Handle (mechanics)

“ 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. ”

“ As the distances of the power and weight from the fulcrum of a lever may be varied at pleasure, and any assigned proportion given to them, a lever may always be conceived having a power equal to that of any given machine. ”

“ Some of these devices are, the wedge, the screw, the pulley and the inclined plane. In some form or other, one or more of these are used in every piece of mechanism in the world.
Because the lever enables the user to raise or move an object hundreds of times heavier than is possible without it, has led thousands of people to misunderstand its meaning, because it has the appearance, to the ignorant, of being able to manufacture power. ”

“ In order to investigate the amount of power lost by winding the rope upon an axle of this size, I shall place a certain weight—suppose 56 lbs.—upon one hook f, and then I shall ascertain what amount of power hung upon the other hook e will be sufficient to raise f. There is here no mechanical advantage, so that the excess of load which e must receive in order to raise f is the true measure of the friction. ”

“ A gigantic hammer might force in a nail by the mere weight of the head resting on the nail, but with the help of inertia we drive the nail by blows from a small hammer. We have here inertia aiding in the production of a mechanical power to overcome the considerable resistance which the wood opposes to the entrance of the nail. To drive in the nail usually requires a direct force of some hundreds of pounds, and this we are able conveniently to produce by suddenly checking the velocity of a small moving body.
Fig. ”

“ As the mechanical power of the screw depends upon the relative magnitude of the circumference through which the power revolves, and the distance between the threads, it is evident, that, to increase the220 efficacy of the machine, we must either increase the length of the lever by which the power acts, or diminish the magnitude of the thread. ”

“ When one end of the lever (A) goes down, the other end goes up, as shown in Fig. 129; and in Fig. 130, when the shaft (C) of one wheel turns in one direction, the shaft of the other wheel turns in the opposite direction.
It is plain that a gear, like a lever, may change direction as well as increase or decrease power. It is the thorough knowledge of these facts, and their application, which enables man to make the wonderful machinery we see on every hand. ”

“ 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. ”

“ For this purpose let us think of some kind of machine constructed according to the laws of mechanics. Iron weights begin the motion by their gravity; copper wheels resist by their rigidity, affect and raise each other and the lever by their impenetrability, and so on. ”

“ The power of the wheel and axle being expressed by the number of times the diameter of the axle is contained in that of the wheel, there are obviously only two ways by which this power may be increased ”

“ Illustrations may be seen on every hand, as when a workman pries up a stone, or when a housewife pries up a tack with the aid of a hammer. The principle here involved is that of the lever—a principle which in its various practical modifications is everywhere utilized in mechanics. Very seldom indeed is the direct push or pull utilized; since the modified push or pull, as represented by the lever in its various modifications of pulley, ratchet-wheel, and the like, has long been known to meet the needs of practical mechanics. ”

“ Of that class of mechanical agents by which motion is transmitted,—the lever, the pulley, the wedge, and many others,—it has been demonstrated, that no power is gained by their use, however combined. Whatever force is applied at one point can only be exerted at some other, diminished by friction and other incidental causes ”

“ Motions Classed.—In problems of mechanism, each solid piece of the machine is supposed to be so stiff and strong as not to undergo any sensible change of figure or dimensions by the forces applied to it—a supposition which is realized in practice if the machine is skilfully designed. ”

“ The reason for this is that the hand naturally grasps the handle in such a manner that the length of the oval of the handle lies in the plane of the line of motion when striking a blow, and it is obvious that to strike a fair blow the length of the hammer should also stand in the plane of motion. ”

“ When the power arm is longer than the load arm, the load is greater than the power; but when the power arm is shorter than the load arm, the power is greater than the load.
We may regard the strain on the balance as a power which supports the weight, just as we regard the weight to be a power producing the strain on the balance. We see, then, that for the lever of the first order to be efficient as a mechanical power it is necessary that the power arm be longer than the load arm. ”

“ In Figure 5, the driver A is twice the diameter of the driven wheel B, and the latter makes two revolutions for one of A, but the speed at the periphery of the two wheels is the same. A pull of one pound at the point a produces a pressure of one pound at b, and this in turn produces a lift of one pound at c because the levers in each wheel are perfectly balanced, that is, each lever has equal effort and weight arms. ”

“ If a force be applied to a turning piece in a line not passing through its axis, the axis will press against its bearings with an equal and parallel force, and the equal and opposite reaction of the bearings will constitute, together with the first-mentioned force, a couple whose arm is the perpendicular distance from the axis to the line of action of the first force. ”

“ Among the moving elements the first to be considered is the lever, which really forms a broad classification comprising many elements that will hardly be recognized as levers at first blush. Levers in some form are to be found in practically every machine. A wheel, a gear, and a pulley are really levers in disguise, as will be explained presently.
Of course everyone knows that a simple lever consists of a rigid bar that swings on a fulcrum. ”

“ In this case, there is something transmitted from my hand along the string to the weight in consequence of which the weight moves: that something is a force. I can also move the weight by pushing it with a stick, because force is transmitted along the stick, and makes itself known by producing motion. The archer who has bent his bow and holds the arrow between his finger and thumb feels the string pulling until the impatient arrow darts off. Here motion has been produced by the force of elasticity in the bent bow. ”

“ A circumstance presents itself, that should be here explained: when the bevil of the wheel w, or the cone of which the wheel is a part, is very obtuse, the cutter-stand e f, can not be driven back by the action of the disk n n on the plane o, without too great a stress being applied from below, to the axis A B. (See the apparatus I M O N, Plate 16, fig. 2.) In this case therefore, the handle R is not used: but a weight is suspended to the end N of the lever M N, sufficient to give the whole System A B, a tendency to rise; and the operator now acts on the screw g, so as to draw back the plane o ”

“ And so the action continues, the lever swinging back and forth and at each complete oscillation releasing one tooth of the escape wheel.
The hairspring takes up the shock of this intermittent motion and a balance wheel carried by the staff to which F is fastened steadies the oscillatory motion of the lever D. A watch is full of microscopic parts. In a small timepiece there are machine-made screws so small that without the aid of a magnifying glass one cannot see the screw threads cut upon them. ”

“ When a lever is applied to raise a weight, or overcome a resistance, the space through which it acts at any one time is small, and the work must be accomplished by a succession of short and intermitting efforts. In fig. 81., after the weight has been raised from W to W′, the lever must again return to its first position, to repeat the action. During this return the motion of the weight is suspended, and it will fall downwards unless some provision be made to sustain it. ”

“ Nor is there any essential difference between the apparatus of Fig. 38 and that of Fig. 20. In Fig. 38 the bar is pulled down by a force at each end, one a weight, the other a spring balance, while it is supported by the upward pressure of the steel edge. In Fig. 20 the bar is being pulled upwards by a force at each end, and downwards by the weight. The two cases are substantially the same. In each of them we find a bar acted upon by a pair of parallel forces applied at its extremities, and retained in equilibrium by a third force. ”

“ These include the thread models, in which threads are drawn tightly between movable bars, cords, wheels, rollers, &c. In mechanics and engineering an endless variety of working models are employed to convey to the eye the working either of machines as a whole, or of their component and subordinate parts. In theoretical mechanics models are often used to exhibit the physical laws of motion in interesting or special cases—e.g. the motion of a falling body or of a spinning-top, the movement of a pendulum on the rotating earth, the vortical motions of fluids, &c. ”

“ If it were now desired to find the power of a man turning a crank or handle, we should take that given in the figure 12, and fix it to the power-axis A. We should also take the fly-system shewn in fig. 19, and place it on the axis-of-resistance H. Then causing the man to turn the Machine, we should put twice as much weight into the scale P, as his strength was thought able to bear. ”

“ Hence, we learn that two equal and directly opposed forces counteract each other, and each may be regarded [Pg 6] as destroying the motion which the other is striving to produce. If I make the weights unequal by adding to one of them, the knot is no longer at rest; it instantly begins to move in the direction of the larger force. ”

“ 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. ”

“ As to the mechanic powers, the single lever makes no resistance by friction; but if, by the motion of the lever in lifting the fulcrum, or place of support, be changed further from the weight, the power will be decreased thereby.
6. In any wheel of any machine, running upon an axis, the friction on the axis is as the weight upon it, the diameter of the axis, and the angular velocity. ”

“ It is often necessary that the rod to which reciprocating motion is communicated shall be urged by the same force in both directions. A wheel partially furnished with teeth, acting on two racks placed on different sides of it, and both connected with the bar or rod to which the reciprocating motion is to be communicated, will accomplish this. Such an apparatus is represented in fig. ”

“ When energy has been stored in a fly-wheel, it can be withdrawn either as a small force acting over a great distance, or as a large force over a small distance. In the latter case the fly-wheel acts as a mechanical power, and in this form it is used in the very important machine to be next described. A model of the punching machine is shown in Fig. ”

“ Of the several parts of a machine, some are designed to move, while others are fixed; and of those which move, some have motions differing in quantity and direction from those of others. The several parts, whether fixed or movable, are subject to various strains and pressures, which they are intended to resist. These forces not only vary according to the load which the machine has to overcome, but also according to the peculiar form and structure of the machine itself. ”

“ When a cord is used to transmit a force from one direction to another, its stiffness renders some force necessary in bending it over the angle P, which the two directions form; and if the angle be sharp, the exertion of such a force may be attended with the rupture of the cord. ”

“ In Plate 5, Fig. 12, A X represents a Crank or Handle with a variable radius, the intent of which is to adapt a man’s strength to the velocity and intensity of any resistance he may have to overcome. The manner is this: B is a Screw pressing on the quadrant, and fixing the arm C X to any required angle with the part A C: thus determining the virtual radius of the handle. ”

“ Let it be required to find the vertical force which must act at the pitch radius of the last wheel t to balance exactly a force ƒs acting vertically downwards on the arm at the point indicated in the figure. The two links concerned are the last wheel t and the arm s, the wheel r being the fixed link of the mechanism. The virtual centres Ors, Ost are at the respective axes of the wheels r and t, and the centre Ort divides the line through these two points externally in the ratio of the train of wheels. ”