Block (mechanics)

“ These experiments demonstrate [Pg 108] that for a three-sheave pulley-block of this construction we may safely apply the rule, that the power is one-quarter of the load.
202. We are thus enabled to see how much of our exertion in raising weights must be expended in merely overcoming friction, and how much may be utilized. Suppose for example that we have to raise a weight of 100 lbs. one foot by means of the pulley-block; the power we must apply is 25 lbs., and six feet of rope must be drawn out from between the pulleys: therefore the power exerts 150 foot-pounds of energy. ”

“ In the several systems of pulleys just explained, the hook to which the fixed block is attached supports the entire of both the power and weight. When the machine is in equilibrium, the power only supports so much of the weight as is equal to the tension of the cord, all the remainder of the weight being thrown on the fixed point, according to what was observed in (225.)
If the power be moved so as to raise the weight, it will move with a velocity as many times greater than that of the weight as the weight itself is greater than the power. Thus in fig. ”

“ If, instead of applying force at one side, we push the block bodily forward by a beam moving parallel to itself, then so long as the guides are straight no strain will be put upon them, even though one side of the block is resisted more than the other; if, however, the guides compelled the block to travel round a curve, then the power, instead of being divided between the two sides in such proportion as is necessary to relieve the guides of all strain, is suddenly applied only to the inside, and the effect is that of a single driver only. ”

“ A case containing several sheaves is called a block. A fall-block is attached to a fixed point; a running-block is movable to and from a fall-block, with which it is connected by two or more plies of a rope. The whole combination constitutes a tackle or purchase. (See Pulleys for practical applications of these principles.)
§ 74. Differential Screw.—On the same axis let there be two screws of the respective pitches p1 and p2, made in one piece, and rotating with the angular velocity α. ”

“ The Block Brake.—The block brake, Fig. 20, consists of one or more wooden blocks or shoes b attached to a lever having a fulcrum at d, and connected by a rod to the lever c. Block brakes are objected to mainly because they throw a great load on the journals of the drum when they are applied; they cannot be relied on when there is a heavy load on the drum, and they require the application of great force to the lever c for a given braking power. They are, however, cheap and easily applied to a drum, and the shoe is readily replaced when worn. ”

“ By this means the weight is distributed over the two sheaves and the two parts of the chain, increasing the safety and diminishing the friction of the block.
"The blocks are very simple in construction, and are not at all liable to get out of order; the construction being such that the weight cannot run down, though the men lifting let go the chain. They hang quite plumb when in action, and the men are able to stand clear away from under the load, as the hand-wheel chain can be worked at any angle." ”

“ When cordage is engaged in the formation of any part of a machine, it has hitherto been considered as possessing perfect flexibility. This is not the case in practice; and the want of perfect flexibility, which is called rigidity, renders a certain quantity of force necessary to bend a cord or rope over the surface of an axle or the groove of a wheel. During the motion of the rope a different part of it must thus be continually bent, and the force which is expended in producing the necessary flexure must be derived from the moving power, and is thus intercepted on its way to the working point. ”

“ The use of the screw bolt is to unite certain parts of machinery in close and firm contact. It is peculiarly adapted for this purpose by the compact form in which it possesses the necessary strength and mechanical power. The extreme familiarity of the object tends to prevent the observation of its peculiar fitness. Yet, among all the applications of mechanics, there is, perhaps, no instance of adaptation more remarkable. ”

“ A simple H-frame hanger is shown in the detail sketch in the page plate. The grooved pulley wheels are set on bolts, and a heavy wire is bent and set through the center block as a support for the car. For experimental purposes, or even for play, when it is not desired to make a more elaborate car, a wooden block or other object of sufficient weight may be used as a load. An interesting feature of the work, especially for a boy, is to devise a realistic coach model, as suggested in the sketch. A wooden block forms the base, and the roof and platforms are made of sheet metal. ”

“ Where great resistances have to be overcome, but where the distance through which the resistance must be urged is short, the lever or the screw is generally found to be the most appropriate means of [Pg 150] increasing power. When, however, the resistance has to be moved a considerable distance, the aid of the pulley, or the wheel and axle, or sometimes of both combined, is called in. The wheel and axle is the form of mechanical power which is generally used when the distance is considerable through which a weight must be raised, or through which some resistance must be overcome. ”

“ P (Fig. 2) is the guide or point to be taken round the primitive. It is attached to a block, D, which works along the bar, B C, which in its turn moves on the four wheels, e e f f, upon the frame R S U T fixed upon the drawing board. O A is fixed perpendicular to R U, and is such that O may be fixed at various points to determine the polar distance. O B D is a light bar passing freely through B and forming one side of a parallel ruler of two or more points, g g, h h, i i. Along i i is a slot and in this works a loaded block containing a wheel P', whose plane is always parallel to i i. ”

“ Successive half-turns about two skew axes a, b are equivalent to a twist about a screw whose axis is the common perpendicular to a, b, the translation being double the shortest distance, and the angle of rotation being twice the acute angle between a, b, in the direction from a to b. It is easily shown that any displacement whatever is equivalent to two half-turns and therefore to a screw.
In mechanics we are specially concerned with the theory of infinitesimal displacements. ”

“ We are now to consider the important subject of the application of mechanical principles to structures. These are fixtures, while machines are adapted for motion; a roof or a bridge is a structure, but a crane or a screw-jack is a machine. Structures are employed for supporting weights, and the mechanical powers give the means of raising them.
344. A structure has to support both its own weight and also any load that is to be placed upon it. Thus a railway bridge must at all times sustain what is called the permanent load, and frequently, of course, the weight of one or more trains. ”

“ The next class of simple machines, which present themselves to our attention, is that which we have called the cord. If a rope were perfectly flexible, and were capable of being bent over a sharp edge, and of moving upon it without friction, we should be enabled by its means to make a force in any one direction overcome resistance, or communicate motion in any other direction. ”

“ The base of a brim block is frequently made of elm, but beech and any really hard wood can be utilized.
Machine blocking necessitates the use of metal blocks, which are cast either in iron, aluminium, or spelter from moulds made from the wooden blocks, so that if only machine blocking is intended, it is first necessary to make the wooden pattern. ”

“ As the wear on a step is generally greatest at the bottom, it is made thicker there than at the sides, except where the fitting strips come in. To prevent the steps turning within the block they are generally furnished with lugs, which enter corresponding recesses in the block and cover. ”

“ If a stone or other weight be placed in a sling, which is whirled round by the hand in a direction perpendicular to the ground, the stone will not fall out of the sling, even when it is at the top of its circuit, and, consequently, has no support beneath it. The centrifugal force, in this case, acting from the hand, which is the centre of rotation, is greater than the weight of the body, and therefore prevents its fall. ”

“ A plane frame which can be built up from a single bar by successive steps, at each of which a new joint is introduced by two new bars meeting there, is called a simple frame; it is obviously just rigid. The stresses produced by extraneous forces in a simple frame can be found by considering the equilibrium of the various joints in a proper succession; and if the graphical method be employed the various polygons of force can be combined into a single force-diagram. ”

“ The blocks are pressed against the calico through the agency of springs, which imitate the elastic pressure of the workman’s hand. Each block receives a coat of coloured paste from a woollen surface, smeared after every contact with a mechanical brush. One man, with one or two children for superintending the colour-giving surfaces, can turn off about 30 pieces English per day, in three colours, which is the work of fully 20 men and 20 children in block printing by hand. It executes some styles of work to which the cylinder machine, without the surface roller, is inadequate. ”

“ Like the weighing machine for carriages, the fulcrum of each lever is at one end, and the force is diminished in passing to the spring, in the ratio of the length of its arms. The spring moves a pinion by means of a rack, upon which pinion a hand is placed, indicating by divisions upon a circular dial-plate, the amount of the force employed. ”

“ Assuming that we have a machine and a support of such dimensions, weight, and construction as to be capable of being readily placed in position, it is evident that we shall still require a much larger number of holes than would be needed if the boring were performed by hand, because they are not placed wholly in accordance with the lines of least resistance. ”

“ If there is the slightest displacement of the centre of gravity of the system from the axis of revolution a force acts on the shaft tending to deflect it, and varies as the deflexion and as the square of the speed. If the shaft is therefore to revolve stably, this force must be balanced at any instant by the elastic resistance of the shaft to deflexion. ”

“ But the materials of which every machine is formed are endued with limited strength, and therefore the load which is placed upon it must be restricted accordingly, else it will be liable to be distorted by the flexure, or even to be destroyed by the fracture of those parts which are submitted to an undue strain. The surfaces of the movable parts, and those surfaces with which they move in contact, cannot in practice be rendered so smooth but that such roughness and inequality will remain as sensibly to impede the motion. ”

“ Each end of the beam is sprung obliquely upwards and towards the middle, so as to form a spring through which a pushing screw passes, which serves to vary the distance of the point of support from the fulcrum, and, at the same time, by its oblique action to raise or depress it, so as to furnish a means of bringing the points of support and the fulcrum into a right line. ”

“ If the direction of the force is vertical, and the beam is inclined, then the strain is increased by as much as the diagonal of inclination exceeds the vertical; for example, let one thousand pounds be suspended from the lower end of a beam ten feet long, inclined at an angle of 45°. The diagonal being ten, the vertical will be 7.07 feet, and the strain is increased as follows:—
7.07 to 10 as 1,000 to 1,414 lbs. As the angle of inclination, from the horizontal, increases, the strain from a given load decreases, until the beam is vertical, when a weight acts with its least power. ”

“ When extraneous forces act on the bars themselves the stress in each bar no longer consists of a simple longitudinal tension or thrust. To find the reactions at the joints we may proceed as follows. Each extraneous force W acting on a bar may be replaced (in an infinite number of ways) by two components P, Q in lines through the centres of the pins at the extremities. In practice the forces W are usually vertical, and the components P, Q are then conveniently taken to be vertical also. We first alter the problem by transferring the forces P, Q to the pins. ”

“ If any disturbing force act sideways upon the wheel, then (if we suppose the material of the wheel, shaft, and bearings to be completely rigid) no alteration of the circular motion occurs; and this is true equally whether be great or small, continuous or intermittent, constant or changing in direction. There is nevertheless continuous equilibrium here, but in another way than before. So soon as the force begins to act it calls forth in the interior of the wheel, the shaft and the supports, internal molecular forces, opposite in direction and exactly equal to it. ”

“ Thus, not so easily as by pushing down, but by motion in the opposite direction, the weight of the load will nevertheless be raised. If, therefore, the tongue of a lever lying on a fulcrum goes too far under the weight, and its head exerts its pressure too near the centre, it will not be able to elevate the weight, nor can it do so unless, as described above, the length of the lever is brought to equilibrium by the depression of its head. ”