Note how the shape varies with the
thickness of the tooth.

Here, then, we have an ideal depth. How shall we obtain the same results in practice? It is comparatively an easy matter to so shape our cutters that the straight faces of our pinion leaves will be straight lines pointing to the center, but to secure just the proper curve for the addenda of our wheel teeth requires rather a more complicated manipulation. This curve does not form a segment of a circle, for it has no two radii of equal length, and if continued would form, not a circle, but a spiral. To generate this curve, we will cut from cardboard, wood, or sheet metal, a segment of a circle having a radius equal to that of our wheel, on the pitch circle, and a smaller circle whose diameter is equal to the radius of the pinion, on the pitch circle. To the edge of the small circle we will attach a pencil or metal point so that it will trace a fine mark. Now we lay our segment flat on a piece of drawing paper, or sheet metal and cause the small circle to revolve around its edge without slipping. We find that the point in the edge of the small circle has traced a series of curves around the edge of the segment.

These curves are called “epicycloids,” and have the peculiar property that if a line be drawn through the generating point and the point of contact of the two circles, this will always be at right angles to a tangent of the curve at its point of intersection. It is this property to which it owes its value as a shape for the acting surface of a wheel tooth, for it is owing to this that a tooth whose acting surface is bounded by such a curve can impel a pinion leaf through the entire lead with little sliding action between the two surfaces. This, then, is the curve on which we will form the addenda of our wheel teeth.

In Fig. 66, the wheel has a radius of fifteen inches and the pinion a radius of one and one-half, and these two measurements are to be added together to find the distance apart of the two wheels; 16.5 inches is then the distance that the centers of revolution are apart of the wheels. Now, the teeth and leaves jointly act on one another to maintain a sure and equable relative revolution of the pair.

In Fig. 66, the pinion has its leaves radial to the center, inside of the pitch line D, and the ends of the leaves, or those parts outside of the pitch line, are a half circle, and serve no purpose until the depthings are changed by wear, as they never come in contact with the wheel; the wheel teeth only touch the radial part of the pinion and that occurs wholly within the pitch line. So in all pinions above 10 leaves in number the addendum or curve is a thing of no moment, except as it may be too large or too long. In many large pieces of machinery the pinions, or small driven wheels, have no addendum or extension beyond their pitch diameter and they serve every end just as well. In watches there is so much space or shake allowed between the teeth and pinions that the end of a leaf becomes a necessity to guard against the pinion’s recoiling out of time and striking its sharp corner against the wheel teeth and so marring or cutting them. In a similar pair of wheels in machinery there are very close fits used and the shake between teeth is very slight and does not allow of recoil, butting, or “running out of time.”

Running out of time is the sudden stopping and setting back of a pinion against the opposite tooth from the one just in contact or propelling. This, with pinions of suppressed ends, is a fault and it is averted by maintaining the ends.

The wheel tooth drives the pinion by coming in contact with the straight flank of the leaf at the line of centers, that is a line drawn through the centers of the two wheels; centers of revolution.

The curve or end of the wheel tooth outside of the pitch line is the only part of the tooth that ever touches the pinion and it is the part under friction from pressure and slipping. At the first point of contact the tooth drives the pinion with the greatest force, as it is then using the shortest leverage it has and is pressing on the longest lever of the leaf. As this action proceeds, the tooth is acted on by the pinion leaf farther out on the curve of the wheel tooth, thus lengthening the lever of the wheel and at the same time the tooth thus acts nearer to the center of the pinion by touching the leaf nearer its center of revolution.

By these joint actions it will appear that the wheel first drives with the greatest force and then as its own leverage lengthens and its force consequently decreases, it acts on a shorter leverage of the pinion, as the end of a tooth is nearer to the center of the pinion, or on the shortest pinion leverage, just as the tooth is about ceasing to act.

The action is thus shown from the above to be a variable one, which starts with a maximum of force and ends with a minimum. Practically the variable force in a train is not recognized in the escapement, as the other wheels and pinions making up the train are also in the same relations of maximum and minimum forces at the same time, and thus this theoretical and virtual variability of train force is to a great extent neutralized at the active or escaping end of the movement.

There is another action between the tooth and leaf that is not easy to explain without somewhat elaborate sketches of the acting parts, and as this is not consistent with such an article, we may dismiss it, and merely state that it is the one of maintaining the relative angular velocities of the two wheels at all times during their joint revolutions.

In Fig. 66 will be seen the teeth of the wheel, their heights, widths and spacing, and the epicycloidal curves. Also the same features of the pinion’s construction. The curve on the end of the wheel teeth is the only curve in action during the rotation between wheel and pinion. Each flank (both teeth and leaves) is a straight line to the center of each. A tooth is composed of two members—the pillar or body of the tooth inside of the pitch line and the cycloid or curve, wholly outside of this line. The pinion also has two members, the radial flank wholly inside of the pitch line, and its addendum or circle outside of this line.

Fig. 66.

In Fig. 66 will be seen a tooth on the line of centers A B, just coming in action against the pinion’s flank and also one just ceasing action. It will be seen that the tooth just entering is in contact at the joint pitches, or radii, of the two wheels, and that when the tooth has run its course and ceased to act, that it will be represented by tooth 2. Then the exit contact will be at the dotted line o o. From this may be seen just how far the tooth has, in its excursion, shoved along the leaf of the pinion and by the distance the line o o, is from the wheel’s pitch line G, at this tooth. No. 2, is shown the extent of contact of the wheel tooth. By these dotted lines, then, it may be seen that the tooth has been under friction for nearly its whole curve’s length, while the pinion’s flank will have been under friction contact for less than half this distance. In brief, the tooth has moved about 8/100 of its curved surface along the straight flank .35 of the surface of the pinion leaf. From this relative frictional surface may be seen the reason why a pinion is apt to be pitted by the wheel teeth and cut away. In any case it shows the relation between the two friction surfaces. In part a wheel tooth rolls as well as slides along the leaf, but whatever rolling there may be, the pinion is also equally favored by the same action, which leaves the proportions of individual friction still the same.

In Fig. 66 may be seen the spaces of the teeth and pinion. The teeth are apart, equal to their own width and the depths of the spaces are the same measurement of their width—that is, the tooth (inside of the pitch line) is a pillar as wide as it is high and a space between two teeth is of like proportions and extent of surface. The depth of a space between two teeth is only for clearance and may be made much less, as may be seen by the pinion leaf, as the end of the circle does not come half way to the bottom of a space.

The dotted line, o o, shows the point at which the tooth comes out of action and the pointed end outside of this line might be cut off without interfering with any function of the tooth. They generally are rounded off in common clock work.

The pinion is 3 inches diameter and is divided into twelve spaces and twelve leaves; each leaf is two-fifths of the width of a space and tooth. That is one-twelfth of the circumference of the pinion is divided into five equal parts and the leaf occupies two and a space three of these parts. The space must be greater than the width of a leaf, or the end of a leaf would come in contact with a tooth before the line of centers and cause a jamming and butting action. Also the space is needed for dirt clearance. As watch trains actuated by a spring do not have any reserve force there must be allowance made for obstructions between the teeth of a train and so a large latitude is allowed in this respect, more than in any machinery of large caliber. As will be seen by Fig. 66, the spans between the leaves are deep, much more so than is really necessary, and a space at O C shows the bottom of a space, cut on a circle which strengthens a leaf at its root and is the best practice.

Having determined the form of our curve, our next step will be to get the proper proportions. Saunier recommends that in all cases tooth and space should be of equal width, but a more modern practice is to make the space slightly wider, say one-tenth where the curve is epicycloidal. When the teeth are cut with the ordinary Swiss cutters, which, of course, cannot be epicycloidal, it is best to make the spaces one-seventh wider than the tooth. This proportion will be correct except in the case of a ten-leaf pinion, when, if we wish to be sure the driving will begin on the line of centers, the teeth must be as wide as the spaces; but in this case the pinion leaf is made proportionately thinner, so that the requisite freedom is thus obtained.

The height of the addenda of the wheel teeth above the pitch circle is usually given as one and one-eighth times the width of a tooth. While this is approximately correct, it is not entirely so, for the reason that as we use a circle whose diameter is equal to the pitch radius of the pinion for generating the curve, the height of the addenda would be different on the same wheel for each different numbered pinion. So that if a wheel of 60 were cut to drive a pinion of 8, the curve of this tooth would be found too flat if used to drive a pinion of 10. Now, since the pitch diameter of the pinion is to the pitch diameter of the wheel as the number of leaves in the pinion are to the number of teeth in the wheel, in order to secure perfect teeth: we must adopt for the height of the addenda a certain proportion of the radius or diameter of the pinion it is to drive, this proportion depending on the number of leaves in the pinion.

A careful study of the experiments on this subject with models of depths constructed on a large scale, shows that the proportions given below come the nearest to perfection.

When the pinion has six leaves the spaces should be twice the width of the leaves and the depth of the space a little more than one-half the total radius of the pinion. The addenda of the pinion should be rounded, and should extend outside the pitch circle a distance equal to about one-half the width of a leaf. The addenda of the wheel teeth should be epicycloidal in form and should extend outside the pitch circle a distance equal to five-twelfths of the pitch radius of the pinion.

With these proportions, the tooth will begin driving when one-half the thickness of a leaf is in front of the line of centers, and there will be engaging friction from this point until the line of centers is reached.

This cannot be avoided with low numbered pinions without introducing a train of evils more productive of faulty action than the one we are trying to overcome. There will be no disengaging friction.

When a pinion of seven is used, the spaces of the pinion should be twice the width of the leaves, and the depth of a space about three-fifths of the total radius of the pinion. The addenda of the pinion leaves should be rounded, and should extend outside the pitch circle about one-half the width of a leaf. The addenda of the wheel teeth should be epicycloidal, and the height of each tooth above the pitch circle equal to two-fifths of the pitch radius of the pinion.

There is less engaging friction when a pinion of seven is used than with one of six, as the driving does not begin until two-thirds of the leaf is past the line of centers. There is no disengaging friction.

With an eight-leaf pinion the space should be twice as wide as the leaf, and the depth of a space about one-half the total radius of the pinion. The addenda of the pinion leaves should be rounded and about one-half the width of a leaf outside the pitch circle. The addenda of the wheel teeth should be epicycloidal, and the height of each tooth above the pitch circle equal to seven-twentieths of the pitch radius of the pinion.

With a pinion of eight there is still less engaging friction than with one of seven, as three-quarters of the width of a leaf is past the line of centers when the driving begins. As there is no disengaging friction, a pinion of this number makes a very satisfactory depth.

A pinion with nine leaves is sometimes, though seldom, used. It should have the spaces twice the width of the leaves, and the depth of a space one-half the total radius. The addenda should be rounded, and its height above the pitch circle equal to one-half the width of the leaf. The addenda of the wheel teeth should be epicycloidal, and the height of each tooth above the pitch circle equal to three-sevenths of the total radius of the pinion. With this pinion the driving begins very near the line of centers, only about one-fifth of the width of a leaf being in front of the line.

A pinion of ten leaves is the lowest number with which we can entirely eliminate engaging friction, and to do so in this case the proper proportions must be rigidly adhered to. The spaces on the pinion must be a little more than twice as wide as a leaf; a leaf and space will occupy 36° of arc; of this 11° should be taken for the leaf and 25° for the space. The addenda should be rounded and should extend about half the width of a leaf outside the pitch circle. The depth of a space should be equal to about one-half the total radius. For the wheel, the teeth should be equal in width to the spaces, the addenda epicycloidal in form, and the height of each tooth above the pitch circle, equal to two-fifths the pitch radius of the pinion.

A pinion having eleven leaves would give a better depth, theoretically, than one of ten, as the leaves need not be made quite so thin to ensure its not coming in action in front of the line of centers. It is seldom seen in watch or clock work, but if needed the same proportions should be used as with one of ten, except that the leaves may be made a little thicker in proportion to the spaces.

A pinion having twelve leaves is the lowest number with which we can secure a theoretically perfect action, without sacrificing the strength of the leaves or the requisite freedom in the depths. In this pinion, the leaf should be to the space as two to three, that is, we divide the arc of the circumference needed for a leaf and space into five equal parts, and take two of these parts for the leaf, and three for the space; depth of the space should be about one-half the total radius. The addenda of the wheel teeth should be epicycloidal, and the height of each tooth above the pitch line equal to two-sevenths the pitch radius of the pinion.

As the number of leaves is increased up to twenty, the width of the space should be decreased, until when this number is reached the space should be one-seventh wider than the leaf. As these numbers are used chiefly for winding wheels in watches, where considerable strength is required, the bottoms of the spaces of both mobiles should be rounded.

Circular Pitch. Diametral Pitch.—In large machinery it is usual to take the circumference and divide by the number of teeth; this is called the circular pitch, or distance from point to point of the teeth, and is useful for describing teeth to be cut out as patterns for casting.

But for all small wheels it is more convenient to take the diameter and divide by the number of teeth. This is called the diametral pitch, and when the diameter of a wheel or pinion which is intended to work into it is desired, such diameter bears the same ratio or proportion as the number required. Both diameters are for their pitch circles. As the teeth of each wheel project from the pitch circle and enter into the other, an addition of corresponding amount is made to each wheel; this is called the addendum. As the size of a tooth of the wheel and of a tooth of the pinion are the same, the amount of the addendum is equal for both; consequently the outside diameter of the smaller wheel or pinion will be greater than the arithmetical proportion between the pitch circles. As the diameters are measured presumably in inches or parts of an inch, the number of a wheel of given size is divided by the diameter, which gives the number of teeth to each inch of diameter, and is called the diametral pitch. In all newly-designed machinery a whole number is used and the sizes of the wheels calculated accordingly, but when, as in repairing, a wheel of any size has any number of teeth, the diametral number may have an additional fraction, which does not affect the principle but gives a little more trouble in calculation. Take for example a clock main wheel and center pinion: Assuming the wheel to be exactly three inches in diameter at the pitch line, and to have ninety-six teeth, the result will be 96÷3=32, or 32 teeth to each inch of diameter, and would be called 32 pitch. A pinion of 8 to gear with this wheel would have a diameter at the pitch line of 8 of these thirty-seconds of an inch or 8/32 of an inch. But possibly the wheel might not be of such an easily manageable size. It might, say, be 3.25 inches, in which case, 96 being the number of the wheel and 8 of the pinion, the ratio is 8/96 or ¹/12, so ¹/12 of 3.25=0.270, the pitch diameter of the pinion. These two examples are given to indicate alternative methods, the most convenient of which may be used. After arriving at the true pitch diameters the matter of the addendum arises, and it is for this that the diametral number is specially useful, as in every case when figuring by this system, whatever the number of a wheel or pinion, two of the pitch numbers are to be added. Thus with the 32 pitch, the outside diameter of the wheel will be 3 in. + ²/32, and if the pinion 8/32+²/32 =¹/32. With the other method the same exactness is more difficult of attainment, but for practical purposes it will be near enough if we use ²/30 of an inch for the addendum, when the result will be 3.25 + ²/30 or 3¼+ ²/30=3?; in. nearly and the pinion 0.270+²/30=0.270+.0666=0.3366; or to work by ? of an inch is near enough, giving the outside diameter of the pinion a small amount less than the theoretical, which is always advisable for pinions which are to be driven.

We represent by Figs. 67 to 71 a wheel of sixty teeth gearing with a pinion of six leaves. The wheel, whose pitch diameter is represented by the line mm is the same in each figure. The pinion, which has for its pitch diameter the line kk, is in Fig. 67, of a size proportioned to that of the wheel, and its center is placed at the proper distance; that is to say, the two pitch diameters are tangential.

In Fig. 68 the same pinion, of the proper size, has its center too far off; the depthing is too shallow. In Fig. 69 it is too deep. Figs. 70 and 71 represent gearing in which the pitch circles are in contact, as the theory requires, but the size of the pinions is incorrect. If the wheels and pinion actuated each other by simple contact the velocity of the pinion with reference to that of the wheel would not be absolutely the same; but the ratio of the teeth being the same, the same ratio of motion obtains in practice, and there is necessarily bad working of the teeth with the leaves.

We will observe what passes in each of these cases, and refer to the suitable remedies for obtaining a passable depthing and a comparatively good rate, without the necessity of repairs at a cost out of all proportion with the value of the article repaired.

Fig. 67.

Fig. 67 represents gearing of which the wheel and pinion are well proportioned and at the proper distance from each other. Its movement is smooth, but it has little drop or none at all. By examining the teeth h, h', of the wheel, it is seen that they are larger than the interval between them. With a cutter FF, introduced between the teeth, they are reduced at d, d', which gives the necessary drop without changing the functions, since the pitch circles mm and kk have not been modified. The drop, the play between the tooth d' and the leaf a, is sufficiently increased for the working of the gearing with safety.

We have the same pair in Fig. 68, but here their pitch circles do not touch; the depthing is too shallow. The drop is too great and butting is produced between the tooth h and the leaf r, which can be readily felt. The remedy is in changing the center distance, by closing the holes, if worn, or moving one nearer the other. But in an ordinary clock this wheel may be replaced with a larger one, whose pitch circle reaches to e. The proportions of the pair are modified, but not sufficiently to produce inconvenience.

Fig. 68.

It may also answer to stretch the wheel, if it is thick enough to be sufficiently increased in size. A cutter should then be selected for rounding-up which will allow the full width to the tooth as at p; but if it is not possible to enlarge the wheel enough, a little of the width of the teeth may be taken off, as is seen at h, which will diminish the butting with the leaf r.

Too great depthing, Fig. 69, can generally be recognized by the lack of drop. When the teeth of the wheel are narrow, the drop may appear to be sufficient. When the train is put in action the depthing that is too great produces scratching or butting and the ’scape wheel trembles. This results from the fact that the points of the teeth of the wheel touch the core of the pinion and cause it to butt against the leaf following the one engaged, as is visible at r in Fig. 69. It should be noticed that in this figure the pitch circles mm and kk overlap each other, instead of being tangential.

Fig. 69.

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Fig. 70.

To correct this gearing, the cutter should act only on the addenda of the teeth of the wheel, so as to diminish them and bring the pitch circle mm to n. The dots in the teeth d, d', show the corrected gearing. It is seen that there will be, after this change, the necessary drop, and that the end of the tooth d' will not touch the leaf r.

In the two preceding cases we have considered wheels and pinions of accurate proportion, and the defects of the gearing proceeding from the wrong center distances. We will not speak of the gearing in which the pinion is too small. The only theoretic remedy in this case, as in that of too large a pinion, is to replace the defective piece; but in practice, when time and money are to be saved, advantage must be taken, one way or another, of what is in existence.

The buzzing produced when the train runs in a gearing with too small a pinion proceeds from the fact that each tooth has a slight drop before engaging with the corresponding leaf. If we examine Fig. 70, it will be easy to see how this drop is produced. The wheel revolving in the direction indicated by the arrow, it can be seen that when the tooth h leaves the leaf r, the following tooth, p, does not engage with the corresponding leaf, s; this tooth will therefore have some drop before reaching the leaf. A friction may even be produced at the end or addendum of the tooth p against the following leaf v.

To obtain a fair depthing without replacing the pinion, the wheels can be passed to the rounding-up machine, having a cutter which will take off only the points of the teeth, as is indicated in the figure; the result may be observed by the dotted lines. The tooth h being shorter, it will leave the leaf r of the pinion when the latter is in the dotted position; that is to say, a little sooner. At this moment the tooth p is in contact with the leaf s, and there is no risk of friction against the leaf v. Care must be taken to touch only the addendum of the tooth so as not to weaken the teeth. The circumference i will be that of a pinion of accurate size, and if the pinion is replaced, it will be necessary to diminish the wheel so that its pitch circle shall be tangential with i.

Fig. 71.

With too small a pinion a passable gearing can generally be produced. In any case stoppage can be prevented. This is not so easy when the pinion is too large. In Fig. 71, the pinion has as its pitch circle the line k, instead of i, which would be nearer the size with reference to that of the wheel. This is purposely drawn a little small for clearness of illustration. The essential defect of such a gearing can be seen; the butting produced between the tooth p and the leaf s will cause stoppage. How shall this defect be corrected without replacing the pinion?

To remedy the butting as far as possible, some watchmakers slope the teeth of the wheel by decentering the cutter on the rounding-up machine. At FF the cutter is seen working between the teeth d and d'. It is evident that when the wheel becomes smaller it is necessary to stretch it out, and to make use of the cutter afterwards. However, the most rational method is to leave the teeth straight, and to give them the slenderest form possible, after having enlarged the wheel or having replaced it with another. The motive force of the wheel being sufficiently weak, the size of the teeth may be reduced without fear. The essential thing is to suppress the butting. Success will be the easiest when the teeth are thinner.

In conclusion, we recommend verification of all suspected gearings by the depthing tool, which is easier and surer than by the clock itself. One can see better by the tool the working of the teeth with the leaves, and can form a better idea of the defect to be corrected. With the aid of the illustrations that have been given it can be readily noticed whether the depthing is too deep or too shallow, or the pinion too large or too small.

The defects mentioned are of less consequence in a pinion of seven leaves, and they are corrected more readily. With pinions of higher numbers the depthings will be smoother, provided sufficient care has been taken in the choice of the rounding-up cutters.

Rounding-Up Wheels.—It is frequently observed that young watchmakers, and (regretfully be it said) some of the older and more experienced ones, are rather careless when fitting wheels on pinions. In many cases the wheel is simply held in the fingers and the hole opened with a broach, and in doing this no special care is taken to keep the hole truly central and of correct size to fit the pinion snugly, and should it be opened a little too large it is riveted on the pinion whether concentric or not. Many suppose the rounding-up tool will then make it correct without further trouble and without sufficient thought of the irregularities ensuing when using the tool.

To make the subject perfectly clear the subjoined but rather exaggerated sketch is shown, Fig. 72. Of course, it is seldom required to round-up a wheel of twelve teeth, and the eccentricity of the wheel would be hardly as great as shown; nevertheless, assuming such a case to occur the drawing will exactly indicate the imperfections arising from the use of a rounding-up tool.

Fig. 72.

Presuming from the drawing that the wheel, as shown by dotted lines, had originally been cut with its center at m, but through careless fitting had been placed on the pinion at o, and consequently is very much out of round when tested in the calipers, and to correct this defect it is put in the rounding-up tool. The cutter commences to remove the metal from tooth 7, it being the highest, next the neighboring teeth 6 and 8, then 5 and 9, and so on until tooth 1 comes in contact with the cutter. The wheel is now round. But how about the size of the teeth and the pitch? The result of the action of the cutter is shown by the sectionally lined wheel. Many will ask how such, a result is possible, as the cutter has acted equally upon all the teeth. Nevertheless, a little study of the action of the rounding-up cutter will soon make it plain why such faults arise. Naturally the spaces between the teeth through the action of the cutter will be equal, but as the cutter is compelled to remove considerable metal from the point of greatest eccentricity, i. e., at tooth 7 and the adjoining teeth, to make the wheel round, and the pitch circle being smaller the teeth become thinner, as the space between the teeth remains the same. At tooth 1 no metal was removed, consequently it remains in its original condition. The pitch from each side of tooth 1 becomes less and less to tooth 7, and the teeth thinner, and the thickest tooth is always found opposite the thinnest.

In the case of a wheel having a large number of teeth and the eccentricity of which is small, such faults as described cannot be readily seen, from the fact that there are many teeth and the slight change in each is so gradual that the only way to detect the difference is by comparing opposite teeth. And this eccentricity becomes a serious matter when there are but few teeth, as before explained, especially when reducing an escape wheel. The only proper course to pursue is to cement the wheel on a chuck, by putting it in a step chuck or in any suitable manner so that it can be trued by its periphery and then opening the hole truly. This method is followed by all expert workmen.

A closer examination of the drawing teaches us that an eccentric wheel with pointed teeth—as cycloidal teeth are mostly left in this condition when placed in the rounding-up tool, will not be made round, because when the cutter has just pointed the correct tooth (tooth No. 1 in the drawing) it will necessarily shorten the thinner teeth. Nos. 6, 7, 8, i. e., the pitch circle will be smaller in diameter. We can, therefore, understand why the rounding-up tool does not make the wheel round.

As we have before observed, when rounding-up an eccentrically riveted wheel, the thickest tooth is always opposite the thinnest, but with a wheel which has been stretched the case is somewhat different. Most wheels when stretched become angular, as the arcs between the arms move outward in a greater or less degree, which can be improved to some extent by carefully hammering the wheel near the arms, but some inequalities will still remain. In stretching a wheel with five arms we therefore have five high and as many depressed parts on its periphery. If this wheel is now rounded-up the five high parts will contain thinner teeth than the depressed portions. Notwithstanding that the stretching of wheels, though objectionable, is often unavoidable on account of the low price of repairs, it certainly ought not to be overdone. Before placing the wheel in the rounding-up tool it should be tested in the calipers and the low places carefully stretched so that the wheel is as nearly round as can be made before the cutter acts upon it.

It is hardly necessary to mention that the rounding-up tool will not equalize the teeth of a badly cut wheel, and further should there be a burr on some of the teeth which has not been removed, the action of the guide and cutter in entering a space will not move the wheel the same distance at each tooth, thus producing thick and thin teeth. From what has been said it would be wrong to conclude that the rounding-up tool is a useless one; on the contrary, it is a practical and indispensable tool, but to render good service it must be correctly used.

In the use of the rounding-up tool the following rules are to be observed:

Making Single Pinions.—There are two ways of making clock pinions; one is to take a solid piece of steel of the length and diameter needed and turn away the surplus material to leave the arbor and the pinion head of suitable dimensions; the other way is to make the head and the arbor of separate pieces; the head drilled and fixed on the arbor by friction. The latter plan saves a lot of work, and the cutting of the teeth may be easier. One method is as good as the other, as the force on the train is very slight and the pinion head may be driven so tightly on the arbor as to be perfectly safe without any other fastening, provided the arbor is given a very small taper, .001 inch in four inches. The steel for the arbor may be chosen of such a size as to require very little turning, and hardened and tempered to a full or pale blue before commencing turning it, but the piece intended for the pinion head must be thoroughly annealed, or it may be found impossible to cut the teeth without destroying a cutter, which, being valuable, is worth taking care of.

Pinions for ordinary work are not hardened; as they are left soft by the manufacturers it would be nonsense for the repairer to put in one hardened pinion in a clock where all the others were soft. Pinions on fine work are hardened. Turning is done between centers to insure truth.

Before commencing work on the pinion blanks it is advisable to try the cutters on brass rod, turned to the exact size, and if the rod is soft enough it will be found that the cutter will make the spaces before it is hardened, which is a very important advantage, admitting of correction in the form of the cutter if required; only two or three teeth need be cut in the brass to enable one to see if they are suitable, and if found so, or after an alteration of the cutter, the entire number may be cut round and the brass pinion made use of for testing its accuracy as to size and shape by laying the wheel along with it on a flat plate, having studs placed at the proper center distance. By this means the utmost refinement may be made in the diameter of the brass pinion, which will then serve as a gauge for the diameter of the steel pinions, it being recollected, as mentioned in a previous paragraph, that a slight variation in the diameter of a pinion may be made to counterbalance a slight deviation from mathematical accuracy in the form of the wheel teeth, such as is liable to occur owing to the smallness of the teeth making it impracticable to actually draw the true curves, the only way of getting them being to draw them to an enlarged scale on paper, and copy them on the cutter as truly as possible by the eye.

Supposing the cutter has been properly shaped, hardened and completed and the steel pinion heads all turned to the diameter of the brass gauge, the cutting may be proceeded with without fear of spoiling, or further loss of time which might be spent in cutting the long pinion leaves; and even what is of more importance in work which does not allow of any imperfection, removing the temptation, which might be strong, to let a pinion go, knowing it to be less perfect than it should be.

Assuming the pinion teeth to be satisfactorily cut, the next operation will be hardening and tempering. A good way of doing this is to enclose one at a time in a piece of gas pipe, filling up the space around the pinion with something to keep the air off the work and prevent any of the products of combustion attacking the steel and so injuring the surface. Common soap alone answers the purpose very well, or it may have powdered charcoal mixed with it; also the addition of common salt helps to keep the steel clean and white. The heating should be slow, giving time for the pinion and the outside of the tube to both acquire the same heat. Over-heating should be carefully avoided, or there will be scaling of the surfaces, injurious to the steel, and requiring time and labor to polish off. There is no better way of hardening than by dipping the pipe with the pinion enclosed in plain cold water, or if the pinion should drop out of the tube into the water it will do all the same. To be sure the hardening is satisfactory it will be as well not to trust to the clean white color likely to result from this treatment, but try both ends and the center with a file. After all this has been successfully accomplished the pinions will require tempering, the long arbors straightening, and the teeth polishing.

The drilled pinion heads, if hardened at all by the method last mentioned, will, on account of their short lengths, be equally hardened all over, but if the pinion and arbor should be all in one piece care will be needed to ensure equal heating all over, or one part may be burnt and another soft. Also, to guard against bending the long arbors, the packing in the tube will need to be carefully done, so as to produce equal pressure all over; otherwise, while the steel is red hot, and consequently soft enough to bend, even by its own weight, it may get distorted before dropping in the water. A long thin rod like this almost invariably bends if heated on an open fire unless equally supported all along; if hardened so, a little tin tray may be bent up, filled with powdered charcoal, and the pinion bedded evenly in it. Either this way or with a tube the long arbor may get bent before being quenched; but if the arbor, though kept straight up to this point, should happen to be dropped sideways into the water the side cooled first would contract most. To avoid this, the arbor should be dropped endways, as vertically as possible.

Tempering the Pinions.—For common cheap work the usual and quickest way is what is called “blazing off.” That is done either by dipping each piece singly in thick oil and setting the oil on fire, allowing it to burn away, or placing a number of pieces in a suitably sized pan, covering with oil, and burning it. The result is the same either way, the method being simply a matter of convenience regulated by the number of pieces to be tempered at one time. As the result of blazing off is to some extent uncertain, and the pinions apt to be too soft, it will be advisable to adopt the process of bluing, by which the temper desired may be produced with more accuracy. The first thing to do will be to clean the surface of the arbor all along on one side; the pinion head may be left alone. As the pinion head would get overheated before the arbor had reached the blue color, if the piece were simply placed on a bluing pan or a lump of hot iron, it will be necessary to provide a layer of some soft substance to bed the pinion on; iron, steel or brass filings answer well because the heat is soon uniformly distributed through the mass, and by judiciously moving the lamp an equable temper may be got all along, as determined by the color. There is another and very sure way of getting a uniform temper, in using which there is no need to polish the arbors. The heat of lead at the point of fusion happens to be just about the same as that required for the tempering of this work; so if a ladle full of lead is available each pinion may be buried in it for a few seconds, holding it down beneath the molten surface with hot pliers. The temper suitable is indicated by a pale blue, a little softer than for springs, and a piece of polished steel set floating on the lead will indicate whether the heat is suitable; if found too great some tin may be added, which will cause the metal to melt at a lower temperature. Over-heating the metal must be avoided: it should go no higher than the bare melting point.

Straightening Bent Arbors.—When all care has been taken in the hardening, the long pieces of wire are still apt to become bent more or less, and this is especially the case with solid pinions; so before proceeding further the pieces must be got true, or as nearly so as possible, and it will be found impracticable to do this by simple bending when the steel is tempered. If the piece is placed between centers in the lathe and rotated slowly, the hollow side will be found; this side must be kept uppermost while the steel is held on a smooth anvil, and the pene, or chisel-shaped, end of a small hammer applied crossways with gentle blows, stepping evenly along so that each portion of the steel is struck all along the part which is hollow; this will stretch the hollow side, and, by careful working, trying the truth from time to time, the piece can be got as true as may be wished, and probably keep so during the subsequent turning and finishing, though it is advisable to keep watch on it, and if it shows any tendency to spring out of truth again, repeat the striking process, which should always be done gently and in such a way as to show no hammer marks. Having got the pieces sufficiently true in this way, each arbor may have a collet of suitable size driven on to it for permanency, and as the collets will probably be a little out of truth they may have a finishing cut taken all over them and receive a final polish.

Polishing.—To polish the steel arbors after turning, a flat metal polisher, iron or steel, is used; this with emery or oilstone dust and oil produces a true surface, with a sharp corner at the shoulder; the polisher will require frequent filing on the flat and the edge to keep it in shape with a sharp corner, and a grain crossing like the cuts on a file to hold the grinding material. The polishing of arbors is not done with the object of making them shine, but to get them smooth and true, so there is no need of using any finer stuff than emery or oilstone dust.

An old way to polish the leaves was to use a simple metal polisher of a suitable thickness, placing the pinion on a cork or piece of wood, or even holding it in the fingers; working away at a tooth at a time until a good enough polish was obtained; but this method, while being satisfactory as to results, was also tedious and very slow. It was in some cases assisted by having guide pinions fitted tight on one or both ends of the arbors to prevent rounding of the teeth, the polisher resting in the guide and the tooth to be polished. On the American lathes an accessory is provided called a “wig wag.” This is a rod fastened at one end to a pulley by a crank pin near its circumference; the pulley being rotated by a belt from the counter shaft pulleys causes the rod to move rapidly backwards and forwards. On the other end of the rod a long narrow piece of lead or tin is fixed, the pinion being fitted by its centres into a simple frame held in the slide rest so that it can be rotated tooth by tooth; the lead soon gets cut to the form of the teeth, and the polishing is quickly effected. Another way is to take soft pine or basswood, shape it roughly to about the form of space between two teeth and use it as a file, with emery and oil or oilstone dust. The wood is soon cut to the exact shape of the teeth, and then makes a quick and perfect job. The pinion is held in the jaws of the vise and the wooden polisher used as a file with both hands.

Where there is much polishing to do a simple tool, which a workman can form for himself, produces a result which is all that can be desired. It consists of an arbor to work between the lathe centres, or a screw chuck for wood, with a round block of soft wood, of a good diameter, fixed on it, and turned true and square across; this will get a spiral groove cut in it by the corners of the pinion leaves. The pinion is set between centres in a holder in the slide rest, with the holder set at a slight angle, so that, instead of circular grooves being cut in the wood a screw will be formed, the angle being found by trial. On the wood block being rotated and supplied with fine emery the pinion will be found to rotate, and, being drawn backwards and forwards by the slide rest, can be polished straight, while the circular action of the polisher will cause the sides of the pinion leaves to be made quite smooth and entirely free from ridges.

If it should be desired to face the pinions, like watch pinions, it may be done in the same way, by cutting hollows so as to leave only a fine ring round the bottoms of the teeth, and using a hollow polisher with a flat end held in the fingers while the pinion is rotating. A common cartridge shell with a hole larger than the arbor drilled in the center of the head makes a fine polisher for square facing on the ends of pinions, while a stick of soft wood will readily adapt itself to moulded ends.

The pinion heads being finished and got quite true, the arbors may be turned true and polished. It is not advisable to turn the arbors small; they will be better left thick so as to be stiff and solid, as the weight so near the center is of no importance, the velocity on the small circumference in starting and stopping being also inappreciable. The thickness of the arbors when the pinion heads are drilled is determined by the necessity of having sufficient body inside the bottoms of the teeth; but when solid they may with advantage be left thicker; however, there is no absolute size. The ends on which the collets for holding the wheels are to be fixed may be turned to the same taper as the broach which will be used for opening the collet holes, while the other ends may be straight.

None of the wheels in a fine clock should be riveted to the pinion heads; even the center wheel, which goes quite up to the pinion head, is generally fixed on a collet. The collets are made from brass cut off a round rod, the outside diameters being just inside the edges of the wheel hubs, and a shoulder turned to fit accurately into the center hole of each wheel. These collets should first have their holes broached to fit their arbors, allowing a little for driving on, as they may be made tight enough in this way without soldering. Be careful to keep the broach oiled to prevent sticking if you want a smooth round hole.

The holes in the wheels being made, each collet may be turned to a little over its final size all over, and then driven on to its place on the pinion, so that a final turning may be made to ensure exact truth from the arbors’ own centers. When the collets are thus finished in their places on the arbors, and the wheels fitted to them, if it is a fine clock, such as a regulator, a hole may be drilled through each wheel and its collet to take a screw, the holes in the collet tapped, the holes in the wheels enlarged to allow the screw to pass freely through, and a countersink made to each, so that the screws, when finished, may be flush with the wheels. One hole having been thus made and the wheel fixed with a screw, the other two holes can be made so as to be true, which would not be so well accomplished if all the holes were attempted at once. The spacing of the three screws will be accurate enough if the wheel arms be taken as a guide. If all this has been correctly done, the wheels will go to their places quite true, both in the round and the flat, and may be taken off for polishing, and replaced true with certainty, any number of times.

The polishing of the pivots should be as fine as possible; all should be well burnished, to harden them and make them as smooth as possible if it is a common job; if a fine one with hardened arbors the pivots may be ground and polished as in watch work; if the workman has a pivot polisher and some thin square edged laps this is a short job and should be done before cutting off the centers and rounding the ends of the pivots. During all this work the wheels, as a matter of course, will be removed from the pinions, and may now be again temporarily screwed on, the polishing of them being deferred till the last, as otherwise they would be liable to be scratched.

Lantern Pinions.—The lantern pinion is little understood outside of clock factories and hence it is generally underrated, especially by watchmakers and those working generally in the finer branches of mechanics. It will never be displaced in clock work, however, on account of the following specific advantages:

The main difference between lantern and cut pinions mechanically is that as there is no radial flank for the curve of the wheel tooth to press against in the lantern pinion the driving is all done on or after the line of centers, except in the smaller numbers, and hence the engaging or butting friction is entirely eliminated when the pinion is driven, as is always the case in clock work. Where the pinion is the driver, however, this condition is reversed and the driving is all before the line of centers, so that it makes a very bad driver and this is the reason why it is never used as a driving pinion. This, of course, bars it from use in a large class of machinery.

The actual making of lantern pinions will be found to offer no difficulties to those who possess a lathe with dividing arrangements, a slide rest, and a drill holder or pivot polisher to be fixed on it. The pitch circle, being through the centers of the pins, can be got with great accuracy by setting the drill point first to the center of the lathe, reading the division on the graduated head of the slide rest screw, and moving the drill point outwards to the exact amount of the semi-diameter of the pitch circle. This presupposes the slide rest screw being cut to a definite standard, as the inch or the meter, and all measurements of wheels and pinions being worked out to the same standard, the choice of the standard being immaterial. If the slide rest screw is not standardized the pitch circle may be traced with a graver and the drill set to center on the line so traced.

The heads of the pinions may be made either of two separate discs, each drilled separately, and carefully fitted on the arbor so that the pins may be exactly parallel with the arbor; or, of one solid piece bored through the center, turned down deep enough in the middle, and the drill sent right through the pin holes for both sides at one operation. The former way will be necessary when the number of pins is small, but the latter is better when the numbers are large enough to allow of considerable body in the center. In either case it is advisable to drill only part way through one shroud and to close the holes in the other with a thin brass washer pressed on the arbor and turned up to look like part of the shroud after the pins are fitted in the holes. This makes a much neater way of closing the holes than riveting and takes but a moment where only one or two pinions are being made.

There is no essential proportion for the thickness of the pins or rounds. In mathematical investigations these are always taken at first as mere points of no thickness at all; then the diameters are increased to workable proportions, and the width of the wheel tooth correspondingly reduced until there is a freedom or a little shake. If much power has to be transmitted, the pins, or “staves,” as they are called in large work, have to be strong enough to stand the strain, but, as the strain in clockwork is very small, the pins need not be nearly as thick as the breadth of a wheel tooth. In modern factory practice the custom is to have the diameter of the rounds equal to the thickness of the leaf of a cut pinion of similar size, the measurement being taken at the pitch circle of the cut pinion. As we have already given the proportions observed in good practice on cut pinions they need not be repeated here. Another practice is to have wheel teeth and spaces equal; when this is done the spacing of all pinions above six leaf is to have the rounds occupy three parts and the space five parts.

In some old church clocks, lantern pinions were much used, in many cases with the pins pivoted and working freely in the ends, or, as they called them, “shrouds,” but this was a mistake, and they are never made so now. A simple way for clock repair work is to get some of the tempered steel drill rod of exactly the thickness desired, hold one end by a split chuck in the lathe, let the other end run free, and polish with a bit of fine emery paper clipped round it with the fingers, when the wire will be ready for driving through the pinion heads, the holes being made small enough to provide for the rounds being firmly held. The drill may be made of the same wire. The shrouds may be made either of brass or steel; the latter need not be hardened, and, when the rounds are all in place and cut off, the ends may be polished as desired. In the case of a center wheel, where the pinion is close up to the wheel, and space cannot be spared, the collet on which the wheel is mounted may form one end of the pinion head.

The Wheel Teeth.—The same principles of calculation belong to these and solid-cut pinions, the only difference being that the round pins require wheel teeth of a different shape from those suited to pinion leaves with radial sides. Both are derived from epicycloidal curves; the curve used for lantern pinions is derived from a circle of the same size as the pitch circle of the pinion, while the curve for wheel teeth to drive radial-sided leaves is derived from a circle of half that diameter, so that the wheel teeth in the former are more pointed than in the latter. There also is a farther difference; as was explained in detail when treating of cut pinions, the curve of the wheel tooth presses upon the radial flank of the leaf inside its pitch circle. Now there is no radial flank in the lantern and the curve is generated from a circle of twice the diameter, so that it is twice as long—long enough to interfere—so it is cut off (rounded) just beyond the useful portion of the working curve of the wheel tooth.

Pillars and arbors are simple parts, yet much costly machinery is used in making them. The wire from which they are made is brought to the factories in large coils, and is straightened and cut into lengths by machines. The principle on which wire is straightened in a machine is exactly the same as a slightly curved piece of wire is made straight in the lathe by holding the side of a turning tool between the revolving wire and the lathe rest, which is an operation most of our readers must have practiced. The rapid revolution of the wire against the turning tool causes its highest side to yield, till finally it presses on the turning tool equally all round, and is consequently straight. However, in straightening wire by machines the wire is not made to revolve, but remains stationary while the straightening apparatus revolves around it. Wire-straightening machines are usually made in the form of a hollow cylinder, having arms projecting from the inside towards the center. The cylinder is open at both ends, and the arms are adjustable to suit the different thicknesses of wire. The wire is passed through the ends of the cylinder, and comes in contact with the arms inside. A rapid rotary motion is then given to the cylinder, which straightens the wire in the most perfect manner, as it is drawn through, without leaving any marks on it when the machine is properly adjusted. The long spiral lines that are sometimes seen on the wire work of clocks is caused by this want of adjustment; and they are produced in the same way as broad circular marks would be made in soft iron wire if the side of the turning tool was held too hard against it when straightening it in the lathe.

After the wire has been straightened it is cut off into the required lengths, and this operation is worthy of notice. If the thick sizes of wire that are used were to be cut by the aid of a file or a chisel, the ends would not be square, and some time and material would be lost in the operation of squaring them; and as economy of material as well as economy of labor is a feature in American clock manufacture, wire of all sizes is sheared or broken off into lengths, by being fed through round holes in the shears, which act the same as when a steady pin is broken when a cock or bridge gets a sudden blow on the side, or in the same manner as patent cutting plyers work. The wire is not bent in the operation, and both ends of it are smooth and flat. The wire for the pillars is then taken to a machine to have the points made and the shoulders formed for the frames to rest against. This machine is constructed like a machinist’s bench lathe, with two headstocks. There is a live spindle running in both heads. In the ends of these spindles, that point towards the center of the lathe, cutters are fastened, and the one is shaped so that it will form the end and shoulder of the pillar that is to be riveted, while the other is shaped so as to form the shoulder and point that is to be pinned. Between these two revolving cutters there is an arrangement, worked by a screw in the end of a handle, for holding the wire from which the pillar is to be made, in a firm and suitable position. The cutters are then made to act simultaneously on the ends of the wire by a lever acting on the spindles, and the points and shoulders are in this way formed in a very rapid manner, all of the same length and diameter. These machines are in some points automatic. The pieces of wire are arranged in quantities in a long narrow feed box that inclines towards the lathe, and the mechanism for holding the wire is so arranged that when its hold is loosened on the newly made pillar, the pillar drops out into a box beneath, and a fresh piece of wire drops in and occupies its place.

In many of the factories, some clocks are manufactured having screws in place of pins to keep the frames together, and the pillars of these clocks are made in a different manner than that we have just described. The wire that is used is not cut into short lengths, but a turret lathe with a hollow spindle is used, through which the wire passes, and is held by a chuck, when a little more than just the length that is necessary to make the pillar projects through the chuck. The revolving turret head of the lathe has cutting tools projecting from it at several points. One tool is adapted to bore the hole for the screw, and when it is bored the next tool taps the hole to receive the screw, while another forms the point and shoulder; and after that end of the pillar is completed another tool attached to the slide of the lathe forms the other shoulder, prepares that end for riveting, and cuts it off at the same time. One thousand of these pillars are in this manner made in a day on each machine. The screws that screw into them are made on automatic screw machines. The latest improvements in this direction being to first turn the blanks and then roll the threads on thread rolling machines.

The pinion arbors, after they have been cut to length, are centered on one end by a milling machine having a conical cutter made for the purpose. The collets for the pinion heads, and the one to fasten the wheel by, are punched out of sheet brass, and a hole is drilled in their centers a little smaller than the wire; and to drive them on, in most instances, is all that is necessary to hold them. At one time it was the practice to drive these collets by hand. One was placed on the point of the arbor, and the point was then placed over a piece of steel, with a series of holes in it of such depths that the collets would be in their proper position on the arbor when the point was driven to the bottom of the hole, but this method has now been superseded by automatic machinery, which will be described later. It is impossible to give an intelligible description of these machines without drawings. All we can say at present is that they perform their work in a very rapid and effective manner, and are in use by all the larger clock factories.

The barrels of weight clocks are mostly made from brass castings, and slight projections are raised on the surface of their arbors by swedging, so as to prevent the arbors from getting loose in the barrels after repeated winding of the clock. This swedging and all the other operations in making arbors used to be done on separate machines; but the largest companies now use a powerful and comprehensive machine that works automatically, and straightens any size of wire necessary to be used in a clock, cuts it to the length, centers it, and also swedges the projections on the barrel arbors, or any of the other arbors that may be necessary. A roll of wire is placed on a reel at one end of the machine, first passing through a straightening apparatus, and afterwards to that portion of the machine where the cutting, swedging and centering are executed, and the finished arbors drop into a box placed ready to receive them. The saving effected by the use of this machine is very great, and in some instances amounts to a thousand per cent over the method of straightening, cutting, swedging and centering on different machines, at different operations.

Boring the holes in the arbors of the locking work, to receive the smaller wires, and the pin holes in the points of the pillars, is done by small twist-drills, run by small vertical drill presses. The work is held in adjustable frames under the drill, and when more than one hole has to be bored this frame is moved backward or forward between horizontal slides to the desired distance, which is regulated by an adjustable stop, so that every hole in each piece is exactly in the same position. In arbors where holes have to be bored at right angles to each other, the arbor is turned round to the desired position by means of an index. The holes in the locking work arbors are bored just the size to fit the wire that is to go into them, and these small wires are easily and rapidly fastened in place by holding them in a clamp made for the purpose, and riveting them either with a hammer or with a hammer and punch.

The Slide Gauge Lathe.—The system of turning with the slide gauge lathe, formerly adopted for lantern pinions in the clock factories, would seem to the watchmaker of a peculiarly novel nature. The turning tools are not held in the hand, in the manner generally practiced, neither are they held in the ordinary slide rest, but are used by a combination of both methods, which secures the steadiness of the one plan and the rapidity of the other. Adjustable knees are fastened to the head and tail stocks of the lathe, Figs. 75 and 76, which answer the purpose of a rest; both the perpendicular and horizontal parts of these knees being fastened perfectly parallel with the centers of the lathe. A straight, round piece of iron, of equal thickness, and having a few inches in the center of a square shape, mortised for the reception of cutters, is laid on these knees, and answers the purpose of a handle to hold the cutting tools. Two handles will thus hold eight tools, one set for brass and one for steel. On every side of the square part of this iron bar, or what we will now call the turning tool handle, a number of cutting tools are fastened by set screws, and the method of using them is as follows: The operator holds the tool handle with both hands on to the knees that are fastened to the head and tail stocks of the lathe, with the turning tool that is desired to be used pointing towards the center, and it is allowed to come in contact with the work running in the lathe in the usual manner practiced in turning. Fig. 76 is from a photo furnished by Mr. H. E. Smith of the Smith Novelty Co., Hopewell, N. J., and shows the tools in the rack, which is wound with leather so that the tools may be rapidly thrown in place without injury.

If a plain, straight piece of work is to be turned, the tool is adjusted in the handle so that the work will be of the proper diameter when the round parts of the handle come in contact with the perpendicular part of the knees or rest; and while the handle is thus held and moved gently along in the corners of the knees, with the tool sliding on the T-rest, the work is easily turned perfectly parallel, smooth and true. Sometimes a roughing cut is taken by holding the bar loosely and then a finishing cut is made with the same tool by holding it firmly in place. In turning a pinion arbor, for instance, the wire having been previously straightened and cut to length and centered, and the brass collets to make the pinion and to fasten the wheel having been driven on, one end is held in the lathe by a spring chuck fastened to the spindle of the lathe, while the other end works in a center in the other head. One turning tool is shaped and adjusted in the handle for the purpose of turning the brass collets for the pinion to the proper diameter, another turns the sides of the brass work, while others are adapted for the arbors, pivots, and so on, pins being placed in holes in the T-rest to act as stops for the tools. After the brass work has been turned, the positions of the shoulders of the pivots are marked with a steel gauge, and by simply turning round the handle of the turning tool till the proper shaped point presents itself, each operation is accomplished rapidly, and the cutting is so smooth that even for the pivots all that is necessary to finish them is simply to bring them in contact with a small burnisher. The article is not taken from the lathe during the whole process of turning, and when completed the centers are broken off, having been previously marked pretty deep at the proper place with a cutting point. Five hundred to 1,200 arbors per day, per man, is the usual output. All the pinions, arbors, and barrels—in fact every part of an American clock movement that requires turning—were formerly done in this manner, at long rows of lathes in rooms, and by workmen set apart for the purpose. But perhaps it may be well to mention that in the machine shops of these factories, where they make the tools, the ordinary methods of turning with the common hand tool, and by the aid of ordinary and special slide rests, are practiced the same as it is among other machinists. In the large factories automatic turret machines are now coming into use and these are shown in Figs. 77, 78 and 79.

The lantern pinions of an American clock have long been a mystery to those unacquainted with the method of their manufacture, and the usual accuracy in the position of the small wires or “rounds,” combined with great cheapness, has often been a subject of remark. The holes for the wires in these pinions are drilled in a machine constructed as follows: An iron bed with two heads on it, Fig. 80, one of which is so constructed that by pulling a lever the spindle has a motion lengthwise as well as the usual circular motion, and on the point of this spindle, which is driven at 22,000 revolutions, the drill is fastened that is to bore the holes in the pinions; the other head has an arbor passing through it with an index plate attached, having holes in the plate, and an index finger attached to a strong spring going into the holes, the same as in a wheel cutting engine; on this head, and on the end of it that faces the drill, there is a frame fastened in which the pinion that is to be bored is placed between centers, and is carried round with the arbor of the index plate, in the same manner as a piece of work is carried round in an ordinary lathe by means of a dog, or carrier; only in the pinion drilling machine the carrier is so constructed that there is no shake in any way between the pinion and the index arbor. This head is carried on a slide having a motion at right angles to the spindle of the other head, by which means the pitch diameter of the proposed pinion is adjusted. The head is moved in the slide by an accurately cut screw, to which a micrometer is attached that enables the workman to make an alteration in the diameter of a pinion as small as the one-thousandth part of an inch. The drill that bores the holes is the ordinary flat-pointed drill, and has a shoulder on its stem that stops the progress of the drill when it has gone through the first part of the pinion head and nearly through the other. All operators make their own drills and the limits of error are for pitch diameter .0005 inch; error of size of drills .0001. The reader can see that these men must know something of drill making.

The action of the machine is simple. The pinion, after it has been turned, pivoted and dogged, is placed in its position in the machine, and by pulling a lever, the drill, which is running at a speed of about 22,000 revolutions a minute, comes in contact with the brass heads of the pinion and bores the one through and the other nearly through. The lever is then let go, and a spring pulls the drill back; the index is turned round a hole, and another hole bored in the pinion, and so on till all the holes are bored. An ordinary expert workman, with a good machine, will bore about fourteen hundred of medium-sized pinions in a day. The wires or “rounds” are cut from drill rod and are put into the holes by hand by girls who become very expert at it. This is called “filling.” We have already stated that the holes are only bored partly through one of the pieces of the brass, and after the wire has been put in, the holes are riveted over, and in this manner the wires are fastened so that they cannot come out. Some factories close the holes by a thin brass washer forced on the arbor, instead of riveting.

Figs. 77, 78 and 79 show the automatic pinion turning machine and its processes in successive operations. These machines are used by most of the large clock manufacturers of the United States and some of the European concerns also. They are entirely automatic, will make 1,500 pinions per day, as an average, and one man can run four machines.

Fig. 79 shows an automatic pinion drilling machine, which takes up the work where it is left by the machine shown in Fig. 77. This machine will drill 4,000 to 5,000 pinions per day according to the size hole and the number of holes. The operator places the pinions in the special chain shown in the front of the machine, from which the transport arms carry them to the spindle, where they are drilled and when completed drop out. One operator can feed three of these machines.

Making Solid Pinions.—The solid steel pinions are not hardened, but are made of Bessemer steel, which could only be case hardened—a thing hardly ever done. The process of making these pinions is as follows: Rods of Bessemer steel are cut into suitable lengths. The pieces obtained are pointed or centered on both ends. The stock not needed for the pinion head is cut away, leaving the arbors slightly tapering, for the purpose of fastening them by this means in a hole on the cutting machine. On the end of the arbor of the index plate are two deep cuts across its center, and at right angles to each other. These cuts are of the same shape that would be made by a knife edged file. The effect of these cuts is to produce a taper hole in the end of the arbor, with four sharp corners. Into this hole the end of the arbor of the pinion or ratchet that is to be cut is placed, and a spring center presses on the other end, and the sharp corners in the hole hold the work firm enough to prevent it from turning round when the teeth are being cut. The marks that are to be seen on the shoulder of the back pivot of the arbor that carries the minute hand of a Yankee clock is an illustration of this method of holding the pinion when the leaves are being cut, and no injurious effects arise from it. The convenience the plan affords for fastening work in the engine enables twenty-five hundred of these pinions to be cut in a day, one at a time. The pinion head is cut subject to the proper dividing plate by a splitting circular saw, and by a milling tool (running in oil) for forming the shape of the leaves, both of which tools are generally carried on the same arbor, both being shifted into their proper places by an adjusting attachment. Pinion leaves of the better class are generally shaped by two succeeding milling cutters, the second one of which does the finishing, obviating any other smoothing. For very cheap work the arbors receive no further finish. The shaping of the pivots, done by an automatic lathe, finishes the job.

Figure 81 shows an automatic pinion cutting machine which has extensive use in clock factories for cutting pinions up to one-half inch diameter and also the smaller wheels. For wheels the work is handled in stacks suited to the traverse of the machine, the work being treated as if the stacks were long brass pinions.

Fig. 81. Automatic Wheel and Pinion Cutters.