CHAPTER I. PRELIMINARY NOTES

Designation of parts

289. This escapement is composed of:

1° The balance staff. On this staff is friction-fitted a steel disc (A, fig. 1, 2, 3, plate V), indifferently called the disc or the plate. This disc carries in relief, underneath and perpendicular to its plane, a small ruby pin (o, fig. 1, 2, 3, plate V), known as the lift finger, or simply the jewel pin.

Fig. 3, pl. V, shows the representation of the bare staff and of the same staff fitted with its plate.

2° An anchor (pallet fork) mounted on a staff, carrying two arms or levers, each most commonly fitted with a ruby pallet (E, G, fig. 2). These two pallets, by analogy with their function, are called the escapement lifts of the anchor, and are distinguished as the recoil lift (E) and the discharge lift (G). The ends of the arms or levers are sometimes also called the beaks of the anchor.

The parts ma, nc of these lifts are called the rests of the anchor; and the parts ah, cd, the inclined planes, or simply the inclines.

The fork, which is only an extension of the anchor toward F, also carries two arms known as fork horns or horns (I, J), and between these two horns, above the notch that separates them, a small bearing surface or angular prism (F, fig. 1 and 2), often called the fork table, but which, to avoid confusion, it seems more rational to call the reversal wedge, by analogy with its shape and function.

3° A flat escape wheel, whose teeth are sometimes pointed and sometimes formed with a head, as in figure 2. In the latter case, their tip ends in a small inclined plane.

Escapement action

290. When the mainspring of the watch is not wound, and the balance is held at rest by the hairspring, the anchor, which has in itself no tendency to move, remains immobile in the position shown in fig. 2, in which it is held by the presence of the pin in the fork notch.

Let us suppose that the tooth of the wheel which will act first is then in the position indicated by the dotted line at II (fig. 2, plate V).

The mainspring being armed, the wheel immediately begins to move and rotates to the right. Tooth H advances onto the incline ab, and, pushing it backward, escapes from it when it has been sufficiently displaced (N, fig. 4). A half-escape is then accomplished, and the wheel comes to rest against arm G, where tooth M comes to bear (fig. 4).

The motion communicated to the anchor by the passage of the tooth over the incline is transmitted to the balance through the fork. The flank r of its notch, pressing against pin o, drives it forward and forces it out of the notch. This pin is then carried along by the rotational motion of the balance, which escapes under the impulse it has just received (fig. 5).

While the balance completes its vibration, without any point of contact with the rest of the escapement, the anchor, resting on the stud K (fig. 5), is maintained in this position by the pressure of tooth M on arm G (fig. 4).

The balance, brought back by the hairspring, returning upon itself, the pin re-enters the notch and draws the fork with it under the effect of the balance’s inertia.

The rest of the wheel ceases because tooth M (fig. 4), having reached the edge of the incline x, z, pushes it strongly while advancing upon it. As a result of this pressure, which accelerates the motion of the anchor, the fork immediately takes an excess of speed on the pin which carries it, and, in turn pushing it vigorously, restores to the balance the force necessary to maintain the vibration which it performs, like the previous one, in complete independence from the rest of the escapement. Then, brought back by the hairspring, it returns to produce a new unlocking, and so on for all successive vibrations.

The wheel performs two functions: producing the rest and communicating the driving force to the anchor.

The fork likewise performs a double role, active and passive: passive when the pin drags it until the release from rest, and active when, in turn pushing the pin, it transmits to the balance the force received from the wheel.

291. Examination of figure 5 (plate V) shows that the fork horns are useless for the action of the escapement, since the pin passes in front of them without touching them and only contacts the flanks of the notch; however, these horns, besides ensuring the return of the pin into the notch, also serve to prevent overturning, the pin striking them externally during excessive vibrations (A, fig. 5).

The travel of the anchor—that is, its angular motion from one rest to the next—is limited either by two pins or studs (K, L, fig. 2, pl. V), or by the walls of the cavity in which the anchor is housed.

Although the anchor is held at rest by the pressure exerted by tooth M (fig. 4) on the arm, it could still happen that a shock detaches the anchor from its supporting stud, thus causing the escapement to fail. This accident is prevented by retaining on the fork at F (fig. 1 and 2) the small triangular prism which we have called the reversal wedge, and which in fact prevents the anchor from overturning. By coming to bear on the plate (fig. 6), this wedge holds the fork in the correct position until the pin re-enters the notch.

The presence of the pin in the notch corresponds to the entry of the wedge into the recess B of the plate (fig. 5 and 6); the plate therefore no longer opposes the anchor being carried to the other side.

As can be seen, the passage of the pin through the fork notch is of equal duration to the passage of the wedge through the recess of the plate.

The contact between the wedge and the edge of the plate can therefore only be accidental. A small safety clearance must be provided between these two parts.

This exposition shows that the anchor escapement, while very secure in operation, combines two considerable advantages: producing large vibrations and not stopping at the finger.

CHAPTER II. PRINCIPLES OF THE ANCHOR ESCAPEMENT

Determining the center of the anchor

293. Let FMNR (fig. 7, pl. V) be the circumference of the wheel. On this circumference are marked two corresponding points M and N, the first at the tip of a tooth, the second at the middle of the third space counted from M.

The two radii MO and NO are drawn, and at the ends of these radii the perpendiculars MA and NA are erected. The point A of intersection of these two lines gives the position of the anchor center so that the escapement is tangent to its wheel. It is sufficient to recall the principles of the introduction (51, etc.) to see that points M and N, assumed as resting points, are placed in the most favorable position.

This condition of tangential rest is not absolutely essential, since the anchor, during the entire duration of this rest, having no communication with the balance, the greater or lesser perpendicular or oblique pressure of the wheel tooth has no influence—or at least very little—on the rate of the watch.

It is all the more useful to make this remark immediately, since we must consider the two other functions of the anchor, namely impulse and unlocking, which, to occur most favorably, would precisely need to take place at the same points as the rests.

Escape detachment — Impulse

294. The detachment occurs when the anchor, driven by the balance, causes the arm pressed by the resting tooth to slide so as to bring this tooth to the edge of the incline; and the impulse, which is immediate, consists in the passage—under pressure—of the tooth over the inclined plane.

If the rest occurs on the tangent, as in fig. 7 (pl. V), the same applies to the detachment. The resistance of this detachment is approximately equal on both arms, apart from the slight recoil and the small difference between the levers AS, AV, a difference intentionally exaggerated in the figure; moreover, both detachments end with equal levers (MA and AN, fig. 7).

But this near equality of the two detachments is the precise cause of the inequality of the two successive impulses; for if the detachments end on circular arcs of the same radius, MA and AN, it is evident that each impulse acts at the end of that same radius or lever only at points M and N, and that, on the recoil lift MX, the resisting lever shortens progressively from M to X—that is, becomes increasingly disadvantageous—whereas on the outgoing lift it lengthens progressively from N to Z. The difference in lever advantage is roughly equal to twice the thickness of a pallet-stone.

Moreover, if one notes that the impulse on the first arm occurs with recoil friction, the motion of the anchor being partly opposed to that of the wheel, and that the impulse on the second arm occurs with outward friction, the tooth and arm moving together while tending to move away from the line of centers, it is clear—although we have neglected decomposition of forces and small velocity differences—that the impulse given on the first arm, i.e. the recoil lift, is much less energetic than the impulse on the outgoing lift.

Here arises a serious difficulty: it is known that inequality of impulse harms rate adjustment, disturbs the regulating organ, and slightly reduces the vibration arc; but it is also known that if the two detachments occur with excessively unequal levers, as happens when impulses are made equal, one of these detachments requires greater force and produces greater friction due to a longer travel over the arm. The balance is again destroyed, and one loses the advantages expected from equal impulses.

Since it is impossible to obtain both equalities simultaneously, an intermediate solution was adopted: placing the point of tangency not on the anchor rests, but at the middle of each beak of the anchor—a compromise that best reconciles all requirements of the problem (fig. 2, pl. V).

By this arrangement, equality of the two detachments no longer exists, but that of the lifts becomes very nearly achieved. The difference between detachment levers is reduced to about the thickness of one beak, instead of twice that thickness as in the previous case. The detachment requiring more force is precisely the one followed by a slightly more favorable impulse, which therefore returns a little more energy to the balance.

In summary: if ED and DG (fig. 2) are drawn from the wheel’s center to the middle of each anchor beak, the center of the anchor must be placed at the intersection of the tangents EB and BG drawn at the ends of these radii, namely at point B.

Practical methods for satisfying these conditions will be given later.

Lift — Incline height — Position of the pin, etc.

299. Tavan and Jürgensen limit the total lift to 40°, while Moinet places it between 50° and 60°. The magnitude of this lift depends on:
     1° the height given to the impulse planes;
     2° the degree to which the pin is brought closer to the center of the balance.

Height of the inclines

300. The anchor is pushed further back the higher the inclined plane is; thus it is the height of this incline that determines the extent of the fork’s motion. The difficulty of detachment and the resistance at the end of the lift increase with the magnitude of this motion; conversely, if the fork travel is very limited, the return of the finger into the notch and the rests occur with little security.

Moreover, considering an escapement beating 18,000 vibrations, one observes that with a low incline the wheel passes too quickly over it and acquires strong force only to fall into rest—a harmful shock that produces a marked flutter in the anchor and may cause contact of the wedge with the disc.

In the first case (incline too high), the watch stops at the finger as soon as oils thicken; in the second case (incline too low), rate regulation is poor and vibration amplitude small.

Experience alone established the middle term: generally, the anchor—and therefore the fork—should be given a total movement of 10°, meaning each incline should produce about 5° of fork travel, or very slightly more.

Position of the finger or pin

306. The arc QT, described from the center of the anchor with a radius equal to BI, gives the length of the fork measured from the anchor center to the base of the horns.

Shape and inclination of the teeth

318. Wheel teeth are made either pointed, or broad and head-shaped like those in fig. 2 (pl. V). If pointed, they must be thin and tapered; if provided with a broad head, they must be relieved at the root, leaving only the material necessary for strength (23).
319. The front face of the teeth (AB, fig. 4, pl. V) must be inclined sufficiently forward so that contact between the tooth and the rest face of the lift occurs only at the corner A of the tooth. The degree of this inclination depends on the amount of draw, on the height of the inclines, and thus on the angular travel of the fork—which determines the penetration of each beak between the teeth, i.e. inside the wheel’s circumference.

When drawing an escapement, it is easy to fix this inclination precisely; but in most cases, all requirements are satisfied by making the front of the tooth form an angle of about 25° with the wheel radius, i.e. angle BAD = 25° (fig. 4, pl. V). The teeth must be undercut at the rear so that the anchor may enter between them without contact.

323.

The width of the anchor beaks equals half the space between one tooth tip and the next when teeth are pointed.

When teeth are wider, the beak width must be such that, combined with the tooth width, both together equal exactly half the distance from one tooth point to the next (F to A, or N to C, fig. 4, pl. V).

At present, and generally, beak and tooth are given the same width. This width is therefore one quarter of the distance between two consecutive tooth tips (fig. 1, pl. VI).

Play of the pin in the fork notch

325. Detachment (294) would occur under the most favorable conditions—that is, on the tangent—if the flank of the fork notch, lying on the line of centers (BP, fig. 2, pl. V), were struck perpendicularly by the pin and under outward friction.

For impulse to also occur tangentially with outward friction, the rear side of the pin would need to be located, at the end of detachment, on the line of centers, where it would receive a perpendicular blow from the opposite flank of the notch.

It is clear that these two conditions cannot be simultaneously fulfilled, since impulse and detachment are two actions extending over a greater distance than the thickness of the pin.

Detachment absorbs and decomposes a quantity of motive force that increases the farther contact occurs from the line of centers and the more oblique the action is to that line. Therefore, the pin encounters less difficulty in detachment when the angular movement of the fork is shorter. It is thus necessary to avoid increasing fork motion beyond the 10° deemed necessary, and not to place the rest studs (K, L, fig. 2, pl. V) too far away, which would unnecessarily increase the resistance encountered by the pin at entry.

326. Examination of fig. 5 (pl. V) shows that the wider the fork notch is made, the closer flank e approaches the line of centers MN, and consequently the more recoil friction is reduced during detachment.

Size of the plate

330. The depth of the fork notch should be only what is necessary for free passage of the pin; otherwise, if too deep, it moves the reversal wedge away from the balance and requires a larger plate. The method for determining the correct size is as follows:

The line CA (fig. 6, pl. V) indicating fork motion of 5° is used; from the anchor center, the arc IJ is drawn passing through the point of the reversal wedge. The intersection of arc IJ with line CA gives the radius of the plate, whose center is at D.

The recess of this plate should be about 1.5 to 2 times the diameter of the pin. This is approximate, as the recess varies with fork angle and plate size.

Anchor opening

332. The anchor opening, measured from the middle of one beak to the other (or from rest to rest), comprises two and a half spaces: thus three teeth are embraced by the two arms. This is not arbitrary: the anchor could embrace more or fewer teeth, but with fewer the contact surfaces would be too small and unreliable; with more, weight and friction would increase excessively.

SUMMARY

333. The anchor center must be placed at the intersection of the two tangents to the wheel drawn from the ends of the two radii terminating at the middle of the beaks.

Anchor opening (rest to rest, or beak midpoint to midpoint): two and a half spaces, or 60° for a 15-tooth wheel, 75° for a 12-tooth wheel, etc.

Draw: 15° on the recoil lift and 12° on the outgoing lift.

Height of beak inclines: 5° to 6°, producing a fork motion of 10° to 12° maximum. These inclines must be straight.

Wheel tooth incline: 2° to 3°, measured over the 5° rest.

Total lift: between 45° and 55°, inversely proportional to watch size.

Front tooth inclination: about 25°. Teeth must be undercut at the rear.

The width of a beak plus the width of a tooth equals exactly half the space between two tooth tips.

Distance from anchor center to balance center is on average equal to the wheel diameter.

Fork length should be:
— for 40° lift: 4/5 of the distance between centers
— for 45° lift: 9/11
— for 50° lift: 5/6
— for 60° lift: 6/7

Pin diameter: about one third of the distance between two tooth tips. The pin should be oval or flattened at the front.

For plate size and pin position, see articles 330 and 305.

DRAWING THE ESCAPEMENT

335. We will pass rather quickly over certain details, those already given in relation to the Duplex escapement (266) being assumed to be present in the reader’s mind.

The anchor we are about to draw is the so-called right anchor; it facilitates, more than any other, the balancing of the pivots, a balance that is always necessary for this part.

Let us take a 15-tooth escape wheel, with a diameter of 4 lignes or 9 millimetres. (The fraction of 23 thousandths of a millimetre completing the value of 4 lignes may be neglected.)

9 millimetres multiplied by 10 gives 90 millimetres for the wheel diameter, and 45 millimetres for the radius.

With a compass opening equal to 45 millimetres, and from point A as center, draw the wheel circumference fgki, etc. (fig. 1, pl. VI).

Draw the two radii AD, AE, forming an angle DAE of 60°, which is the anchor opening (333) for a 15-tooth wheel.

At the ends of these radii, erect the perpendiculars or tangents DC, CE; their point of intersection C is the center of the anchor.

Through points A and C draw the center line ACB.

The width of the beaks, as previously seen, depends on the width of the teeth. Let us assume here that these two quantities are equal, each being 6° (¼ of 24°, or of the distance between two tooth points).

Lightly mark on the wheel circumference the width of the beaks, remembering that lines AD, AE must fall at the middle of these beaks.

From the wheel center A, draw through points a and e the lines AG, AF; then pass through point a the line al, forming with line aG an angle GaI of 15°; and through point e the line eJ, forming with eF the angle FeJ of 12°.

The lines al and eJ will form the rest faces of the anchor lifts, and it will suffice to draw through the points defining the beak width the two parallels bK, dL to obtain the opposite sides of these lifts.

Draw the lines CW, CH making with tangents CD, CE angles ECH, DCW of 6° each (1), thus giving the height of the beak inclines.

Joining point a to point b, and point e to point d, the lifts and dotted construction lines to be retained may be inked in black.

336. From point a draw line aQ, forming with wheel radius aA an angle QaA of 23° to 25°. This line aQ gives the inclination of the front of the tooth.

Since the distance between one tooth point and the corresponding point of the next is 24°, mark on the wheel circumference, starting from radius Aa, the points f’, g’, k’, i’, j’, l’, p’, q’; then behind these points the points f, g, k, i, j, l, p, q, spaced from the first ones by 6°, or the thickness of one beak.

Points f’, g’, k’, etc. give the positions of the front faces of the teeth, and f, g, k, etc. those of the heels.

To draw the front of the teeth, describe from center A a circle tangent to line aQ previously drawn; then, passing through all points f’, g’, f’, etc., draw tangents to this circle to determine the inclination of the tooth faces.

The angle HCP indicating the angular motion of the fork—that is, the depth to which the tip of the beak enters a gap between two teeth—line CP gives the depth of this gap, which, for safety, is brought slightly closer to the wheel center by drawing the pitch circle.

One sees from the drawing that this latter circle lies inside the total wheel circumference by about 1/5 to 1/6 of the radius.

Inside the wheel, from its center, draw the dotted circle f’, g’, k’, etc., which should anticipate the height of the beak inclines by about half that height. The space between the two dotted circles gives the height of the small inclined planes formed at the ends of the teeth. These are drawn, as well as the rear of the teeth, which must be left well clear so that this part is not touched by the moving beak d of the anchor.

All parts of the wheel to be retained are then inked in black, whether solid or dotted.

(1) To avoid overloading and confusing the drawing, these two angles are made 6° instead of 5°. This additional degree compensates for the loss of lift mentioned in article 501, and even that arising from pivot play; in reality the angular movement of the fork remains 5°.

337. From point C, center of the anchor, and with a compass opening equal to the wheel diameter, determine point B, center of the balance.

Draw lines CM, CN forming with the center line CB two angles of 5° each, giving a total angle MCN of 10°.

From center B draw lines BR, BS, each forming with the center line an angle of 22½°, giving a total angle RBS of 45°.

With a compass opening equal to Bo, draw arc TT’. The point where it intersects the center line gives the center of the pin, which is then drawn with a major diameter slightly larger than the width of a beak (329), and a minor diameter equal to two-thirds of the major.

With a compass opening equal to Co, from the anchor center, draw arc VV’, which fixes the length of the fork up to the base of the horns.

Draw the fork notch and the reversal wedge. From the anchor center draw arc RS passing through the tip of the wedge: the intersection of this arc with line CM gives the size of the plate.

To determine the width of the plate recess, draw from its center A (fig. 2) two radii n and m passing on each side of the pin through its extreme contact points.

The depth of this recess is given by the wedge, leaving a proper safety clearance.

Once all proportions are fixed and the essential parts known, only the body of the anchor remains to be drawn, giving it as graceful a form as possible, but above all one suited to ensuring good balance of the part.

The escapement is thus completely drawn in its exact proportions. Indeed:
If the wheel is assumed to be in motion, tooth kk’ (fig. 1), approaching incline ab, pushes it back about 5°, and the half-lift completed, tooth jj’ falls into rest on arm E, which will have penetrated toward the wheel field up to line CP. The rest face of this arm is then enclosed within angle HCE, and since the small tooth incline causes a loss of about 2½° to 3° in the rest, the penetration of the tooth onto the anchor arm stops at about 2° or slightly more.

The motion given to the anchor by the passage of the tooth over the incline being 5°, the center of the fork reaches line CN after having pushed the pin out of the notch, allowing it to exit and re-enter on the return without touching the horns (fig. 2).

The resting position of the anchor is secured by the edge of the plate passing with a slight safety clearance in front of the angle of the wedge, etc.

CONSTRUCTION DIFFERENCES

338. In some highly refined works, the pin is carried on a small lever arm, and the plate is replaced by a strong safety bushing or core, of much smaller diameter than the plate (fig. 4, pl. VI).

A tongue fixed by screws beneath the fork replaces the reversal wedge, and corresponds to the recess of the core during each return of the pin into the fork notch.

This construction, much more delicate than the previous one and requiring great precision, has the advantage of performing its functions more reliably and of producing, when the tongue touches the core, less friction than that caused by accidental contacts between the wedge and the edge of the plate.

The omitted details will be easily completed by examining figures 4 and 5, and by what has been seen in the preceding articles.