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 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 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 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—4:81¼:2½ stroke of heald, and as 24 treadle:162½:1? 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 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). 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 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 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 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 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. 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 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. 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 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 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 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. 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 The chief requirement in a good pick is that as little force as possible shall be wasted in the loom. The relative positions 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 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 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 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 CD2 - ED2 = CE2 122 - 32 144 - 9 ?135 = CE2 length of AE = 15·0000 inches 11·6189 inches AC = 3·3811 inches The answer may be obtained in one calculation as follows:— AE - vCD2-ED2 or 15 - v122-32 15 - v144-9 15 - v135 15 - 11·6189=3·3811 We thus see that the connecting pin moves 3 inches +0·3811 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, sin30° = 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: ED2-DN2 = EN2and CD2-DN2 = CN2 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— ED2-DN2 = EN2 42-22 = EN2 16-4 = EN2 12 = EN2 CD2-DN2 = CN2 122-22 = CN2 144-4 = CN2 140 = CN2 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 - [v(ED2-DN2) + v(DC2-DN2)] =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 42-1·692 = EN2 16-2·856 = EN2 13·144 = EN2 and122-1·692 = CN2 ?144-2·856 = CN2 141·144 = CN2 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 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
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:
and by referring to a table of sines, we find that cosine 0·7262 = angle 43° 26´, therefore angle DAC = 43½°, about. Also
and by referring to a table of sines and cosines, we find cosine 0·8125 = angle 35?°. 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 35?°, 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 35? squared:43½squared 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 = v1-sin2. Thus for an angle of 30°, cosine = v1-0·52, or cos2 = 1-0·52, therefore cos2 = 1-0·25, or cos2 = 0·75, ? cos = v0·75 = 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 We see from Fig. 61 that in a loom with a 4-inch crank and 11-inch arm, the velocity of the slay is much greater when beating up than with the 3-inch crank and 12-inch arm. The effect of the length of the crank-arm on the velocity of the slay can easily be shown by a diagram or by calculation. If the length of the crank-arm be altered without altering the length of the crank, there will be found a somewhat quicker movement of the slay at the beat up in the loom with the shorter arm. The difference is not so great when the crank-arm is a long one in proportion to the crank. The chief cause of the difference in the velocity of C in Fig. 61 is the difference in the length of the crank. It is obvious that the longer the crank the greater the angle which it will cause the arm to make, and therefore the greater will be the acceleration of the velocity of C when the angle is closing and the slay moving forward. Likewise, it is obvious that the shorter the arm the larger will be the angle to close, but the principal thing to notice is that an increase in the length of the crank causes an increase in the velocity of the slay owing to the extra distance which it has to travel in each revolution; so that even if the crank-arm were lengthened in exact proportion to the increase in the length of the crank, so as to keep the angle to be closed in beating up the same, there would still be a considerable increase in the velocity of the slay, caused by the extra distance it has to travel. This lengthening of the crank has obviously much more to do with the increase in velocity of the slay than the shortening of the arm has. The longer the crank the further back from the cloth will the slay be taken, and assuming that the shed is open for the shuttle when the crank is at the bottom centre, a long crank is obviously more suitable for a wide loom, as, having to move further back, it will allow a longer time for the shuttle to pass through the shed than a short crank would; therefore the The time allowed for the passage of the shuttle may also be increased by using a short arm so as to increase the eccentricity of the slay. The longer the crank, the greater the velocity of the slay, therefore a long crank is suitable for heavy work, as it stores up more force in the slay than a short one. The force may also be increased by shortening the crank-arm, thus increasing the eccentricity of the slay. The position of the crank-shaft in relation to the connecting pin has some effect upon the eccentricity of the slay’s movement. Fig. 62 shows this, but to see clearly the effect it would be advisable to make an accurate drawing to a large scale. At the back of the stroke it will be found that in the plane B the distance XY is least; therefore there is here the least dwell of the slay at the back of its stroke with the shaft in this position. This is because the pin moves as nearly as possible on the line B whilst the crank is at the back part of its stroke. As the crank is raised or lowered the dwell at the back increases slightly. Reversing the direction of the loom makes a difference in the beat-up. It will be found that in the circle A, OP and ON are about equal, therefore there will be scarcely any change in the velocity of beat-up by reversing the loom; but as the shaft is In the diagram, Fig. 62, the crank and crank-arm are the same length for each position, the centre of the shaft being indicated by the dotted arc. Timing of the Primary Movements. The primary movements, shedding, picking, and beating up, are timed differently in relation to each other in weaving different classes of fabrics. For plain cloths, or other cloths where a good cover is required—that is, where the warp has to be spread—the crank should be set about the top centre when the healds are crossing each other. At Fig. 38 the loom is timed in this manner. When so timed it is obvious that the shed will be considerably or altogether open when the reed is in contact with the cloth. By sinking the centres of the healds Another advantage of beating up when the shed is crossed or partly open for the succeeding pick is that the pick is held more firmly in position than when the shed is not crossed, and therefore the picks can be got in better. In twilled cloths the boldness of the twill is somewhat affected by the warp being spread, and these cloths are often preferred when made without the healds having been sunk. If the dwell on the tappet is equal to one-third of a pick, as in Fig. 64, the line D will mark the point of the tappet when the crank is at the top centre. When the crank has made one quarter of a revolution and is at the front centre with the reed in contact with the cloth, the point E will be acting on the treadle bowl. It will be seen that If the dwell on the tappet is more than one-third pick, and at the commencement the crank is set on the top centre with the healds level, the shed will keep open longer for the shuttle to pass through, and would be more open when the crank reached the front centre. It will be obvious that for a wide loom a longer dwell is required than for a narrow loom. By having the shed fully open before the shuttle enters the shed, the warp is spread and a good cover put on the cloth, but all this dwell is taken off the time which would otherwise be allowed for opening and closing the shed, and therefore means extra strain on the warp. If it is not necessary to spread the warp, the shed need not be fully open until the shuttle is entering the shed. In this case the greatest possible amount of time is allowed for opening and closing the shed, thus putting as little strain as possible on the warp. Speed of Tappets. As previously stated, the bottom shaft in the loom, being the one used for picking, revolves at one-half the speed of the crank-shaft, and therefore plain cloth tappets may be fastened on the bottom shaft. Tappets of more than two picks to the round are usually fixed on a counter-shaft, S (Fig. 65), in looms with inside tappets. Sometimes the wheel E is geared directly If the wheel on the crank-shaft A contains 45 teeth, and the wheel B 90 teeth, C 40 teeth, and E 60 teeth, the tappet-shaft S will be making one revolution for three revolutions of the crank-shaft; therefore these wheels will do for three-end twill tappets. This may be proved by multiplying the drivers together and the drivens together, and dividing one by the other, thus—
It is usual to place two or three wheels on the bottom shaft of the loom, so that any one of them may be geared into the carrier wheel D, each giving the required speed for different tappets. If a 40 wheel, a 30 wheel, and a 24 wheel are placed on the bottom shaft in such a manner that they can be moved along the shaft and any one of them be geared into the carrier wheel, any 3, 4, or 5 pick tappets can be driven with these wheels. We have seen that a 40 wheel at C gives three picks to the round. Suppose the 30 wheel at C is geared into the carrier wheel, we get—
or the relative speed of the tappets and crank-shaft are as If the 24 wheel is at C, we get:
and thus we get the proper rate of speed for tappets five pick to the round. Some loom makers use the wheel E as a change wheel. With a 24 wheel C and a 36 wheel E we get three picks to the round, thus—
With a 24 wheel C, a 48 wheel E gives 4 picks, With a 24 wheel C, a 60 wheel E gives 5 picks, With a 24 wheel C, a 72 wheel E gives 6 picks. Example.—Find the number of teeth for the wheel C on the bottom shaft to drive tappets seven picks to the round, wheel on tappets 63 teeth.
Woodcroft’s tappets, as a rule, are driven directly from the crank-shaft. As these tappets are usually of a large circumference, a large wheel on them is of no disadvantage, although sometimes intermediate wheels are used. If the tappets are twelve to the round, and the wheel on the tappets contains 192 teeth, a driving wheel of 16 teeth will be required on the crank-shaft.
For driving outside tappets, as in Fig. 39, a driving wheel on the crank-shaft and two intermediate wheels are generally used. To find the wheel on the crank-shaft, or the first driver, the other wheels being as follows: first driven wheel, B, 36 teeth; second driver, C, 12 teeth; tappet wheel, D, 120 teeth. Multiply the two driven wheels together, and divide by the given driver multiplied by the picks to the round, thus—
To find the second driver for eight picks, the other wheels being: first driver, A, 20; first driven, B, 40; second driven, D, 60. The given driver multiplied by the picks to the round, 20×8 = 160; the drivens multiplied together, 40×60 = 2400; 2400÷160 = 15wheel required. To find either of the driven wheels, multiply the two drivers and the picks together, and divide by the driven given wheel, thus— Example.—Find the wheel for the tappets, D, for 10 picks to the round,
To find both intermediate wheels, multiply the given driver by the picks to the round, and as the product is to the teeth in the tappet wheel, so is the required driven to the required driver. Example.—Find the two intermediates for 10-pick tappets, if the wheel on the crank-shaft has 18 teeth, and the wheel on the tappets 120 teeth. The 18 × 10 = 180, and therefore the two required wheels must be in the proportion of 180 to 120, the former being the driven wheel. Thus a 36 driven and a 24 driver will give the required speed to the tappets. That this is correct may be seen from the following:—
That the required wheels must be in this proportion will be apparent from the fact that if the wheel B has ten times the number of teeth in A, then B is revolving at the speed at which the tappets are to move; therefore if the wheel C has the same number of teeth that D has, the speed of the tappets will remain the same. One of the most important motions in the power loom is that by which the loom is stopped automatically when the shuttle is caught in the shed or for some reason does not enter the shuttle-box. A motion of this kind has always been considered necessary since the introduction of the power loom. If the shuttle be caught in the shed as the reed is beating up, it is obvious that great damage to the warp must result unless the loom is brought to a sudden stop or the reed thrown out. The loose reed is a better way of preventing damage to the warp by the shuttle being caught. If the shuttle is caught in the shed it throws out the reed and stops the loom. Its action will be understood from Fig. 68. A rod, C, runs underneath the shuttle-race at the back of the slay, and the finger B is fastened to it. The reed is held in position by a board, A, which is also connected to the rod C, as shown in the diagram. If the shuttle is caught in the shed, it presses back the reed and The invention of the loose reed is generally attributed to Mr. James Bullough. It was invented about 1842. One of the most useful adjuncts to the power-loom is the motion for stopping the loom when the weft breaks or runs out. Fig. 69 will explain the principle of this useful contrivance. The grid A is placed at the side of the reed between the reed and the shuttle-box, and the fork is so placed that as the grid moves forward the prongs of the fork pass through it. In looms with change boxes at both sides the weft fork is often placed in the middle of the loom. It is obvious that when several shuttles are used there will always be some weft threads opposite the grid in the ordinary weft fork motion, and this renders it inoperative in this class of looms. It is therefore necessary to have a fork to feel for each pick separately. There are two distinct classes of taking-up motions—the positive, and the negative or drag motion. In the former the cloth is taken up a small but regular distance each pick, and the number of picks per inch can be regulated to a fraction. Fig. 71 is the common form of positive take-up motion. A ratchet wheel or “rack wheel,” A, is moved forward one tooth every pick by a click or catch, M, operated by a projection, G, on the slay sword. As the slay moves forward the rack wheel is moved one tooth, and the holding catch or detent N prevents it from going back. There are five wheels in the train, and the The speed at which the emery beam roller is turned regulates the number of picks per inch, and as changes are constantly required in most weaving mills, the wheel B is usually taken as a change wheel. As this wheel is a driver, a smaller wheel will make the emery roller move slower, and therefore more picks will be put in the cloth, and a larger wheel will drive the emery roller quicker, and as a consequence a smaller number of picks will be put in. If the rack wheel has 50 teeth, This may be proved by multiplying the drivers together and by the circumference of the emery beam roller in quarter-inches for a divisor, and multiplying the drivens together for a dividend: the quotient will be the number of picks per quarter-inch. DRIVERS. 25 15 125 25 375 60 quarter-inches inbeam 22500 DRIVEN. 50 120 6000 75 22500) 450000 (20picksper quarter-inch 45000 0 When the cloth is taken out of the loom, rather more than this number of picks will be counted, as there is not the same tension as when the cloth is being woven. It is usual to allow about 1½ per cent. for this shrinkage. For the purpose of easy calculation the dividend of the loom is obtained; that is, the change wheel required to give one pick per quarter-inch. By using this as a dividend and dividing by the number of picks required in a quarter-inch, the quotient will be the change wheel required; and, vice versÂ, by dividing by the change wheel, the number of picks given by that wheel can be obtained. To find the dividend of a loom— Multiply the rack, stud, and beam wheel together for a dividend, and the stud pinion and the number of quarter-inches in a circumference of the emery beam for a divisor, and the quotient will be the mathematical dividend. Add 1½ per cent. to this for the practical dividend. With the wheels given in Fig. 71 the dividend will be as follows:—
Having the dividend, it is only necessary to divide by the picks to obtain the change wheel required, or to divide by the teeth in the change wheel to obtain the picks which it will give, thus—
The following are the wheels used by various loom makers: Rack wheel. Stud wheel. Stud pinion. Beam wheel. Circumference of beam in inches. Dividend. 50 120 15 75 15 507 60 120 15 75 15 609 50 146 14 90 15 794 50 100 12 75 15 528 60 100 12 75 15 634 Example.—Find the dividend of a loom with a rack wheel 60 teeth, stud wheel 100 teeth, stud pinion 12 teeth, beam wheel 75 teeth, beam 15 inches circumference. rackstudbeam wheel 60×100×75 12×60 studquarter-inches pinionin beam =625mathematical dividend 9=1½percent. 634practicaldividend. It is not possible by changing one wheel only to obtain any number of picks or fraction of a pick, as will be seen from the following examples:— picks 50740 = 12·67 picks 50741 = 12·12 picks 50742 = 12·07 For the lower number of picks the motion does fairly well, but for the higher numbers of picks the changes cannot be made with sufficient exactitude by changing a single wheel. Even in the lower picks it is now required to make the smallest fractional changes. An improved arrangement of wheels is now largely adopted. This is Pickles’ motion. Fig. 72 shows the train of wheels. The change wheel B is in this case a driven wheel, and therefore if a larger wheel is used it will give a larger number of picks in the cloth, and if a smaller wheel is used it will give a smaller number of picks; so that if the wheels are so proportioned that the change wheel B has the same number of teeth that there are picks per quarter-inch, it will always remain so, whatever size the wheel is. If a 20 driven wheel gives 20 picks, a 30 will give 30 picks, and so on. The wheel A is also changed, and this is usually called the “standard” wheel. This is a driver wheel, and therefore a smaller wheel gives more picks, and vice versÂ. The wheels are so proportioned that if A, the standard wheel, has nine teeth, each tooth in B, the change wheel, represents one pick, The wheels mostly used are those in the diagram, and supposing we have a 36 standard and a 45 change wheel, and taking the emery beam as 15·05 inches in circumference, we get—
Thus with a 36 standard a 45 change wheel, B, gives 11¼ picks per quarter-inch, or each tooth in the change wheel gives a quarter of a pick per quarter-inch. By changing these two wheels any fraction of a pick can be obtained. Thus if 13½ picks per quarter-inch are required, the wheels used would be an 18 standard and a 27 change wheel. For 13? picks a 27 standard and a 41 change wheel would be used, and so on. The following examples will fully illustrate the principle of this motion:— Picks per quarter-inch. Standard wheel. Change wheel. 20 9 20 15½ 18 31 14? 27 43 14? 27 44 13¼ 36 53 13¾ 36 55 12? 45 61 It is not always customary to change the wheels in the above manner, as a different value is often given to each tooth in the change wheel by altering the standard wheel, otherwise than by multiples of nine. Any number may be made the basis of a train of wheels of this kind; there is no reason why it should be nine more than any other number, and in adapting looms from the ordinary five-wheel motion to this principle, it is not necessary to get all new wheels, as sow of the old ones may be made to form part of the train. There are several kinds of negative or drag take-up motions. One of the older forms is that given in Fig. 73. A lever, AB, centred at C is weighted on the arm B. A small cam, D, on the crank-shaft presses down A every pick and lifts the catch E, which operates the ratchet wheel F. The action of a negative motion is as follows:—As the slay beats up, the cloth between the cloth beam and the reed is slackened a little, and the weights on the lever at that moment act as a drag upon the ratchet wheel F. The holding catch is usually a double one, and will hold the ratchet wheel when taken forward the space of half a tooth. By increasing the drag upon the ratchet wheel, a slighter blow from the slay will enable the weights to act, and thus less weft is put into the cloth. If a loom is regulated so as to put a certain number of picks per inch into the cloth of a given count of weft, and weft of a finer count is then used, it is obvious that the number of picks per inch would be increased. If the weft varies in thickness As the cloth is wound on the beam the circumference of the latter gradually increases, and consequently there would be a gradual alteration in the amount of weft put into the cloth, owing to the difference in leverage. It is necessary, therefore, to count the cloth and adjust the weights at intervals in order to keep the number of picks regular. Another kind of negative take-up motion is shown at Figs. 74 and 75. This is now more generally used than the other kind. The cloth beam A is driven by a screw, S. The ratchet wheel B is fastened to the screw-shaft, and the method of operating the ratchet wheel will be seen from Fig. 75, which is another view of the mechanism. A short lever, E, is attached to the rocking shaft K, and as the slay moves backwards from the cloth the weights W are lifted a little, and when the slay moves forward, the weights, acting Another ready method of obtaining any required pick in 507·5 × 24 standard B15 picks =812 This 812, then, is the product of the two drivers, and any two convenient wheels which, multiplied together, give this number can be used—thus 81228 = 29. Therefore the two drivers may have 28 and 29 teeth respectively. The two wheels are found by experiment. If the dividend of the five wheels is 609 a 20 standard wheel is used, and the same drivers as in the preceding case will do. If it is required to change only one wheel, and to have the arrangement such as to give an exact number of picks, or half-picks, or quarter-picks, in the quarter-inch of cloth, by taking the two drivers A and C of such numbers that their product amounts to 507, the number of teeth in the driven wheel B will always equal the number of picks per quarter-inch exactly. Thus 507/13 = 39. Therefore if the drivers A and C have respectively 13 and 39 teeth, every tooth in the driven wheel B will represent one pick per quarter-inch. Suppose half-picks are required exactly, the method of obtaining the wheels is as follows:—Multiply the 507·5 by 2, which equals 1015, then find two convenient wheels which, multiplied together, produce this number; 35 × 29 = 1015, and the two drivers A and C may be 35 and 29. This will cause every tooth in the driven wheel B to represent half a pick exactly. Thus with a 35 wheel A, and a 29 wheel C, a 31 wheel B will give 15½ picks per quarter-inch, the other wheels being the same as in an ordinary 507 dividend motion. The following examples will prove this:— 50 rack × 31 B × 120 stud × 75 beam wheel35 A × 29 C × 15 pinion × 60 quarter-inches =15·27 and 15·27 0·23 =1½percent.shrinkage 15·50 picks. When quarter-picks are required exactly, by changing one wheel only—multiply 507·5 by 4, and the product of the two drivers A and C must equal this. Then every tooth in the driven wheel B will represent a quarter-pick per quarter-inch. There are many methods of letting off the warp positively, but none are likely to succeed in displacing the older and quite satisfactory method of levers, ropes, and weights. The very fact of making the let-off positive, causes too great a rigidity in the hold of the warp, which is detrimental to the yarn. The frictional let-off is not likely to be replaced in cotton goods weaving unless it be in some of the heavier kinds of fabrics. Where it is a question of putting in as much weft as possible, the positive let-off has an advantage. |