Chapter II: Hand and Power Looms (1)

The three principal movements in weaving are shedding, picking, and beating up the weft. By shedding is meant opening the warp threads to allow the shuttle containing the weft to pass over certain ends and under others. In the common hand loom the shed is made by the weaver operating treadles with his feet. Fig. 35 shows the method of connecting the shafts or staves with the treadles for weaving a plain cloth. There are two treadles, A and B, placed underneath the loom, and centred at C. The stave E is connected to the treadle A through the lever G. The stave F is connected to the same treadle through the “tumbler” T and the lever M. When the treadle A is pressed down it will take the stave E down, and the stave F up. For the second pick, the stave F is connected to the treadle B through the lever H, and the stave E is connected to the same treadle through the “tumbler” R and the lever N. Therefore, when the treadle B is pressed down, it will take the stave F down and stave E up. By alternately pressing first one treadle and then the other, we get each stave up for one pick and down for the next, alternately, as required for weaving plain cloth. The levers M and N are usually called “long lams,” the levers G, H “short lams,” and the top levers R, T “tumblers.” The cords PP connect the long lams and tumblers together at the side of the loom.

In mounting this loom for weaving a three-shaft twill, three treadles are required, one treadle for each pick in the pattern. Supposing one stave to be down and two up for each pick. The stave required to be taken down for the first pick must be connected to the first treadle through a short lam, and the two staves required to be taken up must be connected to the same treadle through their long lams and tumblers. Each pick in the pattern must be gone through in this manner. A separate treadle is required for every pick in the pattern, unless the same pick is repeated, in which case one treadle will do for more than one pick. It is not advisable to break the regularity in the order of treading in order to save a treadle; but in diaper patterns and similar weaves the effect of a point draft is obtained by reversing the order of treading.

Figs. 36 and 37 show the design and cording plan respectively for a twill cloth requiring eight treadles.

The hand loom is practically obsolete in the cotton trade, but it is still extensively used in silk manufacture, where power looms, as at present constructed, are not found advantageous for weaving the finer classes of goods.

The chief shedding motions in power looms are tappets, dobbies, and jacquards.

There are various kinds of tappets, the simplest and best for plain or twill weaving being those shown at Figs. 38 and 39. The former is the more general arrangement. In this the tappets are placed under the loom, inside the framework. In the arrangement shown at Fig. 39 the tappets are placed _outside_ the loom, and thus a larger amount of floor space is taken up by the latter than the former.

Outside tappets are mostly used in the Yorkshire weaving districts, and are commonly made for weaving with about eight shafts. The top levers, with “half moons,” are centred at the cross rods EE (Fig. 39), and the heald is lifted from both sides of the loom. The top levers are very useful for equalizing the shed, as the connection with the upright rod can be altered without difficulty.

In a power loom there are two horizontal shafts, the top shaft A (Fig. 38) and the bottom shaft B. The former is used for working the slay, by means of the crank C, and the connecting rod or “crank arm” D (Fig. 38). The bottom shaft is used for “picking,” and for this purpose it is necessary that the shaft should revolve at one-half the speed of the top or crank shaft. The toothed wheel on the bottom shaft must therefore contain twice the number of teeth in the wheel on the crank shaft which drives it. As a plain cloth contains two picks to the round, and the bottom shaft makes one revolution for two picks, the tappets are fixed to the bottom shaft. Each tappet acts upon treadle bowl E, and therefore the size of the bowl will require to be taken into consideration in shaping the tappets. For weaving plain cloth four staves are usually taken, in order to prevent overcrowding the healds on each stave, the ends being drawn through the staves in the order 1, 3, 2, 4. As the staves are fastened together in pairs, this is the same as two staves.

The kind of movement to be given to the staves is very important, especially in quick-running looms. The staves should be moving quickest when they are level, and their speed should gradually decrease as the shed opens. It is obvious that a movement of this kind will put as little strain as possible on the warp, and therefore cause the fewest breakages. The depth of the shed should only be sufficient to allow the shuttle to pass, therefore the “lift” or stroke of the heald is dependent upon the depth of the shuttle used. The shed when opened should remain open only long enough to allow the shuttle to pass through.

_Example._--What lift should a tappet have to make a plain cloth,
the other arrangements in the loom being as follows: Sweep of slay
5½ inches, distance of healds from cloth 8 inches, heald connected
to treadle 24 inches from fulcrum, distance from fulcrum to centre
of treadle bowl 16 inches, size of shuttle 1½ inch broad, 1¼ inch
deep?

Assuming that the tappets are under the loom, as in Fig. 38, the
treadle bowl E is 16 inches from M, and the heald connected 24
inches from M. If slay moves back from cloth 5½″, and the shuttle
is 1½″ broad and 1¼″ deep, it follows that the shed must be 1¼″
deep, or a little over, at a point 4″ from the cloth (5½-1½ = 4).
Then if the heald is 8″ from cloth, the stroke of heald may be
obtained--4: 8 ∷ 1¼: 2½″ stroke of heald, and as 24″ treadle: 16
∷ 2½: 1⅔ lift of tappet required.

To obtain the proper shape of the tappets for a plain cloth, the lift or stroke of the tappets to give the required lift to the healds must be obtained. If the lift of the heald is required to be 4 inches, and the centre of the treadle bowl E (Fig. 38) is situated 12 inches from the fulcrum of the treadle M, the heald being connected to the treadle at, say, 18 inches from the fulcrum, the lift or stroke of the tappet will be obtained as follows:--

As 18 : 12 ∷ 4
4
----
18) 48 ( 2⅔ lift of tappet
36
--
12

In some makes of looms the staves are connected to the treadles at a point between the fulcrum and the treadle bowl, the fulcrum being at the front of the loom. This necessitates a larger lift of tappet than lift of heald. The tappets in this case are very large, and are preferred by some manufacturers.

=To construct a tappet for a plain cloth from the following dimensions.=--Lift of tappet, 4 inches. Distance from centre of shaft to nearest point of contact with treadle bowl, 2 inches; dwell one-third of a pick. Diameter of treadle bowl, 2 inches.

At a radius of 2 inches describe the circle A (Fig. 40). This circle represents the distance from the centre of the shaft to the nearest point of contact with the treadle bowl.

At a radius of 3 inches describe the circle B. One inch added for radius of treadle bowl.

At a radius of 7 inches describe the circle C. Four inches added for lift.

The circle B represents the centre of the treadle bowl when the inner circle of the tappet is acting upon the bowl.

The circle C represents the centre of the bowl when pressed down by the tappet.

The pattern being a plain one, the circle must be divided into two equal parts, and each half-circle will then represent one pick. By the line DE divide the circle into two equal parts. Then, as the healds must have a pause or dwell equal to one-third pick when at the top and bottom of their stroke, divide each half-circle into three equal parts by the lines FK, GH. Divide FH and GK each into six equal parts, and divide the space between the circles B and C into the same number of unequal parts, the largest being in the middle, gradually decreasing towards the circles B and C.

From the corners of these unequal spaces, and with the radius of the treadle bowl in the compasses, describe circles representing the position of the treadle bowl at different parts of its movement.

Draw the curved line touching the extremities of the treadle bowl. This gives the outline of the tappet.

As previously stated, the movement of the heald must be quickest when the shed is nearly closed, and must gradually decrease in speed as the shed opens. The unequal spaces into which the lift of the tappet was divided give this eccentric movement to the heald. The curve of the tappet will approach nearer to a radial line as the shed closes, and the heald approaches the centre of its stroke. Referring to Fig. 40, it will be seen that the treadle bowl is at rest from F to G and from H to K, or one-third of a pick at both the top and bottom of the stroke. Therefore the time allowed for change, or for moving the heald from top to bottom, or _vice versâ_, is equal to two-thirds of a pick. If a dwell equal to half a pick is required, it can be obtained by dividing the pick into four equal parts and taking the middle two parts for dwell. If two-thirds dwell is required, divide the pick into six parts and take four parts for dwell.

It is usual to give the tappet which operates the back heald a slightly larger lift than the tappet which operates the front heald. The difference required can be easily calculated. In looms with the fulcrum of the treadles at the front, and the healds connected to the treadles between the fulcrum and the treadle bowls, some of the required extra lift is obtained by connecting the back heald to the treadle at a point further from the fulcrum than the front heald is connected. In looms with the fulcrum of the treadles at the back of the loom, and the tappets acting between the heald and the fulcrum, there will be a greater difference between the size of tappets in proportion to the lift than in the former case.

Tappets for twills, and other simple weaves, having more than two picks to the round, are usually placed upon a counter-shaft, but outside tappets are usually worked loose upon the bottom shaft.

The following example will illustrate the principle of constructing twill tappets:--

Draw a tappet for a 3 up and 1 down twill. Distance from centre of shaft to nearest point of contact with treadle bowl 3 inches, lift 3 inches, bowl 2 inches diameter, dwell ½ pick.

At a radius of 3 inches describe the circle A (Fig. 41). At a radius of 4 inches describe the circle B (one inch added for treadle bowl). At a radius of 7 inches describe the circle C (3 inches added for lift). There being four picks in the pattern, divide the circles into four equal parts by the lines DE, FG. Then each quarter-circle represents one pick, and the tappets must be made to make one revolution for four revolutions of the crank shaft. As the dwell of the heald (when the shed is open) must be equal to half a pick, or half a revolution of the crank shaft, divide the first pick into four equal parts by the points O, L, M; make DP equal to DO, and FN equal to FM, and rule lines from P, O, M, N to the centre. The distance OM represents the half-pick dwell, and the distances OP and MN represent the half-pick which will be allowed for changing the heald from bottom to top of its stroke, and _vice versâ_. Divide OP and MN into six equal parts, and the lift of tappet, or the distance between the circles B and C, into six unequal parts, the largest in the middle and gradually decreasing towards the two circles. From the corners of the unequal spaces describe the small circles representing the treadle bowl at different parts of its stroke, and draw the outline of the tappet touching the extremities of these circles.

A tappet of this shape acting upon a treadle bowl two inches in diameter will take the heald down for one pick and allow it to go up for three picks. The heald will be held stationary for exactly half a pick when at the bottom of its stroke, and will begin to rise slowly, and gradually increase in speed as it approaches the centre of its stroke, and will gradually decrease in speed as it approaches the top of its stroke. The downward movement will be an exact counterpart of this. In this kind of tappet it will be noticed that the heald, when it gets to the top (if it is required up for more than one pick), remains stationary until it is required to come down. Thus the heald remains at the top while the circles revolve from N to P.

For this twill there will be four treadles, each treadle being operated by a tappet of the same shape; but the tappet operating each succeeding treadle will be placed one quarter of a revolution later than the previous one.

The size of the treadle bowl has a very appreciable effect upon the shape of the tappet, more especially when there are several picks to the round. The movement imparted to the _centre_ of the treadle bowl will be the exact movement given to the heald as far as regards dwell and eccentricity, and as the tappet acts on the treadle bowl at a distance of 1 or 2 inches from the centre, the required amount of dwell and eccentricity must be given to the centre of the bowl, and the shape of the tappet obtained accordingly. It will be noticed at Fig. 41, that to give a dwell of half a pick to the centre of the treadle bowl, a slightly longer dwell is on the tappet at the inner circle; and as the size of the treadle bowl increases, this hollowing out of the tappet must be increased in order to keep the dwell of the heald the same.

Fig. 42 is a drawing of a tappet for a 3 down, 1 up, 1 down, 1 up (six to the round) twill. Centre of tappet shaft to nearest point of contact with bowl 4 inches, lift of tappet 2 inches, bowl 1½ inch diameter, dwell one-third of a pick.

To construct this tappet:--At a radius of 4 inches describe the circle A. At a radius of 4¾ inches describe the circle B. At a radius of 6¾ inches describe the circle C. As there are six picks to the round, divide the circles into six equal parts by the lines D, E, F, G, H, I. As there is one-third pick dwell, divide each pick into three equal parts, and take the middle one for dwell. Rule the lines L, M, N, O, P, Q, R, S to the centre, and divide the spaces allowed for change into six equal parts, and the distance between the circles B and C into six unequal parts, as in the previous examples. From the corners of the unequal spaces describe the circles representing the movement of the treadle bowl, and obtain the shape of the tappet accordingly. It will be noticed that at point L the treadle bowl begins to dwell, and remains stationary until it reaches the point S, when it begins to go up. The heald will thus be down for the first, second, and third picks, up for the fourth, down for the fifth, and up for the sixth.

Woodcroft Section Tappet.--Sect. 1, riser (heald-up); sect. 2,
faller (heald-down); sect. 3, left-hand riser; sect. 4, neutral
riser; sect. 5, right-hand riser; sect. 6, left-hand faller; sect.
7, neutral faller; sect. 8, right-hand faller.]

=Woodcroft’s Section Tappets= are much used in weaving heavy goods, such as velveteens and corduroys. They are made with various numbers of sections to the round. A single tappet plate of one twelve picks to the round is given at Fig. 43. Sections are sometimes made in two kinds only. These are termed “risers” and “fallers,” according as they raise or depress a heald respectively. Each heald requires one plate and lever L, and as the tappets revolve, the lever L is moved up and down. When the lever L is lifted, the heald is moved downwards. A difference in the character of the shed produced by these tappets as compared with ordinary tappets will be noticed. When the lever L is lifted for two or more picks in succession, it comes down about half-way each pick. This is unavoidable in section tappets consisting only of “riser” and “faller” sections, which must join together exactly wherever inserted, thereby causing all the healds to come towards the centre of the shed after every pick. If there are twelve sections to the round, any pattern repeating on three, four, six, or twelve picks may be woven.

It is sometimes considered an objectionable feature of section tappets (as represented in Fig. 43) that they cause all healds to be brought level after every pick, thereby producing jerky shedding. This objection, however, has been overcome by the construction of eight distinct varieties of sections, as shown in Fig. 44, whereby healds may remain either up or down for several picks in succession on the “open-shed” principle, as with ordinary box-plate tappets cast in one piece.

OSCILLATING TAPPETS.

Another form of shedding device, which embodies certain features of ordinary rotary tappets and dobbies, is that known as the oscillating or rocking tappet, an example of which is shown in Fig. 45. This type of shedding motion consists of a series of plates, B, cast with upper and lower projecting ridges, C, D, and fulcrumed on shaft A, upon which they oscillate in a manner indicated by arrows, E. A movement in either direction represents one pick. On each side of the rocking shaft A, and oscillating with the tappets, is a pattern chain, F and F′, composed of bowls and bushes threaded upon spindles, G. Pattern chains, which represent odd and even picks respectively, are rotated alternately and intermittently, one spindle for each pick, thereby causing elbow-levers H to be raised or depressed, according to whether a bowl or a bush is presented underneath them respectively. The vertical arms of H act upon loose plates, I (termed “duck-bills”), which are fulcrumed upon short studs, J. Grooves may thus be formed between either the upper or lower ridges of tappet plates, and the upper or lower edges of “duck-bills,” which grooves, by acting upon treadles K, governing healds, will operate the latter in a manner determined by the pattern chains.

Oscillating tappets are situated at one end of a loom, above the crank shaft, from which they are driven by wheel gearing and suitable connecting arms. They are chiefly employed on looms weaving fustians and similar heavy and strong fabrics.

In plain looms with under tappets, the healds are generally connected round a top roller or cone, so that when the tappet is pressing one stave down, it is also taking the other stave up. The shedding is thus positive. For weaving twills, satins, and such weaves, either spring, roller, or pulley top motions are used. Where spring tops are used, the tappet pulls the heald down, and the spring pulls it up again. Of course, the speed at which the heald moves upward will be controlled by the shape of the tappet exactly as it is in its downward stroke, but in the up stroke of the heald, the tappet is only acting negatively. With roller tops the movement is positive, as the rollers are so constructed that as one stave is taken down by the tappets another is taken up. If two staves are taken down, two will be taken up, and the tappets must be constructed so as to allow this. It is very important also that the tappets should be of the proper shape, and the exact counterpart of each other, so that any one stave is allowed to go up at exactly the same speed, and with the same amount of eccentricity in its movement, as any other stave which is being taken down by the tappets. Fig. 46 shows the top roller arrangement for plain cloth. Straps are connected to the staves over the rollers K, K^1; so that when one stave is taken down by the tappet, the other is taken up.

For three staves the arrangement of rollers as shown at Fig. 47 is used. The diameter of B must be twice that of A. Sometimes a pulley is used at C, but when it is a roller, it is fitted into slots at the ends so as to allow of its being lifted. The diameter of C is immaterial, but the reason for B and A being as 2: 1 is that when the first heald is taken down, either the second or third must be taken up the same distance. Suppose the first stave is pulled down a distance of 4 inches, the strap E, being fastened to the roller A, which is half the size of B, will be taken up only two inches; and as the tappets are constructed so as to allow only one heald to go up each pick, if this heald is the second one, the third being immovable, the second will be taken up 4 inches, or the same distance that the first was taken down. If the strap E were fastened to B, the stave would be taken up eight inches instead of four. This arrangement of rollers is suitable for a 2 and 1 twill; either 2 down and 1 up, or 1 down and 2 up.

For four staves the arrangement shown at Fig. 48 is used. The relative size of the rollers in this case is immaterial. If the first stave is pulled down by the tappet 4 inches, and the second is the one allowed to go up, it will be taken up the same distance. If the first is being pulled down 4 inches, and the third is the one allowed to go up, the fourth being immovable, the strap A is pulled down 2 inches, and B lifted two inches, and the third stave will be lifted 4 inches. If any one of the four healds is pulled down, another will be lifted the same distance. This motion can be used for either a 3 and 1 twill or a 2 and 2 twill, or any four-stave pattern with the same number of staves going up as are going down each pick. The arrangement shown at Fig. 49, in which the top roller is dispensed with, is sometimes used for a 2 and 2 twill. It will not work a 3 and 1 pattern. The principle of this will be understood by carefully following the movement of staves in weaving a 2 and 2 twill. The draft used with Fig. 49 must be 1, 3, 2, 4, or the first end must be drawn through the first stave, the second end through the third stave, the third end through the second stave, and the fourth through the fourth stave. If the pattern is the one shown at Fig. 50, in which the first and second ends are down for the first pick, it is obvious that to effect this the first and third staves will be down for that pick, and the second and fourth staves will be up. For the second pick the second and third ends are down, and as these are drawn through the third and second staves respectively, these staves must be down for the second pick. As the third is already down, it is only necessary to take the second down, which will pull the first up as required. The changes in this pattern will be easily understood from the following:--

1st pick: 1st and 3rd staves down, 2nd and 4th staves up.
2nd pick: 3rd and 2nd staves down, 5th and 3rd staves up.
3rd pick: 2nd and 4th staves down, 1st and 3rd staves up.
4th Pick: 4th and 1st staves down, 3rd and 2nd staves up.

Fig. 51 shows a top-roller device for five healds, with bottom heald staves connected to treadles that are operated by tappets, J, fixed upon a shaft underneath, but a little in front of the healds, and driven by a train of wheels from a pinion, B, on the end of the crank shaft A. This top-roller motion is designed for a five-end weave in which either one heald only or else four healds, must be raised or depressed for every pick, uniformly. Therefore, four of the five healds must be suspended from one pair of rollers C, and one heald from another pair of rollers D, with both pairs of rollers firmly secured to the same shaft. Also, in order to obtain the proper leverage that will ensure the four healds that are suspended from rollers C, exactly counterbalancing the one heald suspended from rollers D, the diameters of the pairs of rollers C and D must be in the ratio of one to four, respectively.

All shedding motions of this type are based on the principle of equilibrium, whether they are designed as top-roller motions, to operate above the healds, or as stocks and bowls to operate below the healds. Therefore, in all top-roller motions, the diameters of the rollers on the same shaft must always be in inverse ratio to the number of healds suspended from them. Likewise with stocks and bowls, the leverage of the stocks must be in inverse ratio to the number of healds to which the respective ends of the stocks or levers are connected.

An arrangement for seven staves is given at Fig. 52. The two pulleys A and B, on the same centre, are in the ratio of 3: 4, and the pulley D must be twice the diameter of C, the relative size of the remaining pulleys being immaterial. If the first stave is pulled down, say, 6 inches, and the seventh stave is the one allowed to go up; then the strap E will be pulled down 2 inches, and the strap F taken up 1½ inches, the strap G 3 inches, and the stave 6 inches, which is the same distance that the other stave was pulled down. It will be the same with any other healds in the set. If one stave is taken down, any other one left loose by the tappet will be taken up the same distance. Instead of the pulleys A and B, a lever may be used with its two arms in the ratio of 3 to 4, the four staves being connected to the shorter arm, and the three staves to the longer arm.

In some looms the positions of tappets and roller heald-motions are inverted: tappets being fixed above, and roller motions below, healds. In such cases the roller motions are known as “stocks and bowls,” which terms, however, more correctly describe those devices consisting of a combination of levers and bowls, or rollers, and not those consisting of rollers upon shafts. In either case, they are based upon the same principle of leverage, and act in an exactly similar manner to each other. These devices are very limited in their scope, as regards variety of weaves for which they are suitable, and may only be employed for weaves of a regular character, in which the number of healds up and down is the same for every pick. Of course, any number of healds in a set may be up or down as required, but when once that number is selected, and healds are tied up accordingly, it may not be changed without re-tieing up.

Fig. 53 shows a front and end elevation of what is known as the Yorkshire shedding motion, in which tappets are cast upon a sleeve slid upon one end of the second motion or picking shaft D, to operate treadles, M, fulcrumed at N. Connecting rods, J, connect treadles, M, with quadrant jacks, O, secured to cross-bars, K. These serve as fulcra for the jacks, which are connected to upper heald staves, P, by means of straps and cords, R, whilst bottom heald staves are attached by cords to springs, S, for the purpose of pulling healds down, after being raised by the tappets.

PICKING.

As soon as a warp-shed is sufficiently opened by the healds, the shuttle, containing weft, is propelled through it. That operation is termed “picking,” and may be accomplished by either of two types of picking motions known as “over” and “under” picking motions. The “over-pick,” also known as the “cone” and Blackburn pick (Fig. 54), is in most general use, especially for narrow and quick-running looms weaving light and medium-weight fabrics; whilst the “under-pick” (Figs. 56 and 57), of which there are many modifications, is chiefly confined to medium and broad looms, which require a picking motion capable of developing greater force. A shuttle is propelled by a picker made of hide, which is connected by means of a leather strap to the picking stick A (Fig. 54). The upright shaft B is the fulcrum of the lever. The cone C is the short arm of the lever which receives the force from the picking tappet D. The tappet is so shaped that as it revolves it gives a sudden quick movement to the cone-shaped stud, and therefore to the shuttle. It is obvious that as the shuttle must move from one side of the loom to the other, and back again, for two revolutions of the crank shaft, the picking tappets must be placed on a shaft whose speed is one-half that of the crank shaft; therefore the bottom shaft in the loom on this account is made to move at the required speed, and the picking tappets are placed on this shaft at opposite sides of the loom.

The chief requirement in a good pick is that as little force as possible shall be wasted in the loom. The relative positions of the tappet shaft and cone should be such that the force is exerted as nearly as possible in the direction of the dotted line E at right angles with the upright shaft B. It is impossible to effect this throughout the whole course of the stroke, but it is obvious that if this is approached as nearly as possible, the pick will be smooth, and the wear and tear reduced to a minimum. A very considerable amount of power is wasted if the direction of the force is too much downward.

The direction of the force is at right angles to a line drawn tangent from the cone at the point of connection with the picking tappet. Thus in Fig. 54 the direction of the force is indicated by the dotted line M, which is at right angles to the dotted line N, drawn tangent to the cone at the point of connection with the tappet.

The intensity of the force depends on the length of the stroke of the tappet and on the suddenness of the curve of the working face. If in two looms the length of tappet is the same, but in one the portion of a revolution occupied in making the stroke is less than in the other, there will be a greater intensity of force in the loom with the quicker stroke. In Fig. 55 the portion of a revolution occupied in making the stroke is indicated by the angle AB. If this angle is increased, the force of the pick will be lessened, and if the angle be decreased, the force of the pick will be augmented. It will be understood from this that if the picking tappets are short the pick is liable to be harsh. If a fair length of tappet is given, a smoother and better-timed pick can be made. The curve on the picking tappet gradually approaches a radial line as it nears the end of the stroke, but the combined influence of the change in the position of the cone and the backward movement of the slay causes the shuttle to move quickest in the early part of its movement in the box.

There is a relation between the length of the shuttle-box and the length of the picking tappet. If the tappet is a short one, the shuttle-box must be short; and if a longer tappet is used--the leverage of the picking arm and other parts being the same--the shuttle-box will be longer.

It is obviously inadvisable to have too short a tappet, as the movement of the shuttle in the box must in that case be extremely sudden, in order to have the necessary force.

An underpick motion is given at Fig. 56. A picking treadle, A, centred at C, is pressed suddenly down by the picking bowl B, which is fastened on to the wheel on the bottom shaft in the loom. A strap, E, connects the treadle and the picking lever. In Fig. 57 this connection is shown. The strap from the treadle is fastened to the quadrant, and as the treadle is pressed suddenly down, the picking lever H is moved forward. The shape of the curve E, which the picking bowl strikes, regulates the character of the movement given to the lever H, and it is well not to have the curve too small and sudden, or the pick will not be satisfactory. The curve on the treadle in Fig. 88 (p. 120) is perhaps better than the one in Fig. 56, as it is longer, and is therefore not liable to be so jerky.

There are numerous other picking motions, which chiefly differ in the mechanism for actuating the picking lever.

=Beating up the Weft= is the third primary movement in weaving. This movement is performed by a crank on the top shaft in the loom and a connecting rod or crank-arm which connects the crank and the slay together. This is shown at Fig. 38, where the crank C and crank-arm D give a reciprocating movement to the slay S. The slay moves upon a rocking shaft, E, as a fulcrum, and when the crank is at the front centre the slay-swords should be perpendicular, or nearly so. Sometimes the fulcrum is taken a little forward, but it is never advisable to have the slay over the perpendicular when in contact with the cloth.

The movement of the slay should be eccentric. It is obvious that when the slay is at the back of its stroke its movement should be sufficiently slow to allow time for the shuttle to pass through the shed; and that when beating up, the speed of the slay should be sufficient to knock the weft firmly into the cloth. A crank and crank-arm give the kind of movement required.

The eccentricity of the slay’s movement depends upon the length of the crank and crank-arm, and upon the position of the crank-shaft in relation to the point of connection of the crank-arm with the slay. The position of the crank-shaft in relation to the connecting pin varies in different makes and widths of looms. We shall see that the position of the shaft and the direction in which the loom runs have an important bearing on the force exerted by the slay in beating up the weft. For ordinary looms the usual position of the shaft is a little below the level of the connecting pin when at the front centre, and when the shaft is in this position the movement of the slay is the most even and least eccentric. To obtain this position of the crank-shaft in a diagram, first draw the line SA (Fig. 58) to represent the slay-sword when the reed is in contact with the cloth; this we will assume is perpendicular. We will suppose SA to be 24 inches, S being the rocking shaft and A the connecting pin which connects the crank-arm with the slay. Suppose the loom we are dealing with to have a 3-inch crank and a 12-inch crank-arm. Describe the arc AN from the centre S, and mark off on the arc a distance from A equal to twice the length of the crank. As the crank is 3 inches long, mark off the point B, 6 inches from A. This point B represents the position of the connecting pin when the slay is at the back of its stroke.

From A, rule the line AX in such a position that the arc AB makes the least possible departure from it. It will be found that this necessitates AX cutting the arc AB at a point a little past the middle of the arc. With the length of the crank and crank-arm, viz. 15 inches, in the compasses, from A as the centre cut the line AX at E, and this gives the position for the crank-shaft which will give the least possible eccentricity to the slay. This will be obvious, as the nearer the connecting pin moves on the straight line AX, the less will be the eccentricity of the slay.

That the movement of the slay in the back half of its stroke is slower than in the front half can easily be proved by taking the length of the crank-arm in the compasses, and, after bisecting the arc AB at C, from C marking off the points D and H on the crank circle. It will be seen that both these points are somewhat inside the top and bottom centres of the crank indicated by the dotted line, and therefore the slay moves from C to A and back, the front half of its stroke, in less time than it moves from C to B and back to C. The reason for this eccentricity or unevenness in the movement of the slay is that when the crank is moving from the back centre to the top centre the crank-arm is oscillating and opening an angle with AX while the slay is moving forward, and therefore while the crank is making this quarter of a revolution, the connecting pin of the slay will move something less than from B to C; and while the crank is moving from the top centre to the front centre, the crank-arm is straightening or closing the angle while the slay is moving forward, and thus the connecting pin will move a greater distance than from C to A while the crank is making this quarter of a revolution. When the crank moves from front to bottom centre the angle is opening while the slay is moving backwards, and therefore the pin will move a little more than from A to C; and when the crank moves from bottom to back centre the angle is closing while the slay moves backwards, thus retarding the velocity of the slay.

This will be better understood from Fig. 59, where CD is the crank-arm, and ED the crank at the top centre. A is the position of the connecting pin when at the front of its stroke, and B its position when at the back of its stroke. The dimensions are as in Fig. 58--viz. 12-inch arm, 3-inch crank--and for simplicity we will assume the connecting pin moves on the straight line AE. From A to B is 6 inches, and therefore it is obvious that AC is something over 3 inches, and that the connecting pin moves this distance whilst the crank is making the quarter of a revolution from top to front centre. The distance AC can be obtained as follows. It is obvious that CDE is a right-handed triangle, and therefore CD^2 is equal to CE^2 + ED^2. Therefore CD^2-ED^2 = CE^2, and having obtained the length of CE, we can subtract this from AE, which leaves the length of AC. The formula will stand thus--

CD^2 - ED^2 = CE^2
12^2 - 3^2
144 - 9
∴ 135 = CE^2
and CE = √(135) or 11·6189
length of AE = 15·0000 inches
11·6189 inches
-------
AC = 3·3811 inches

The answer may be obtained in one calculation as follows:--

AE - √(CD^2 - ED^2) = AC
or 15 - √(12^2 - 3^2)
15 - √(144 - 9)
15 - √(135)
15 - 11·6189 = 3·3811

We thus see that the connecting pin moves 3 inches + 0·3811 inch while the crank is moving from the top to front centre. It will also move the same distance while the crank moves from front to bottom centre.

When the crank is moving from the bottom to the back centre, the connecting pin will move 3 inches - 0·3811.

3·0000
0·3811
------
2·6189 inches,

and the same distance when the crank moves from back to top centre.

It is often necessary in comparing looms to obtain the distance travelled by the connecting pin for a smaller movement of the crank than a quarter of a revolution.

Suppose it is desired to find the distance travelled by the connecting pin while the crank moves through 30 degrees to the front centre.

Take a 4-inch crank and 12-inch crank-arm. In Fig. 60, ED is the crank, 4 inches, and DC the crank-arm, 12 inches, the angle O = 30 degrees. P is the position of the connecting pin when at front of its stroke.

To find the distance CP. From a table of natural sines we can obtain the sine of an angle of 30 degrees, viz, sin 30° = 0·5, and therefore, knowing the length of ED, viz. 4 inches, we can obtain the length of DN, it being 0·5, or half of ED, in an angle of 30 degrees.

Having two sides of a triangle, we can obtain the third side thus:

ED^2 - DN^2 = EN^2 and
CD^2 - DN^2 = CN^2

Having obtained the length of CN and EN, we can easily obtain CP by subtracting CF from the length of crank and crank-arm together. Working out the problem in figures we get--

ED^2 - DN^2 = EN^2
4^2 - 2^2 = EN^2
16 - 4 = EN^2
12 = EN^2
∴ EN = √(12) or 3·4641. And
CD^2 - DN^2 = CN^2
12^2 - 2^2 = CN^2
144 - 4 = CN^2
140 = CN^2
∴ CN = √(140) or 11·8321
and 11·8321 + 3·4641 = 15·2962

Therefore CE = 15·2962 inches, and subtracting this from PE, which is 16 inches (12 + 4 = 16), we get 16-15·2962 = 0·7038 as the distance CP, which is the distance moved by the connecting pin for the 30 degrees movement of the crank.

The complete formula is as follows:--

PE-[√[(ED^2-DN^2)] + √[(DC^2-DN^2)]] = CP, or distance moved by the connecting pin for the given number of degrees through which the crank moves, ND being obtained from a table of sines.

To find the distance moved by the connecting pin while the crank moves through 5 degrees--say, from 30 degrees to 25 degrees in beating up.

To solve this it will only be necessary to subtract the length of CE when the crank is forming an angle of 30 degrees from the length of CE when the crank forms an angle of 25 degrees. In the previous example we found that for 30 degrees, CE = 15·2962 inches, and therefore proceeding in the same manner for 25 degrees, we get from table of sines, sin 25° = 0·4226, and 0·4226 of 4 inches 1·69; therefore ND =1·69 inches, and

4^2 - 1·69^2 = EN^2
16 - 2·856 = EN^2
13·144 = EN^2
∴ EN = √(13·144) or 3·626
and 12^2 - 1·69^2 = CN^2
∴ 144 - 2·856 = CN^2
141·144 = CN^2
∴ CN = √(141·144) = 11·88;

therefore CN = 11·88 inches, and CE will equal 11·88 + 2·626, or 15·506 inches, when the crank is forming an angle of 25 degrees.

15·506 length of CE for 25 degrees
15·296 length of CE for 30 degrees
------
inches 0·210 distance moved by pin whilst crank moves
through 5 degrees, from 30 degrees to 25
degrees, in beating up.

In this manner it is easy to calculate the distance travelled by the pin for any number of degrees moved by the crank, and by comparing the velocity of the slay in different looms, the force of the beat up can be compared.

_The force exerted by the slay varies as the square of its velocity._ Thus, if in two looms where the _weight_ of the two slays and the tension on the two warps are the same, the velocity of the slay in one loom is twice that of the other at a certain point in the beat up, the force of the former slay at that particular point will be four times the force of the latter, 1^2: 2^2 ∷ 1: 4.

We can thus compare the force exerted by the slay in different looms at any point of the beat up.

The force of the beat up is chiefly exerted upon the pick when the crank is nearly at the front centre, and the force exerted will also depend considerably upon the tension on the warp; but the slay is doing some work in beating up from the moment the reed begins to move the pick forward.

Possibly the most reliable method of comparing the force of the beat up in different looms is to calculate the time occupied by the slay in moving through a specified distance at the front of its stroke in beating up. This necessitates a rather different calculation to the preceding examples, but is equally as simple.

Suppose it is required to compare the force exerted by the slay in beating up (say the front 1 inch of its stroke) in two looms, one with a 12-inch crank-arm and 3-inch crank and the other with an 11-inch arm and 4-inch crank. The weight of the slays, the speed of the looms, the tension on the warps, and the timing of the primary movements, the same in each case.

In Fig. 61 the smaller circle represents the 3-inch crank and the larger one the 4-inch crank. CP = 1-inch, CB = 11-inch arm, and CD = the 12-inch arm. It is obvious that if we can obtain the two angles made by the cranks, viz. ∠ CAB and ∠ CAD, we shall be able to get the time, or fraction of a revolution, occupied in moving the slay from C to P. As we know the three sides of the triangle we can obtain the angle enclosed by any two sides, and what is required in this case is to obtain the angles BAC and DAC. In triangles of this kind where there is no right angle, we can obtain the cosine of the angle as follows:--

CA^2 + AD^2 - DC^2
------------------ = AQ, the cosine of angle DAC,
2CA.AD

and CA^2 + AB^2 - BC^2
------------------ = AN, the cosine of angle BAC.
2CA.AB

The proof of this formula is given in Euclid, Book 2.

Having obtained the cosines of the two angles, we can find the angles themselves by referring to a table of sines and cosines.

Then as AP = 15 inches,

CA = 14, AD 3 inches, DC 12 inches, BA 4 inches, BC 11 inches; and reducing the formulæ to figures, we get:

14^2 + 3^2 - 12^2 196 + 16 - 144
----------------- = -------------- = 0·7262 cosine,
2 × (14 × 3) 84

and by referring to a table of sines, we find that cosine 0·7262 = angle 43° 26´, therefore angle DAC = 43½°, about. Also

14^2 + 4^2 - 11^2 196 + 16 - 121 91
----------------- = -------------- = --- = 0·8125,
2 × (14 × 3) 112 112

and by referring to a table of sines and cosines, we find cosine 0·8125 = angle 35⅔°.

We thus find that to move the connecting pin 1 inch to the front of the stroke, in the loom with 11-inch arm, the 4-inch crank will move through 35⅔°, and in the loom with the 12-inch arm the 3-inch crank will move through 43½° for the same movement of the slay. Assuming the force exerted by the latter to be 1, the force of the former will be as 35⅔ squared: 43½ squared ∷ 1: _Ans._

It may be as well here to give a short explanation of the system of obtaining angles by sines and cosines.

As the crank moves forward it is obvious that the line DQ will become shorter, and as the angle becomes larger the line DQ will increase in length. In trigonometry, the ratio between the length of the line DQ and the radius AD is called the _sine_ of the angle, and if the radius is 1, the length of DQ will be the value of the sine. In an angle of 30° the sine is exactly ½ the radius, and the relation between the radius and the sine for every angle is known, and arranged in “tables of sines.” The length of AQ will also vary with the angle, and the length of this line is called the “cosine” of the angle QAD. The _cosine_ of an angle of 30° is therefore the same as the _sine_ of an angle of 60°. When the sine is known it is easy to obtain the cosine as follows:--

Cosine = √(1-sin^2). Thus for an angle of 30°, cosine = √(1-0·5^2), or cos^2 = 1-0·5^2, therefore cos^2 = 1-0·25, or cos^2 = 0·75, ∴ cos = √0·75 = 0·866. By reversing, the sine may be obtained from the cosine.

The value given to the sines and cosines must not be taken for the _actual_ length of the lines; they are simply the ratio to the radius. Thus in an angle of 30°, if the radius is 1 inch the length of the sine will be ½ inch and the cosine 0·866 inch. If the radius is 2 inches, the actual length of the sine will be 1 inch and of the cosine 1·732 inches.

TABLE OF SINES AND COSINES.

+--------+--------+--------+------+
|=Angle.=| Sine. | Cosine.|Angle.|
+--------+--------+--------+------+
| =0°= |=0·00= |=1·00= | =90°=|
| 1° | ·0175 | ·9998 | 89° |
| 2° | ·0349 | ·9994 | 88° |
| 3° | ·0523 | ·9986 | 87° |
| 4° | ·0698 | ·9976 | 86° |
| =5°= | =·0872=| =·9962=| =85°=|
| 6° | ·1045 | ·9945 | 84° |
| 7° | ·1219 | ·9925 | 83° |
| 8° | ·1392 | ·9903 | 82° |
| 9° | ·1564 | ·9877 | 81° |
| =10°= | =·1736=| =·9848=| =80°=|
| 11° | ·1908 | ·9816 | 79° |
| 12° | ·2079 | ·9781 | 78° |
| 13° | ·2250 | ·9744 | 77° |
| 14° | ·2419 | ·9703 | 76° |
| =15°= | =·2588=| =·9659=| =75°=|
| 16° | ·2756 | ·9613 | 74° |
| 17° | ·2924 | ·9563 | 73° |
| 18° | ·3090 | ·9511 | 72° |
| 19° | ·3256 | ·9455 | 71° |
| =20°= | =·3420=| =·9397=| =70°=|
| 21° | ·3584 | ·9336 | 69° |
| 22° | ·3746 | ·9272 | 68° |
| 23° | ·3907 | ·9205 | 67° |
| 24° | ·4067 | ·9135 | 66° |
| =25°= | =·4226=| =·9063=| =65°=|
| 26° | ·4384 | ·8988 | 64° |
| 27° | ·4540 | ·8910 | 63° |
| 28° | ·4695 | ·8829 | 62° |
| 29° | ·4848 | ·8746 | 61° |
| =30°= | =·5000=| =·8660=| =60°=|
| 31° | ·5150 | ·8572 | 59° |
| 32° | ·5299 | ·8480 | 58° |
| 33° | ·5446 | ·8387 | 57° |
| 34° | ·5592 | ·8290 | 56° |
| =35°= | =·5736=| =·8192=| =55°=|
| 36° | ·5878 | ·8090 | 54° |
| 37° | ·6018 | ·7986 | 53° |
| 38° | ·6157 | ·7880 | 52° |
| 39° | ·6293 | ·7771 | 51° |
| =40°= | =·6428=| =·7660=| =50°=|
| 41° | ·6561 | ·7547 | 49° |
| 42° | ·6691 | ·7431 | 48° |
| 43° | ·6820 | ·7314 | 47° |
| 44° | ·6947 | ·7193 | 46° |
| =45°= | =·7071=| =·7071=| =45°=|
| Angle | Cosine | Sine | Angle|
+--------+--------+--------+------+