55

C D, then coinciding with C B, will have passed through

an angle equal to 1' C B, and again, at the next point in

the revolution, will coincide with C 21. Therefore, the

portion B D of the curve, will impel the given point

through the arc 1' 2', in the same time and with the same

velocity, as the part A B will have raised it from A to 1'.

By a similar process of reasoning, it will be manifest that,

the angle l'CB being just one-third of 3' C I, the point

A will also traverse the space 2' 3' with a uniform motion.

By a glance at the figure, it will be seen that this curve

is not symmetrical, in other words, that the part A F E is

not equal or similar to A D E. This may be accounted

for by observing that the arc b T, for instance, is equal to

1 B, and consequently the point b, (which is determined

by the intersection of the circle passing through T with

the arc described from the centre a), cannot be situated

in the same position in relation to A as the point B, since

the radius C A does not pass through 1'; the same re-

mark applies to all the other arcs d 2', &c. It is not the

less certain, however, that the part A F E of the eccentric

will cause the given point to descend through the arc A/ A,

in the same uniform manner as it had been elevated by

the part A D E. Fig. 5 is a model of an eccentric of the

kind just described.

In the two preceding examples of eccentrics, it has

been shown that the point A moves through equal spaces

in equal times, both in ascending and descending. In some

cases, however, this is by no means desirable; thus, if the

eccentric is destined to give motion to a mass of matter

which offers considerable resistance, such a form would

give rise to injurious and destructive shocks. In such

cases, it is necessary so to regulate the curvature of the

eccentric, that the point A shall move at the beginning

and end of its stroke with diminished velocity; and that,

for this purpose, the space A A, should be unequally

divided, as in the example which comes next under notice.

Fig. 6. To draw a double and symmetrical eccentric

curve such as to cause the point A to move in a straight

line and with an unequal motion; the velocity of ascent

being accelerated in a given ratio from the starting

point to the vertex of the curve, and the velocity of descent

being retarded in the same ratio.

Upon A A' as a diameter describe a semicircle, and

divide it into any number of equal parts; draw from

each point of division V, 21, 3', &c., perpendiculars upon

C A'; and through the points of intersection l2, 22, 32, &c.,

draw circles having for their common centre the point C,

which is to be joined, as before, to all the points of divi-

sion on the circle (A' 48.) The points of intersection of

the concentric circles with the radii C 1, C 2, C 3, &c.,

are points in the curve required.

Fig. 7 represents a model of the above eccentric, in a

practical form.

Construction of Eccentric Curves and Wheels.—

Plate XIX.

Fig. 1. To construct a double and symmetrical eccen-

tric, which shall produce a uniform rectilinear motion,

with periods of rest at the points nearest to, and farthest

from the axis of rotation.

The lines in the figure above referred to, indicate suffi-

ciently plainly, without the aid of further description, the

construction of the curve in question, which is simply a

modification of the eccentric represented at Figs. 1, 2, and

3 of our last plate. In the present example, the eccentric

is adapted to allow the movable point A to remain in a

state of rest during the first quarter of a revolution B D;

then, during the second quarter, to cause it to traverse

with a uniform motion, a given straight line A A, by

means of the curve D G; again, during the next quarter

E F G, to render it stationary at the elevation of the

point A'; and finally, to allow it to subside, along the

curve B E, with the same uniform motion as it was ele-

vated, to its original position, after having performed the

entire revolution.

Fig. 7 exhibits both the geometrical and practical con-

struction of this eccentric; Fig. 2 being an edge view, and

Fig 3 a vertical section of it.

Figs. 4, 5, 6, 7, and 8. Circular Eccentrics. These

figures represent models of two distinct varieties of the

circular eccentric, which is the contrivance usually adopted

in steam-engines for giving motion to the valves regulat-

ing the action of the steam upon the piston. The circular

eccentric is simply a species of disc or pulley fixed upon

the crank-shaft, or other rotating axis of an engine, in

such a manner that the centre or axis of the shaft shall be

at a given distance from the centre of the pulley. A ring

or hoop, either formed entirely of, or lined with brass or

gun-metal, for the purpose of diminishing friction, is ac-

curately fitted within projecting ledges on the outer cir-

cumference of the eccentric, so that the latter may revolve

freely within it; this ring is connected by an inflexible

rod with a system of levers by which the valve is moved.

It is evident that as the shaft to which the eccentric is

fixed revolves, an alternating rectilinear motion will be

impressed upon the rod, its amount being determined by

the eccentricity, or distance between the centre of the

shaft and that of the exterior circle. The throw of the

eccentric is twice the eccentricity C E; or it may be ex-

pressed as the diameter of the circle described by the point

E. The nature of the alternating motion generated by

the circular eccentric is identical with that of the crank,

which might in many cases be advantageously substi-

tuted for it.

Figs. 4, 5, and 6 exhibit a specimen of a circular ec-

centric formed in a single piece, and which can be ap-

plied only when the shaft to which it is to be attached

is straight and uninterrupted by cranks, &c. The mode

of representing the arm in Fig. 6, which is a section on

the line D F, is not strictly accurate, but is a license

frequently practised in similar cases, and which is at-

tended with obvious advantage.

Figs. 7 and 8 represent the kind of eccentric usually

employed in marine steam-engines; these are, in most cases,

loose upon the shaft, so as to admit of their being used

for working the engines either backwards or forwards;