Machine

are either simple or compound: the simple ones are the seven mechanical powers, viz. lever, balance, pully, axis, and wheel, screw, and inclined plane. See Mechanical Powers. If the given power is not able to overcome the given resistance when directly applied, that is, when the power applied is le than the weight or resonance given; then the thing is to be performed by the help of a machine , made with levers, wheels, pullies, screws, . so adjusted, that when the weight and power are put in motion on the machine , the velocity of the power may be at least so much greater than that of the weight, as the weight and friction of the machine , taken together, is greater than the power; for on this principle depends the mechanism or contrivance of all mechanical engines used to draw or raise heavy bodies, or overcome any other force; the whole design of these being to give such a velocity to the power, in respect of the weight, as that the momentum of the power may exceed the momentum of the weight: for if machines are so contrived, that the velocity of the agent and resistant are reciprocally as their forces, the agent will just sustain the resistant, but with a greater degree of velocity will overcome it. So that if the exce of motion or velocity in the power is so great as to overcome all that resistance which commonly arises from the friction or attraction of contiguous bodies, as they slide by one another, or from the cohesion of bodies that are to be separated, or from the weights of bodies that are to be raised: the exce of the force remaining, after all these resistances are overcome, will produce an acceleration of motion thereto, as well in the parts of the machine , as in the resisting body. Compound Machines , are formed by various combinations, and serve for different purposes; in all which the same general law takes place, viz. that the power and weight sustain each other, when they are in the inverse proportion of the velocities they would have in the directions wherein they act, if they were put in motion. Now, to apply this law to any compound machine , there are four things to be considered: 1. The moving power, or the force that puts the machine in motion; which may be either men or other animals, weights, springs, the wind, a stream of water, . 2. The velocity of this power, or the space it moves over in a given time. 3. The resistance, or quantity of weight to be removed. 4. The velocity of this weight, or the space it moves over in the same given time. The two first of these quantities are always in the reciprocal proportion of the two last; that is, the product of the first two must always be equal to that of the last; hence, three of these quantities being given, it is easy to find the fourth; for example, if the quantity of the power be 4, its velocity 15, and the velocity of the weight 2, then the resistance, or quantity of the weight, will be equal to 4 × 15 2 = 60 2 = 30. The following rules will direct the mechanic how he may contrive his machine , that it may answer the intended purpose, to the best advantage. 1. Having a igned the proportion of your power, and the weight to be raised, the next thing is to consider how to combine levers, wheels, pullies, . so that working together they may be able to give a velocity to the power, which shall be to that of the weight something greater than in the proportion of the weight to the power. This done, you must estimate your quantity of friction; and if the velocity of the power be to that of the weight still in a greater proportion than the weight and friction taken together are to the power; then your machine will be able to raise the weight. And note, this proportion must be so much greater, as you would have your engine work faster. 2. But the proportion of the velocity of the power and weight must not be made too great: for it is a fault to give a machine too much power, as well as too little; for if the power can raise the weight and overcome the resistance, and the engine perform its proper effect in a convenient time and work well, it is sufficient for the end proposed; and it is in vain to make additions to the engine to increase the power any farther; for that would not only be a needle expence, but the engine would lose time in working. 3. As to the power applied to work the engine, it may either be a living power, as men, horses, . or an artificial power, as a spring, . or a natural power, as wind, water, fire, weights, . When the quantity of the power is known, it matters not, as to the effect, what kind of power it is; for the same quantity of any sort will produce the same effect; and different sorts of powers may be applied in an equal quantity a great variety of ways. The most easy power applied to a machine is weight, if it be capable of effecting the thing designed. If not, then wind, water, . if that can be conveniently had, and without much expence. A spring is also a convenient moving power for several machines : but it never acts equally as the weight does; but is stronger when much bent, than when but a little bent, and that in proportion to the bending, or the distance it is forced to; but springs grow weaker by often bending or remaining long bent: yet they recover part of their strength by lying unbent. The natural powers, wind and water, may be applied to vast advantage in working great engines, when managed with skill and judgment.—The due application of these has much abridged the labors of men; for there is scarce any labor to be performed, but an ingenious artificer can tell how to apply these powers to execute his design, and answer his purpose; for any constant motion being given, it may, by due application, be made to produce any other motions we desire. Therefore these powers are the most easy and useful, and of the greatest benefit to mankind. Besides, they cost nothing, and do not require any repetition nor renewing, like a weight or a spring, which require to be wound up. When these cannot be had, or cannot serve our end, we have recourse to some living power, as men, horses, . 4. Men may apply their strength several ways in working a machine . A man of ordinary strength, turning a roller by the handle, can act for a whole day against a resistance equal to 30 pounds weight; and if he works ten hours in a day, he will raise a weight 30lb. 3¹⁄₂ feet in a second; or if the weight be greater, he will raise it so much le in proportion. But a man may act, for a small time, against a resistance of 50lb. or more. If two men work at a windla or roller, they can more easily draw up 70lb. than one man 30lb. provided the elbow of one of the handles be at right angles to that of the other: and with a fly or heavy wheel applied to it, a man may do ¹⁄₃d part more work; and for a little while act with a force, or overcome a continual resistance of 80lb. and work a whole day when the resistance is but 40lb. Men used to carrying weighty burdens, such as porters, will carry some 150lb. others 200lb. or 250lb. according to their strength. A man can draw but about 70 or 80lb. horizontally; for he can but apply half his weight. If the weight of a man be 140lb. he can act with no greater force in thrusting horizontally, at the height of his shoulders, than 27lb. A horse draws to greatest advantage, when the line of direction is a little elevated above the horizon, and the power acts against his breast: and can draw 200lb. for eight hours in a day, at two miles and an half an hour. If he draws 240lb. he can work but six hours, and not quite so fast; and, in both cases, if he carries some weight he will draw better than if he carried none. And this is the weight a horse is supposed to be able to draw over a pully out of a well. In a cart a horse may draw 1000lb. The most force a horse can exert is when he draws something above a horizontal direction. The worst way of applying the strength of a horse, is to make him draw or carry up a hill: and three men with 100lb. on their backs, will climb up a steep hill faster than a horse with 300lb. A round walk for a horse to draw in at a mill, . should not be le than 40 feet diameter. 5. Every machine should be made of as few parts, and those as simple as po ible, to answer its purpose; not only because the expence of making and repairing will be le , but it will also be le liable to be put out of order. 6. If a weight is to be raised but a very little way, the lever is the most simple, easy, and ready machine; or, if the weight be very great, the common screw is most proper; but if the weight is to be raised a great way, the wheel and axle is a proper power, but blocks and pullies render the labor still more easy: the same may be done by the perpetual screw. Great wheels, to be wrought by men or cattle, are of most use and convenience when their axles are perpendicular to the horizon; but if by water, . then it is best to have their axles horizontal. 7. As to the combination of simple machines to make a compound one, though the lever when simple cannot raise a weight to any great height, and in this case is but of little service; yet it is of great use when compounded with others. Thus the spokes of a great wheel are all levers perpetually acting; and a beam fixed to the axis to draw the wheel about by men or horses, is a lever. The lever also may be combined with the screw, but not conveniently with pullies or with the wedge. The wheel and axle is combined to great advantage with pullies: but the perpetual screw, with the wheel is very serviceable. The wedge cannot be combined with any other mechanical power; and it only performs its effect by percu ion; but this force of percu ion may be increased by engines. Pullies may be combined with pullies, and wheels with wheels. Therefore if any single wheel would be too large, and take up too much room, it may be divided into two or three more wheels and trundles, or wheels and pinions, as in clock work, so as to have the same power, and perform the same effect. In wheels with teeth, the number of teeth that play together in two wheels, should be prime to each other, that the same teeth may not meet at every revolution: for when different teeth meet, they by degrees wear themselves into a proper figure: therefore they should so be contrived that the same teeth meet as seldom as po ible. 8. The strength of every part of the machine should be made proportional to the stre it is to bear: and therefore let every lever be made so much stronger, as its length and the weight it is to support are greater; and let its strength diminish proportionally from the fulcrum, or point where the greatest stre is to each end. The axles of wheels and pullies must be so much stronger as they are to bear greater weight. The teeth of wheels, and the wheels themselves, which act with greater force, must be proportionally stronger; and in any combination of wheels and axles, make their strength diminish gradually from the weight to the power, so that the strength of every part be reciprocally as its velocity. The strength of ropes must be according to their tension; that is, as the squares of their diameters: and, in general, whatever parts a machine is composed of, the strength of every particular part of it must be adjusted to the stre upon the whole; therefore in square beams the cubes of the diameters must be made proportional to the stre they bear: and let no part be stronger or bigger than is nece ary for the stre upon it; not only for the ease and well going of the machine , but for diminishing the friction; for all superfluous matter in any part of it, is a dead weight upon the machine, and serves only to impede its motion: hence he is the most perfect mechanic, who not only adjusts the strength to the stre , but who also contrives all the parts to last equally well, so that the whole machine may fall together. 9. To have the friction as little as po ible, the machine should be made of the fewest and simplest parts. The diameters of the wheels and pullies should be large, and the diameters of the arbors or spindles they run on, as small as can be consistent with their strength. All ropes and cords must be as pliable as po ible, and for that end rubbed with tar or grease: the teeth of wheels must be made to fit and fill up the openings, and cut into the form of epicycloids. All the axles, where the motion is, and all teeth where they work, and all parts that in working rub upon one another, must be made smooth: and when the machine goes, must be oiled or greased. 10. When any motion is to be long continued, contrive the power to move or act always one way, if it can be done, for this is better and easier performed than when the motion is interrupted, and the power is forced to move first one way, and then another; because every change of motion requires a new additional force to effect it. Besides, a body in motion cannot suddenly receive a contrary motion, without great violence: and the moving any part of the machine contrary ways by turns, with sudden jerks, tends only to shake the machine to pieces. 11. In a machine that moves always one way, endeavor to have the motion uniform. 12. But when the nature of the thing requires that a motion is to be suddenly communicated to a body, or suddenly stopped: to prevent any damage or violence to the engine by a sudden jolt, let the force act against some spring, or beam of wood, which may supply the place of a spring. 13. In regard to the size of the machine , let it be made as large as it can conveniently; the greater the machine, the more exact it will work, and perform all its motions the better; for there will always be some errors in the making, as well as in the materials, and consequently in the working of the machine . The resistance of the medium in some machines has a sensible effect; but all these mechanical errors bear a le proportion in the motion of great machines, than in that of little ones; being nearly reciprocally as their diameters, supposing they are made of the same matter, and with the same accuracy, and are equally well finished. 14. For engines that go by water, it is nece ary to measure the velocity, drop in pieces of sticks, . and observe how far they are carried in a second, or any given time. But if it flows through a hole in a reservoir, or standing receptacle of water, the velocity will be found from the depth of the whole below the surface. Thus let s = 16¹⁄₁₂; v = velocity of the fluid per second; B = the area of the hole; H = the height of the water; all in feet. Then the velocity of v = √ 2 s H ; and its force = the weight of the quantity vv 2 s B or H B of water, or = 62¹⁄₂ 112 H B hundred weight: because a cubic foot = 62¹⁄₂ lb. avoirdup. Also a hogshead is about 8¹⁄₂ feet, or 531lb. and a tun is 4 hogsheads. When you have but a small quantity of water, you must contrive it to fall as high as you can, to have the greater velocity, and consequently more force upon the engine. 15. If water is to be conveyed through pipes to a great distance, and the descent be but small, much larger pipes must be used because the water will come slow. Water should not be driven through pipes faster than four feet per second, by reason of the friction of the tubes; nor should it be too much wire-drawn, that is, squeezed through smaller pipes, for that creates a resistance, as water-way is le in narrow pipes. 16. When any thing is to be performed by a water-wheel, moved by the water running under it and striking the paddles or ladle-boards, the channel it moves in ought to be something wider than the hole of the adjutage, and so close to the floats on every side as to let little or no water pa ; and when past the wheel, to open a little, that the water may spread. It is of no advantage to have a great number of floats or paddles; for those past the perpendicular are resisted by the back water, and those before it are struck obliquely. The greatest effect that such a wheel can perform, in communicating any motion, is when the paddles of the wheel move with one-third the velocity of the water; in which case, the force upon the paddle is four-ninths only; supposing the absolute force of the water against the paddle, when the wheel stands still, to be 1: so that the utmost motion which the wheel can generate, is but ⁴⁄₂₇ths of that which the force of the water against the paddles at rest would produce.