MECHANIC
, or Mechanical, something relating to Mechanics, or regulated by the nature and laws of motion.
Mechanical is also used in Mathematics, to signify a construction or proof of some problem, not done in an accurate and geometrical manner, but coarsely and unartfully, or by the assistance of instruments; as are most problems relating to the duplicature of the cube, and the quadrature of the circle.
Mechanical Assections, such properties in matter, as result from their figure, bulk, and motion.
Mechanical Causes, are such as are founded on Mechanical Affections.
Mechanical Curve, called also Transcendental, is one whose nature cannot be expressed by a finite Algebraical equation.
Mechanical Philosophy, also called the Corpuscular Philosophy, is that which explains the phenomena of nature, and the operations of corporeal things, on the principles of Mechanics; viz, the motion, gravity, figure, arrangement, disposition, greatness,| or smallness of the parts which compose natural bodies.
Mechanical Solution, of a Problem, is either when the thing is done by repeated trials, or when the lines used in the solution are not truly geometrical, or by organical construction.
Mechanical Powers, are certain simple machines which are used for raising greater weights, or overcoming greater resistances than could be effected by the natural strength without them.
These simple machines are usually accounted fix in number, viz, the Lever, the Wheel and Axle, or Axis in Peritrochio, the Pulley, the Inclined Plane, the Wedge, and the Screw. Of the various combinations of these simple powers do all engines, or compound machines, consist: and in treating of them, so as to settle their theory and properties, they are considered as mathematically exact, or void of weight and thickness, and moving without friction. See the properties and demonstrations of each of these under the several words Lever, &c. To which may be added the following general observations on them all, in a connective way.
1. A Lever, the most fimple of all the mechanic powers, is an engine chiefly used to raise large weights to small heights; such as a handspike, when of wood; and a crow, when of iron. In theory, a lever is considered as an inslexible line, like the beam of a balance, and subject to the fame proportions; only that the power applied to it, is commonly an animal power; and from the different ways of ufing it, or applying it, it is called a lever of the first, second, or third kind: viz, of the 1st kind, when the weight is on one side of the prop, and the power on the other; of the 2d kind, when the weight is between the prop and the power; and of the 3d kind, when the power is between the prop and the weight.
Many of the instruments in common use, are levers of one of the three kinds; thus, pincers, sheers, forceps, snuffers, and such like, are compounded of two levers of the first kind; for the joint about which they move, is the fulcrum, or centre of motion; the power is applied to the handles, to press them together; and the weight is the body which they pinch or cut. The outting knives used by druggists, patten-makers, blockmakers, and some other trades, are levers of the 2d kind: for the knife is fixed by a ring at one end, which makes the fulcrum, or fixed point; the other <*>nd is moved by the hand, or power; and the body to be cut, or the resistance to be overcome, is the weight. Doors are levers of the 2d kind; the hinges being the centre of motion; the hand applied to the lock is the power; while the door or weight lies between them. A pair of bellows consists of two levers of the 2d kind; the centre of motion is where the ends of the boards are fixed near the pipe; the power is applied at the handles; and the air pressed out from between the boards, by its resistance, acts against the middle of the boards like a weight. The oars of a boat are levers of the 2d kind: the fixed point is the blade of the oar in the water; the power is the hand acting at the other end; and the weight to be moved is the boat. And the same of the rudder of a vessel. Spring sheers and tongs are levers of the 3d kind; where the centre of motion is at the bow-spring at one end; the weight or resistance is acted on by the other end; and the hand or power is applied between the ends. A ladder reared by a man against a wall, is a lever of the 3d kind: and so are also almost all the bones and muscles of animals.
In all levers, the effect of any power or weight, is both proportional to that power or weight, and also to its distance from the centre of motion. And hence it is that, in raising great weights by a lever, we chuse the longest levers; and also rest it upon a point as far from the hand or power, and as near to the weight, as possible. Hence also there will be an equilibrium between the power and weight, when those two products are equal, viz, the power multiplied by its distance, equal to the weight multiplied by its distance; when, also, the weight and power are to each other reciprocally as their distances from the prop or fixed point.
2. The Axis in Peritrochio, or Wheel and Axle, is a simple engine consisting of a wheel fixed upon the end of an axle, so that they both turn round together in the same time. This engine may be referred to the lever: for the centre of the axis, or wheel, is the fixed point; the radius of the wheel is the distance of the power, acting at the circumference of the wheel, from that point; and the radius of the axle is the distance of the weight from the same point. Hence the effect of the power, independent of its own natural intensity, is as the radius of the wheel; and the effect of the weight is as the radius of the axle: so that the two will be in equilibrio, when the two products are equal, which are made by multiplying each of these, the weight and power, by the radius, or distance at which it acts; and then also, the weight and power are reciprocally proportional to those radii.
In practice, the thickness of the rope, that winds upon the axle, and to which the weight is fastened, is to be considered: which is done, by adding half its thickness to the radius of the axis, for its distance from the fixed point, when there is only one fold of rope upon the axle; or as many times the thickness as there are folds, wanting only one half when there are several folds of the rope, one over another: which is the reafon that more power must be applied when the axis is thus thickened; as often happens in drawing water from a deep and narrow well, over which a long axle cannot be placed.
If the rope to which the power is fastened, be successively applied to different wheels, whose diameters are larger and larger; the axis will be turned with still more and more ease, unless the intensity of the power be diminished in the same proportion; and if so, the axis will always be drawn with the same strength by a power continually diminishing. This is practised in spring clocks and watches; where the spiral spring, which is strongest in its action when first wound up, draws the fuzee, or continued axis in peritrochio, first by the smaller wheels, and as it unbends and becomes weak, draws at the larger wheels, in such manner that the watch work is always carried round with the same force.
As a very small axis would be too weak for very great weights, or a large wheel would be expensive as| well as cumbersome, and take more room than perhaps can be spared for it; therefore, that the action of the power may be increased, without incurring either of those inconveniences, a compound Axis in Peritrochio is used, which is effected by combining wheels and axles by means of pinions, or small wheels, upon the axles, the teeth of which take hold of teeth made in the large wheels; as is seen in clocks, jacks, and other compound machines. And in such a combination of wheels and axles, the effect of the power is increased in the ratio of the continual product of all the axles, or small wheels, to that of all the large ones. Thus, if there be two small wheels and an axle, turning three large wheels; the axle being 2 inches diameter, and each of the small wheels 4 inches, while the large ones are 2 feet or 24 inches diameter; then is the continual product of the small diameters, and is that of the large ones; therefore 13824 to 32, or 432 to 1, is the ratio in which the power is increased: and if the power be a man, whose natural strength is equal, suppose, to 150 pounds weight, then , or 28 ton 18 cwt 64lb, is the weight he would be able to balance, suspended about the axle.
3. A Single Pulley, is a small wheel, moveable round an axis, called its centre pin; which of itself is not properly one of the mechanical powers, because it produces no gain of power; for, as the weight hangs by one end of the cord that passes over the pulley, and the power acts at the other end of the same, these act at equal distances from the centre or axis of motion, and consequently the power is equal to the weight when in equilibrio. So that the chief use of the single pulley is to change the direction of the power from upwards to downwards, &c, and to convey bodies to a great height or distance, without a person moving from his place.
But by combining several single pulleys together, a considerable gain of power is made, and that in proportion to the additional number of ropes made to pass over them; and yet it enjoys at the same time the properties of a single pulley, by changing the direction of the action in any manner.
4. The Inclined Plane, is made by planks, bars, or beams, laid aslope; by which, large and heavy bodies may be more easily raised or lowered, by sliding them up or down the plane; and the gain in power is in proportion as the length of the plane to its height, or as radius to the sine of the angle of inclination of the plane with the horizon.
In drawing a weight up an inclined plane, the power acts to the greatest advantage, when its direction is parallel to the plane.
5. The Wedge, which resembles a double inclined plane, is very useful to drive in below very heavy weights to raise them but a small height, also in cleaving and splitting blocks of wood, and stone &c; and the power gained, is in proportion of the slant side to half the thickness of the back. So that, if the back of a wedge be 2 inches thick, and the side 20 inches long, any weight pressing on the back will balance 20 times as much acting on the side. But the great advantage of a wedge lies in its being urged, not by pressure, but usually by percussion, as the blow of a hammer or mallet; by which means a wedge may be driven in below, and so be made to lift, almost any the greatest weight, as the largest ship, by a man striking the back of a wedge with a mallet.
To the wedge may be referred the axe or hatchet, the teeth of saws, the chisel, the augur, the spade and shovel, knives and swords of all kinds, as also the bodkin and needle, and in a word all sorts of instruments which, beginning from edges or points, become gradually thicker as they lengthen; the manner in which the power is applied to such instruments, being different according to their different shapes, and the various uses for which they have been contrived.
6. The Screw, is a kind of perpetual or endless Inclined Plane; the power of which is still farther assisted by the addition of a handle or lever, where the power acts; so that the gain in power, is in the proportion of the circumference described or passed through by the power, to the distance between thread and thread in the screw.
The uses to which the screw is applied, are various; as, the pressing of bodies close together; such as the press for napkins, for bookbinders, for packers, hotpressers, &c.
In the screw, and the wedge, the power has to overcome both the weight, and also a very great friction in those machines; such indeed as amounts sometimes to as much as the weight to be raised, or more. But then this friction is of use in retaining the weight and machine in its place, even after the power is taken off.
If machines or engines could be made without friction, the least degree of power added to that which balances the weight, would be sufficient to raise it. In the lever, the friction is little or nothing; in the wheel and axle, it is but small; in pulleys, it is very considerable; and in the inclined plane, wedge, and screw, it is very great.
It is a general property in all the Mechanic powers, that when the weight and power are regulated so as to balance each other, in every one of these machines, if they be then put in motion, the power and weight will be to each other reciprocally as the velocities of their motion, or the power is to the weight as the velocity of the weight is to the velocity of the power; so that their two momenta are equal, viz, the product of the power multiplied by its velocity, equal to the product of the weight multiplied by its velocity. And hence too, universally, what is gained in power, is lost in time; for the weight moves as much slower as the power is smaller.
Hence also it is plain, that the force of the power is not at all increased by engines; only the velocity of the weight, either in lifting or drawing, is so diminished by the application of the instrument, as that the momentum of the weight is not greater than the force of the power. Thus, for instance, if any force can raise a pound weight with a given velocity, it is impossible by any engine to raise 2 pound weight with the same velocity: but by an engine it may be made to raise 2 pound weight with half the velocity, or even 1000 times the weight with the 1000th part of the velocity.|
See Maclaurin's Account of Newton's Philos. Difcov. book 2, chap. 3; Hamilton's Philos. Ess. 1; Philos. Trans. 53, pa. 116; or Landen's Memoirs, vol. 1, pa. 1.
