0.5

1 cm

54

ENGINEER AND MACHINIST’S DRAWING-BOOK.

It is almost unnecessary to observe, that the instructions

we have given for the drawing of the anterior face F' G' of

the wheel, are equally applicable to the posterior FT T

which is parallel to it, and in all respects the same; the

common centre of all the circles in it being at O', Fig. 4,

is projected to 0 in Fig. 3. Hence, it will be easy to

construct the ellipses representing these circles in the

oblique projection, and consequently to determine the

points e, f Jc, &c., in the curvature of the teeth; observing

that, as their centre lines converge to C in the front face,

they all tend to 0 in the remoter surface, which is, how-

ever, for the most part concealed by the former.

It would be superfluous to enter into any details re-

garding the construction of the oblique view of the rim,

eye and arms, which are drawn upon precisely similar

principles to those we have already so fully explained.

Projections of Eccentrics.—Plate XYIII.

The term eccentric is applied in general to all such

curves as are composed of points situated at unequal dis-

tances from a central point or axis. The ellipse, the curve

called the heart, and even the circle itself when supposed

to be fixed upon an axis which does not pass through its

centre, are examples of eccentric curves.

The object of such curves, which are of frequent occur-

rence in machinery, is to convert a rotatory into an alter-

nating rectilinear motion ; and their forms admit of an

infinite variety, according to the nature of the motion de-

sired to be imparted. Examples of their application occur

in many arrangements of pumps, presses, valves of steam-

engines, spinning and weaving machines, &c.

Fig. 1. To draw the eccentric symmetrical curve called

the heart, which is such as, when revolving with a uni-

form motion on its axis, to communicate to a movable

point A, a uniform rectilinear motion of ascent and

descent

Let C be the axis or centre of rotation upon which

the eccentric is fixed, and which is supposed to revolve

uniformly; and let A A' be the distance which the

point A is required to traverse during a half revolution

of the eccentric. From the centre C, with radii re-

spectively equal to C A and C A', describe two circles ;

divide the greatest into any number of equal parts,

(say 16), and draw through these points of division the

radii C 1, C 2, C 3, &c. Then, divide the line A A' into

the same number of equal parts as are contained in the

semicircle, (that is, into 8, in the example now before us),

and through all the points V, 21, S', &c., draw circles con-

centric with the former ; the points of their intersection

B, D, E, &c., with the respective radii C 1, C 2, C 3, &c.

are points in the curve required, its vertex being at the

point 8.

It will now be obvious that when the axis, in its ano-u-

lar motion, shall have passed through one division, in

other words, when the radius C 1 coincides with C A', the

point A, being urged upwards by the curvature of the

revolving body on which it rests, will have taken the

position indicated by 1' ; and further, when the succeed-

ing radius C 2 shall have assumed the same position, the

point A will have been raised to 2' ; and so on till it

arrives at A', after a half revolution of the eccentric. The

remaining half A G F 8 of the eccentric, being exactly

symmetrical with the other, will enable the point A to

descend in precisely the same manner as it is elevated.

It is thus manifest that this curve is fitted to impress a

uniform motion upon the point A itself; but in practice a

small friction roller is usually interposed between the

surface of the eccentric and the piece which is to be actu-

ated by it. Accordingly the point A is to be taken as the

centre of this roller, and the curve whose construction we

have just explained is replaced by another similar to, and

equidistant from it, which is drawn tangentially to arcs

of circles described from the various points in the primary

curve with the radius of the roller. This second curve is

manifestly endowed with the same properties as the other;

for supposing the point e, for example, to coincide with A,

if we cause the axis to revolve through a distance equal to

one of the divisions, the point f which is the intersection

of the curve with the circle whose radius is C 1', will then

obviously have assumed the position 1'; at the next por-

tion of the revolution, the point g, (which is such that the

angle / C g is equal to e C /), will have arrived at 2', and

so on. Thus it is plain that the point a will be elevated

and depressed uniformly by means of the second curve, in

the same manner as that denoted by A is actuated by

the first.

It is worthy of remark that all the diameters A 8, B F,

D G, &c., of the eccentric are equal; this circumstance

may, in some instances, be taken advantage of by placing

two friction rollers diametrically opposite to each other,

which will thus be alternately and similarly impelled, and

so perform the functions of a spring.

Fig. 2 is an elevation, and Fig. 3 a vertical section of

an eccentric such as we have just described, in the form in

which it would be applied in practice.

Fin. 4. To draw a double eccentric curve which shall

o

impart a uniform motion of ascent and descent to the

point A, traversing an arc of a circle A A'.

First, divide the given arc A A' into any number of

equal parts, (8 in the present example), and from the com-

mon centre, or axis C of the eccentric, describe circles

passing through each of the points of division V, 2', S', &c.

Divide also the circle passing through 0, the centre of the

arc A A', into twice the number of equal parts; then taking

up in the compasses the length A 0, and placing one of the

points at the division marked 1, describe an arc of a circle,

which will cut at B the circle drawn with the radius Cl';

from the next point of division 2, mark off, in the same

manner, the point D in the circle whose radius is C 2',

and so on. The points B; D, E, &c., thus obtained, are

points in the curve required, which, supposing the eccen-

tric to revolve uniformly, will possess the property of com-

municating to the point A a uniform motion of ascent and

descent along the arc A A'. This admits of easy demon-

stration. The angle B C F is half of 21 C D, and conse-

quently, when the point B has arrived at 1', the radius

ENGINEER AND MACHINIST’S DRAWING-BOOK.

It is almost unnecessary to observe, that the instructions

we have given for the drawing of the anterior face F' G' of

the wheel, are equally applicable to the posterior FT T

which is parallel to it, and in all respects the same; the

common centre of all the circles in it being at O', Fig. 4,

is projected to 0 in Fig. 3. Hence, it will be easy to

construct the ellipses representing these circles in the

oblique projection, and consequently to determine the

points e, f Jc, &c., in the curvature of the teeth; observing

that, as their centre lines converge to C in the front face,

they all tend to 0 in the remoter surface, which is, how-

ever, for the most part concealed by the former.

It would be superfluous to enter into any details re-

garding the construction of the oblique view of the rim,

eye and arms, which are drawn upon precisely similar

principles to those we have already so fully explained.

Projections of Eccentrics.—Plate XYIII.

The term eccentric is applied in general to all such

curves as are composed of points situated at unequal dis-

tances from a central point or axis. The ellipse, the curve

called the heart, and even the circle itself when supposed

to be fixed upon an axis which does not pass through its

centre, are examples of eccentric curves.

The object of such curves, which are of frequent occur-

rence in machinery, is to convert a rotatory into an alter-

nating rectilinear motion ; and their forms admit of an

infinite variety, according to the nature of the motion de-

sired to be imparted. Examples of their application occur

in many arrangements of pumps, presses, valves of steam-

engines, spinning and weaving machines, &c.

Fig. 1. To draw the eccentric symmetrical curve called

the heart, which is such as, when revolving with a uni-

form motion on its axis, to communicate to a movable

point A, a uniform rectilinear motion of ascent and

descent

Let C be the axis or centre of rotation upon which

the eccentric is fixed, and which is supposed to revolve

uniformly; and let A A' be the distance which the

point A is required to traverse during a half revolution

of the eccentric. From the centre C, with radii re-

spectively equal to C A and C A', describe two circles ;

divide the greatest into any number of equal parts,

(say 16), and draw through these points of division the

radii C 1, C 2, C 3, &c. Then, divide the line A A' into

the same number of equal parts as are contained in the

semicircle, (that is, into 8, in the example now before us),

and through all the points V, 21, S', &c., draw circles con-

centric with the former ; the points of their intersection

B, D, E, &c., with the respective radii C 1, C 2, C 3, &c.

are points in the curve required, its vertex being at the

point 8.

It will now be obvious that when the axis, in its ano-u-

lar motion, shall have passed through one division, in

other words, when the radius C 1 coincides with C A', the

point A, being urged upwards by the curvature of the

revolving body on which it rests, will have taken the

position indicated by 1' ; and further, when the succeed-

ing radius C 2 shall have assumed the same position, the

point A will have been raised to 2' ; and so on till it

arrives at A', after a half revolution of the eccentric. The

remaining half A G F 8 of the eccentric, being exactly

symmetrical with the other, will enable the point A to

descend in precisely the same manner as it is elevated.

It is thus manifest that this curve is fitted to impress a

uniform motion upon the point A itself; but in practice a

small friction roller is usually interposed between the

surface of the eccentric and the piece which is to be actu-

ated by it. Accordingly the point A is to be taken as the

centre of this roller, and the curve whose construction we

have just explained is replaced by another similar to, and

equidistant from it, which is drawn tangentially to arcs

of circles described from the various points in the primary

curve with the radius of the roller. This second curve is

manifestly endowed with the same properties as the other;

for supposing the point e, for example, to coincide with A,

if we cause the axis to revolve through a distance equal to

one of the divisions, the point f which is the intersection

of the curve with the circle whose radius is C 1', will then

obviously have assumed the position 1'; at the next por-

tion of the revolution, the point g, (which is such that the

angle / C g is equal to e C /), will have arrived at 2', and

so on. Thus it is plain that the point a will be elevated

and depressed uniformly by means of the second curve, in

the same manner as that denoted by A is actuated by

the first.

It is worthy of remark that all the diameters A 8, B F,

D G, &c., of the eccentric are equal; this circumstance

may, in some instances, be taken advantage of by placing

two friction rollers diametrically opposite to each other,

which will thus be alternately and similarly impelled, and

so perform the functions of a spring.

Fig. 2 is an elevation, and Fig. 3 a vertical section of

an eccentric such as we have just described, in the form in

which it would be applied in practice.

Fin. 4. To draw a double eccentric curve which shall

o

impart a uniform motion of ascent and descent to the

point A, traversing an arc of a circle A A'.

First, divide the given arc A A' into any number of

equal parts, (8 in the present example), and from the com-

mon centre, or axis C of the eccentric, describe circles

passing through each of the points of division V, 2', S', &c.

Divide also the circle passing through 0, the centre of the

arc A A', into twice the number of equal parts; then taking

up in the compasses the length A 0, and placing one of the

points at the division marked 1, describe an arc of a circle,

which will cut at B the circle drawn with the radius Cl';

from the next point of division 2, mark off, in the same

manner, the point D in the circle whose radius is C 2',

and so on. The points B; D, E, &c., thus obtained, are

points in the curve required, which, supposing the eccen-

tric to revolve uniformly, will possess the property of com-

municating to the point A a uniform motion of ascent and

descent along the arc A A'. This admits of easy demon-

stration. The angle B C F is half of 21 C D, and conse-

quently, when the point B has arrived at 1', the radius