0.5

1 cm

52

ENGINEER AND MACHINIST’S DRAWING-BOOK.

teeth, describe arcs from the centres i, j, with the radius

of the curve, intersecting at the centre g, and on the centre

0, with the radius 0 g, describe an arc; then the centres

g, h, &c., of all the circular arcs forming the curved teeth

will be found in this circle.

Figs. 7, 8, 9, illustrate the construction of fluted columns,

and are sufficiently intelligible without further description.

SECTION III.

Drawing of Spur Wheels, and Eccentrics.

Projections of a Spur Wheel.—Plate XVI.

Spur wheels enter largely into the composition of most

machines, and to delineate them with accuracy and des-

patch requires the application of some of the most generally

useful processes in mechanical drawing. We have, there-

fore, taken as our next example of projection, a specimen

of a spur wheel with six arms, and of the most approved

modern form and proportions. It may be remarked,

however, that the curvature of the teeth is here taken

quite arbitrarily; for the true form depends upon the re-

lation between the wheel and the pinion into which it

works. We shall have occasion, in a subsequent part of

this work, to develop fully the principles which determine

the true form of the teeth of wheels; the method here

pointed out is the most convenient and simple, and wifi

be found to be a sufficiently near approximation to the

truth for all drawings executed to a scale.

Definitions. The pitch of the teeth is their distance

apart from centre to centre; and is equal to the thickness

of a tooth plus the interspace. In a wheel or pinion the

pitch is measured upon the primitive or pitch circle;

and, in a rack, on the pitch line; which pass through the

teeth midway, or nearly so, between the root and the

extremity.

Fig. 1 is a side elevation, Fig. 2 an edge view, and Fig. 3

a vertical section of a spur wheel with 54 teeth and a

pitch of 2 inches.

On the centre C, describe the pitch circle, and divide it

into 54 equal parts. To effect this division without fray-

ing by repeated trials that part of the paper on which the

teeth are to be represented, draw from the same centre C,

and with any convenient radius, a circle abed, and,

preserving the same radius with which it was drawn,

divide its circumference into six equal parts, and subdivide

each sixth into nine equal parts, and draw radii to the

centre C; these will cut the pitch circle at the required

number of points. This done, set off upon Figs. 2 and 3

the breadth of the wheel, represented by perpendiculars

drawn at equal distances on each side of E G and H I;

and, having divided the length of the pitch into 15 equal

parts, mark off, beyond the pitch circle a distance equal to

5 \ of these parts, and within it a distance equal to 61

parts, and from the centre C draw circles passing through

these points; these circles are the projections of the cylin-

ders bounding the points of the teeth and the roots of the

spaces respectively, and are to be represented on Figs. 2

and 3 by straight lines passing through the points F. G,

H, I, e, /, set off on either side of A B with the distance

of the radii of the circles above referred to.

In forming the outlines of the teeth, the radii which,

by their intersections with the pitch circle, divide it into

the required number of parts, may be taken as the centre

lines of each tooth. The thickness of the tooth, measured

on the pitch circle, is T7-g-ths of the pitch, and the width

of the space is equal to ysTths* These distances being set

off, take up in the compasses the length of the pitch, and

from the centre g describe a circular arc li i; and from

the centre j, with the same radius, describe another arc h h

touching the former; these arcs being terminated at the

circles bounding the points of the teeth and the bottoms

of the spaces respectively, form the curve of one side of a

tooth. The other side is formed in a similar manner, by

drawing from the centre l the arc m n, and from the centre

p the arc m o; and so on for all the rest of the teeth. It

is obvious that, when the length of the pitch is taken as

the radius of curvature for the teeth, as in the present

instance, the centres being all in the pitch circle, the centre

of each arc for any individual tooth wifi be in the corres-

ponding point of the contiguous tooth, which circumstance

wifi in most cases render the previous division of the pitch

circle unnecessary, and so far facilitate the operations,

but, when this method is resorted to, the utmost care must

be taken in setting and using the instruments. The teeth

are projected upon Fig. 2 by simply drawing through all

the visible angular points straight lines parallel to A B,

and terminated at either extremity by the verticals repre-

senting the outlines of the breadth of the wheel.

The teeth having been thus completed, we proceed to the

delineation of the rim, arms, and eye of the wheel. The

thickness of the rim is usually made equal to that of one

of the teeth, namely, TUths of the pitch, which distance is

accordingly set off on a radius within the circle of the

bottoms of the spaces, and a circle is described from the

centre C through the point q thus obtained. Within the

rim, a strengthening feather, q r, in depth about fths of

the thickness of the rim is generally formed as shown in

the plate. The eye, or central aperture for the reception of

the shaft, is then drawn to the specified diameter, as also the

circle representing the thickness of metal round the eye,

which is usually made equal to the pitch of the wheel;

these various circles are projected upon the section Fig. 3

* For the convenience of reference, we give the proportions of

the teeth of wheels in a tabular form.

Supposing the pitch to be divided into 15 equal parts, then the

Depth from point to pitch-line, . — 5^ parts.

Depth from pitch-line to root of tooth, — 64 „

Total depth of tooth, ... ... ... =12 „

Working depth, ... ... ... ... = H „

Thickness of tooth (also of arms and rim), =7 „

Width of space, ... ... ... ... =8 „

These proportions, to which we shall adhere throughout this work

in our examples of toothed gearing, are those adopted by the most

experienced millwrights of the present day, and we would recom-

mend the student to impress them upon his memory.

ENGINEER AND MACHINIST’S DRAWING-BOOK.

teeth, describe arcs from the centres i, j, with the radius

of the curve, intersecting at the centre g, and on the centre

0, with the radius 0 g, describe an arc; then the centres

g, h, &c., of all the circular arcs forming the curved teeth

will be found in this circle.

Figs. 7, 8, 9, illustrate the construction of fluted columns,

and are sufficiently intelligible without further description.

SECTION III.

Drawing of Spur Wheels, and Eccentrics.

Projections of a Spur Wheel.—Plate XVI.

Spur wheels enter largely into the composition of most

machines, and to delineate them with accuracy and des-

patch requires the application of some of the most generally

useful processes in mechanical drawing. We have, there-

fore, taken as our next example of projection, a specimen

of a spur wheel with six arms, and of the most approved

modern form and proportions. It may be remarked,

however, that the curvature of the teeth is here taken

quite arbitrarily; for the true form depends upon the re-

lation between the wheel and the pinion into which it

works. We shall have occasion, in a subsequent part of

this work, to develop fully the principles which determine

the true form of the teeth of wheels; the method here

pointed out is the most convenient and simple, and wifi

be found to be a sufficiently near approximation to the

truth for all drawings executed to a scale.

Definitions. The pitch of the teeth is their distance

apart from centre to centre; and is equal to the thickness

of a tooth plus the interspace. In a wheel or pinion the

pitch is measured upon the primitive or pitch circle;

and, in a rack, on the pitch line; which pass through the

teeth midway, or nearly so, between the root and the

extremity.

Fig. 1 is a side elevation, Fig. 2 an edge view, and Fig. 3

a vertical section of a spur wheel with 54 teeth and a

pitch of 2 inches.

On the centre C, describe the pitch circle, and divide it

into 54 equal parts. To effect this division without fray-

ing by repeated trials that part of the paper on which the

teeth are to be represented, draw from the same centre C,

and with any convenient radius, a circle abed, and,

preserving the same radius with which it was drawn,

divide its circumference into six equal parts, and subdivide

each sixth into nine equal parts, and draw radii to the

centre C; these will cut the pitch circle at the required

number of points. This done, set off upon Figs. 2 and 3

the breadth of the wheel, represented by perpendiculars

drawn at equal distances on each side of E G and H I;

and, having divided the length of the pitch into 15 equal

parts, mark off, beyond the pitch circle a distance equal to

5 \ of these parts, and within it a distance equal to 61

parts, and from the centre C draw circles passing through

these points; these circles are the projections of the cylin-

ders bounding the points of the teeth and the roots of the

spaces respectively, and are to be represented on Figs. 2

and 3 by straight lines passing through the points F. G,

H, I, e, /, set off on either side of A B with the distance

of the radii of the circles above referred to.

In forming the outlines of the teeth, the radii which,

by their intersections with the pitch circle, divide it into

the required number of parts, may be taken as the centre

lines of each tooth. The thickness of the tooth, measured

on the pitch circle, is T7-g-ths of the pitch, and the width

of the space is equal to ysTths* These distances being set

off, take up in the compasses the length of the pitch, and

from the centre g describe a circular arc li i; and from

the centre j, with the same radius, describe another arc h h

touching the former; these arcs being terminated at the

circles bounding the points of the teeth and the bottoms

of the spaces respectively, form the curve of one side of a

tooth. The other side is formed in a similar manner, by

drawing from the centre l the arc m n, and from the centre

p the arc m o; and so on for all the rest of the teeth. It

is obvious that, when the length of the pitch is taken as

the radius of curvature for the teeth, as in the present

instance, the centres being all in the pitch circle, the centre

of each arc for any individual tooth wifi be in the corres-

ponding point of the contiguous tooth, which circumstance

wifi in most cases render the previous division of the pitch

circle unnecessary, and so far facilitate the operations,

but, when this method is resorted to, the utmost care must

be taken in setting and using the instruments. The teeth

are projected upon Fig. 2 by simply drawing through all

the visible angular points straight lines parallel to A B,

and terminated at either extremity by the verticals repre-

senting the outlines of the breadth of the wheel.

The teeth having been thus completed, we proceed to the

delineation of the rim, arms, and eye of the wheel. The

thickness of the rim is usually made equal to that of one

of the teeth, namely, TUths of the pitch, which distance is

accordingly set off on a radius within the circle of the

bottoms of the spaces, and a circle is described from the

centre C through the point q thus obtained. Within the

rim, a strengthening feather, q r, in depth about fths of

the thickness of the rim is generally formed as shown in

the plate. The eye, or central aperture for the reception of

the shaft, is then drawn to the specified diameter, as also the

circle representing the thickness of metal round the eye,

which is usually made equal to the pitch of the wheel;

these various circles are projected upon the section Fig. 3

* For the convenience of reference, we give the proportions of

the teeth of wheels in a tabular form.

Supposing the pitch to be divided into 15 equal parts, then the

Depth from point to pitch-line, . — 5^ parts.

Depth from pitch-line to root of tooth, — 64 „

Total depth of tooth, ... ... ... =12 „

Working depth, ... ... ... ... = H „

Thickness of tooth (also of arms and rim), =7 „

Width of space, ... ... ... ... =8 „

These proportions, to which we shall adhere throughout this work

in our examples of toothed gearing, are those adopted by the most

experienced millwrights of the present day, and we would recom-

mend the student to impress them upon his memory.