Cutting, wheel. The wheel cutting engine is a tool used by horologists to lay out and cut the teeth on the wheels of clocks, watches, etc., as required by the mechanisms for which the wheels are intended.

Few machines are more essential to the crafts, and few whose accuracy is as critical, as the cutting engine . On it depends the quality of timekeepers like clocks, watches, etc., for whatever the nature of the regulator, if the teeth of the wheels and pinions are uneven, the imperceptible motion of the hands cannot be uniform, nor can the power of the driving force be even, unless the wheels themselves are so; consequently, the regulator itself accelerates or slows as a result of those inequalities.

I need not pause to prove the usefulness of the engine (it is well known); my purpose must be to describe it, explain its various uses, and give the means or point out the care required in its construction.

I should have great difficulty in identifying the inventor of this splendid machine; he is unknown to us, like almost all those who have made discoveries that are useful to the nation, while we know by name the inventors of several frivolous things.

All I have been able to learn is that the machine comes from England, and the first to build one here was M. Taillemard, a very good machinist who died about twenty years ago. I was given this information by M. Camus, of the Académie des Sciences.

The first means employed by workmen who had wheels to cut was marking out with dividers the number of units needed, then cutting them with files. This practice was still followed not long ago, but those operations demanded a great amount of time, and how much accuracy could be expected from this method? However, one intelligent workman did not leave the craft in that state for long; he saw a better way, which was to draw various concentric circles on a large brass plate, which he then divided into the numbers of units he used in the mechanisms he was making. Once this was completed, he had only to center the wheel to be cut on the plate used as a pattern; then using a rule or alidade pivoted at the center of the plate and laid in succession on each point dividing a given circle, he marked these divisions on the wheel. Thus it was divided into exactly the same number of units as the pattern circle, and all that remained was to shape the teeth with suitable files. Some craftsmen were able to take advantage of this simple machine and develop it to the point where it would cut teeth as it laid them out; instead of cutting wheels by hand with files, they used a file moving up and down in a slide mounted on a frame, which also carried the pattern and the wheel to be cut . Next came a circular file (called a cutter ), turned by a bow in pivots mounted on the frame (made of wood); the frame also carried the pattern plate, which turned on the frame together with the wheel to be cut , and the latter was secured to the arbor carrying the pattern. In order to mark and shape the teeth, there remained only to immobilize the main plate or pattern and determine the motion it must make from one tooth to the next; that was the function of a part mounted on the frame and carrying a point that rested on a dividing point on the dividing plate, and thus kept the plate from turning. Meanwhile, by turning the cutter with the bow, a tooth was shaped, a slot was made; then lifting the point of the alidade that kept the pattern from turning, and moving the plate to the first division, the point was lowered into the hole, blocking the plate again. A second slot was cut into the wheel, and so on until the plate had completed a revolution, and consequently there were as many teeth slotted into the wheel as there were dividing points on the circle selected.

Such was the origin of the wheel cutting engine , a mechanism that can be envisioned fairly well from the outline I have just given; the illustrations and explanation to follow will make its construction much better understood. The same is true for the wheel cutting engine that has since been developed and operates in the same way; so what I have said about the origin and development will help to understand the machines I shall now describe.

I shall begin with the most advanced cutting engine built until now, which is also the simplest. Then I shall give a description of Sully's. Then I shall add a summary of the machines built to cut any kind of number. I shall close the article with some comments on the care with which a cutting engine must be constructed.

Since Sully's machine is more complex than the one built since, I thought it best to begin with the latter, built by M. Taillemard and developed by his pupil, M. Hulot, who is well known, perhaps not as much as he deserves, for his talent with machines. I have added to this machine a part that may contribute to its improvement, a device whereby mounted escape wheels, contrate wheels, etc. may be positioned instantly, and centered perfectly, on the pattern plate.

Description of the cutting engine designed and built by M. Hulot, Machinist to the King.

The frame, ABCDIFG (Plate XXIV, Figure 1), is made of two pieces in the shape of a Y. Each end of part AEC is bent at a right angle, so that parts GFD are extensions and serve as pillars; they fit into mortises in the other part of the frame, which is seen only at ends BI. The portions of GFD extending through part BI of the frame are threaded so that feet a, b, c serve both as nuts joining the two parts of the frame and as feet supporting the machine; its weight is enough to steady it when stood on any table, MN, to cut all possible wheels.

P is the dividing plate; it is mounted on arbor OPq (Plate XXV, Figure 1). The arbor is carried in the frame and rotates. The two bearings for the arbor are located farther apart than the frame members themselves, by means of bridge rs  [1] beneath frame part BI, and round plate t attached on top of the other frame part, AC. The hole in plate t , in which the arbor turns, is tapered, as is the corresponding part of the arbor. This part, plate t , is the upper bearing of arbor OP q . The other bearing is the lower end, p , of the arbor, which rests on a point at the center of screw O. The screw gives the arbor greater or less freedom of motion; raising or lowering screw O shifts the tapered portion of the arbor farther into the tapered hole or out of it, making it turn less or more freely.

Arbor OP q is drilled lengthwise, a cylindrical hole for the centers or screw plates, m . These centers hold the wheels to be cut , and the size of the plates and center screws is proportional to the size of the wheels. The portions of the centers inside the arbor OP q are turned on their points, as are the plates and the screws. The underside of the plate is cone shaped, as shown in Plate XXVI, Figure 3; it fits in part q of the cylindrical hole in arbor OP q , which is likewise turned in a cone shape. To secure the screw plates in arbor OP q in such a way that the plate is centered in the arbor, a large nut, ef (Plate XXV, Figure 1), is threaded onto arbor OP q . A key is inserted through a slot in arbor OP q and the stem of plate m , and the nut presses the key down in the arbor. Key f bears against the lower end of the opening (Plate XXVI, Figure 3), so when the nut is screwed down the plate is drawn against the conical part q , securing it firmly and centering it. The pressure of the nut keeps the plate from turning in the arbor, and the key, fitting closely the opening through the arbor, gives even more stability.

Part QR (Plate XXIV, Figure 1) moves along beam A x ; it is mounted as follows: the sides of beam A x (only side g is shown here) are not at right angles with the top. They form an acute angle; the channel in part QR has the same shape, so it bears against beam A x on three faces (a type of joint called "dovetail"). Tightening screw i , perpendicular to plane g , locks part QR very securely in place. Along the frame there is a long screw, VV (Plate XXV, Figure 1). At D on the frame the screw has a shoulder or head, fitting into a recess in the frame and covered by plate i , secured to the frame with two small screws. Thus the screw can only turn and not shift endwise; when screw VV is turned with a crank at square c , the threads in part z attached to part QR cause it to move with the screw. The motion of part QR determines the depth of the teeth in flat wheels; it is brought nearer or farther from the center of the pattern plate according to the diameter of the wheel to be cut .

Part QR carries other parts that allow giving various angles to the H piece or cutter carrier, to cut ratchet teeth, worms, contrate wheel teeth, etc., as will be seen in the description I shall give of this part.

KL (Plate XXV) is a stout piece of iron bent at a right angle, its base resting on the upper surface of part QR. In the center of this surface, part QR has a peg that fits a socket machined in the base of part KL, so that the latter can rotate on surface QR and assume various angles to the center of the pattern plate. It has a pointer, 2, that indicates on surface QR the 360 degrees of a circle. The angle of part QR and the H piece it carries allows the cutting of ratchet wheels, etc. To secure part KL to surface QR a large screw, v , is threaded into a hole in the peg mentioned above, for this purpose.

In order that the roots of the teeth may always be perpendicular to their faces, the axis of H must be as far above A x as the midpoint of the wheel is when mounted on the screw plate. For this purpose, screw 3 (Plate XXV, Figure 1) raises or lowers the H piece, in a similar way as part QR is moved along plane A x .

Screws T on the H piece or cutter carrier (Plates XXIV & XXV, Figure 1) turn at two opposing points on part U (Plate XXIV, Figure 1). Part U has at its center a stout rod that extends through part L and is threaded at the end, so with nut 4 (Plate XXV, Figure 1) part U and thus H are secured; the latter can only rotate on its center, T.

Part U (Plate XXIV, Figure 1) has a pointer that reads on dial 6, showing the 360 degrees of a circle, the angle of H relative to surface A x , and consequently the wheel and the dividing plate. This is used for making worm wheels and the inclined teeth of contrate wheels.

Screw 5 adjusts the depth given to the teeth of contrate wheels, since depending on the height, the H plate and the cutter are more or less close to surface A x . This screw is also used when cutting ordinary wheels, to bring the axis of the cutter below the thickness of the wheels (Plate XXIV & XXV, Figure 1).

The alidade or index arm is hh ; it pivots at y . The function of this part is to keep the pattern plate from turning by placing point 9 in one of the holes of the pattern.

Once a number has been chosen, the index arm is locked against sector z by tightening screw 7, so that the arm cannot move from the circle selected. The sector can slide the length of part 8 (Plate XXIV, Figure 1), in which it dovetails, and it moves when screw VV is turned (Plate XXV, Figure 1). [2] Since sector z carries the index arm, clearly the motion of this sector moves the arm as well, bringing center y nearer or farther from the center of the plate. Now assuming point 9 of screw d of the index arm is placed on a point of the plate, and screw V moves the sector, plainly the plate will turn in the direction of screw V. This motion is very often used, and one example will show its usefulness.

I wish to cut a wheel with 120 teeth, but my pattern only has 60. I start by cutting the wheel with 60 teeth, and then without disturbing the index arm, I turn screw V, and consequently the pattern and the wheel, until the middle of one of the teeth already cut is brought to the middle of cutter H. Then I shall cut that tooth and the others as usual, which will give me a wheel of double 60. Such is the nature of this adjustment that it moves the pattern imperceptibly and as much as desired, without removing the wheel from the plate, where centering it is often difficult.

The cutter, f , is mounted on the H piece (Plate XXIV, Figure 1); it is secured by a nut on an arbor that also carries pinion p . The arbor turns on points in recesses in the center of screws v v  [3], parallel to screws T T, on which the H piece pivots.

A crank, 1 2, is fitted to a square on the arbor that carries wheel b ; the wheel has 40 teeth and meshes with pinion p of 16. Turning the crank drives the cutter and makes the openings or slots for the teeth. A bow can also be used, with the cord wound around a pulley in place of the pinion; but this becomes too inconvenient, and I prefer the crank.

To cut thick wheels with heavy teeth, M. Hulot uses a large crank fitted to a square on the end of the same arbor that carries the cutter. See Plate XXVI, Figure 1. For this purpose he drilled screw V its full length and squared the shank of the arbor carrying cutter y to fit the crank; he gains force thereby, since the cutter turns more slowly, at the same speed as the crank.

M. Hulot uses an excellent means of locking screws TT and vv of the H piece (Plate XXVI, Figure 1), namely pressure perpendicular to the axis of the screws, as for locking the centers of a clockmaker's lathe. He cut mortises e e through the threaded arms of the H piece, and into them fit collars C, drilled and tapped like the screws. The collars have threaded stems d , with nuts f that bear against the underside of openings e e of the H piece; tightening the nut tightens the collar against the screw and thus keeps it from turning. This lock has the advantages of being sturdy and not changing the position of the screws. Beneath the H piece there is a spring that raises it unless it is pressed down; this releases the cutter from the teeth and allows the pattern to be turned.

The dividing plate, P, as we have seen, is a large brass plate on which as many concentric circles have been drawn as there are numbers to lay out; each circle is marked with a different number. Here are the dividing numbers: 720, 487, 396, 366, 365, 360, 249, 192, 186, 150, 144, 142, 120, 110, 108, 102, 101, 100, 96, 90, 88, 85, 84, 80, 78, 76, 74, 72, 70, 69, 68, 66, 64, 63, 60, 59, 58, 56, 54, 52, 50, 48, 46. Using the method I explained previously, all these numbers can be doubled by moving the alidade after cutting the wheel with the number on the pattern, and using a cutter that leaves enough width in the teeth for them to be divided in two; so much for the large numbers. To obtain numbers lower than the ones on the plate, look for a multiple of the number sought. Example: I wish to cut a wheel with 73, which is not on the pattern. I look at the large numbers to see if 73 is exactly contained in one of them. I take 365 at random, which is divisible by 3, 4 and 5, giving me a quotient of 73, which is the number I am seeking; so by setting the alidade on the number 365 and stopping the pattern on every fifth division, a wheel of 73 teeth will be cut , and similarly for the other numbers. See Aliquot, Divisor, etc.

To cut ordinary clock wheels, start by fitting the wheel accurately to screw plate m (Plate XXVI, Figure 3); it is secured by means of a nut and a machined washer between the nut and the wheel. Then position point 9 of the alidade [Plate XXV] on the circle with the number chosen for cutting the wheel. Then move part QR towards the center of the pattern, by means of the crank and screw V, until the cutter extends over the wheel by about the depth of a tooth. Take care also that the cutter is aligned precisely with the center of the pattern, so that if it were advanced as far as the center, the tip of the screw plate would divide the thickness of the cutter in two; this is essential in order that the teeth be straight. To avoid moving cutter H towards the center of the pattern every time the cutter is replaced, part S (Plate XXVI, Figure 5) may be used, and in place of roller A, a point may be set in such a way that when the cutter is aligned with the center of the screw plate it coincides exactly with the point and aligns with the center of the plate. So whatever the distance between the cutter and the center, the point on part S will always show whether the cutter is properly aligned. Tighten screw i (Plates XXIV & XXV) to secure part QR to the frame; then, turning the cutter with the crank, make the cut for one tooth. Having done that, raise point d of the alidade to release the dividing plate. Move it to the next point on the same circle; resting the point of the alidade on this point (point 9 enters by the spring action of the alidade), cut a second tooth; continue, stopping on each dividing of the circle, until the revolution is complete.

To cut wheels of large diameter, like one pied , etc., they must be supported near the place where the cutter is operating, to keep the wheel from bending; this is the function of part S (Plate XXVI, Figure 5). It is mounted on arm A x of the frame. Roller A of this part is raised to the wheel from beneath and provides a support that makes it steady.

To cut watch wheels, the only difference with large ones is the method of securing the wheel to the screw plate. Clock wheels, as we have seen, are secured by the means of a nut; for watch wheels part a (Plate XXVI, Figure 2) is used for pressure; it is cone-shaped, its base rests on the wheel, and the apex fits in a recess at the end b of lever L [4]. The cone, a , has a hole in its base to admit the point of the screw plate centering the wheel and protruding above the top face of the wheel.

Part A is attached to part B, which is secured to frame pillar F by screw V, which also secures part C. Part C carries a roller, r , which is a fulcrum for lever L. The roller eases the motion of the lever.

The lever bears on the apex of cone a . Screw T bears on lever L near its middle, so tightening it lowers part b of the lever and cone a until the base presses on the wheel, and the wheel on the plate. This pressure secures the wheel to the plate and forces them to turn together. For further assurance that the wheel cannot turn on the plate, the base of the cone and the face of the plate are cut like a file and tempered. Thus they embed themselves in the brass and secure the wheel very solidly. The pressure of the lever on the cone may be lessened or increased according to which hole in part B is chosen for pin C.

Part A has two motions, one around pin C and the other around pin d , which allows it to move in two directions; this is useful in case the cone is not perfectly centered on the plate. These motions avoid the necessity of centering.

For greater precision, contrate and escape wheels are cut when mounted on their pinions; now since the screw plates must be drilled to admit the arbors and it is no longer possible to use a nut, several means have been used to secure them, like wax, collars the size of the wheels, etc. I shall dwell only on the means that seems to me the best for clocks, a plate m n (Plate XXVI, Figure 3) on which the wheel is secured by means of four screws on plate P, which presses the wheel against face A of the plate. This secures it, but centering it perfectly on the plate is done only by trial and error; that is why I built the machine shown in the same plate, Figure 4. It mounts on the frame, as shown in Figure 2. A is a dial divided into 60; the hand is carried on the arbor of a small pulley in a kind of cage formed by the dial and part B, in dotted lines; part C is assembled in the same cage and turns at i ; part op of part C is a spring shaped like a bow with a silk thread tied to each end and wrapped around pulley n carrying the hand. Two lignes from the center of part C a pin, S, is located, which bears against part b of piece D, which in turn slides in part E along the slot for screw v . Spring r is designed to press pin S against part l of part D, so if D slides, its slightest motion will cause a very great one in the needle. Now let us assume escape wheel R [5] (Plate XXVI, Figures 2 & 3) secured to screw plate m n by the pressure of the screws on plate P, the plate secured to the arbor OP q , and end d of piece D resting against the edge of the escape. If the dividing plate is turned, the variation of the hand on the dial in one revolution of the escape will show the number of degrees it moved. Now pushing the escape from the side opposite part D, by an amount that brings the hand back half the distance it moved, will center it for that point. Continue turning the pattern plate and escape until the hand no longer moves; then the escape will surely be centered on the pattern.

Of M. Sully's wheel cutting engine

Plates XX, XXI, XXII, XXIII, etc. show this machine, which is described and illustrated in M. Thiout's Traité d'horlogerie mécanique et pratique . I give the author's description, vol. I, p. 46; since the plates I provide for this machine were copied from the ones in M. Thiout's book, I have made no changes.

"Plate P is enclosed in a frame, ABCD; the lower part, BC, is removable whenever the plate, which has divisions on both sides, is to be turned over; these two parts make up the frame and are supported by two beams, D and E, which rest on four columns of a certain height.

Wheel F (Plate XX), which drives the cutter, is mounted on an arbor that rotates freely in two uprights, G and H, when crank I is turned. Uprights G and H are fixed to bed K L, which is adjusted up and down by two screws like M, on a second bed, M N. This bed can rotate around point N in slots O and R and be tilted more or less, which is done when cutting contrate wheels. In addition to this motion, the assembly can also be moved nearer or farther from the center of the dividing plate by turning screw S (Plate XXI). Slots O and R, in which the bed assemblies turn, are mounted on two studs, V V, which are locked at the desired point with screws T T. S is a nut fixed to the frame for screw f f, [6] which moves the assemblies forward and back; the screw is secured at N by a collet, and the end is swaged, held by a spring located at the bar that supports the slot plate. The arbor of cutter X turns on points K and L; it carries pinion Y, which meshes with wheel F. The depth of cut is adjusted by screw Z, which rests on a piece not shown in this illustration, attached to bed M at G. Note that bed M remains at the place where it is set, and only bed K L can be raised and lowered, by means of lever W attached to it. Screw Z is also locked by lowering lever 4, which carries a horizontal screw and clamps the former in its threads.

I shall save for the description of plate XXIII and its detailed illustrations an account of various parts and mechanisms of the machine. I shall also explain how to secure the wheel to be cut on the platform arbor. The wheel, shown at number 5 (Plates XX, XXI, XXII), is held at the center by part 6, mounted at the end, 7, of cock 7 8 9. The cock pivots on screws 8 and 10, so turning screw 11 to raise end 9 lowers the other end, 7, pressing firmly on the cap that holds the wheel to its arbor. An alidade or pointer, 12 [7] (Plates XX, XXI), from the midpoint of bed K towards point N, is used to align the cutter with the center. A line is drawn along this part corresponding to the vertical plane of the center; the pointer pivots on a screw and bears on the width of the cutter. The large screw, 15 (Plate XXII), steadies cock 7 8 and eliminates any play and flexing there may be in the screws when a wheel has been secured on its center. Screw 16 is merely a part of the frame structure. Screw 17 (Plates XX, XXI) secures the index arm or alidade, 18 19, with two chief parts: arm 18, and a brass strip, 19 21, similarly secured on top of beam D. Arm 18 19 (Plate XX) makes a right angle at 20 and has an S curve at the upper end. A curved fork, 22, pivoting on pin 22, retains it with the S-shaped piece. Part 23 bears on a rod, 25; the rod presses on brass strip 19 21, so that spring 24, mounted at 20, the other end of which presses on a pin at the fork, tends to press down on end 23. When this happens, rod 25 relays the force of the spring to part 19 21, for the fork cannot slide along the rod, being retained at 23. The force of the spring is relayed to tip 19 of pin 26, which locks the plate while a tooth is being cut. The index arm or alidade is shown better in side view in Plate XXIII, Figure 13.

The tub, 28 (Plate XX), is to catch the filings while a wheel is being cut; another of the same shape is placed on beam A beneath wheel F, overhanging the edge of the first one a little.

Explanation of the top view of the engine (Plate XXI)

M M is the first bed, which may be tilted more or less, as it pivots around point N. The bed is locked in the required position by means of screws Q Q, which extend through slots O R. The second bed, KHHG, is secured to the first by screws B B; it can pivot on them. C C is a horizontal arbor that turns freely in uprights H H and carries wheels F and E. The first, F, meshes with pinion Y and turns the cutter at moderate speed; the second, E, is used for higher speed with a pinion on arbor L L that meshes with it. Plate XXIII will show the method of fixing these cutters on the arbor.

A 12 (Plate XXI) is the alidade, which directs the cutter to the center, 5, of the wheel to be cut ; it rotates around screw A.

K and G are screws that support arbor L L for the cutter and the pinion.

Z is a screw that determines the height of movable bed H H, raising it with arm W. Lever 4 is for locking screw Z. 5 is the wheel to be cut , secured by the piece labeled 6. This piece is fork-shaped and extends beneath bridge 29, where it is secured with a screw; the other end, 30, is retained by a steel T-shaped piece, under which the blades of the fork are caught. Thus, when wheel 5 is to be removed from its arbor, one need only loosen screw 29 and slide piece 6 out after releasing it from under the T; then it is very easily taken from under the wheel.

7 9 is the cock on which bridge 29 is mounted, and under which piece 6 is inserted. The cock is hinged on two screws at 8 and 10, so that raising end 9 with screw 11 lowers the other end, 7, and secures wheel 5 on its arbor by means of piece 6.

16 is an assembly screw that retains the bracket for screw 15, which secures the cock. The bracket is fixed to beam D D.

Screw 17 retains the alidade on the same beam. Piece 23 is the surface for the fork that bears on arm 25. Under the action of spring 24 (see Plate XX), the fork relays the force of the spring to blade 21, and consequently to point 26, which enters the plate divisions in succession, as they are used.

Side view of the engine (Plate XXII)

A B is the last piece of the bed, solidly joined to the beams resting on the columns.

C D is a piece similar to the previous one, but it can be removed when it is desired to turn the dividing plate over; this is done by removing nut I, which releases the collars between which end D is retained. The other end, C, is retained by a sliding bolt, C E, which secures the piece. The bolt is set with screw E L; end C dovetails into upright 26, so that when the plate is to be inverted, first one removes nut L; then the two screws L and E are loosened, and the bolt is drawn towards E by means of knob F. End D is raised a little to release it from under support 10, where it snaps into place. Then when the other screws, Y and AE, have been loosened, plate F is easily taken out and turned over, for screw AE only meets the tip of the plate screw, and screw Y holds it in position.

S V is the screw that moves beds M K and slots R and all the parts connected to them nearer and farther from center 5. M is the first bed, pivoting at point N and locked by screws Q. The second bed, K, carried on bed M, is centered at 24. Center K is that of the cutter and the pinion. Center H is the arbor for the wheels labeled F and E in plate XXI. It drives the pinion, and consequently the cutter. Screw G is for locking the arbor of the pinion.

O X is the alidade, which is used to center the cutter, aligning its edge or thickness with the center of wheel 5.

W is the lever used to raise and lower bed K on its center, 24. Small lever 4 is for locking screw Z; this is done by lowering 4. Screw Z bears against support 21, which moves from point 23 in guide 22 [8], which is attached to bed M. Piece 21 is secured to the guide with a screw, the tip of which is seen at 22; it is also held by spring 27.

6 7 8 and 9 mark the edge of piece 6, which holds wheel 5, and the cock, 7 9, which hinges at 8.

29 and 30 mark the piece and the screw called the T, which retain arm 6. Screw 11 raises the cock. Screw 15 locks it. Finally, screw 16 secures bracket 8 31 32 to the frame of the engine.

Explanation of Plate XXIII

ABCD (Figure 112) is the incline or slot plate in profile; the beds move in curved slots EC, ED, FA and FB. The beds are centered at G; they are locked, as we have said, by means of screws E F. Plate ABCD is joined to slides H and I by brackets K L. Similarly, the slides are locked with screws T T.

Nut M retains the collars on piece N, which can be removed when desired, to invert the plate or any other purpose.

Figure 113 shows the dividing plate index or alidade in side view; it is attached to the frame by screw A, on which it can pivot. Part BC, atop beam D, carries movable rod E in fork FGH and in part C, where it is held. The fork also pivots at point G. Since pin F holding the fork is pushed up by spring K, tip H tends to press down following arc H ; thus rod E relays the force of spring K to strip LM, which carries point N. The strip is attached to beam D only at L; it flexes under the force of the spring, and the point holds the platform by its divisions with the whole force of spring K. Plainly, when the alidade is lifted in order to change division, spring K is compressed; once released, it presses full force on pin F and so on rod E, since fork H cannot slide down the rod.

Screw P tightens the fitting that carries point N. The fitting is attached to strip M by a second screw, R. Cutter Q (Figure 114) is secured on the arbor of pinion O by means of a second piece, S, which has a pin T that fits a hole in the cutter at V; the assembly is tightened with nut X. Note that piece S fits a squared portion of the arbor.

The wheel to be cut , Y, is mounted in the following way. There are (Figure 116) several steel arbors, like Z, that fit into barrel W of the platform. The steel arbor has two pins, 4 and 5, that fit slots cut into opposite sides of the upper part of barrel W, at 6 and 7. Arbor Z can turn only when barrel W turns. Then wheel Y is placed at Z, and it is secured by cap AE, threaded like a nut; part 6 bears on this cap, as described in the preceding plates. Flange 9 of barrel W is secured at the center of the platform with three screws like 10; when the platform is inverted, the barrel must be removed and mounted on the other side, as chosen for the work.

Here is how screws are used in this machine. Assume 11 is part of one side of the bed, tapped for screw 12, which holds the pivot of the arbor for pinion O. The screw extends through block 13, inserted in a mortise cut in piece 11. The block has a second screw, 14, on which collar 15 is fitted, and atop the collar is nut 16, of the same thread as screw 14. Tightening the screw raises it and draws the tenon, tightening screw 12 against the sides of piece 11, which it traverses. In this way the screws are kept from loosening in the nuts. Figure 115 is one of the trays that catch the filings as the wheel is being cut .

There are several advantages in this construction:

1) The use of screws eliminates play, which no matter how small, is always harmful in teeth.

2) Aligning the cutter with the center is enormously useful, since the teeth can only be cut straight.

3) The wheel to be cut on its center is very effectively secured; the screws retaining the cock are firm and cannot flex.

4) The alidade for the dividing plate looks complex, but it should be considered a single well-built part, having a spring with very gentle action, which allows moving the alidade more easily than others with springs that act directly. Most of the improvements that will be observed when using this machine were made by M. de la Fautrière, who was its owner."

Of the engine for cutting any number

Pierre Fardoil is a Paris horologist and an excellent machinist who has designed several complex tools, illustrated in M. Thiout's Traité d'horlogerie mécanique et pratique . He is the inventor of an ingenious engine for cutting wheels of any number ; it can be fitted to a cutting engine using all the original parts for cutting except for the alidade, which is eliminated, and the dividing plate, which has teeth like a wheel; this takes the place of the division points.

The dividing plate is cut with worm teeth to the number 420 (he chose the number for the aliquots it contains). The plate meshes with a single worm mounted as required on the frame of the conventional cutting engine , so that turning the worm one revolution advances the plate one tooth. Now if the wheel, secured to the plate as we described earlier, is cut with a tooth on every revolution of the worm, obviously the resulting wheel will have 420 teeth. If the worm is given only a half-turn and a tooth is cut , and so on with every half-revolution, the wheel will be 840; if the worm is given only a quarter-turn and a tooth is cut , the wheel will be 1680, and so on. The number of teeth will be greater the smaller part of a revolution the worm makes. If, on the other hand, the worm makes two turns for every tooth, the wheel will be 210; if four turns, 105, etc.

The arbor extension of the worm gear is squared for a plate to which a sturdy ratchet is attached, numbered as desired. On the part carrying the worm gear a spring and pawl act upon the ratchet, preventing it and the worm gear from turning backwards. To the plate carrying the ratchet a second ratchet is attached (changeable according to the number of the wheel), with a number related to the wheel to be cut , as will be shown below. Finally, on the end of the worm arbor there is a crank with a pawl and spring that act on the second ratchet; when the crank is turned backwards, the worm gear remains stationary. Only when the crank is turned to the right does the worm gear move. Backwards motion determines the amount by which the worm is to advance for each tooth of the wheel to be cut , as will be shown in the following example. "Assume a wheel is to be cut with 249 on this machine, whose pattern is 420. To find the number of ratchet teeth, divide 420 and 249 by three, which is the only common divisor for these two numbers. The quotients are 140 and 83. Therefore a ratchet of 83 will be chosen, and for each tooth to be cut the ratchet will be advanced 140 teeth; first a complete revolution of 83 teeth, followed by 59, making the 140 teeth. This is determined in the following way."

At every turn the crank encounters a piece that blocks its motion; it cannot turn further unless the piece is removed. The crank is turned backwards the number of ratchet teeth that must go past after the complete revolution. In the present example, this is 57 ratchet teeth. To keep the crank from turning backwards more than 57 teeth, it is fitted with a second arm at a chosen location. In this example, between the two arms of the crank there must be an interval of 57 ratchet teeth. This arm will encounter the same piece that keeps the crank from turning forward, which also keeps it from turning backwards more than 57 teeth. Then the crank is turned to the right until it encounters the stop. The crank is advanced another revolution, and turned backwards by the amount stated above. A second tooth is cut , and so on until the wheel is cut . A plan and description of this machine will be found in M. Thiout's Traité... , together with a table of the various numbers that can be cut with it, from 102 to 800; the various ratchets required for such wheels; the numbers of revolutions or part revolutions to be made; etc. Now since a considerable difficulty in this mechanism is that different ratchets must be used, we must seek to eliminate it, for it is no less difficult to cut a ratchet to a number that is not available than it is to cut a wheel to one that we do not have.

Nevertheless, the principle of using a worm gear for dividing motion is very sound and most advantageous, as can be seen in the article Engine for cutting any number.

The plan of an engine for cutting any number with the ratchets eliminated can be seen in M. Thiout's Traité... ,; it was designed by M. Varinge, who was horologist to the Duke of Tuscany. [9]

As in M. Fardoil's machine, a worm gear moves the dividing plate, which he has cut to 360. The worm gear carries a crown wheel of 60, which engages a pinion of 10. The pinion arbor has an indicator on a dial divided in 60. The indicator is in two parts, one steel and one brass; they can turn relative to each other by friction. Beneath the dial there is a plate that also turns by friction; it bears an index for the steel indicator, showing the starting point for cutting . In addition, behind the crown wheel there is a plate that can turn by friction; it carries a knob that snaps a spring at each revolution of the crown wheel, counting the turns.

The crown wheel is turned by means of a crank fitted to a square on the worm gear arbor; if a tooth is cut on every revolution, the wheel will be 360; in this case, each turn of the crank will have turned the indicator mentioned above six times, six times 60 degrees on the dial, or 360 degrees. To obtain a number less than 360, as with M. Fardoil's machine, the worm gear must make more than one revolution for each tooth; so for a wheel of 90, it must make 4 turns, etc.

If a number greater than 360 is desired, the worm must make less than one revolution; in each case, the indicator and dial are used for the partial revolutions. Thus one can have the 360th part of a revolution for the crown wheel, so by this method a wheel with 129,600 teeth could be cut , turning the crown wheel only one degree for each tooth.

If the indicator makes one revolution for each tooth being cut , the result will be a wheel with 2,160 teeth, etc.

By eliminating M. Fardoil's ratchet, M. Varinge did not avoid one defect, that of lost motion, gear lash, unevenness, etc.; but it is still a step towards perfecting this machine, and M. Varinge's is preferable to the one that inspired it, which is Fardoil's.

To remedy the defects observed in these two machines, and to simplify them further, here is the design I wish to have built.

I shall have the dividing plate of my cutting engine cut to number 720. It will be moved by a single screw turning at the center of a large plate mounted to the frame of the machine with two screws. The plate will be divided in 720. The arbor of the worm gear will be squared for a crank and an indicator; thus turning the crank will turn the indicator the number of teeth to be cut in the wheel. A pressure clip will set the indicator on a degree and keep it stationary during the cutting . I shall give a table of some of the numbers that can be cut , and the number of degrees to move the indicator, and a rule for finding them. See Engine for cutting any number .

In case 720 does not contain enough aliquots for all numbers, others can be marked on other concentric circles on the plate divided in 720; by this method all numbers can be cut that may be needed, especially for complex machines like orreries, planispheres, instruments, etc.

On the construction of cutting engines, I have agreed to close this article with a discussion of the care required in order that a cutting engine may be well made and accurate. I cannot be expected to treat it at the length it deserves; this article is already too long, and I can pause only on the most essential parts.

To appreciate all the care, delicate work, thought, etc. involved, one need only examine the cutting engine I have described, by M. Hulot; that skillful craftsman has brought it to a point of perfection that leaves nothing to be desired. I shall therefore simply follow him in his operations. One of the main parts of a cutting tool is the dividing plate; on it depends in part the accuracy of the wheels. It must be as large as possible; only then is it simple. If there is unevenness, either it is obvious, and it is corrected; or it is very small, and it becomes less noticeable for wheels that are infinitely smaller.

For similar reasons, the plate must be marked off following another that is much larger. In order to come as close as possible to perfection, M. Hulot made a master plate for marking dividing plates that is six pieds in diameter; it is sturdily made and divided with precision; the parts that are used to mark the plates are designed and made with great care, so all possible accuracy can be expected from plates marked from this pattern; I am judging from experience.

Since this element also involves astronomy, horology and various mathematical instruments, I believe nothing should be overlooked in order to perfect it; if the talented are allowed to benefit from their achievements, contributions can be made. For this purpose, they must be informed of the progress made in their craft. I can therefore give the description of M. Hulot's master plate in the article Engine for cutting any number.

The arbors carrying the division plates require infinite care. In order to make them perfect, M. Hulot drills them lengthwise, and not content to turn them on smooth arbors, he turns them on a smooth arbor which does not turn, thereby ensuring that the hole has the same center as the outer surface of the arbor, and that the screw plates, once turned, have the same center. Once the arbor is turned, it is fitted by friction into the lower part of the bearing hole for the arbor, a tempered steel cylinder about three pouces long, pointed at the end so that part P [Plate XXV] rests on point O of the screw, forming the lower support for the arbor.

The plate is turned on its arbor, and the lines on which the various numbers are marked are drawn while turning the arbor in the frame.

The tapered bearing at the upper end is made by turning the plate and the arbor in the frame.

The frame must be solid and proportional to the size of the wheels to be cut . To give an idea, I include the dimensions of M. Hulot's cutting engine , which can cut very heavy wheels up to 18 pouces in diameter; it can very well serve as a guide, for it is rationally designed.

The dividing plate is 17 and one-half pouces in diameter. The length of frame parts E and C (Plate XXIV), measured from center m , is just sufficient to accommodate the plate. Frame arm A x is 13 pouces long, 2 1/2 pouces wide, and 9 lignes thick. The other frame arms have the same width and thickness. The bearing for arbor OP q (Plate XXV) is 4 pouces in diameter, the body of the arbor 1 pouce and one-half in diameter, and the length from pivot O to t 8 pouces . The screw plates stand about 2 pouces 2 lignes above surface A x. The height of the frame, including the components, is 6 pouces and a quarter.

All surfaces of the frame components must be perfectly dressed, and the lower parts, parallel to the ones above the platform, must be perpendicular to all these surfaces in every direction. Surface A x above all requires infinite care. As I have said, it must be perfectly dressed and perpendicular to the axis of the arbor. The sides of this part must be not only parallel and well dressed, but they must in addition align at the same distance from the center of the arbor; a line bisecting the width of plane A and parallel to the sides, passes exactly through the center of arbor OP q. Thus slide QR, the H plate and the cutter can be moved forward or back without changing the position of the cutter in relation to a tooth being cut.

The slide or assembly QR and all the parts fitted to it require the greatest possible care; above all, part QR must be very stable. In M. Hulot's engine, the slide is 4 and one-half pouces long; the width is that of surface A x , 2 pouces and a half. Screw 2 (Plate XXV) is perpendicular to surface A, but it does not bear on it. A plate as wide as surface A and as long as part QR takes the pressure of the screw, so not only does the screw not mark surface A, but its pressure is distributed the whole length of the plate. In this way part QR is always secured to part A x by three surfaces.

In order to make part K (Plate XXV) as solid as possible on slide QR, base K must be broad and well dressed, and likewise for part U carrying the H plate.

In M. Hulot's engine, the H plate (Plate XXIV, Figure 1) is 5 pouces long; from f to g the distance between screws T and U is 2 pouces and a half, from one center to the other. The holes for these screws must be exactly parallel and their axes on the same plane, quite cylindrical, with fine threads, etc.

All this fitting, attention, reasoning, etc., goes to constitute the accuracy of a cutting engine . I am far from having listed them all, and I noted that such was not my intention, but an intelligent workman building a cutting machine may find ideas in the outline I have given of M. Hulot's engine; he must also understand the reasons for what he is doing, and any further guidance from me would be useless for him. As for the workman with no talent, he always leaves something to be desired, and machines requiring as much precision and understanding as these must not be made by him.

Article by M. Ferdinand Berthoud

1. Reference omitted from figure (translator's note).

2. Error: this screw is the smaller one below VV and is not labeled (translator's note).

3. Some references omitted (translator's note).

4. References omitted from the plate (translator's note).

5. References omitted from the plate (translator's note).

6. Reference omitted from plate (translator's note).

7. In this article "alidade" is used to designate both the index arm that locks the dividing wheel, and the pointer for centering the cutter (translator's note).

8. Reference missing from figure (translator's note).

9. From 1569 on the title was Grand Duke (translator's note).