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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and it is necessary that they should be fitted to the
shaft in two distinct pieces. The part B is very ac-
curately fitted to the body of the eccentric A; the joints
being rebated to prevent lateral displacement; and the
parts are held immovably together by round steel pins
a, a, passing through the lines of junction. A catch or
projection b is cast upon one side of the boss of the ec-
centric, which is carried round with the crank-shaft by
either of two similar catches affixed to the latter; the
position of these, as well as the length of the part b, being
so adjusted that, when, in the revolution of the shaft, one
of its catches abuts against one end of the part b, the ec-
centric shall then be in its proper position for effecting the
forward action of the engine; and similarly, when the
opposite catch is in contact with the other extremity of
the projection on the eccentric, the reversing or backward
motion of the engine is produced.

Fig. 9. To describe the involute of a circle.

The involute is the curve described by the development
or resolution of the successive parts of another given curve
into their equivalent straight lines. The mode of its
generation is as follows:—Suppose an inelastic thread to
be accurately applied to the outline or circumference of
the curve o, 1, 2, 8-9; if we cause the extremity o to
move by unwinding the thread gradually from off the
circumference, the curve 1', 2', S',-9', described by that
point, will be the involute of the given curve. This
definition obviously suggests a mode of drawing the curve
mechanically. The application of this curve in machinery
is of not unfrequent occurrence; it is the form given to
many cams or wypers for various purposes; it is also the
curve proper to be given to the teeth of a pinion driving
a rack.

The geometrical construction of the involute of a circle
is as follows:—Describe a circle from the centre C, with
the radius C A, and, commencing at o, divide its circum-
ference into any number of equal parts, (which must be
so small that each may be looked upon as a straight
line). Then draw indefinitely through each of the points
1, 2, 3, &c., tangents to the given circle, and upon the
first, set off from 1 to 1' the length of the arc o 1; upon
the second, from 2 to 2', twice the length of the arc o 1,
in other words the arc o 2 reduced approximately to a
straight line, and so on. The curve which passes through
all the points thus obtained will be the involute of the
circle o A 9.

Supposing it is required, by means of an involute cam
or wyper to raise a point A to A', a circle described
from the centre C, and passing through A', will intersect
the curve at a point 5', such that the portion o 5' will
represent the length sufficient to produce the required

The involute may also be described mechanically thus:
let A (Fig. 178, annexed), be the circle ot which the
involute is required, and let R be a straight ruler, at
whose extremity a pin p is fixed with the point resting
upon the initial point q of the curve; then by rolling the
straight ruler upon the circumference, so that the point

at which it touches the circle may move gradually from q
towards r, the curve traced by the pin p will be the
involute required.

Fig. 10. To produce the involute of a circle so as to
form a spiral.

If we continue or prolong the involute of the circle a e
f i indefinitely, the curve will then assume the form and

title of a spiral. This curve is such that, after the first
revolution round the axis, the generating point a having
arrived at b, all straight lines such as b c, c d, l m, &c., are
equal to a b, and consequently to the circumference of the
primary circle or nucleus. This curve may be described
by means of a succession of circular arcs, whose centres are
taken successively upon the points of contact of tangents
drawn from various points e, f i, &c., taken upon the cir-
cumference of the primary circle. Thus, from the point of
contact e, with the radius e g, equal to the arc a e reduced
to a straight line, draw the arc a g, from f with the radius
h f, equal to the arc a e f, describe the arc g h from i the
arc h k, and so on. Also, from a, with the radius a b
draw the arc b l; and, with the radius a c, the arc c m, &c.

Classification of Gearing.

Combinations of toothed gearing, as is well known, are
employed for the transmission of motive power with a
determinate velocity. To produce a regular, smooth, and
equable motion by means of toothed gearing, and thus to
prevent shocks which might be injurious and destructive
to the machinery, the form of the teeth must be such that
the wheels shall work together in precisely the same man-
ner as if they were impelled merely by the friction of the
circumferences of their pitch circles. To attain this object,
the form of the teeth must be subjected, as we shall now
proceed to point out, to certain invariable laws depen-
dent upon the relative diameters of the gearing pairs.

Toothed gearing may be divided into two great classes,
spur and bevel wheels; in the former, the axes of the
driving and driven wheels are parallel to each other;
in the latter, they may be situated at any angle. Of
these classes there are numerous varieties, distinguished
by appropriate names.

Thus we have spur gearing, strictly so called, consisting
of wheels of which the teeth are disposed at the circumfer-
ence and converge towards the centre (see Fig. 1, Plate
XXI.) Trundle gear, in which a spur or face wheel moves a
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