Armengaud, Jacques Eugène; Leblanc, César Nicolas   [Hrsg.]; Armengaud, Jacques Eugène   [Hrsg.]; Armengaud, Charles   [Hrsg.]
The engineer and machinist's drawing-book: a complete course of instruction for the practical engineer: comprising linear drawing - projections - eccentric curves - the various forms of gearing - reciprocating machinery - sketching and drawing from the machine - projection of shadows - tinting and colouring - and perspective. Illustrated by numerous engravings on wood and steel. Including select details, and complete machines. Forming a progressive series of lessons in drawing, and examples of approved construction — Glasgow, 1855

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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;
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