Mecaenas

“ While in appearance a machine differs greatly from any of the force- or motion-distributors of nature, yet for the theoretical or pure mechanician no such difference exists,—or rather it completely disappears on analysis, so that to him the problems of machinery fall into the same class as those of the mechanical phenomena of nature. He sees in both forces and motions existing, and subject to the same great laws which, developed in their most general form, govern and must govern every single case. In pure Mechanics machines are now treated only as illustrations ”

“ Many would not call the balance which we have just mentioned a machine, in consquence of the narrowness of the limits within which, its motion is confined; but force and motion are employed in it in exactly the same way as in other machines; it certainly ought there- fore to receive the same name. We may much rather say that the Engineer's measuring instruments, the theodolite, level and so on, are not machines. Here indeed mechanisms, in exactly the above de- scribed meaning, are used, and forces must be applied to these in just the way we have supposed in order that they may be used. ”

“ Two bodies, such for instance as a screw and nut, having such forms that at any instant there is only one possible motion for each relatively to the other, form the simplest combination available for machinal purposes—such bodies he calls a pair of elements. Two or more elements from as many different pairs can be combined into a link, and such links united into kinematic chains, and it is by fixing, that is, preventing the motion of, some one link of such a chain that a mechanism is obtained. ”

“ This shows within what distinct limits machine-problems lie, and that they allow themselves to be readily separated from the general problems of Mechanics, as we have already maintained.
While the science of Mechanics examines motion caused in the most general cases by the action of mechanical forces, Machine-mechanics occupies itself with certain special cases only, with motions produced by a limited circle of means. It draws its first laws from the same fountain as Mechanics, to which, as the more comprehensive science, it is subordinate. ”

“ In 1841 he published his ‘Principles of Mechanism.’ In this work he reduced the study of what he called pure mechanism to a system. It is the earliest attempt to develop, with anything like completeness, the science of machines considered from the kinematic point of view, without reference to the forces which are at work or to the energy which is transmitted. A machine, according to him, is a contrivance for producing a specific relation between the motions of one of its parts and another. ”

“ Whilst in the first system, which we may call kosmical, the external measurable mechanical forces are opposed by similar external forces, in the second, the machine system, there are opposed to all external forces others concealed in the interior of the bodies forming the system, and appearing there,—and acting in exactly the required manner,—in consequence of the action of the external forces. ”

“ In practical mechanics, however, it is at least very rarely that the momentum of bodies is in any degree an object of consideration: the strength of machinery being in every case to be adapted to the quantitas motrix, and the extent and value of the effect to be produced depending upon the quantitas mechanica of the force applied, or in other words to the space through which a given vis motrix is exerted. ”

“ We have already seen how a mechanism becomes a machine. In its complete form the machine consists of one or more mecha- nisms, which can, in the way we have already pointed out, be separated into kinematic chains, and these again into pairs of elements. This separation is the analysis of the machine, the investigation of its kinematic contents, arranged in mechanisms, kinematic chains, and pairs of elements. ”

“ The prevention of disturbing motions by latent forces is then a principle in the machine. Its application is connected with various objects. When a machine is constructed it is meant to be an arrangement for carrying on some definite mechanical work—it may be the moving of some body, or the alteration of its form, or both together. For such a purpose we require that so soon as motion is caused by any effort in any part of the machine that motion shall be of an absolutely defined nature. ”

“ But to treat of Mechanics is not my present business. I was only willing to show by those examples the great extent and certainty of the third Law of motion. For if we estimate the action of the agent from its force and velocity conjunctly; and likewise the reaction of the impediment conjunctly from the velocities of its several parts, and from the forces of resistance arising from the attrition, cohesion, weight, and acceleration of those parts; the action and re-action in the use of all sorts of Machines will be found always equal to one another. ”

“ The modification of motion and the modification of force take place together, and are connected by certain laws; but in the study of the theory of machines, as well as in that of pure mechanics, much advantage has been gained in point of clearness and simplicity by first considering alone the principles of the modification of motion, which are founded upon what is now known as Kinematics, and afterwards considering the principles of the combined modification of motion and force, which are founded both on geometry and on the laws of dynamics. ”

“ Every military engineer who had watched the flight of a projectile was aware that the received notions of mechanics would not explain its motions. No theory of the impact of such projectiles had even been proposed. A whole science was to be created. The doctrine of mechanical equilibrium is statics—and this science was founded by Archimedes. The doctrine of mechanical motion is dynamics—and nothing was done in this science till the time of Galileo. ”

“ I have thought it necessary to do, because, if I mistake not, I see almost all mechanics deceiving themselves in the belief that, by the help of a machine, they can raise a greater weight than they are able to lift by the exertion of the same force without it.—Now if we take any determinate weight, and any force, and any distance whatever, it is beyond doubt that we can move the weight to that distance by means of that force ”

“ Energy distributed between two Bodies: Projection and Propulsion.—Hitherto the effort by which a machine is moved has been treated as a force exerted between a movable body and a fixed body, so that the whole energy exerted by it is employed upon the movable body, and none upon the fixed body. This conception is sensibly realized in practice when one of the two bodies between which the effort acts is either so heavy as compared with the other, or has so great a resistance opposed to its motion, that it may, without sensible error, be treated as fixed. ”

“ When the nature and properties of the mechanic powers and other machines have been explained, the force of these observations will be more distinctly perceived. The effects of props and fixed points in sustaining a part of the weight, and sometimes the whole, both of the weight and power, will then be manifest, and every machine will furnish a verification of the remarkable proportion between the velocities of the weight and power, which has enabled us to explain what might otherwise be paradoxical and difficult of comprehension. ”

“ One train of mechanism may diverge into two or more—as when a single shaft, driven by a prime mover, carries several pulleys, each of which drives a different machine. The principles of comparative motion in such converging and diverging trains are the same as in simple trains.
Division 6.—Aggregate Combinations.
§ 72. General Principles.—Willis designated as “aggregate combinations” those assemblages of pieces of mechanism in which the motion of one follower is the resultant of component motions impressed on it by more than one driver. ”

“ It is indeed astonishing to how small a depth the methods hitherto used have penetrated into their real nature, and how incompletely known therefore are most of the mechanisms in common use. To the thorough, thoughtful mechanician who looks at his work as a serious matter, a scientific investigation of the Kinematics of Machinery will in this respect be specially valuable. It will relieve him of the minute and often worrying search after solutions of his problems by rendering it possible for him to work systematically. ”

“ Well over a century later we still are nibbling at the fringes of the problem. Willis did, nonetheless, give the thoughtful reader a glimpse of the most powerful tool for kinematic synthesis that has yet been devised; namely, kinematic analysis, in which the argument is confined to the relative displacements of points on links of a mechanism, and through which the designer may grasp the nature of the means at his disposal for the solution of any particular problem. ”

“ 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. ”

“ Commencing with the generalization that " a mechanical force, or the cause of a mechanical motion, we know to be in general the condition of a difference of pressure," he infers, "hence it appears that if a general mechanical theory is possible, the ultimate property of matter must be conceived to be a mutual repulsion of its parts, and the indubitable Newtonian law of universal attraction be deduced herefrom, under the actual conditions of the world. ”

“ When the axis is that of greatest pressure, the force along the axis will be a pressure. When the axis is that of least pressure, the force along the axis will be a tension.
If we observe the lines of force between two magnets, as indicated by iron filings, we shall see that whenever the lines of force pass from one pole to another, there is attraction between those poles; and where the lines of force from the poles avoid each other and are dispersed into space, the poles repel each other, so that in both cases they are drawn in the direction of the resultant of the lines of force. ”

“ It is obvious that this mechanical improvement is especially applicable wherever cycles occur in the mathematical operations, and that, in preparing data for calculations by the engine, it is desirable to arrange the order and combination of the processes with a view to obtain them as much as possible symmetrically and in cycles, in order that the mechanical advantages of the backing system may be applied to the utmost. It is here interesting to observe the manner in which the value of an analytical resource is met and enhanced by an ingenious mechanical contrivance. ”

“ The sciences we have been considering under the general name of mechanics, which is derived from a Greek word that means to contrive, invent, construct, have much to do with machinery, with the methods of construction, the propelling forces, and the phenomena produced. There were machinists and some simple machines propelled by human or brute force, by weights and springs, by falling or running water, and air in motion before the laws of motion and forces were understood, or the rude mechanic arts began to assume the character of a science. ”

“ Even if it were supposed that the function of the science did not extend beyond arranging the mechanisms in classes, still their division cannot be made according to the changes of motion, for this would necessitate endless repetitions. Almost all mechanisms might be looked for, and might also be placed, in at least two such classes, and most in from four to six or even ten to fifteen, for they can be used, and in practice are actually employed, for just so many different kinds of change. ”

“ In a machine of which each piece is to move with a uniform velocity, if the effort and the resistance be constant, the weight of each piece must be balanced on its axis, so that it may produce lateral pressure only, and not act as a reciprocating force. ”

“ No mechanical contrivance, no mechanism furnishes any power, but is only a means of applying power; and, even if the term mechanical embraces all the phenomena of matter in motion, we still have the question as to whether the mechanism or the matter moves by its own power, or is moved by the effort of some intelligent being. ”

“ 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. ”

“ As little as one examines the conditions of equilibrium in the lever and in other machines, it is easy to recognize this law, that the weight and the force are always in inverse ratio to the spaces that the one and the other can travel through in the same time. ”