Kinematics

“ The term 'kinematic' is used when motion is considered abstractly without reference to force or mass. Kinetics is applied kinematics, or, as pointed out above, dynamics treated with kinematic concepts. ”

“ The lecture then proceeded to state the province of dynamics, to define its different parts, and to insist on the importance of kinematics, which was described as a purely geometrical subject, the geometry of motion, considerations from which entered into every dynamical problem. This distinction between dynamical and kinematical considerations—between those in which force is concerned and those into which enter only the idea of displacement in space and in time—is emphasised in Thomson and Tait's Natural Philosophy, which commences with a long chapter devoted entirely to kinematics. ”

“ 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. ”

“ The study of kinematics has been considered for nearly 80 years as a necessary part of the mechanical engineer's training, as the dozens of textbooks that have been published over the years make amply clear. ”

“ By kinematic synthesis is meant the designing of a linkage to produce a given series of motions for a particular purpose.
That a rational—numerical or geometrical—approach to kinematic synthesis is possible is a relatively recent idea, not yet fully accepted; but it is this idea that is responsible for the intense scholarly interest in the kinematics of mechanisms that has occurred in this country within the last 10 years. ”

“ If I have devoted more space to particular people and episodes than is warranted by their contributions to the modern treatment of the subject, it is because I have found that the history of kinematics of mechanisms, like the history of any other branch of engineering, is more interesting and more plausible if it is recognized that its evolutionary development is the result of human activity. ”

“ An abstract system of kinematics, under any geometrical arrangement or conception, is indeed quite irreconcilable with the actual system of dynamics found in nature and subject to our observation. All gases would under the operation of the first law of motion, tend to infinite and equable diffusion ”

“ I adhere to the term virtual mainly because the adjective effective is required in its usual meaning in kinematics to represent the resolved part of a force which acts obliquely to the line of motion, the effective force being the whole force multiplied by the cosine of the angle at which it acts with respect to the direction of motion. ”

“ 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. ”

“ Every time, however, that we have to choose between the useful and the useless, we are compelled to return from the abstract to the concrete. In the school, therefore, kine- matic science must frequently be connected with its practical applications it has not only to show what theoretical solution applies to problems already solved empirically, but in. most cases to construct the theory as well as to find it. It is remarkable that there is scarcely any kinematic problem, scarcely any turning, however bold, in the theoretical propositions, for which we cannot find an example in practice. ”

“ Every motion then which varies from the one intended will be a disturbing motion, and we therefore give beforehand to the parts which bear the latent forces—the bodies, that is, of which the machine is constructed,—such arrangement, form and rigidity that they permit each moving part to have one motion only, the required one. ”

“ 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. ”

“ 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. ”

“ These principles are demonstrated by a study of mechanisms already in existence, such as the linkage of a retractable landing gear, computing mechanisms, mechanisms used in an automobile, and the like. A systematic, if not rigorous, approach to the design of gears and cams also is usually presented in such a course. Until recently, however, no serious attempt was made to apply the principles developed in kinematic analysis to the more complex problem of kinematic synthesis of linkages. ”

“ The scholarly interest in a subject is fairly represented by the papers that are published in the transactions of professional societies and, more recently, by original papers that appear in specialized magazines. From 1900 to 1930 there were few papers on mechanisms, and most of those that did appear were concerned with descriptions of new "mechanical motions." ”

“ 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. ”

“ You are quite right; and the return of the ball, after having struck the wall, affords an example of what is termed reflected motion, upon which I shall have to remark when we come to the interesting subject of ‘Compound Forces;’ but at present, my only wish is to render the property of elasticity intelligible to you. It is a force of very extensive application; there is scarcely a machine wherein the elasticity of one or more solids is not essentially concerned. Nature, also, avails herself of this property to accomplish many of her purposes. ”

“ In the selection of the subjects, the question of practical utility has in many cases been regarded as the one of paramount importance. The elementary truths of Mechanics are too well known to admit of novelty, but it is believed that the mode of treatment which is adopted is more or less original. This is especially the case in the Lectures relating to friction, to the mechanical powers, to the strength of timber and structures, to the laws of motion, and to the pendulum. The illustrations, drawn from the apparatus, are nearly all original, and are beautifully executed. ”

“ Thus, it is a law of motion, discovered by experience, that the moment or force of any body in motion is in the compound ratio or proportion of its solid contents and its velocity; and consequently, that a small force may remove the greatest obstacle or raise the greatest weight, if, by any contrivance or machinery, we can increase the velocity of that force, so as to make it an overmatch for its antagonist. Geometry assists us in the application of this law, by giving us the just dimensions of all the parts and figures which can enter into any species of machine ”

“ It has been confounded, under the common name of Mechanics, with the other science, Mechanics Proper, or Machinery, which considers the effect of force transmitted by Mechanism from one part of a material combination to another. For example, the Mechanical Powers, as they are usually termed, (the Lever, the Wheel and Axle, the Inclined Plane, the Wedge, and the Screw,) have almost always been treated with reference to the relation between the Power and the Weight, and not primarily as a mode of changing the velocity and kind of the motion. ”

“ Action and reaction are equal, and in contrary directions. In all cases the quantity of motion gained by one body is always equal to that lost by the other in the same direction. Thus, if a ball in motion, strikes another at rest, the motion communicated to the latter will be taken from the former, and the velocity of the former be proportionately diminished.
Centre of Gravity.
Centre of Gravity,—is that point at which the whole weight of the body may be considered to act, and about which consequently, the body, when subjected to the force of gravity only, will balance in all positions. ”

“ Caroline. Yes; I have the most weight, he the greatest velocity; so that upon the whole our momentums are equal. But you said, Mrs. B., that the power should be greater than the resistance, to put the machine in motion; how then can the plank move if the momentums of the persons who ride are equal?
Mrs. B. Because each person at his descent touches and pushes against the ground with his feet; the reaction of which gives him an impulse which produces the motion; this spring is requisite to destroy the equilibrium of the power and the resistance, otherwise the plank would not move. ”

“ The principles of the science of Mechanics were discovered by observations made upon bodies within the reach of men; as we have seen in speaking of the discoveries of Stevinus, Galileo, and others, up to the time of Newton. And when there arose the controversy about vis viva (Chap. v. Sect. 2 of this Book) ;—namely, whether the “living force” of a body is measured by the product of the weight into the 537 velocity, or of the weight into the square of the velocity;—still the examples taken were cases of action in machines and the like terrestrial objects. ”

“ The rotatory motion prevented the sword from falling, just as you will hereafter find the spinning of the top will preserve it in an erect position. There is also another effect produced by rotatory motion, with which it is essential that you should become acquainted. You, no doubt, remember that momentum, or the velocity of a body, will compensate for its want of matter. A number of bodies, therefore, although incapable of balancing each other when in a state of rest, may be made to do so, by imparting to them different degrees of motion. ”

“ One and the same movement may vary in velocity, as in watching the ascent or descent of a projectile thrown up vertically. So different movements may present a difference of velocity as in the sequences of a ballet. Such contrasts plainly answer to the most favorable mode of expending motor energy. Again, our movement may be followed by another of different direction; that is to say, one that involves the action of fresh muscular elements, or a change in the relative amounts of action of two or more combining muscles. ”

“ 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. ”

“ Seymour; “viz. some exertion which is called Force; thus the force of my hand put your ball in motion; while gravitation was the force which made it fall to the earth; and I must, moreover, inform you, that a body always moves in the direction of the force which impels it, and with a velocity, or rate of motion, which is proportional to its degree, or strength; and, were there no other forces in action but that which originally produced the motion, the body would proceed onwards in a right line, and with a uniform velocity for ever.” ”

“ Hence it is the height that matters; none of the speed of the ball is destroyed unless it rises. If the second plane be made horizontal, the ball will thus run on for ever unless stopped by friction or some other applied force. This fundamental result, put into definite words by Newton, is known as the first law of motion, and is the foundation of the whole science of dynamics. ”

“ IN the sciences of Mechanics and Physical Astronomy, Motion and Force are the direct and primary objects of our attention. But there is another class of sciences in which we endeavor to reduce phenomena, not evidently mechanical, to a known dependence upon mechanical properties and laws. In the cases to which I refer, the facts do not present themselves to the senses as modifications of position and motion, but as secondary qualities, which are found to be in some way derived from those primary attributes. ”

“ To understand the principle of a mechanical power, we must revert to the doctrine of momentum. It will be remembered, that a small ball, weighing only two pounds, and moving at the rate of 500 feet in a second, will produce as much effect as a cannon ball of ten pounds in weight, provided it only moved at the rate of 100 feet in the same time; in like manner a ball weighing one pound may be made to balance another of five pounds, by placing it five times farther from the centre of motion ”