In Fig. 2656 the oblong portion between the two belly parts marked g g is known as the “butt,” and when split down the ridge, as shown by the dotted line down the centre, the two pieces are known as “bends;” the two pieces marked y are “belly offal;” d is known as “cheeks and faces.” The butt within the dotted line may extend in length from a to b, or from a to c; if cut off between b and c that portion is called the “range” or the whole from b to x may be cut in one piece and termed a “shoulder.”

Sometimes the range is cut off and the rest would be called a shoulder with “cheeks and faces” on; or, again, the range and shoulder may be in one nearly square piece. The manner of cutting this part depends upon the spread and size of the hide.

The part of the hide that is used to manufacture the best belting is shown in Fig. 2657, on which the characteristics of the various parts are marked. The piece enclosed by the dotted lines is that employed in the manufacture of the commonest belting, while that enclosed by the full lines b, c, d is that used for the best belting. The former includes the shoulder, which is more soft and spongy, while it contains numerous creases, as shown. These creases are plainly discernible in the belt when made up, and may be looked for near the belt points.

The centre of the length of the hide will stretch the least, and the outer edges on each side of the length of the hide the most. Hence it follows that the only strip of leather in the whole hide that will have an equal amount of stretch on each edge is that cut parallel to line a, and having that line as a centre of its width. All the remaining strips will have more stretch on one edge than on the other, and it follows that, to obtain the best results the leather should be stretched after it is cut into strips, and not as a whole in the hide, or in that part of it employed for the belt strips. It is found, indeed, that, even though stretched in strips, the leather is apt in time to curve. Thus a belt that is straight when rolled in the coil will, on being unrolled, be found to be curved. It is to be observed, also, that each time the width of the strips is reduced, this curving will subsequently take place; thus, if a belt 8 inches wide and quite straight, be cut into two belts of 4 inches wide, the latter will curve after a short time. The reason of this is almost obvious, because it is plain that the edge that was nearest the centre line of the hide offers the greatest resistance to stretching; hence, when the strip is stretched straight, and an equilibrium of tension is induced, reducing the width destroys to some extent this equilibrium, and the leather resumes, to some extent, its natural conformation. This, however, is not found to be of great practical importance, so long as the outer curve of one piece is on the same side as the outer curve of its neighbor, as shown on the left view in Fig. 2658, in which case the belt will run straight, notwithstanding its curve; but if the curves are reversed, as on the right in Fig. 2658, the belt will run crooked, wabbling from side to side on the pulley. To avoid this, small belts may be made continuous by cutting them from the hide, as shown in Fig. 2659; but in this case it is better that the belt be cut from the centre strip of the hide.

If the leather is stretched in strips after being cut from the hide, the amount of the stretch is about 6 inches in a length of 4¹⁄₂ feet of a belt, say, 4 inches wide, but the stretch will be greater in proportion as the width of the strip is reduced. But if stretched as a whole, the amount of stretch will be about 1 inch per foot of length, the shoulder end stretching one-third more.

If the leather has been properly stretched in strips the length of the belt may be cut to the length of an ordinary tape line drawn tightly over the pulleys, which allows the same stretch for the belt as there is on the tape line, added to the degree of tension due to cutting the belt too short to an amount equalling its thickness (as would be the case if the belt is cut of the same length as the tape line); or if the belt is a double one, the belt thus cut to length would be too short to an amount equal to twice the thickness of the strips of leather of which it is composed.

When the amount to which the leather has been stretched is an unknown quantity (as is commonly the case), the workman cuts the belt too short, to an amount dictated solely by judgment, following no fixed rule. If, as in the case of narrow belts, the stretching be done by hand, the belt is placed around the pulleys, stretched by hand, and cut too short to an amount dictated by judgment, but which may be stated as about 2¹⁄₂ per cent. of its length.

But the stretch of a belt after it is put to work proceeds very much more rapidly if it has been stretched in the piece and not in the strip, hence it gets slack in the course of a few hours, or of a day or more, according to how much it has been stretched; whereas one properly stretched in the strip will last for weeks, and sometimes for months, without getting too slack.

The results of some experiments made by Messrs. J. B. Hoyt & Co. on the strength of the various parts of a hide are given in Fig. 2660. One side of the part of the hide used for leather belting was divided off into 48 equal divisions, each piece being 11³⁄₄ inches long, and two inches wide, the results of each test being marked on the respective pieces. The first column is the strain under which the piece broke; the second column is the amount in parts of an inch that the piece stretched previous to breaking; and the third column is the weight of the piece in ounces and drachms.

From the table it appears that the centre of the hide which has the most equal stretch has the least textile strength, while in general that which has the most stretch has the greatest textile strength, but at the same time the variations are in many cases abrupt.

A single belt is one composed of a single thickness of leather put together, to form the necessary length, in pieces, riveted and cemented together at the joint, or sewed or pegged as hereafter described.

A double belt is similarly constructed, but is composed of two thicknesses of leather cemented and riveted, pegged, or sewed together throughout its whole length, as hereafter described. The object of a double belt is to increase the strength without increasing the width of the belt. Belts are usually made in long lengths coiled up for ease of transportation, the length of belt required being cut from the coil.

To find the length in a given coil that is closely rolled—Rule: the sum of the diameter of the roll and the eye in inches, multiplied by the number of turns made by the belt, and this product multiplied by the decimal .1309, will equal length of the belt in feet.

The grain or smooth side of the leather is the weakest, as may be readily found by chamfering it to a thin edge, when it will tear like paper, and a great deal more easily than will the flesh side under similar treatment. Again, it will crack much more readily: thus, take a piece of leather and double it close with the grain side outward, and it will crack, as shown in Fig. 2661 at c, whereas if doubled, however closely, on the flesh side no cracks will appear. If the edge of a clean-cut piece of leather be examined, there will be found extending from the grain side inward a layer of lighter color than the remainder of the belt; and this whole layer is less fibrous and much weaker than the body of the belt, the strongest part of which is on the flesh side. If the grain side is shaved off thin and stretched slightly with the fingers it will exhibit a perfect network of small holes showing where the hair had root. Here, then, we have weakness and excessive liability to crack on the grain side of the leather, and it is obvious that if this side is the outside of the belt, as in Fig. 2662, at a, the tendency is to stretch and crack it, especially in the case of small pulleys, whereas if the grain side were next to the pulley the tendency would be to compress it, and therefore, rather to prevent either cracking or tearing. Furthermore, very little of the belt’s strength is lost by wearing away its weakest side.

For open belts let the distance between the shaft centres, as a b in Fig. 2663, be the base of a right angle triangle, and the difference between the semi-diameters, as b c, the perpendicular. Square the base and the perpendicular, and the square root of the sum of the two will give the hypothenuse, and this multiplied by 2 and added to one-half the circumference of each pulley is the required length for the belt. This will give a belt too long to the amount to be cut out of the belt to give it the necessary tension when on the pulleys.

Example.—Let the distance between centres in Fig. 2663 be 48 inches; diameter of large pulley 24 inches; diameter of small pulley 4 inches—

A simpler rule which gives results sufficiently accurate for practical purposes is as follows:—

Rule.—Add the diameter of the two pulleys together, divide the result by 2, and multiply the quotient by 3¹⁄₄, then add this product to twice the distance between the centres of the shafts, and you have the length required.

When the length of a crossed belt is required, and the pulleys are not erected upon the shafts, it is, on account of the abstruseness of a calculation for the purpose, preferred in workshop practice to mark off by lines the pulleys set at their proper distance apart (either full size or to scale), and measure the length of the side of the belt, supposing the belt to envelop one-half the circumference only of each pulley, and to add to this one-half the circumference of each pulley; or if there is a great difference between the relative diameters of the pulleys and the distance apart of the shafts is unusually small, the lengths of the straight sides of the belt are measured and the arcs of contact around the pulleys are stepped around by compasses, the set of the compasses being not more than about one-tenth the circumference of the pulleys. This gives a more near result than that obtained by calculation, because although it will give a belt shorter than by calculation, yet the belt will be too long on account of the stretch necessary to the tension required for ordinary conditions.

In narrow belts, as, say, three inches and less in width, the belt may be cut to the length of a tape line passed over the pulleys, and when placed over the pulleys it may be strained under a hand pull and cut as much shorter as the tension under hand pressure indicates as being necessary.

But if the belt is a wide one a stretching clamp, such as shown in Fig. 2664, is employed, the screws being right hand at one end and left hand at the other, so that operating them draws the clamps, and therefore the ends of the belt, together.

The stretch of a belt not stretched in the piece proceeds slowly when the belt is at work, hence if laced at first to a proper degree of tension it will get slacker in a few hours or in a day or so, and must be tightened, or taken up as it is termed, by cutting a piece out. For this purpose a butt joint possesses the advantage that the piece to be taken out may be less, and still leave the end clear for new holes to be punched, than is the case with a lap joint, which occurs because the butt joint occupies a shorter length of the belt than is the case with a lap joint.

When a belt is under tension upon two pulleys and at rest, the friction or grip of the belt upon the respective pulleys (supposing them to be of the same diameter and therefore to have the same arc and area of contact) will depend upon the relative positions of the pulleys; thus suppose one pulley to be above the other as in Fig. 2665, the upper pulley p will have the grip due to the tension of the belt added to that due to the weight of the belt, whereas if placed horizontally, as in Fig. 2666, the weight of the belt will fall equally on the two pulleys, and for this reason vertical belts of a given width require to have a greater tension to transmit the same amount of power as the same belt would if placed horizontally. But as soon as motion was transmitted, by the belt, from one pulley to the other, the belt on one side of the pulley would be under greater tension then that on the other.

Suppose, for example, a belt to transmit motion and power from pulley a in Fig. 2667, to pulley b, then the side c of the belt is that which drives or pulls b, and it is therefore called the driving side of the belt, the resistance to rotation offered by b causing the driving side of the belt to be the most strained; and hence the straightest, whereas the side d will be free of the tension due to the resistance of b.

But if the direction of motion be reversed as in Fig. 2668, a still being the driving pulley, the side d will be the one most tightly strained, and therefore, the driving side of the belt; or, in other words, the driving side of a belt is always that side which approaches the driving pulley, and the slack side is always that which recedes from the driving pulley. In horizontal belts, however, the driving side of the belt is not a straight line, because of the belt sagging from its own weight no matter how tightly it may be strained, but the shorter the belt the less the sag.

It is always, therefore, desirable, so far as the driving power of the belt is concerned, to have the lower half (of belts running horizontally) the driving side, because in that case the sag of the belt causes it to envelop a greater arc of the pulley, which increases its driving power. If the circumstances will not permit this and the sag of the belt operates to practically incapacitate the belt for its duty, what is termed an idle wheel or idler may be employed as shown in Fig. 2669 at e, serving to prevent the sag and to cause the belt on the driving side to envelop a greater portion of the pulley’s circumference, and hence increase its friction on the pulley and therefore its driving power. In the example the two pulleys a and b are of equal diameters; hence the idle wheel is placed midway between them, but when such is not the case the idle wheel should be located according to the circumstances and the following considerations. The idle wheel requires a certain amount of power to drive it, and this amount will be greater as the idle wheel is nearer to the smallest wheel of the pair connected; but on the other hand, the closer the idle wheel to the small pulley (all other factors being equal) the greater the arc of small pulley surface enveloped by the belt, and hence the greater the belt’s driving power. When therefore a maximum increase of driving power is required, the idler must be placed near to the smallest pulley, the desired effect being paid for in the increased amount of motive power required to rotate the driving pulley.

But under equal conditions the larger the diameter of the idle wheel the less the power required to drive it, because the less its friction on its journal bearing. A belt tightener should whenever practicable be placed on the slack side of the belt.

Belt tighteners are sometimes used to give intermittent motion, as in the case of trip hammers; the belt being vertical is made long enough to run loose, until the tightening pulley closes the belt upon the pulley, taking up its slack and increasing the arc of contact.

When the direction of rotation of the driven pulley requires to be reversed from that of the driving pulley, the belt is crossed as in Fig. 2670. A crossed belt has a greater transmitting power than one uncrossed (or, as it is termed, than an “open belt”) because it envelops a greater arc of both pulleys’ circumference. This is often of great advantage where the two pulleys are of widely varying diameter, especially if the small pulley requires to transmit much power, and be of very small diameter.

But a crossed belt is open to the objection that the surfaces of the belt rub against each other at the point of crossing, which tends to rapidly wear out the laced joint of the belt. By crossing a vertical belt the lower pulley receives part of the weight of the belt.

When a belt connects two pulleys whose respective planes of revolution are at an angle one to the other, it is necessary that the centre line of the length of the belt shall approach the pulley in the plane of the pulley’s revolution, which is sufficient irrespective of the line of motion of the belt when receding from the pulley. This is shown in Fig. 2671, which represents what is known as a quarter twist; a, b are two pulleys having their planes of revolution at a right angle, the belt travelling as denoted by the arrows, then the centre line c of the belt being in the plane of rotation of a on the side on which it advances to a, the belt will continue to run upon the same section of a. If the pulley positions be reversed, as in Fig. 2672, the same rule applies, and the side d in the figure being that which advances upon b must travel to b in the plane of b′s rotation, otherwise the belt would run off the pulley; hence it is obvious that the belt motion must occur in the one direction only.

Shafts at any angle one to another may have motion communicated from one to the other by a similar belt connection, providing that a line at a right angle to the axis of one shaft forms also a right angle with the axis of the other. Thus in Fig. 2673 the axis of shaft a may be set at any required angle to the plane of rotation of pulley b, provided that the axial line of a be made to lie at a right angle to the imaginary line l, which is at a right angle to the axis of the shaft of b, and that the side of the driving pulley which delivers the belt (as c, Fig. 2671) is in line with the centre line of the driven pulley, as denoted by the dotted line c.

But when this provision cannot be carried out, pulleys to guide the direction of motion of the belt must be employed; thus in Fig. 2674 are an elevation and plan[39] of an arrangement of these guide or mule pulleys; a b is the intersection of the middle planes e e and f f of the pulleys p and p′ to be connected by belt. Select any two points, a and b, on this line and draw tangents a c, b d to the principal pulleys. Then c a c and d b d are suitable directions for the belt. The guide pulleys must be placed with their middle planes coinciding with the planes c a c, d b d, and the belt will then run in either direction.

In Fig. 2675 is an arrangement of guide pulleys by which two pulleys not in the same plane are connected, while the arc of contact of the smaller pulley c is increased by the idlers or guide pulleys a b, while either c or d may be driven running in either direction.

In Fig. 2676 is shown Cresson’s adjustable mule pulley stand, which is a device for carrying guide pulleys, and admitting of their adjustment in any direction. Thus the vertical post being cylindrical, the brackets can be swung around upon it and fastened in the required position by the set-screws shown. The brackets carrying the pulleys are also capable of being swung in a plane at a right angle to the axis of the guide pulleys, and between these two movements any desired pulley angle may be obtained. It is obvious that by moving the brackets along the cylindrical post their distance apart may be regulated.

When a belt is stretched upon two pulleys and remains at rest there will be an equal tension on all parts of the belt (that is to say, independent of its weight, which would cause increased tension as the points of support on the pulleys are approached from the centre of the belt between the two pulley shafts); but so soon as motion begins and power is transmitted this equality ceases, for the following reasons:—

In the accompanying illustration, Fig. 2677, a is the driving and b the driven pulley, rotating as denoted by the arrows; hence c is the driving and d the slack side of the belt. Now let us examine how this slackness is induced. It is obvious that pulley a rotates pulley b through the medium of the side c only of the belt, and from the resistance offered by the load on b, the belt stretches on the side c. The elongation of the belt due to this stretch, pulley a takes up and transfers to side d, relieving it of tension and inducing its slackness. The belt therefore meets pulley b at the point of first contact, e, slack and unstretched, and leaves it at f, under the maximum of tension due to driving b. While, therefore, a point in the belt is travelling from e to f, it passes from a state of minimum to one of maximum tension. This tension proceeds by a regular increment, whose amount at any given point upon b is governed by the distance of that point from e. The increase of tension is, of course, accompanied by a corresponding degree of belt stretch, and therefore of belt length; and as a result, the velocity of that part of the belt on pulley b is greater than the velocity of any part on the slack side of the belt; hence the velocity of the pulley is also greater than that of the slack side of the belt. In the case of pulley a the belt meets it at g under a maximum of tension, and therefore of stretch, but leaves it at h under a minimum of tension and stretch, so that while passing from g to h the belt contracts, creeping or slipping back on the pulley, and therefore effecting a reduction of belt velocity below that of the pulley. To summarize, then, the velocity of the part of the belt enveloping a is less than that of a to the amount of the creep; hence the velocity of the slack side of the belt is that of a minus the belt creep on a. The velocity of the part of the belt on b is equal to that of the slack side of the belt plus the stretch of the belt while passing over b; and it follows that if the belt or slip creep on one pulley is equal in amount to the belt stretch on the other, the velocities of the two pulleys will be equal.

Now (supposing the elasticity of the belt to remain constant, so that no permanent stretch takes place) it is obvious that the belt-shortening which accompanies its release from tension can only equal the amount of elongation which occurs from the tension; hence, no matter what the size of the pulleys, the creep is always equal in amount to the stretch, and the velocity ratio of the driven pulley will (after the increase of belt length due to the stretch is once transferred to the slack side of the belt) always be equal to that of the driving pulley, no matter what the relative diameters of the pulleys may be. In Fig. 2678, for example, are two pulleys, a and b, the circumference of a being 10 inches, while that of b is 20; and suppose that the stretch of the belt is an inch in a revolution of a (a being the driving pulley). Suppose the revolutions of a to be one per minute, then the velocity of the belt where it envelops a and b, and on the sides c and d, will be as respectively marked.

Thus the creep being an inch per revolution of a, the belt velocity on the side c will be nine inches per minute, and its stretch on b being an inch, the velocity of b will be ten inches per minute, which is equal to the velocity of the driving pulley.

It is to be observed, however, that since a receives its motion independently of the belt, its motion is independent of the creep, which affects the belt velocity only: but in the case of b, which receives its motion from the belt, it remains to be seen if stretch is uniform in amount from the moment it meets this pulley until it leaves it, for unless this be the case, the belt will be moving faster than the pulley at some part of the arc of contact.