THE ANATOMY OF A MACHINE
EVERY animal is a complex machine, provided with its own motive power
and a brain for directing the operation of its own mechanical elements.
Not satisfied with the mechanism that nature has put into the human
machine, man has reached for other elements and devised mechanisms
of his own in order to supplement the human machine and increase its
efficiency. At first, as we have seen, these elements were hand tools
of the crudest sort; but they were gradually improved and then they
were combined into what we term machines. In developing these machines,
he naturally took his own system as a pattern and was guided to a
large extent by an examination of his own physical structure. We see
this very clearly in the names of the different parts of machinery,
which are taken from the names of similar parts in the human frame.
Almost every member of the body is used in mechanical terminology. For
instance, we have the “head” and the “foot,” the “arms” and the “legs,”
the “fingers” and the “ankles,” “elbows,” “shoulders,” “trunk,” “hips,”
and various parts of the face, such as the “eyes,” “ears,” “nose,”
“mouth,” “teeth,” “lips,” and even the “gums,” to indicate parts of
machinery which have some remote resemblance to these features.
Before we can understand machinery we must have some general knowledge
of the elements of which it is composed. Probably most of the readers
of this book already possess a fair knowledge of machine elements and
mechanical movements and they can well afford to skip this chapter.
However, for the benefit of the uninitiated, we must put a machine on
the operating table, dissect it, and explain its anatomical structure.
We cannot attempt a very detailed study, but will confine ourselves to
the most important elements.
Every machine is made up of movable parts and fixed parts, the latter
serving to guide or constrain the motion of the former; for no
combination of elements will constitute a machine unless the parts are
_constrained_ to move in certain predetermined directions.
THE LEVER
Among the moving elements the first to be considered is the lever,
which really forms a broad classification comprising many elements that
will hardly be recognized as levers at first blush. Levers in some form
are to be found in practically every machine. A wheel, a gear, and a
pulley are really levers in disguise, as will be explained presently.
Of course everyone knows that a simple lever consists of a rigid bar
that swings on a fulcrum. The fulcrum may be a knife edge, a shaft
passing through the bar or any element on which the bar can be swung
or oscillated. The purpose of the lever is to give a certain advantage
in the application of a force to a load. This may be a change of speed
and distance of travel, and hence of power, or merely a change of
direction.
[Illustration: FIG. 1.--THREE ORDERS OF SIMPLE LEVERS]
There are three types or _orders_ of levers produced by varying the
relative positions of the points where the fulcrum, the force or
effort, and the weight or load are applied. These are shown in Figure
1. In the lever of the _first order_ the fulcrum is placed between the
effort and the weight; in the lever of the _second order_ the weight
is applied between the fulcrum and the effort; and in the lever of the
_third order_ the effort is applied between the fulcrum and the weight.
In each case that part of the lever which extends from the fulcrum to
the point where the effort is applied is called the _effort arm_, and
that which extends from the fulcrum to the point where the weight is
supported is the _weight arm_. The weight that can be lifted with a
given effort depends upon the ratio of the effort arm to the weight
arm. If the two arms are of equal length, the effort is equal to the
weight, but twice the weight can be lifted with the same effort if the
effort arm is twice as long as the weight arm. You can lift a ton with
an effort of only 100 pounds if your effort arm is twenty times as long
as your weight arm but the end of your effort arm would have to move
twenty inches to raise the ton weight one inch. We are assuming in all
these cases that the lever itself has no weight and that there is no
friction at the fulcrum.
Of course levers are not used merely for the purpose of lifting weight,
but to overcome any resistance or merely to apply pressure upon an
object. In almost every household we may find examples of the three
orders of levers. A pair of shears, for instance, is composed of two
levers of the first order, swinging on a common fulcrum. The effort is
applied at the handles, and the weight or load is the material that is
cut by the blades or, speaking more technically, the handles are the
_effort arms_ and the blades are the _weight arms_. A material that
is too tough to be cut at the tip ends of the blades may be easily
cut if we move it in near the fulcrum or pin that hinges the blades
together; for by doing this we shorten the weight arms, because the
weight arm is measured not to the end of the blade, but to the point
where it is cutting into the material. To cut very tough material, such
as heavy tin or sheet steel, we use long-handled short-bladed shears.
The cutting pressure depends upon the ratio of the effort arm to the
weight arm. If the effort arms are twice as long as the weight arms,
the cutting pressure is twice as great as that applied at the handles.
A nutcracker consists of a pair of levers of the second order. The
fulcrum is at one end and the effort or pressure is applied at the
opposite end of the levers or handles, while the equivalent of the
weight (in this case the nut) is placed between the effort and the
fulcrum. Again the _effort arm_ is measured from the fulcrum or hinge
pin of the tool to the point where the hand pressure is applied, and
the weight arm is measured from the fulcrum to the nut. The effort
arm may be four or five times as long as the weight arm, so that the
pressure exerted on the nut is four or five times as great as that
exerted by the hand on the ends of the handles.
[Illustration: FIG. 2.--AN ANGULAR OR BELL-CRANK LEVER]
In the case of a pair of sugar tongs we have another tool something
like the nutcracker in construction, but here the weight, i.e., the
lump of sugar, is seized by the ends of the tongs while the hand
pressure is applied somewhere between the fulcrum and the weight. Hence
we have here a lever or pair of levers of the third order. The _effort
arm_ of a pair of tongs is always shorter than the _weight arm_ and
the pressure on the sugar lump is always less than that exerted on the
tongs by the hand. Evidently the most powerful tool of the three is the
nutcracker, because the effort arms extend over the full length of the
tool and are always longer than the weight arms.
A lever need not consist of a straight bar; the effort arm may form
an angle with the weight arm, forming what is known as an angular or
bell-crank lever (Figure 2). When a common claw hammer is used to pull
out a nail, the claws that slip under the head of the nail form the
weight arm and the hammer handle the effort arm. A horizontal pull on
the handle produces a vertical lift on the nail.
Sometimes two or more levers are interconnected, as in Figure 3, the
effort arm of one being linked to the weight arm of the other. This
serves to increase the lifting force at the weight and at the same time
keep the mechanism within compact limits. Such compounding can go on
indefinitely and is subject to all sorts of variations.
[Illustration: FIG. 3.--COMPOUND LEVERAGE]
One thing we must not forget, and it is a matter that is commonly
overlooked by perpetual motion cranks, namely, that while a pound of
pressure on the effort arm may be made to lift two, four, or a hundred
times as many pounds on the weight arm by varying the relative length
of these arms, it has to move two, four, or a hundred times as far as
the weight arm, so that the work done on one side of the fulcrum is
always exactly equal to that done on the other side.
CONTINUOUS REVOLVING LEVERAGE
[Illustration: FIG. 4.--PRIMITIVE GEAR WHEELS--TWO COACTING GROUPS OF
LEVERS]
If we take a number of levers radiating from a common fulcrum like the
spokes of a carriage wheel, we have a primitive gear wheel. Two such
groups of levers may be mounted on parallel shafts so that when one
is turned its spokes will successively engage the spokes of the other
group and make the latter turn (see Figure 4). Each spoke is first
an effort arm on one side of the wheel and then a weight arm as it
turns around to the other side of the wheel, and as the effort arms
and weight arms are of the same length there is no multiplication of
power. A pound on one side of the wheel cannot lift more than a pound
on the other. The driven wheel receives the same power as the driving
wheel except for such loss as may be due to friction at the bearings or
where the spokes contact. The only advantage of such a pair of gears
is that the direction of rotation of the driven wheel is the reverse
of that of the driving wheel. If the spokes of one wheel are longer
than those of the other, we have at once a variation in the rate of
rotation proportional to the relative diameters of the two wheels. In
Figure 5, for instance, the diameter of the driving wheel A is twice
the diameter of the driven gear B, and so, for each revolution of A, B
must make two revolutions, i.e., the driver must make two revolutions
for each revolution of the driven wheel. In other words, the speed of
revolution is doubled. However, if we make B the driver the speed of
the driven wheel A will be half of that of wheel B.
[Illustration: FIG. 5.--COACTING LEVERS OF UNEQUAL LENGTH]
In primitive machines spoke gears were seldom mounted on parallel
shafts because of the difficulty of keeping the spokes in alignment.
Instead, one shaft was mounted at right angles to the other so that
one set of spokes would cross the other (Figure 6), thus producing
the equivalent of a bevel gear. This was of advantage in changing the
plane of rotation. A later development was the _barrel_ or _lantern
gear_, which permitted transfer of power without changing the plane of
rotation. A cylindrical bundle of rods constituted one of the wheels
(as shown in Figure 7). Instead of being crudely formed of spokes, the
other wheel sometimes consisted of a disk with pins radiating from
its rim. Such gears in far more refined form are still used in modern
clocks and watches. A still further development for transmitting motion
to a plane at right angles to that of the driving shaft is shown in
Figure 8. Here we have a _crown_ gear in which the pins instead of
radiating from the periphery of the disk project from the side face of
the gear.
[Illustration: FIG. 6.--PRIMITIVE EQUIVALENT OF THE BEVEL GEAR]
[Illustration: FIG. 7.--PRIMITIVE LANTERN GEAR]
Turning back to our first spoked wheels, it is very evident that we
may put a rim over the spokes or even fill in between the spokes and
convert the wheels into solid disks that are in frictional engagement
with each other without getting away from the fact that we are dealing
with levers. Each wheel, then, consists of a continuous revolving
lever. Friction gears are used quite commonly in machinery when it is
desirable to have the wheels slip if subjected to excessive strain.
TOOTHED GEARS
By forming teeth on one gear to mesh between similar teeth on the
other, we convert the friction gears into a pair of spur gears (Figure
9). We need not go into the intricacies of the form of gear teeth.
They are designed to be in continuous rolling contact while they are
in mesh. The novice is apt to call all spur gears “cogwheels” and
gear-teeth “cogs.” Mechanics, however, recognize a difference between
cog wheels and spur wheels. In the former, the teeth, or cogs, are not
cast upon or cut out of the wheel body, but are separate pieces fitted
to the wheel. Such wheels are found in old water mills. They consist of
wooden wheels with iron or steel teeth mortised in the wooden rim of
the wheel. In general it is safer to speak of spur gears because there
are few cogwheels now in use.
[Illustration: FIG. 8.--CROWN AND LANTERN GEAR]
When a small gear engages a large one, the former is commonly known as
a _pinion_.
[Illustration: FIG. 9.--SPUR AND PINION GEAR]
[Illustration: FIG. 10.--BEVEL FRICTION GEARS]
If two friction wheels are to turn at right angles one to the other,
they must have conical bearing surfaces, as in Figure 10. The angle
between the shafts of the two gears and the relative size of the gears
may be changed as desired, provided each cone surface has its apex at
the intersection of the two shafts or axes. It is easy to understand
how such conical friction gears may be converted into toothed bevel
gears (Figure 11), by forming teeth on the conical surfaces, and it
will be evident that the teeth must taper toward the apex of the two
cones. Two bevel gears of equal diameter, and with shafts set at right
angles one to the other, are known as _miter_ gears.
[Illustration: FIG. 11.--TOOTHED BEVEL GEARS]
So far we have not shown any combination of gearing that will multiply
power. In Figure 5, the driver A is twice the diameter of the driven
wheel B, and the latter makes two revolutions for one of A, but the
speed at the periphery of the two wheels is the same. A pull of one
pound at the point _a_ produces a pressure of one pound at _b_, and
this in turn produces a lift of one pound at _c_ because the levers
in each wheel are perfectly balanced, that is, each lever has equal
effort and weight arms. The way to obtain an increase of power and of
peripheral speed is to fasten two wheels of unequal diameters together
on the same center and apply the effort to one of the wheels (as in
Figure 12) and the weight to the other wheel. This gives us what is
technically known as a _wheel and axle_. The dotted lines show that
we have here a lever of the first order which can be used to multiply
power in the same way that a bar lever does. If one wheel is twice the
diameter of the other then a pound of effort will lift two pounds of
weight.
[Illustration: FIG. 12.--WHEEL AND AXLE OR REVOLVING LEVER OF FIRST
ORDER]
[Illustration: FIG. 13.--REVOLVING LEVERS OF THE 2D AND 3D ORDER]
Figure 13 shows how the effort and weight can be shifted about in such
fashion as to give us a lever of the second and one of the third order.
The power may be enormously increased and the speed of the final wheel
greatly reduced by setting up a train of gears in which the effort
is received by the larger one of each couple and is delivered by the
smaller one. In Figure 14 the smaller wheels are half the diameter of
the larger ones. A pound of pressure at A will amount to 2 at B, 4 at
C, 8 at D, 16 at E, and 32 at F. On the other hand, point A will have
to move through 32 inches to make the point F move an inch.
[Illustration: RAISING WATER WITH A CHAIN OF POTS
A primitive pump still used in Egypt]
[Illustration: A HORSE-OPERATED CHAIN-PUMP USED IN GREECE]
[Illustration: MULTIPLE SPINDLE DRILL IN MOTOR CAR FACTORY]
[Illustration: FIG. 14.--A TRAIN OF SPUR GEARS]
[Illustration: FIG. 15.--PULLEYS OF THE 1ST, 2D, AND 3D ORDERS]
[Illustration: FIG. 16.--TYPICAL ARRANGEMENT OF BLOCK AND TACKLE]
A pulley is merely a modification of the wheel. Figure 15 shows how it
may be arranged to correspond to the three orders of simple levers.
If the pulley axis is fixed, as in the first order, the effort and
weight arms are equal and hence balanced. In the second order the
wheel is bodily movable, hence one pound will raise two pounds of
weight because the power arm is twice as long as the weight arm, while
in the third order it takes two pounds of lift to raise one pound of
weight. There is no end of possible combinations of pulleys which will
multiply power in the same way that bar levers do when compounded. A
common arrangement of block and tackle is given in Figure 16. There is
a four-sheave pulley block above and a three-sheave block below, but
in order to trace the rope clearly the pulley wheels or sheaves are
represented as of different diameters. The arrangement consists of a
series of levers of the first order in the upper pulley block coupled
to a series of levers of the second order in the lower block. To find
the weight that a given power will lift, multiply the effort by the
number of strands of rope that are supporting the weight. In this case
there are seven such strands, not counting the strand E, to which the
effort or pull is applied. This means that a pull of a hundred pounds
at E will lift 700 pounds at W. Of course a pull of seven feet at E
will raise the weight only one foot.
[Illustration: FIG. 17.--INCLINED PLANE WITH EFFORT PARALLEL TO THE
INCLINED FACE]
THE INCLINED PLANE AND ITS FAMILY
The inclined plane constitutes a second broad classification of machine
elements. The wedge, the screw, the cam, and the eccentric, all belong
to the family of the inclined plane.
[Illustration: FIG. 18.--INCLINED PLANE WITH EFFORT PARALLEL TO THE
BASE]
A simple form of inclined plane is pictured in Figure 17, which shows
a weight W being rolled up an incline. The effort required to carry it
to the top of the incline depends, of course, upon the steepness of the
incline. The drawing shows a rise of 3 feet on a slope 5 feet long, and
the weight of the wheel is, say 20 pounds. To find the effort required,
the weight is multiplied by the rise (20 × 3 = 60) and divided by
the length of the slope (60/5 = 12) and we find that it takes only
12 pounds to roll the 20-pound wheel to the top of the incline. This
holds true when the pull is parallel to the inclined face. If the
pull is parallel to the base of the incline, as in Figure 18, we must
divide by the length of the base instead of the length of the incline
(60/4 = 15) and we find that it takes 15 pounds of effort to pull the
weight up the incline. If the pull is exerted at an angle both to the
base and the inclined face, we have a problem that is slightly more
complicated and we need not go into it here because it involves a bit
of trigonometry. In all cases, however, it may be noted that the amount
of rope that is taken in, in hauling the weight up the incline, bears a
definite relation to the amount of effort required to raise the weight.
In Figure 17, 5 feet of rope must be pulled in, in order to raise the
weight 3 feet, so that ⅗ of 20 or 12 pounds is all that is required
to pull up the weight, while in Figure 18, 4 feet of rope is hauled
in for a lift of 3 feet, so that ¾ of 20 or 15 pounds is required to
pull up the weight. In this respect the inclined plane is exactly like
the lever or the pulley, for the _effort_ multiplied by the _distance_
through which it is exerted is always exactly equal to the _weight_
multiplied by the _distance_ through which it moves. Thus in Figure
17, the effort 12 pounds multiplied by the distance 5 = the weight 20
pounds times the distance 3, and in Figure 18, effort 15 x distance 4
= weight 20 x distance 3. Of course, we are ignoring the weight of the
rope and the friction which, in actual practice, are important factors
to be reckoned with.
[Illustration: FIG. 19.--ENDLESS SCREW OR WORM GEAR]
So far we have considered a fixed inclined plane, but when the inclined
plane is moved between the weight and a fixed base it is known as a
wedge, and in this case, too, the effort required to move the wedge
multiplied by the distance the wedge moves is equal to the weight
multiplied by the distance it is lifted.
The commonest form of inclined plane is the screw which is merely an
inclined plane bent around a cylinder. A screw engaging a toothed
wheel, as in Figure 19, gives a combination known as an “endless
screw,” or, more commonly, as a worm gear. The screw or worm is always
the driver, and as it must make a complete turn to move the gear
through a space of one tooth, the power of this combination is very
great. It is practically impossible to turn the worm by using the gear
wheel as a driver because the friction developed at the point where
the worm and gear contact is very great. For this reason worm gearing
is used in the steering gear of automobiles. The shaft of the steering
wheel is fitted with a worm which meshes with a worm gear on the parts
connected with the wheels. It is very easy to turn the wheels by
operating the steering wheel, but if the wheels strike a rut or a stone
they are not deflected from their course, because the worm makes it
impossible for them to turn the steering wheel.
[Illustration: FIG. 20.--HELICAL OR SPIRAL GEARS]
The spiral gear shown in Figure 20 is a cross between a worm gear and
spur gear. The teeth are spirals set at an angle of 45 degrees to the
axis of the wheel. In this case either gear can be used to drive the
other, and the advantage of such a pair is that power is transmitted
from one shaft to another in a different plane and at right angles to
the first.
[Illustration: FIG. 21.--DRUM CAM]
[Illustration: FIG. 22.--PROFILE OR DISK CAM]
Cams are usually irregular revolving inclined planes. Figure 21, shows
a cylinder or drum cam. A groove is cut in the cylindrical wall of the
cam and an arm or lever is provided with a roller which rolls in the
groove. When the cam is revolved the lever is constrained to follow all
the twists and turns of the groove. A different form of cam is shown in
Figure 22. It is formed with an irregular periphery against which the
roller is pressed by a spring. As the cam wheel revolves, the roller
and the arm to which it is attached must move in and out over all the
hills and valleys of the periphery. The cam is one of the most useful
elements in modern machinery, for it provides a very simple means of
producing the most complicated and irregular motions.
[Illustration: FIG. 23.--ECCENTRIC BY WHICH ROTARY MOTION IS CONVERTED
INTO RECTILINEAR MOTION]
We cannot attempt to describe all the different types of cams, but
reference should be made to the eccentric, which is a form of cam
commonly used to operate the valves of a steam engine. The cam in this
case is a perfectly circular disk, but the shaft that turns it does not
lie at the center of the disk, consequently an object bearing against
the periphery must move toward and away from the center as the disk
revolves. Instead of using a spring-pressed roller to bear against one
side of the disk, the whole disk is encircled with a ring of steel
known as an eccentric strap. This strap is bolted to a valve rod and
as the eccentric revolves the strap makes the valve rod move back and
forth. (See Figure 23.)
A description of all the various combinations of gearing, link motions,
ratchets, escapements, clutches, and miscellaneous movements would
easily fill the rest of this book, and we must therefore content
ourselves with this very brief survey of a few of the more important
elements employed in the construction of modern machinery.