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. Thus, there are four principal species of
motion which more frequently than any others act upon, or are required
to be transmitted by, machines:--
1. _Continued rectilinear motion._
2. _Reciprocating rectilinear motion._
3. _Continued circular motion._
4. _Reciprocating circular motion._
These will be more clearly understood by examples of each kind.
Continued rectilinear 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.
Reciprocating rectilinear 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-engine, the stampers of a fulling mill.
Continued circular motion is exhibited in all kinds of wheel-work, and
is so common, that to particularise it is needless.
Reciprocating circular motion is seen in the pendulum of a clock, and
in the balance-wheel of a watch.
We shall now explain some of the contrivances by which a power having
one of these motions may be made to communicate either the same species
of motion changed in its velocity or direction, or any of the other
three kinds of motion.
(314.) By a continued rectilinear motion another continued rectilinear
motion in a different direction may be produced, by one or more fixed
pulleys. A cord passed over these, one end of it being moved by the
power, will transmit the same motion unchanged to the other end. If the
directions of the two motions cross each other, one fixed pulley will
be sufficient; see _fig. 113._, where the hand takes the direction
of the one motion, and the weight that of the other. In this case the
pulley must be placed in the angle at which the directions of the two
motions cross each other. If this angle be distant from the places at
which the objects in motion are situate, an inconvenient length of rope
may be necessary. In this case the same may be effected by the use of
two pulleys, as in _fig. 158._
If the directions of the two motions be parallel, two pulleys must
be used as in _fig. 158._, where P′ A′ is one motion, and
B W the other. In these cases the axles of the two wheels are
parallel.
It may so happen that the directions of the two motions neither cross
each other nor are parallel. This would happen, for example, if the
direction of one were upon the paper in the line P A, while the
other were perpendicular to the paper from the point O. In this case
two pulleys should be used, the axle of one O′ being perpendicular to
the paper, while the axle of the other O should be on the paper. This
will be evident by a little reflection.
In general, the axle of each pulley must be perpendicular to the
two directions in which the rope passes from its groove; and by due
attention to this condition it will be perceived, that a continued
rectilinear motion may be transferred from any one direction to any
other direction, by means of a cord and two pulleys, without changing
its velocity.
If it be necessary to change the velocity, any of the systems of
pulleys described in chap. XV. may be used in addition to the fixed
pulleys.
By the wheel and axle any one continued rectilinear motion may be
made to produce another in any other direction, and with any other
velocity. It has been already explained (250.) that the proportion of
the velocity of the power to that of the weight is as the diameter of
the wheel to the diameter of the axle. The thickness of the axle being
therefore regulated in relation to the size of the wheel, so that
their diameters shall have that proportion which subsists between the
proposed velocities, one condition of the problem will be fulfilled.
The rope coiled upon the axle may be carried, by means of one or more
fixed pulleys, into the direction of one of the proposed motions, while
that which surrounds the wheel is carried into the direction of the
other by similar means.
(315.) By the wheel and axle a continued rectilinear motion may be made
to produce a continued rotatory motion, or _vice versâ_. If the power
be applied by a rope coiled upon the wheel, the continued motion of
the power in a straight line will cause the machine to have a rotatory
motion. Again, if the weight be applied by a rope coiled upon the
axle, a power having a rotatory motion applied to the wheel will cause
the continued ascent of the weight in a straight line.
Continued rectilinear and rotatory motions may be made to produce each
other, by causing a toothed wheel to work in a straight bar, called a
_rack_, carrying teeth upon its edge. Such an apparatus is represented
in _fig. 159._
In some cases the teeth of the wheel work in the links of a chain. The
wheel is then called a _rag-wheel_, _fig. 160._
Straps, bands, or ropes, may communicate rotation to a wheel, by their
friction in a groove upon its edge.
A continued rectilinear motion is produced by a continued circular
motion in the case of a screw. The lever which turns the screw has
a continued circular motion, while the screw itself advances with a
continued rectilinear motion.
The continued rectilinear motion of a stream of water acting upon a
wheel produces continued circular motion in the wheel, _fig. 93_,
_94_, _95_. In like manner the continued rectilinear motion of the wind
produces a continued circular motion in the arms of a windmill.
Cranes for raising and lowering heavy weights convert a circular motion
of the power into a continued rectilinear motion of the weight.
(316.) Continued circular motion may produce reciprocating rectilinear
motion, by a great variety of ingenious contrivances.
Reciprocating rectilinear motion is used when heavy stampers are to
be raised to a certain height, and allowed to fall upon some object
placed beneath them. This may be accomplished by a wheel bearing on
its edge curved teeth, called _wipers_. The stamper is furnished with
a projecting arm or peg, beneath which the wipers are successively
brought by the revolution of the wheel. As the wheel revolves the
wiper raises the stamper, until its extremity passes the extremity of
the projecting arm of the stamper, when the latter immediately falls
by its own weight. It is then taken up by the next wiper, and so the
process is continued.
A similar effect is produced if the wheel be partially furnished with
teeth, and the stamper carry a rack in which these teeth work. Such an
apparatus is represented in _fig. 161._
It is sometimes necessary that the reciprocating rectilinear motion
shall be performed at a certain varying rate in both directions. This
may be accomplished by the machine represented in _fig. 162._
A wheel upon the axle C turns uniformly in the direction
A B D E. A rod _mn_ moves in guides, which only permit
it to ascend and descend perpendicularly. Its extremity _m_ rests
upon a path or groove raised from the face of the wheel, and shaped
into such a curve that as the wheel revolves the rod _mn_ shall be
moved alternately in opposite directions through the guides, with the
required velocity. The manner in which the velocity varies will depend
on the form given to the groove or channel raised upon the face of the
wheel, and this may be shaped so as to give any variation to the motion
of the rod _mn_ which may be required for the purpose to which it is to
be applied.
The _rose-engine_ in the turning-lathe is constructed on this
principle. It is also used in spinning machinery.
It is often necessary that the rod to which reciprocating motion is
communicated shall be urged by the same force in both directions. A
wheel partially furnished with teeth, acting on two racks placed on
different sides of it, and both connected with the bar or rod to which
the reciprocating motion is to be communicated, will accomplish this.
Such an apparatus is represented in _fig. 163._, and needs no
further explanation.
Another contrivance for the same purpose is shown in _fig. 164._,
where A is a wheel turned by a winch H, and connected with a rod or
beam moving in guides by the joint _ab_. As the wheel A is turned
by the winch H the beam is moved between the guides alternately
in opposite directions, the extent of its range being governed by
the length of the diameter of the wheel. Such an apparatus is used
for grinding and polishing plane surfaces, and also occurs in silk
machinery.
An apparatus applied by M. Zureda in a machine for pricking holes in
leather is represented in _fig. 165._ The wheel A B has its
circumference formed into teeth, the shape of which may be varied
according to the circumstances under which it is to be applied. One
extremity of the rod _ab_ rests upon the teeth of the wheel upon which
it is pressed by a spring at the other extremity. When the wheel
revolves, it communicates to this rod a reciprocating rectilinear
motion.
Leupold has applied this mechanism to move the pistons of pumps.[5]
Upon the vertical axis of a horizontal hydraulic wheel is fixed another
horizontal wheel, which is furnished with seven teeth in the manner
of a crown wheel (263.). These teeth are shaped like inclined planes,
the intervals between them being equal to the length of the planes.
Projecting arms attached to the piston rods rest upon the crown of this
wheel; and, as it revolves, the inclined surfaces of the teeth, being
forced under the arm, raise the rod upon the principle of the wedge.
To diminish the obstruction arising from friction, the projecting arms
of the piston rods are provided with rollers, which run upon the teeth
of the wheel. In one revolution of the wheel each piston makes as many
ascents and descents as there are teeth.
[5] Theatrum Machinarum, tom. ii. pl. 36. fig. 3.
(317.) Wheel-work furnishes numerous examples of continued circular
motion round one axis, producing continued circular motion round
another. If the axles be in parallel directions, and not too distant,
rotation may be transmitted from one to the other by two spur-wheels
(263.); and the relative velocities may be determined by giving a
corresponding proportion to the diameter of the wheels.
If a rotary motion is to be communicated from one axis to another
parallel to it, and at any considerable distance, it cannot in
practice be accomplished by wheels alone, for their diameters would
be too large. In this case a strap or chain is carried round the
circumferences of both wheels. If they are intended to turn in the same
direction, the strap is arranged as in _fig. 100._; but if in
contrary directions it is crossed, as in _fig. 101._ In this case,
as with toothed wheels, the relative velocities are determined by the
proportion of the diameters of the wheels.
If the axles be distant and not parallel, the cord, by which the motion
is transmitted, must be passed over grooved wheels, or fixed pulleys,
properly placed between the two axles.
It may happen that the strain upon the wheel, to which the motion is to
be transmitted, is too great to allow of a strap or cord being used. In
this case, a shaft extending from the one axis to another, and carrying
two bevelled wheels (263.), will accomplish the object. One of these
bevelled wheels is placed upon the shaft near to, and in connection
with, the wheel from which the motion is to be taken, and the other at
a part of it near to, and in connection with, that wheel to which the
motion is to be conveyed, _fig. 166._
The methods of transmitting rotation from one axis to another
perpendicular to it, by crown and by bevelled wheels, have been
explained in (263.).
The endless screw (299.) is a machine by which a rotatory motion round
one axis may communicate a rotatory motion round another perpendicular
to it. The power revolves round an axis coinciding with the length of
the screw, and the axis of the wheel driven by the screw is at right
angles to this.
The axis to which rotation is to be given, or from which it is to
be taken, is sometimes variable in its position. In such cases, an
ingenious contrivance, called a _universal joint_, invented by the
celebrated Dr. Hooke, may be used. The two shafts or axles A B,
_fig. 167._, between which the motion is to be communicated,
terminate in semicircles, the diameters of which, C D and
E F, are fixed in the form of a cross, their extremities moving
freely in bushes placed in the extremities of the semicircles.
Thus, while the central cross remains unmoved, the shaft A and its
semicircular end may revolve round C D as an axis; and the shaft
B and its semicircular end may revolve round E F as an axis. If
the shaft A be made to revolve without changing its direction, the
points C D will move in a circle whose centre is at the middle of
the cross. The motion thus given to the cross will cause the points
E F to move in another circle round the same centre, and hence the
shaft B will be made to revolve.
[Illustration: _C. Varley, del._ _H. Adlard, sc._
_London, Pubd. by Longman & Co._]
This instrument will not transmit the motion if the angle under the
directions of the shafts be less than 140°. In this case a double
joint, as represented in _fig. 168._, will answer the purpose.
This consists of four semicircles united by two crosses, and its
principle and operation is the same as in the last case.
Universal joints are of great use in adjusting the position of large
telescopes, where, while the observer continues to look through the
tube, it is necessary to turn endless screws or wheels whose axes are
not in an accessible position.
The cross is not indispensably necessary in the universal joint. A
hoop, with four pins projecting from it at four points equally distant
from each other, or dividing the circle of the hoop into four equal
arcs, will answer the purpose. These pins play in the bushes of the
semicircles in the same manner as those of the cross.
The universal joint is much used in cotton-mills, where shafts are
carried to a considerable distance from the prime mover, and great
advantage is gained by dividing them into convenient lengths, connected
by a joint of this kind.
(318.) In the practical application of machinery, it is often necessary
to connect a part having a continued circular motion with another which
has a reciprocating or alternate motion, so that either may move the
other. There are many contrivances by which this may be effected.
One of the most remarkable examples of it is presented in the
scapements of watches and clocks. In this case, however, it can
scarcely be said with strict propriety that it is the rotation of
the scapement-wheel (266.) which _communicates_ the vibration to the
balance-wheel or pendulum. That vibration is produced in the one case
by the peculiar nature of the spiral spring fixed upon the axis of the
balance-wheel, and in the other case by the gravity of the pendulum.
The force of the scapement-wheel only _maintains_ the vibration,
and prevents its decay by friction and atmospheric resistance.
Nevertheless, between the two parts thus moving there exists a
mechanical connection, which is generally brought within the class of
contrivances now under consideration.
A beam vibrating on an axis, and driven by the piston of a
steam-engine, or any other power, may communicate rotary motion to
an axis by a connector and a crank. This apparatus has been already
described in (311.). Every steam-engine which works by a beam affords
an example of this. The working beam is generally placed over the
engine, the piston rod being attached to one end of it, while the
connecting rod unites the other end with the crank. In boat-engines,
however, this position would be inconvenient, requiring more room than
could easily be spared. The piston rod, in these cases, is, therefore,
connected with the end of the beam by long rods, and the beam is placed
beside and below the engine. The use of a fly-wheel here would also
be objectionable. The effect of the dead points explained in (311.)
is avoided without the aid of a fly, by placing two cranks upon the
revolving axle, and working them by two pistons. The cranks are so
placed that when either is at its dead point, the other is in its most
favourable position.
A wheel A, _fig. 169._, armed with wipers, acting upon a
sledge-hammer B, fixed upon a centre or axle C, will, by a continued
rotatory motion, give the hammer the reciprocating motion necessary
for the purposes to which it is applied. The manner in which this acts
must be evident on inspecting the figure.
The treddle of the lathe furnishes an obvious example of a vibrating
circular motion producing a continued circular one. The treddle acts
upon a crank, which gives motion to the principal wheel, in the same
manner as already described in reference to the working beam and crank
in the steam-engine.
By the following ingenious mechanism an alternate or vibrating force
may be made to communicate a circular motion continually in the same
direction. Let A B, _fig. 170._, be an axis receiving an
alternate motion from some force applied to it, such as a swinging
weight. Two ratchet wheels (253.) _m_ and _n_ are fixed on this axle,
their teeth being inclined in opposite directions. Two toothed wheels C
and D are likewise placed upon it, but so arranged that they turn upon
the axle with a little friction. These wheels carry two catches _p_,
_q_, which fall into the teeth of the ratchet wheels _m_, _n_, but fall
on opposite sides conformably to the inclination of the teeth already
mentioned. The effect of these catches is, that if the axis be made
to revolve in one direction, one of the two toothed wheels is always
compelled (by the catch _against_ which the motion is directed) to
revolve with it, while the other is permitted to remain stationary in
obedience to any force sufficiently great to overcome its friction with
the axle on which it is placed. The wheels C and D are both engaged by
bevelled teeth (263.) with the wheel E.
According to this arrangement, in whichever direction the axis
A B is made to revolve, the wheel E will continually turn in
the same direction, and, therefore, if the axle A B be made to
turn alternately in the one direction and the other, the wheel E will
not change the direction of its motion. Let us suppose that the axle
A B is turned against the catch _p_. The wheel C will then be
made to turn with the axle. This will drive the wheel E in the same
direction. The teeth on the opposite side of the wheel E being engaged
with those of the wheel D, the latter will be turned upon the axle,
the friction, which alone resists its motion in that direction, being
overcome. Let the motion of the axle A B be now reversed. Since
the teeth of the ratchet wheel _n_ are moved against the catch _q_, the
wheel D will be compelled to revolve with the axle. The wheel E will be
driven in the same direction as before, and the wheel C will be moved
on the axle A B, and in a contrary direction to the motion of the
axle, the friction being overcome by the force of the wheel E. Thus,
while the axle A B is turned alternately in the one direction and
the other, the wheel E is constantly moved in the same direction.
It is evident that the direction in which the wheel E moves may be
reversed by changing the position of the ratchet wheels and catches.
(319.) It is often necessary to communicate an alternate circular
motion, like that of a pendulum, by means of an alternate motion in
a straight line. A remarkable instance of this occurs in the steam
engine. The moving force in this machine is the pressure of steam,
which impels a piston from end to end alternately in a cylinder. The
force of this piston is communicated to the working beam by a strong
rod, which passes through a collar in one end of the piston. Since it
is necessary that the steam included in the cylinder should not escape
between the piston rod and the collar through which it moves, and yet,
that it should move as freely and be subject to as little resistance as
possible, the rod is turned so as to be truly cylindrical, and is well
polished. It is evident that, under these circumstances, it must not be
subject to any lateral or cross strain, which would bend it towards one
side or the other of the cylinder. But the end of the beam to which it
communicates motion, if connected immediately with the rod by a joint,
would draw it alternately to the one side and the other, since it moves
in the arc of a circle, the centre of which is at the centre of the
beam. It is necessary, therefore, to contrive some method of connecting
the rod and the end of the beam, so that while the one shall ascend
and descend in a straight line, the other may move in the circular arc.
The method which first suggests itself to accomplish this is, to
construct an arch-head upon the end of the beam, as in _fig. 171._
Let C be the centre on which the beam works, and let B D be an
arch attached to the end of the beam, being a part of a circle having C
for its centre. To the highest point B of the arch a chain is attached,
which is carried upon the face of the arch B A, and the other end
of which is attached to the piston rod. Under these circumstances it is
evident, that when the force of the steam impels the piston downwards,
the chain P A B will draw the end of the beam down, and will,
therefore, elevate the other end.