Mechanics is the science which treats of the effect of forces upon the form or motion of bodies.


The science of mechanics is divided into statics and dynamics. When the forces which act on a body are so balanced as to cause no change in its motion, the problem of finding the relations of these forces falls under the division of statics. When the forces which act on a body cause some change in its motion, the problem of finding the relation of the forces to the mass of the body and to the change of its motion falls under the division of dynamics. The division of dynamics is frequently called kinetics.

Machines are arrangements receiving work from some outside source of supply, which work is modified by the machine and delivered in some form more suitable for the purpose required. A machine is an instrument or apparatus by which a force applied at a certain point, and having a certain determinate intensity and direction, is made to exert a force at another point, more or less distant from the former, and generally different in intensity and direction. Thus, for example, a horse moving on a horizontal road in a circle is made to raise a weight vertically in the shaft of a mine, or water from the shaft of a well. Men pulling at a rope in some direction more or less oblique are enabled to raise a mass of heavy matter from the hold of a ship, and to transfer it to an adjacent wharf. The Mechanical Advantage of a machine is the ratio of two forces. The efficiency of any machine is measured by the ratio of energy actually given out as useful work to the energy supplied.

KISS principles

Everything is a spring

Everything is a spring. Everything. No exceptions.

Project planning follows the rule of pi.

Take how much time you think you can complete something in, multiply it by pi, and that will be the actual length of time it takes.

Parkinson’s Law

Work expands so as to fill the time available for its completion. The amount of time in which one has to perform a task is the amount of time it will take to complete said task. Don’t give too much time for a project or it will never get done. The demand upon a resource tends to expand to match the supply of the resource. The reverse is not true.

Document everything

Justify your design, especially on collaborative projects

Design is an iterative process

The necessary number of iterations is one more than the number you have currently done. This is true at any point in time. Design for disassemble and assembly. Design for the Tesla Principle.

Ask questions

If you don’t know something, say so.

Understand capitalism and business

Don’t work for free (unless you really want to) and don’t work without a contract. Products selling are not necessarily technologically superior.

Design is based on requirements

One bit “Better” than requirements is the enemy of "Good" enough. 'Get 'er done', then go play.

Engineering takes numbers

Analytic principles and processes of properties and state of systems, devices or mechanisms take numbers. Design takes numbers, but is not numbers only.

Simple machines

That branch of the sciences, which treats of motion, and developes the effects of powers or moving forces, so far as they are applied to engines. Mechanical powers are certain simple instruments employed for raising greater weights, or overcoming greater resistance, than, without their aid, could be effected by mere natural strength. The classes of simple machines denominated mechanic powers, have relation chiefly to the peculiar principle which determines the action of the power on the weight or resistance. In explaining this arrangement various other reflections have been incidentally mixed up with our investigations; yet still much remains to be unfolded before the student can form a just notion of those means by which the complex machinery used in the arts and manufactures so effectually attains the ends, to the accomplishment of which it is directed.

By a power of a given energy to oppose a resistance of a different energy, or by a moving principle having a given velocity to generate another velocity of a different amount, is only one of the many objects to be effected by a machine. In the arts and manufactures the kind of motion produced is generally of greater importance than its rate. The latter may affect the quantity of work done in a given time, but the former is essential to the performance of the work in any quantity whatever. In the practical application of machines, the object to be attained is generally to communicate to the working point some peculiar sort of motion suitable to the uses for which the machine is intended; but It rarely happens that the moving power has this sort of motion. Hence, the machine must be so contrived that, while that part on which this power acts is capable of moving in obedience to it, its connection with the other parts shall be such that the working point may receive that motion which is necessary for the purposes to which the machine is applied.

To give a perfect solution of this problem it would be necessary to explain, first, all the varieties of moving powers which are at our disposal; secondly, all the variety of motions which it may be necessary to produce; and, thirdly, to show all the methods by which each variety of prime mover may be made to produce the several species of motion in the working point. It is obvious that such an enumeration would be impracticable, and even an approximation to it would be unsuitable to the present treatise. Nevertheless, so much ingenuity has been displayed in many of the contrivances for modifying motion, and an acquaintance with some of them is so essential to a clear comprehension of the nature and operation of complex machines, that it would be improper to omit some account of those at least which most frequently occur in machinery, or which are most conspicuous for elegance and simplicity.

The varieties of motion which most commonly present themselves in the practical application of mechanics may be divided into rectilinear and rotatory. In rectilinear motion the several parts of the moving body proceed in parallel straight lines with the same speed. In rotatory motion the several points revolve round an axis, each performing a complete circle, or similar parts of a circle, in the same time.

Each of these may again be resolved into continued and reciprocating. In a continued motion, whether rectilinear or rotatory, the parts move constantly in the same direction, whether that be in parallel straight lines, or in rotation on an axis. In reciprocating motion the several parts move alternately in opposite directions, tracing the same spaces from end to end continually.

Implemented machines

Simple achines are seven in number, viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, the Screw, and the Funicular Machine.

The Lever
Any inflexible rod, bar, or beam which serves to raise weights, while it is supported at a point called the fulcrum or prop, which is the centre of motion. There axe four kinds of levers. The first, is that in which the rod is supported in some part of its length by a. fulcrum, and the moving and resisting bodies are at the opposite extremities; of this kind are, balances, scales, crows, handspikes, scissors, and pincers. The second, is that which has the weight between the moving power and the fulcrum; such as, oars, rudders, and cutting knives which are fixed at one end. The third, is that in which one end rests on the fulcrum, the resistance is at the other end, and the moving power is in some part of the intermediate length; this is exemplified in tongs, the bones and muscles of animals, and men raising a scaling ladder; in this latter instance, the ground is the fulcrum, the weight of the ladder the resistance, and the men raising it the moving power. The fourth kind, called the bended lever, resembles the first, excepting that the rod is bent for convenience, and that the fulcrum is at the angular point; for instance, a hammer drawing a nail. The levers are supposed to be void of gravity or weight, or their arms to be in equilibrio before the weights are applied. The moving and resisting powers are supposed in all cases, to act perpendicularly to the length of the arms of the levers to which they are applied.

Wheel and Axle
The cord by which the power acts, is placed about the circumference of the wheel, while that of the weight goes round its axle, or round a smaller wheel attached to the larger, and having the same axis or centre. To this power belong all turning or wheel machines, such as cranes, windlasses, capstans, &c. The Wheel and Axle possess a great advantage over the simple Lever, in point of convenience; for a weight can be raised but a short distance by the Lever, while, by the continued turning of this wheel and roller, the weight may be raised from any depth, and to any height.

A small wheel, commonly made of wood or brass, which turns about an iron axis, passing through its centre, and fixed in a block, by means of a cord passing round its circumference; it serves to draw up any considerable weight. The Pulley is either single, or combined with others to increase the power; it is also fixed or moveable, according as it is fixed to one spot, or moves up and down with the weight and power.

Inclined Plane
A plane surface, inclined, or making an angle with the horizon. This power becomes available in some situations where the other mechanical powers cannot be conveniently applied; as in sliding heavy weights either up or down a plank or plane laid sloping, letting casks down into a cellar, or drawing them out from it: also, when removing earth from a low to a higher situation, by means of wheel-barrows, or otherwise, inclined planes made of boards laid aslope serve for the barrows to run upon.

A piece of wood or metal, in the form of a rectangular prism. In this power, the friction against the sides is very great, equalling at least the force to be overcome, because the wedge retains any position to which it is driven, and therefore the resistance is doubled by the friction. But the Wedge possesses one great advantage over the other mechanical powers, arising from the force of percussion, or the blow with which the back is struck. Accordingly, we find it produces effects vastly superior to those of any other machine; for instance, the splitting and raising the largest timber, or the hardest rocks; the raising the largest ships, by driving a wedge beneath them, which can be performed by the blow of a mallet; and thus it appears that the blow of a hammer on the back of a wedge is incomparably greater than any mere pressure, and will overcome it. The thinner the wedge, the more effect it has in splitting a body, or overcoming resistance against its sides. All cutting instruments may be referred to the wedge; a chisel or an axe is a simple wedge; a saw is a number of chisels fixed in a line; a knife may be considered as a wedge, when employed in splitting; but if attention be paid to its edge, it will be found to be a fine saw, as is evident from the greater effect produced by a drawing stroke than a direct action of the edge.

A spiral thread or groove, cut round a cylinder, making everywhere the same angle with its length. It is chiefly used in compressing or squeezing bodies, in stamping coins, or making impressions on paper, linen, or cards, and is of vast utility in science, by enabling us to measure or subdivide small spaces. A very ordinary screw will divide an inch into 5000 parts, but the fine hardened steel screws, applied to astronomical instruments, will divide much more minutely.

Funicular Machine
Formed by a cord being made to pass over two fixed pulleys, and a weight being applied to the cord, in any position between the Pulleys, and another weight at each of the extremities, the ratio of the three weights, or any of them being unknown, can be ascertained by forming a triangle, with lines drawn parallel to the directions in which they pull, from the points of application of the weight between the Pulleys.

Species of motion

The force which is applied to and transmitted by a machine is technically called the power; the point at which it is applied is called the point of application; its direction is the line in which the force has a tendency to make the point of application move; and its intensity is usually expressed by a weight which, acting at the same point of application, would produce a like effect upon it.

The moving powers applied to and transmitted by machinery are infinitely various. In the capstan of a ship, the moving power is human force applied to it; in a common pump, the same moving force is used; a horse is the moving power applied to vehicles of transport on common roads, and a steam-engine on railways; the wind is the moving power applied to a sailing-vessel, and to a windmill; the momentum of water acting against the float-boards of a wheel, or its weight acting in the buckets, is the moving power of a water-wheel; the elastic force of steam acting on the piston in the cylinder is the moving power of the steam-engine.

There are four principal species of motion which more frequently than any others act upon, or are required to be transmitted by, machines: —

  • Continued rectilinear motion.
  • Reciprocating rectilinear motion.
  • Continued circular motion.
  • Reciprocating circular motion.

These will be more clearly understood by examples of each kind.

Continued rectilinear Reciprocating rectilinear Continued circular Reciprocating circular
motion is observed in the flowing of a river, in a fall of water, in the blowing of the wind, in the motion of an animal upon a straight road, in the perpendicular fall of a heavy body, in the motion of a body down an inclined plane motion is seen in the piston of a common syringe, in the rod of a common pump, in the hammer of a pavier, the piston of a steam-enginey the stampers of a fulling mill. motion is exhibited in all kinds of wheel-work, and is so common, that to particularise it is needless. motion is seen in the pendulum of a clock, and in the balance-wheel of a watch

If work is imparted to a body so that it stores it up and is capable of giving it out again, the body is said to possess Energy. A force is said to be doing work when it acts through a distance, overcoming resistance. The quantity of work done is proportional jointly to the magnitude of the force and the distance through which it acts, the distance being always measured along or parallel to the line of action of the force. The unit of work used by engineers in this country is the foot pound, and is that quantity of work which is done when a force of one pound acts through a distance of one foot in its line of action. The inch-ton and foot-ton are also sometimes used, these being the work done when a force of one ton acts through a distance of one inch or one foot respectively. The work done by any force is calculated by taking the product of the magnitude of the force and the distance through which it acts.


Energy means capability of doing work. The principle of the Conservation of Bnergy asserts that man is not able to create or destroy energy, he can only transform it from one form into another. This principle is the result of the observation and experiment of many people, including those who have sought in vain for perpetual motion. To the engineer, it is of extreme importance. Thus, if we impart to any machine a certain quantity of energy, and no energy is lost in the machine or used to coil up a spring belonging to the machine or do any other form of work in the machine, then the machine will deliver an exactly equal quantity to that given to it. It cannot deliver more, for then it would create energy; nor can it deliver less, for then energy would be destroyed in the machine. Actually, it is impossible to construct a machine in which there is no energy lost, whether by the rubbing of surfaces on one another, by churning the atmosphere, or by the development of sound and other causes. But we can assert about all machines:

Energy supplied = Energy given out + energy lost in overcoming resistances in the machine.

If the machine is running light, i.e. doing no useful work against resistances, then we must supply energy sufficient to make good that lost by resistances in the machine. If the machine is doing useful work, then we must in addition supply energy equivalent to this useful work.

Mechanical power application

• Power is always the product of Nature. God has not vouch-safed to man the means of its primary creation.

One of the most fruitful-sources of error and deception with regard to inventions, arises from misconceptions of the nature and application of mechanical power. By the term mechanical power that which moves machinery, transports heavy bodies, shapes the raw material into useful forms, and, to use the short but expressive phrase of the mechanic, "that which does work." Mechanical power, when properly understood, is a condition or state of matter. Thus, a quantity of burning fuel, a moving mass of water or of air, are bodies in the condition of power, and, by communicating a portion of their motion to other bodies, they produce in them certain changes which are denominated work. The change thus produced is the measure of the amount of power in a given quantity of matter. For example, the number of bushels of grain which can be ground during the combustion of a bushel of coal is the measure of the amount of power in this quantity of fuel.

Power is always expended in doing work, and it is in the highest degree absurd to think of applying it to useful purposes without exhausting it. Every change of condition, every transformation of matter, every new motion, and every manifestation of life, is at the expense of some motive power which, having performed its part, is for ever neutralized. Man finds power in the moving air and the rapid cataract; in the burning coal, the heaving tide. He transfers it from these to other bodies, and renders it the obedient slave of his will — the patient drudge which, in a thousand ways, administers to his wants, his convenience, and his luxuries, and enables him to reserve his own energy for the higher purpose of the development of his mind and the expression of his thoughts.

The following is a list of all the primary powers which as yet have been used by man in accomplishing his varied purposes in the wide domain of practical life. These are:

  1. Water power.
  2. Wind power.
  3. Tide power.
  4. The power of combustion; and
  5. The power of vital action.

To this list may hereafter be added the power of the volcano and the internal heat of the earth; and, besides these, science at the present time gives no indications of any other. These are denominated primary powers, though, in reality, when critically studied, they may all, except the two last mentioned, be referred to actions from without the earth, and principally to emanations from the sun.

Gravitation, electricity, galvanism, magnetism, and chemical affinity can be employed as sources of power. At the surface of the earth, they are forces of quiescence, the normal condition of which must be disturbed (as with other previously mentioned sources) before they can manifest power; and then the work which they are capable of performing is equivalent of the power which was communicated to them.

There is no more prevalent and mischievous error than the idea that there is, in what are called the imponderables, a principle of spontaneous activity. Heat is the product of chemical action; and electricity manifests power when its equilibrium is disturbed by an extraneous force, and then the effect is proportional to the disturbing cause. It was for this reason that the existence of electricity remained so long unknown to man. Though electricity is not in itself a source of power, yet, from its extreme mobility and high elasticity, it affords the means of transmitting power with scarcely any loss, and almost inconceivable velocity, to the greatest distance. A wave of disturbance, starting from the impulse given at the battery, will traverse the circumference of the earth in less time than has been occupied in stating the fact.

Besides electricity and the principles before mentioned, there are other agents employed between the primary power and the work — namely, the elastic force of steam, of air, and of springs; also, various instruments called machines. But these mnst not be confounded, as they frequently are, with the sources of power. It is not the engine which is the source of motion of the cars, nor yet the steam, but the repulsive energy imparted to the expanding water from the burning fuel.

A machine is an intermediate instrument to transmit, to modify, and to apply power; and, with the exception of the power consumed in wearing away the rubbing parts — that is, in producing friction — and the small portion imparted to the air, the amount of power transmitted is jnst equal to that received.

The human body is itself an admirably contrived complex machine, furnished with levers, pulleys, cords, valves, and other appliances for the application and modification of the power derived from the food. It is, in fact, a locomotive engine, impelled by the same power which, under another form, gives activity and energy to the iron horse of the railway. In both the power is derived from combustion of the carbon and hydrogen of the organic matter employed for food or fuel. In both the direction of power is under the influence of an immaterial, thinking, willing principle, called the soul. But this must not be confounded, as it frequently is, with the motive power. The soul of a man no more moves his body than the soul of the engineer moves the locomotive and its attendant train of cars. In both cases the soul is the directing, controlling principle, not the impelling power. Let, for example, a locomotive engine be placed upon the track, with water in the boiler and flro in the grate, in short, with all the potentials of motion, and it will still remain quiescent. In this state, let the engineer enter the tender and touch the valve; the machine instantly becomes instinct with life and volition ; it has now a soul to govern its power and direct its operations; and, indeed, as a whole, it may be considered as an enormous animal, of which the wheels and other parts are additions to the body of the engineer.

The facts given as to the source of power and its application rest upon the widest and best-established inductions of physical science; and a knowledge of them is absolutely essential to every one who desires to improve the art of applying the powers of the elements to useful purposes with elementary machines—viz., the lever, the wheel and axis, the inclined plane, the pulley, and the screw. These employed, separately, as instruments for the application of power, or in combination, as the elementary parts of complex machines. Every tyro (novice) in science knows that they have no power in themselves; yet the name, mechanical powers, by which they are designated, tends to perpetuate a pernicious error long after the fallacy is understood.

See also

External articles


Further reading


  • Cooper, P. US Patent, X5086.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License