PART I
READING
MACHINE DRAWINGS

BY
FREDERICK H. EVANS, M. E.
THE MANUAL ARTS PRESS
PEORIA, ILLINOIS
D R A F T IN G R O O M S E R I E S, P A R T I
READING
MACHINE DRAWINGS
J -
By Frederick H. Evans, M. E.
Assistant Professor of Manual Arts, Bradley Polytechnic Institute, Peoria, Ill.
Formerly Draftsman for the Ironton Engine Co., Ironton, O.,
the Link Belt Machinery Co. and Sarge
and Lundy, Chicago.
nt
2
Q
s
J.
o
s
THE MANUAL ARTS PRESS
PEORIA, ILLINOIS

coPYRIGHT, 1913,
FREDERICK H. Eva N.S.
FOREWORD.
On account of the recent increase in the use of the language
of mechanical drawing in technical literature, and its wide
adoption in construction work there are many persons who
need to know how to read it, yet comparatively few need to
be able to use mechanical drawing instruments.
In learning to read mechanical drawing, as it is usually
taught, the greatest obstacle in the way of many is the cost
of a set of instruments and the time and care required to learn
to use them. This pamphlet is designed as a text to teach
reading of machine drawings without the use of any other
materials than an ordinary lead pencil and a pad of cross-lined
paper, preferably ruled with uniform lines of about five to the
inch.
MACHINE DRAWING.
1. Purpose. It is the purpose of machine drawing to
accurately represent the shape and size of machine parts.
2. The Means of Representation are straight and curved
lines of different weights or widths made on a plane surface,
such as a piece of paper or cloth tacked to a board.

FIG. 1.
3. Representation. A familiar representation of a rect-
angular block is shown in Fig. 1, the straight lines representing
its edges. Such a drawing gives an idea of the shape of the
object, yet exact proportions can not be determined from it.
If, however, a view of the block is drawn as seen from a great
distance along OY in Fig. 2, the top view Y of Fig. 3 is
obtained which shows the exact ratio of the width to the length
of the block. The side or end view X of Fig. 3 is drawn from
a point of sight a great distance along OX, Fig. 2, and shows
the exact ratio of the thickness to the width of the block. In
a similar manner the front view Z, Fig. 3, is drawn from a
point of sight along OZ, Fig. 2, and shows the exact ratio of
the length to the thickness of the block.
READING MACHINE DRA WINGS 5
Any two of these views show completely the exact proportion
of the block, and if the drawing is made to a known scale the
exact dimensions of the block can be determined. Other views
*
FIG, 2.
called auxiliary views can be drawn from points of sight not on
the axes OX, OY, or OZ.
A draftsman in making the top view of an object may
imagine the paper on which he is drawing to be in the position

6 READING MACHINE DRA WINGS
Y of Fig. 4, and that he is looking at the object along lines
perpendicular to the paper. In a similar manner, he may
imagine his paper in the position X while drawing the front
21
21
|
|
2(
2
2%
C.
>4.
21
ye
N N
y
FIG. 4.
2'
view, and in the position Z while drawing the side, or end
view, each position of the paper being perpendicular to the
other two.
Another way to state it is: The top view is projected on a
horizontal plane, the front view is projected on a vertical
plane, and the side, or end view is projected on a profile plane
which is perpendicular to both.

READING MACHINE DRA WINGS

E. |
| |
tºil #—!
| ſº * --||
|| |||—| #—H
li Hill
li #–H
H I
F </
I
=
FIG. 5.

8 READING MACHINE DRA WINGS
Another way of looking at it, is to imagine the object turned
for each of the three views, the result is the same in either case.
Notice that in Fig. 1 each line represents an edge of the
block. In Fig. 3, in each view, it would be correct to say that
each line represents either an edge, two edges, or a surface of
the block. It is best to consider that each line represents a
surface.
4.%. /77. /7 * /*- */
(a) (b) (c)
FIG. 7.
Top and front views of objects are shown in Fig. 7. In
Fig. 7(a) k represents an edge only; in Fig. 7 (b) m and n
each represent a surface only; while in Fig. 7 (c) h and j each
represent only the small parts of the cylindrical surface that is
parallel to the lines of sight of that view.
Surfaces and edges hidden from view are represented by
short dashed lines, Fig. 8.
The only other case in which a line, or lines are used to
represent parts of an object is illustrated in Fig. 9. If a pattern
is made for a casting, as drawn in Fig. 9(a), the pattern is
first made with sharp corners or edges at a, b, c, d, e, and f.
In finishing, the corners at b, d, e, and g are rounded or
“knocked” off, and the corners c and f are filled in or become
“fillets.” In this case it is clearer to represent the edges in

READING MACHINE DRA WINGS 9
the front view by the lines aſ, b’, c’, etc. This cannot cause the
pattern-maker to make a mistake.
In a case like Fig. 9(b) where there is no abrupt break in
the surface, and no corners to take into consideration, there
|
(a)
(
b
)
(
C
)
FIG. 8.
|-
2, dºi i
(a) -- (b)
FIG. 9.
II
should be no other lines in the front view than those drawn.
In drafting rooms where it is customary to use shade lines, the
front view is shown as in Fig. 9(c).
Objects in which the surfaces are perpendicular to each other
can be represented by views taken along lines of sight perpen-
dicular to their respective surfaces, such as the top, front, and


10 READING MACHINE DRA WINGS
side views described. For complicated pieces, it is sometimes
necessary to take a view from a point of sight on a line oblique
to the other lines of sight. Such a view is called an auxiliary
view.
4. Arrangement. The terms top view, front view, and
side, or end view refer to what would naturally be taken for
the top, front, and side or end of an object. The top view
* * * *
|- ºr ºm aſ
FIG. 10.
is placed above the front view, and the side or end view is
placed at the right side of the front view—if a right side view,
it is placed at the right of the front view, if a left side view, it
is placed at the left of the front view. In a similar manner, a
bottom view is placed below the front view.
The right ends of the top, front, and bottom views should
be in the same vertical line. The same is true for the left
ends of the same views, or the representations of any point on
these views.
In a similar manner, the tops of the left side view, front
view, and right side view should be in the same horizontal line,
also the bottoms of the same views, and the representations of
any point in these views.
Lines drawn to carry the eye from the representation of
parts on one view to their representations on other views are
the object.

READING MACHINE DRA WINGS 11
In making a working sketch or drawing of a machine part,
any side may be assumed as the top, and any adjacent side as
one side, or end, and the views arranged accordingly.
O

ſº
Aſ4&A'ſ V/ATV/
S | -4 \ S
- - —tº SI.
/77 Eä '•l.” U /7
§ 7 O/* V/AF// §
U Ş
SJ [S
––– *º º cº-ºº:
/AF7 J//7Flſº AT/TO/V7 //ETV/ Aſ/6//7 J//7′
|
29-––– * *-* - º ºs - ºr ––––le/2
AfC277 (2/M 1//AT
y
FIG. 11.
Brief rules for arrangement are as follows:
In a drawing of two or more views of an object, if the
pencil point is placed on one view, the view on which the pencil
point rests represents the side of the object that would be illu-
minated if the pencil point were a lantern and the nearest view
the object.
12 READING MACHINE DRA WINGS
In general, the views should be so arranged that a horizontal
or vertical line drawn from any point represented on one view
will pass thru the representation of the same point on any other
view which the line intersects. (See m n, gr, and o p, Fig.
11.)


— — —
A +--G–--Ha - G)—-
| |


(a)
H –l-
|eo of º
| t | | | | |


(c) (d)
FIG. 12.
5. Sections. An object can often be best represented by
the aid of a section view, Fig. 12. In Fig. 12(a), the line
A B represents the top view of a plane cutting the object. The
section view represents what would be seen of the object if
everything between it and the surface cut by the plane were
removed.
It assists the imagination to regard the section lines as saw
marks made in sawing the object in the cutting plane.
READING MACHINE DRA WINGS 13
Section lines never cross visible lines but cross every other
kind.
Different pieces in the same view should be distinguished by
a difference in the slant of the section lines, and, if a different
material, by a difference in the spacing and the weight and
kind of section lines.
2
ſ
2
2.
i %
%
2 º
22222222222222% 3
| R-
! / Hº
(a) (b)
FIG. 13.
2
%
%
2
%
|
2
Where it is desired to show a part section it should be done
as in Fig. 12(b), or Fig. 12(c). The wavy line in Fig. 12(b)
conveys the impression that the object has been cut and then
broken off. A section may be taken as in Fig. 12(d).
If the rules of intersection were strictly followed, section
A B of Fig. 13(a) would be as shown at 2 and not as shown
at 1. Since 1 gives a better idea of mass than 2, and requires
less work in drawing, the former is more often used; that is,
thin strips of metal cut by a section plane are bounded by full
lines, and the cross-hatching is omitted. The same is true of
rods and shafts, Fig. 13(b).
















14. READING MACHINE DRA WINGS
In Fig. 14 are shown other ways of taking sections. Figs.
14(a) and 14(b) are self explanatory, Fig. 14(c) is a dotted
longitudinal section taken thru the center of the object.
No more hidden lines should be used than are required to
make the drawing clear.
Z2/.
% | --,-l.--
Z * * *
*% F-ºf-ty.
%%.3% || ----|
4% ºft ! --|--| --
4% }%2%.2% ; r
4%%22% } ---4
*2. 22, Z -;
£3%%% ——t !---'
|
FIG. 14.



READING MACHINE DRA WINGS 15
CoNVENTIONAL SCREw THREADs.
PLATE R–1.
Section of V Thread.
Section of U. S. Standard Thread.
Section of Whitworth Standard Thread.
Shaded Drawing of Screw Thread.
. Line Drawing of Screw Thread.
6, 7. Ordinary Conventional Forms of Representing Screw
Threads. 7 is adapted to smaller sizes than 6.
8. A Conventional Form Adapted to Very Small Sizes.
9. Top View of a Tapped Hole.
10, 11. Easy Conventional Forms Especially Adapted to
Hasty Sketches.
12, 14. Conventional Forms of Hidden Threads.
13. Conventional form of Section thru a Tapped Hole.
All of these represent right-hand screw threads. Left-hand
threads are slanted in the opposite direction.
6. Symbols. Mechanical drawing has been called a
“graphic language:” as such, in its development, symbols are
taking the place of picture representation. For an illustration
of this study Plates R–1, R-2, and R–3.
i
16 READING MACHINE DRA WINGS
PROBLEMS.
The following problems are to be done freehand with a soft
pencil on cross-ruled paper. Paper with uniform light blue
lines about three-sixteenths inch apart is the best. The drawing
should be well arranged on the paper. Begin by laying out the
general arrangement in very light sketchy lines, leaving details
for the last.


Nºz
NLZ
CZ
FIG. 15. FIG. 16. & FIG. 17. FIG. 18.



FIG. 19. FIG. 20. FIG. 21.
Problem 1. Figs. 15–21 represent top views of figures that
are cut from lumber one inch thick with a band saw. Draw
the front view of each.
Problem 2. Draw the side view of Figs. 15–21. For Fig.
15 see Fig. 26.
Problem 3. Draw three views each of Figs. 15–21.
READING MACHINE DRA WINGS 17
Problem 4. Draw three views each of Figs. 22–25. (Two
views are given.)
Problem 5. Copy Figs. 27–38 and supply the omitted view
in each one.
Nº. Nº NIZ ex
FIG. 22. FIG. 23. FIG. 24. FIG. 25.
In Fig. 28 would the front and the top view be sufficient to
show the shape of the piece?
In Fig. 29 notice the change made in the front view by
rounding the corners of the base.

18 READING MACHINE DRA WINGS
| |
| | |
Filſ. Iſſy_ _l. ... TI I
— i) |
- i - -
FIG. 3ſ). FIG. 31.
| i
| |
- | |
| |
FIG. 33. FIG. 34.
FIG. 36.
| | | | | _1_Hill-
| | | | |
FIG. 37. FIG. 38.




READING MACHINE DRA WINGS 19
In Fig. 30 notice how a fillet is shown in the front view.
In Fig. 31 compare the top view with the top view of Fig.
30.
In top view of Fig. 32 omit the hidden lines.
In Figs. 33–37 study the use of hidden lines.
In Fig. 38 draw the top view in section and compare with
the top view of Fig. 37. Is the end view a true section? Why?
Problem 6. Redraw Fig. 39 and use a better arrangement
of views and sections.

20 READING MACHINE DRA WINGS
Problem 7. Copy Figs. 40–43 and draw a third view in
each case. Notice that the two views of Fig. 43 are not drawn
to the same scale.

—&


FIG. 40. FIG. 41.




FIG. 42. FIG. 43.
Problem 8. Draw three views of a piping arrangement
using every fitting represented in Plate R–3.
Problem 9. Draw an assembled view of the connecting-rod
detailed in Plates D–1, D–2, and D–3.
Problem 10. Draw a section of the engine main bearing
shown in Plates D-4, D–5, D–6, and D–7a, D–7b, D–7c.
Problem 11. Find how the pieces detailed in Plates D–1
to D–12, inclusive, go together.
, UN 2 1 1918
The Drafting Room Series
By FREDERICK H. EVANS, M. E.
I. READING MACHINE DRAWINGS.
Pamphlet of 20 pages and 17 plates.
Price, in Filing Box, 75 cts.
Without Box, 50 cts.
II. MACHINE DRAFTING.
Pamphlet of 48 pages and 44 plates.
Price, in Filing Box, $1.25
Without Box, 1.00
III. INTERFERENCE OF Moving PARTs
AND TOOTH GEARS.
Pamphlet of 40 pages and 21 plates.
Price, in Filing Box, 90 cts.
Without Box, 65 cts,
THE SERIES COMPLETE WITHOUT
DUPLICATE PLATES.
Pamphlet of Parts I, II and III, with 54 plates.
Price, in Filing Box, $2.00
Without Box, $1.75
- % -
f : .
**.
- 3%
ºr “ , , * . -- t
- x. $. 1 - #
... 3 3 * - ,” -
* * ..." +. - -
-** J .-- : <- - - - * *
* ºf -
... …" -
* †. * -, -
º } = - 5
f T -
*: ' . . . . , -
#4.” ... " -- ... "
| 1-3 - - -
štº".]". " , , .
sº • * * *,
º, *-* - - ‘. .
#1- º -
3. … h -
gº.T. - $– …" -
| -- i. - --
t , --
+: c 3. -
- * * *
| * – a
. t
•, -
- | " .. * → x
*.. 3. ~
3 -
- I 3r
-: *
t -- 3. V- *... •
s * : 4.
3 * *
• ? º
~ * ,
***",
cº- § - i
*_ - ;
Tº t x- - t - + *-
* I' - - ^* - r
*: * - * - * -
g: • 3. z - -
:... ." a. - -
º A. - - *
:* * , t -
*"... . , - - -- -
- 4 +
* *, * + -
# * * -
§§. 4.
* ~~ * f : - -
# * {
º
* .
i- * { R
º - - -
º ". . . ' … 2.
- s • -
ſº. -
-, s * - Y.
- § -
º:- *.
: r * - - - - - - --> - ww.
e; - - - * t ~3 *
Pºe - -
-- - , - $ -
*;. i- - -- - -
- - x- |
š. - t t * 3.
x * - 3. - r * ,
,3 . • § 3. *š. - - -8. - “. . . 's bºx
* - * - - t w” - -- : ** - -
# , . . - - - º - - - : *
‘....' - t t” -
* * - - - -
* r y x
º,” - , , ; * • * 3r * - & a “ ”
* ...,& - - *~ * 4 -- --
# * * * *. ... “ t -
s: - - * . * * . - & 8 K. -
} | .. * - - - * r - . • :-
#3 º' - - -- - * • - - - >. - ... *
º, w - * 3 - 3. - ‘. - * , ~ *
" . . . - : - - f
* * ; : *- f -: * * * - { * * ! ~~ #
- * - + T & - - - - -
1,\ - a- ... " - - ... * - -: - # - - * - - g rº
•' ... * * - r - - - - -- - ----- -- * 4. & ... ', ' ' ' ', e.
*-*.*. - - - - - .
rº-. 3 * *, -- - -- º - - - ;:
* , a “ r - ~ : ** - * .. s - ' º
*** * * * -- * 4. - .. r - - º -- - r x- * , - • *-ºr
1 : *** •r * * f -- - * - - - 3. - -- - -- ~ * *
2: 4 -- ... * - > • . - - A ~ *
it ºr ..— ... ". ." -- * ~~ - - * -- - -- s - ~ * f.” .
* - -
* † - . . . " z 3. - * , , ” “ - * * * *, *. - - - ! + , * * ~ *
Eºr } - * * –. ~ * -- 3. • - 3 * - * *
*::, . **** ***.*-*- * * *-* -- ...,' ... * < 3. - - - - . k --
- - - - - - & - -
×3 - ". i & * * $t - . . . - º g
: - - - a • - - - r. *. -> . - - , - . s
& | 1 . . . . . : * - * * - ..'. -
- _ _ " : * , * * ... "
... < * , - i -Y - - - ... ." . T. --- - - - - -
- 2 * j . . - • * * - - - :- --
i - - - - t - * * , } - * > . ~ – - h
- • 3. * : * - - - } - - - *.*
- i. & > . * -- * -' { -*
º- - - * . º 3-
- ** rº. 3. [. -
- i - *. -- - t
- - -- J 4. ; & &
… * * . | *. $. * ... * ~f~
- - y r * .
a * 1 M. * - s- 5 $ x
:- x - - * * b --
.# *- - - - #
> 4. - - $ •. . . .--
- - * %.
x - *. … " • *, *
+ k ~. > - " ;
- - t = - t
• * , ". - § - . 1" - ~ -.
- - * ~. - → *. *
-- * * -- *
-- . . - - - - $. - * { * * * * -- .* 3r *
t & - -- - , r .-
is: . . . . ** • .’ * .* ... * -. - ~ *
*- * { z - - • * - - ~ -- • * *
y * - - ‘. * . * * - - - * *
* - - * * * -: ~. -
º, { - - - - - - h
* f -$. --
- .* - r k h - + 3
- > ** + - ſº ‘. . . - * }
* - *: - ~t * ... f : * * > : f - *
t + - ... * . -* r: *:
i. * * , - + - * , ºr - y §
*-3 - - 3. - - - * * ~ - 4. *. -
* -- -- " - * * . * - * * , - *
... º. º: * - - -3 * - - - * * * - --- } * -
* ... "… 3. * > * . . . . *** - f § . . . * - # *
* * * * $ - • * : ... " .. s: - Y- r -
- * ! * * * : . * * *- ... * - .*
-. - *. | ,- - - 3. w -
--- ... • * , , . - - - - i - & sº •'
• * * … sº ". * → -. -
. . . . , < : --.
: " ' ". wa - → . - * *
sº y - f - < - - u-
." : - , *2 - - - - , , --, r " * vº -
- × * - * * • *. - - -:
*-* < x. * - a r * . . & - * :-T
- - 4 *
. . . ... ." t - *
$ * - * -- -, - x + xi § * T. A
.* * * ,. -: ---- - 3. } -* * 3. “… • .
1 * * . . . - * * ... * * 7 . - .
- - * " - « »- 3.
• *-*- ; ~ *. . . * * * - - - -
* * * * * { - - ... *s }
* , # --- *. * - ... *
" . -> * { 3 - - # :- … *
- + - : -.'" 3 * * r -- * - -" - - * * , ,”, “ . *:-- º: , - x - - : ** : * ,
** * <º # - s - * t # p * - r * *
F."...sº : * - * • *- |- * - - - - * * - ... " " :
- * ! 3 - 3. ~r & -> * - - 2.
i. --->
- 1, * * *
# , " '
3.”
$º '.'
§
g: J'
A'. …. ."
!.
s: • **-
§º,
º, º.º.
º º - **
* . . a. k * - ... *- " ... " .
* †. ::: *...*"º:, ; ºf , º, . *:::#sº
.*.*.*, *, *...* : 5 * : . . . . .';* * *
". . . . . . . . . . . * * *, *, . **-*.-->
**::::. . . . . . . . . . . . .' * * * *
- § 3 ; - ~
... x - 3 $ ** }:
§ -- le.-: , ;
f a'ºxº §:
* xº-. ...ºr ºf







































































* --> , “.
4 * f 3.
f -
4 * ~ J
3.
THE DRAFT IN
|
MACHINE
FREDERICK F
THE MANUAL A
PEORIA, IL



D R A FTI N G R O O M S E R I ES, P A R T I I
MACHINE DRAFTING
THE DRAFTING ROOM
DETAILING
TRACING
THE GEOMETRY OF DRAFTING
KINKS AND SHORT CUTS
By FREDERIck H. Ev ANS, M. E.
Assistant Professor of Manual Arts, Bradley Polytechnic Institute, Peoria, Ill.
Formerly Draftsman for the Ironton Engine Co., Ironton, O.,
the Link Belt Machinery Co. and Sargent
and Lundy, Chicago.
THE MANUAL ARTS PRESS
PEORIA, ILLINOIS
coPYRIGHT, 1913,
FREDERICK H. EVANS.
FOREWORD.
To learn of the modern drafting room, and to do the work
that is done there, is worth while, for the drafting room is the
“thinking shop” of any large organization doing construction
work. The thinking in the drafting room directing the skill
in the shops produces modern machinery, and machinery
characterizes modern civilization.
The most valuable thinkers in the drafting room come from
the shops. The student will find in the use of this book that
while shop experience is not essential to its beneficial study,
yet, it is essential in order to derive the greatest benefit from it.
Few students, having had plane and solid geometry, are able
when beginning machine drafting to efficiently apply their
knowledge of geometry to the drawing board.
In the text that follows are presented geometrical problems
that have risen in the author's work in machine drafting,
covering a period of over ten years, and the solutions given are
the best solutions arrived at after many hours of study. The
problems are presented in their own language, in the drawing
board language of conventional lines.
In Kinks and Short Cuts are presented some time-savers and
error-reducers.
Draftsmen are so in the habit of thinking of paper as a
material that they generally neglect its use as a tool. The
“templet methods” here shown make very useful tools out of
paper.
THE DRAFTING ROOM.
7. The Work of the Machine Draftsman lies between
the conception of a mechanical idea in the mind of an inventor,
and the giving of comprehensive detailed instructions to the
men who are to build and set to work the machine that em-
bodies the idea.
The inventor may be the president of a manufacturing con-
cern, or a man in the shops who makes a suggestion. The
drafting room work may be done by a large office force con-
stituting the drafting room, or it may be done by one person
who may be both the inventor and the maker of the machine.
We may for convenience consider the drafting room work
divided into five classes, as follows: the work of the (1)
designer, (2) detailer, (3) tracer, (4) blue-printer, and (5)
checker. This classification is not a rigid one. One person
may do two or more classes of work, or the work of any or all
classes may be subdivided.
8. The Designer. The designer must, in his imagination,
see the completed machine as a whole. He generally makes
freehand sketches which he changes and modifies until the
proper relation of parts is obtained. He calculates certain im-
portant general dimensions which are determined by the kind
of work the machine is to do, the space it is to occupy, the
necessary strength and weight of parts, etc. After his idea of
the machine is formed, he consults with the inventor, and then
gives his sketches and necessary explanations to the detailer.
9. The Detailer. It is for the detailer to work out the
parts. He makes an assembly drawing accurate to scale, tests
for interference of moving parts, and decides how each part
can be most easily and cheaply made. He must consider the
shop equipment and facilities for doing work. He makes de-
tailed working drawings in pencil, grouping on one sheet the
pieces that will be made by one person, or in one part of the
5
6 MACHINE DRAFTING
shop. He must, in his mind, go thru the process of manufactur-
ing, and place the dimensions and notes on the drawings so that
they will be most convenient for those who are to work from
them. He suggests to the designer any alteratoins in design
that are necessary, or, that will be an improvement. When
his work is completed he submits it to the designer for approval.
The pencil drawings are then turned over to the tracer who
traces them on tracing cloth in ink. The tracings are given to
the blue-printer who makes a set of blue-prints for the checker.
10. The Checker. It is the work of the checker to find
things wrong with drawings. He plainly and prominently
marks all of the mistakes, omissions, and errors that he can
find. After he corrects them, the blue-prints go to the persons
who made the mistakes to be approved and altered or redrawn.
New prints are then made and sent to the shops.
11. Erecting Card. For a complicated machine, an erect-
ing card is made and sent to the erecting floor. An erecting
card is a drawing showing how a machine is assembled, and
having on it dimensions to aid in fitting the parts accurately
to place and detecting any errors of construction.
12. Mistakes on drawings are generally found in the shops,
and improvements in the design are suggested. A list of these
mistakes and profitable changes is kept in the drafting room,
and the tracings are altered when convenient.
13. Foundation Plans and Limit Drawings of large
machines are sent to prospective purchasers. These give all of
the information necessary to lay the foundation, shows how
much space must be allowed for the machine when set up, and
what connections must be made to it.
14. Lay-out Drawings. Where a number of machines
are being installed, a lay-out drawing is made which shows the
positions the machines occupy in relation to each other and to
surrounding objects.
Title. On drawings that are to be filed for reference a
space should be left for a title. In the title is placed the in-
formation one needs before using the drawing. The uses to
MACHINE DRAFTING 7
which the drawing is to be put, and the system of filing de-
termines the character of the title.
The title should be placed in a corner of the drawing—
generally the lower right-hand corner, for then it can be seen
by lifting the corners of the drawings, making it unnecessary
to remove any drawings from the drawer. In the title the
number of the drawing should be placed nearest the corner.
In some systems the title contains, the name and address of
the company, the name of the machine, the type of drawing
(detail, lay-out, or assembly), the names of parts drawn, the
scale or scales used, date of completion, drawing number, and
initials of all persons responsible for the drawing. Besides this,
there is often a bill of materials.
On the other hand, where it is desirable to save space on
the drawing, the drawing number only is necessary. All other
information can be kept in the card index which includes all
drawings.
In the problems at the end of this chapter, the title should
be considered and a form selected and rigidly adhered to, in
order to make the drawings uniform.
15. Records. Drawings not only serve the purpose of a
set of instructions to workmen, but they serve as a complete
record of the machine that makes it possible to replace broken
parts from the factory without having the broken part returned.
Factories manufacturing high grade machines generally keep
drawings for this purpose for many years, and thereby many
bad deeds of draftsmen live after them and are multiplied many
times.
16. System. When one considers the many tracings that
accumulate in a drafting room, that they are constantly being
sent to the blue-printer, that they are frequently corrected and
altered, thereby invalidating all prints made before, it can
readily be seen that not the least of a drafting room is its
system.
8 MACHINE DRAFTING
DETAILING.
The first work the detailer should learn to do is to make
pencil drawings ready for tracing, either from scale drawings
or from dimensioned sketches.
17. The Tools used by the detailer are the drawing board
and tee-square, 30°–60° and 45° transparent triangles, 4H
and 6H pencils, scale and pricker point, bow-pencil, bow-
dividers, hair-spring dividers, pencil eraser, thumb tacks, and
sometimes an irregular curve.
18. The Paper should be tough, and should withstand
erasing. Brown, or cream color is less trying on the eyes than
white.
19. Aims. In detailing drawings that are to be traced
and blue-printed, the results to be striven for, in order of im-
portance, are:
(a) To arrange the drawing so that it will be most con-
venient for those who are to work from it.
(b) To lay it out so that the tracer can do his best work.
This requires that the drawing be neat, and that the centers
of arcs be accurately and visibly located for tracing.
(c) Speed and ease of execution.
(d) Accuracy to scale.
THE INSTRUMENTS.
20. The Drawing Board should be about six inches
larger each way than the drawing paper sheets. It should be
made of soft wood, should have one edge true, and be con-
structed so that it will not warp. *
21. The Tee-Square should be light, and the blade should
have transparent edges, and be no longer than to reach over the
longest drawing for which it is used.
22. The Triangles should be transparent. It is con-
venient but not essential to have two pairs of triangles, one
with edges long enough to reach across the drawing, and each
of the other pair much smaller for small detail work.
MACHINE DRAFTING 9
23. The Scale may be made of boxwood, steel, or boxwood
with white edges. The 12” triangular boxwood scale gradu-
ated to 12”, 4”, 3”, 2”, 14”, 1”, #”, #", 3”, +”, and 4”=1:
is a good all-round scale. For small work, a 6" flat boxwood
scale with bevel edges graduated to 3”, 1}^, #”, and 3’’=1’, is
very convenient. Flat boxwood scales as long as 12” are apt
to warp. *

|- mTºmmy'ſ
O }
7/re "Av// Scaſe ºraavarea’ fo
six fee/7//is.
O
S
|
sº
|
\)
| |
"In '1'1' 1" | 1 | | | | º
HTTTTTTTI-I-I-II r",
5.ca/e &raa'ozarea’ fo
. or # 3/ze ana.

3. ... .ºrf
& orsz Jize
#.6'
==
FIG. 44.
In Fig. 44, is shown two edges of a draftsman's scale. The
edge shown in the top figure is graduated to sixteenths. In
the lower figure, on the left from 0 to the left a space of three-
fourths of an inch is laid off and graduations made as tho the
three-fourths of an inch were one foot laid off to read down to
half-inches. To the right of 0, the figures 1, 2, 3, etc., repre-
sent feet to the same scale.
In the same way, three-eights of an inch is laid off to the
right of 0 near the right end to represent one foot graduated
down to inches, and the figures 2, 4, 6, etc., to the left of this
0 on the right, represents feet to the three-eights-equal-one-foot
scale.
The distance between the line AB and the line CD, by the
#” scale is 3'-74”.
The distance between CD and EF by the 3’ scale is 7–5”.
10 MACHINE DRAFTING
24. The Pricker Point. In marking off distances from
the scale, the conical pencil point should be used, or, for very
accurate work, the pricker point. A very good pricker point
can be made by removing the eraser from a hexagonal pencil
and inserting a needle held by sealing wax in its place. An
ordinary sewing needle is best on account of its flexibility.
The side of the needle can be pressed into an indentation of a
division on the scale without digging into it. This is a very
handy instrument, in many ways, to have on the drawing table.



A * Z3 sº º'
.5ecr A-A
sº-sº ºmº
Weſz Gar CTO/Y / CT/4 4. Æ4 G GATA’
Aro//v7r /*o//yr A-2//yr
FIG. 45.
25. The Hard Pencil. The accuracy and neatness of a
drawing depend largely on the point of the pencil with which
it is made. In Fig. 45 are shown three pencil points, the
wedge, conical, and dagger points. In sharpening a pencil
point to any shape, the wood is first removed with a knife,
after which the lead is brought to the correct shape by rubbing
it over a file held in the left hand. A file is much better for
this purpose than either sandpaper or emery paper. No at-
tempt should be made to cut the lead with a knife.
26. The Wedge Point. In unskilled hands, difficulty is
experienced in keeping the flat side of the wedge flat against
the ruler edge of the triangle or tee-square, as it should be.
MACHINE DRAFTING 11
It is also more difficult to sharpen than the conical point, can-
not be used to point off distances, and renders it difficult to
stop a line in exactly the right place. On the other hand, it
can be sharpened to a more acute angle than the conical point
without weakening it too much; it does not wear dull so
rapidly, requires less sharpening, and, carefully used, makes
lines more sharply defined. It should be held flat against the
ruling edge and only slightly inclined in the direction in which
the lines are drawn.
27. The Conical Point. The conical point should be
twirled while drawing a line, and slanted in the direction in
which the pencil is being moved. In sharpening, care should
be taken not to file the point so sharp that it will immediately
break on using. A test will best demonstrate the relative
merits of the different kinds of points.
28. Accuracy Test. Plate D–13 shows how the tee-
square and the two triangles may be used to obtain the half,
fourth, eighth, sixteenth, etc. of a line AB by a series of bi-
sections. By reversing the process, a line GH may be multi-
plied two, four, eight, sixteen, etc. times.
This problem is a test of a draftsman's accuracy and his
ability to sharpen a pencil to do accurate work. The student
should use the problem to experiment on different shapes of
pencil points.
29. The Compass Lead. Fig. 46 shows steps in sharpen-
ing the lead for either the bow-pencil or the compass. This
is done by holding the file in the left hand and rubbing the
lead back and forth over it. The edge ab should be less the
smaller the circles to be drawn.
The point should be finished by very lightly rubbing the
back of the lead c over the file, giving it a rocking motion to
round it.
The lead should be brought to this shape before inserting it
in the instrument. When the lead wears dull, it should be
sharpened without removing it, by filing the back.
It is essential that the edge de be kept perpendicular to a
12 MACHINE DRAFTING
line passing through its center and the needle-point of the
compasses and that the face gf, as well as the needle-point, be
kept perpendicular to the paper.
30. Making a Detail Drawing from the Sketch. The
following steps are given as an example of the process of
making a detail drawing. The method should be studied, yet
77/E COM/FAS.5 / FTAA’
(£
º
—z—,
J
it should be borne in mind that each drawing is a problem in
itself, and no set of fixed rules can be laid down by which to
proceed. For rapid and accurate work, not only should the
correct use of the instruments be reduced to a habit, but, also,
the use of plane geometry in the preliminary construction.
The light construction lines here plainly shown are mis-
leading, for on the drawing they are done with a very sharp
6H pencil, and are made with a light touch only heavy enough
to be barely visible.

MACHINE DRAFTING 13
Fæ ºv.--
{
*
§
\\
yº
2A. AT&2/~7 AA-2/P/Y& A-Zoº. 23
// A/ */ &/o/* fy f'ſ 2-2.
2222222 22-22,222 °33/.3T
yezºe:- dºes oºza era&memočevo Žev
THE SKETCH AS THE DETAILER GETS IT.
Fig. 48.
SPACING.

14 MACHINE DRAFTING
(1). Light Penciling. A horizontal and vertical line drawn
in each view, from which it is convenient to measure.
(2). Light Penciling. The principal vertical distances laid
off with the scale and pricker point, and horizontal lines drawn
thru the dots as shown.
(3). Light Penciling. Horizontal distances laid off and
vertical lines drawn thru them.
The space the drawing is to occupy is now laid out and there
should be enough room left for dimensions and notes. If the
space is likely to be crowded, lines should be drawn for the
lettering. There is nothing more annoying than to work a
drawing out in detail and find at the last that it must be done
over because “there isn't room.” Such a waste of time can be
prevented by doing the spacing first.
Fig. 49.
BLOCKING OUT DETAILS AND GEOEMTRICAL
CONSTRUCTION.
(4). Light and Heavy Penciling. Centers located. Con-
struction lines that are to be object lines should be drawn
heavy. -

MACHINE DITAFTING 15
Fig. 50.
FINAL CONSTRUCTION UP TO STRAIGHT OBJECT LINES.
( 5). Light Penciling. Geometrical construction finished.
( 6). Heavy Penciling. Circular arcs drawn.
Fig. 51.
THE FINISHED DRAWING.
( 7). Heavy Penciling. Horizontal object lines drawn.
(8). Heavy Penciling. Vertical object lines drawn.
( 9). Heavy Penciling. Slant lines drawn.


16 MACHINE DRAFTING
(10.) Heavy Penciling. Freehand arcs drawn. See Fig.
52. w
(11). Medium Penciling. Dimension lines drawn.
(12). Heavy Penciling. Dimensions and arrow points.
(13). Freehand Penciling. Cross sectioning.
(14). Indicated but not drawn in pencil. Threads.
It is convenient to do light pen-
ciling with a 6H pencil, and

medium and heavy penciling with
a 2.H. |
In inking and tracing the final
steps beginning with (6) are
followed.
For methods of sectioning, see
Art. 56.
31. Dimensioning. Plates
D–14 to D–18, inclusive, should
be carefully studied. It is important that the student study
out “the reason why” in each example where “Avoid” is used.
Plate D–14 shows different methods of dimensioning, and
what to avoid. Where all dimensions are in inches, the inch
mark (*) should not be used.
Each drafting room has a style of its own which a new
draftsman is supposed to adopt. -
In Plate D–17 “polish” indicates that the surface is to be
polished without conforming accurately to any dimension.
“Fin. & Polish” means, finish to dimensions before polishing.
“Fin. & Scrape” means, finish to dimensions and scrape until
the surfaces are in contact over their entire area.
“Fin. & Grind” means, finish close to dimensions and com-
plete the machining process by grinding. -
“Spot Face” means, finish to dimension only the spot so
designated.
“Trim” generally means, trim with a cold chisel.
A “Cored” hole is made in casting.
A “Drilled” hole is drilled from solid metal.

FIG, 52.
MACHINE DRAFTING 17
“Bore” indicates that the hole is to be “Cored,” allowance
being made for finish.
TRACING.
32. The Work of the Tracer is to copy pencil drawings
in ink. This is generally done on transparent tracing cloth,
or tracing paper, securely fastened over the pencil drawing.
The traced drawing is called a tracing. Blue-prints are made
from tracings by a process similar to the way in which photo-
graphs are made from negatives.
33. Legibility. To the tracer belongs the art of delinea-
tion, and his first concern should be to make his tracings legible.
This is done by choosing the proper weight for each kind of
line, and drawing it accurately; by making neat legible letters
and figures; and by placing dimensions, notes, etc. where they
best serve their purpose. The tracer should consider who is
to read his drawings, and make them accordingly. The con-
ventions of drawings are not everywhere the same, because
mechanical drawing is a language, and must necessarily have
different “dialects” in different localities, and under different
conditions.
The drawings in this book were traced according to what
the author believes to be the most generally used standard.
34. Lines. The general shape of the object represented
is the first thing looked for on a drawing, hence, the object
lines should be the most prominent lines.
The object lines are: visible lines, shaded lines—if used,
and hidden lines. All other lines are auxiliary lines. These
are: projection lines, dimension lines, extension lines, center
lines, cross-section lines, and leading lines. These lines should
be made so as to be readily distinguished from each other.
It is not good practice to ink a drawing that must be ac-
curate to scale; such drawings are generally made in pencil.
If inked at all, they should be inked with as fine lines as will
serve the purpose.
18 MACHINE DRAFTING
Most of the tracing done is of working drawings. If the
drawings are fully dimensioned, as they should be, neither the
tracings nor the blue-prints should be scaled for exact dimen-
sions by persons who read them.
&o/e7 //me
of Cy/maer &emſer //mes
Jeaſon //memofon Line,
4//7e5
W3///e//ne
/// A//7e
eaa/72 4//7e
A xfension or
Projection Al//7e
FIG. 53.
In inking, for the sake of legibility, the object lines should
not be so heavy as to obscure the smaller details, nor so light
as to necessitate making the lighter auxiliary lines too light
to be easily followed, yet, there should be an easily discernable
contrast between them.
For expediency, lines excessively heavy should be avoided
because of liability to blots, and the longer time required to
dry. Unnecessarily light lines should be avoided because of
the extra time required in cleaning and refilling the pen, for
the ruling pen clogs more often in drawing light lines. Other
determining factors are the kind and the size of the drawing,
the kind of surface on which it is drawn, the quality of work
that should be done, and the time limit of doing it.







MACHINE DRAFTING 19
Until the young draftsman has had sufficient experience to
temper his taste by good judgemnt and develope a “line sense,”
it is well to follow some arbitrary standard such as is given in
Figs. 53, 54.
The figures in dimensioning should be large enough to be
distinct, yet, not large enough to crowd.
The arrow points should catch the eye but not disfigure the
drawing.
35. Rapidity. Next to legibility the tracer should strive
for rapidity of execution.
Time should not be spent in making short dashes in auxiliary
lines when longer ones will do just as well.
Before starting to trace, the drawing to be traced, and the
process by which it was made should be thoroly understood.
The instruments should be in good condition and adapted
to the work to be done.
Care should be taken to eliminate unnecessary motion.
Correct habits of work should be formed.
This chapter should be carefully studied, for, what does not
apply to the quality of a tracer's work, applies to ease and
rapidity of execution.


20 MACHINE DRAFTING
36. Light. The ideal source of light is the one that will,
while at work, evenly light the field of vision with the proper
intensity.
Too bright a light is as bad as not enough.
Light concentrated on the drawing, with dimly lighted sur-
roundings should be avoided; nor should any object in sight,
while the eyes are on the work, appear brighter than the
drawing.
The light should be diffused and in such a position that if a
mirror were laid flat on the table just beyond the upper left
hand corner of the drawing, the center or brightest part of the
source of light could be seen in the center of the mirror when
the draftsman is in a working position. This position of the
light will cast the fewest annoying shadows from the hands
and the instruments, and will not be reflected directly into the
eyes by the drawing.
Whatever the light, the draftsman should be careful to
shade his eyes from all glare.
The best source of light is daylight thru high north windows.
If a draftsman has any choice in the location of his table, he
should choose a position by a window with a northern exposure
—provided that the room has ample heating facilities.
A draftsman should bear in mind that his eyes are his
greatest asset, and that they are subject to greater strain in
drawing than in most kinds of work.
37. Position of the Board. The drawing board should
be a little higher than the elbow in its natural position when
the draftsman stands or sits ready for work. The board should
not be slanted more than twenty degrees, a greater slant causes
the ink to flow down vertical lines, and any objects on it to
roll or slip.
Draftsmen often injure their health by leaning on the draw-
ing table while at work. This is a bad habit that should be
avoided.
38. Preparation of Tracing Cloth. The tracing cloth
should be cut large enough to allow for trimming square when
MACHINE DRAFTING 21
the tracing is finished. The extra margin is very convenient
to try the pens on when adjusting to the proper weight of
lines. When a number of tracings of the same size are to be
made, it saves time to cut a number of pieces of cloth to the
most economical size and lay them away flat in a drawer or
envelope.
For a small tracing, square up the drawing to be traced,
inserting a tack in each of the upper corners, place the tracing
cloth—glossy side up—over the drawing, insert a tack in each
of the lower corners, remove the upper tacks, draw the cloth
tight and re-insert the upper tacks.
A large tracing should first be drawn tight by placing a
tack about the middle of each of the longer edges, then, draw-
ing from the center, insert a tack near the middle of each of
the shorter edges, and finally tack down the corners. This
prevents the cloth from wrinkling.
Opinion differs concerning the proper side of tracing cloth
to use. The glazed side was glazed for the purpose of being
used, and, lacking other information, the beginner should use
it. There are purposes for which the unglazed side is better,
these will be learned by experience.
Before tracing, sprinkle fine powder such as chalk dust,
talcum powder, or soapstone on the cloth and rub it with the
fingers until the cloth loses its oily feeling. Brush off loose
particles with a lintless cloth. -
39. Uses of Instruments. The drawing table should be
kept as clear as possible of things seldom used. The in-
struments and articles for tracing are:
For Applying and Preparing the Cloth; thumb tacks and
some finely pulverized powder.
For Guiding the Ruling Pen; the tee-square, 30°–60° and
45° triangles, and irregular curves.
For Applying the Ink; the ruling pen, compasses with pen
point, bow-pen, and freehand pens.
For Filling and Cleaning the Pens; the ink bottle with a
quill, and a lintless cloth pen wiper.
22 MACHINE DRAFTING
For Removing Ink Blots, Cleaning, Erasing, and Burnish-
ing; a piece of absorbent cotton rolled in a paper, or a blotter,
an ink eraser, an erasing shield, a soft rubber eraser, a sharp
steel eraser, a dust cloth, and a burnisher. -
40. Arrangement on the Table. No definite rule can
be laid down as to the exact spot each article used should
occupy on the table, yet, for easy, rapid work there should be
a system in laying down and picking up instruments. Bad
habits formed in handling instruments are as fatal to a drafts-
man as the “forefinger” habit is to one who would become an
expert on the typewriter, or a pianist.
In the groups named above, there are instruments for the
right hand, and instruments for the left hand. In moving
instruments out of the way it is natural for the right hand to
move about the elbow as a center to the right, and the left hand
to move about the left elbow as a center to the left. There-
fore, the right-hand instruments should be placed in an arc
that the right hand will sweep over when moving about the
elbow in its natural position on the table. The instruments
oftenest picked up and laid down should be nearest the draw-
ing. The same principle holds for left-hand instruments.
When done with an instrument, it should be carried to its
place in the same motion that another one is picked up. The
draftsman should be able to pick up any instrument without
taking his eyes from his work.
A natural and handy arrangement is shown in Fig. 55.
41. Instrument Testing. Ruling Pen Points. With a
piece of white paper for a background see that the point is as
follows:
The nibs are of equal length when closed.
The profile of the nibs is regular and without sharp angles.
The nibs are not too blunt, nor yet so sharp as to cut into
the paper.
The screw works smoothly and without slipping threads.
42. Bow-Pen. Test the pen point and screws as above.
Fic. 55.

MACHINE DRAFTING 23
See that there is sufficient tension in the springs to open to
the widest.
That the needle point and the pen point come together when
closed.
Adjust the needle point so that it is about ºf" longer than
the pen point when closed. *
The needle point should be sharp enough not to slip with the
weight of the instrument.
43. Compasses. Make the same tests of the pen point
and the needle as of the bow-pen. º
The compass has three joints, to test for alignment, see that
the pen point and the needle point can be brought together
when the lower joints are straight, and when they are bent to
nearly their limit.
The lower joints should not bend when the upper one is
bent while holding the compass by its points.
The tighter the joint, the less accurately can measurements
be made. The looser the joint, the more delicate must be the
handling of the instrument to prevent its slipping.
To obtain the proper adjustment, a number of concentric
circles should be drawn in pencil and traced very accurately in
ink, trying different adjustments of the upper joint until the
right one is obtained. -
44. Order of Procedure in Tracing. The same order
should be followed as for pencilling after the construction lines
are drawn. See Art. 30.
For particular work, the detailer should mark centers and
points of tangency of arcs, tho as a rule it is not done. One
soon acquires the ability to find centers and radii by guess. The
width of lines should be decided upon before beginning to
trace, drawing them, if necessary, on a scrap piece of paper for
comparison.
It is very convenient to have a mark scratched on each of
the ruling pen adjusting screw heads. By remembering the
position of the mark for a certain weight of line, the adjustment
can be easily and quickly made. See Fig. 56.
24 MACHINE DRAFTING
45. Balky Ruling Pen. Causes:–A great deal of a
tracer's time and patience is wasted by the ruling pen
refusing to draw a line. Such a failure is caused by a
lack of contact between the liquid ink in the pen and
the surface being inked. This trouble may come from
either a solid or a liquid, over which ink will not flow,
coming between the liquid in the pen and the surface
to be inked.
Ink is composed of a solid coloring matter held in
solution by a volatile liquid. When an ink line dries,
the liquid evaporates and leaves the solid coloring
matter clinging to the surface to which the ink is
applied. While ink is in the ruling pen, the part that
is exposed to the air is drying and forming a film or crust
around the liquid ink, which sometimes clogs the pen.
If the stopper is left out of the bottle the ink becomes too
thick, or dust and lint may get in, either of which may clog
the pen.
If the nibs of the pen touch each other by too fine an adjust-
ment, or by pressing the pen too hard against a ruling edge,
the pen balks.
Oil on the nibs of a ruling pen prevents the ink from flowing.
The surface being inked should neither absorb nor repel ink.
Tracing cloth and some papers have oil in their composition
that works to the surface and repels ink. The moisture from
the hands sometimes has the same effect.
46. Remedies. If the ink it too thick, thin according to
the directions on the bottle.
If it has been in the pen but a short while, squeeze the nibs
together to break the crust, or touch the point to the back of
the fingers to start it—black ink will wash off.
In making heavy lines with the compass or with the bow-pen
the ink can be started, while the instrument is in position, by
running the pricker point or pen point between the nibs to the
paper.
If these fail, clean the pen and refill.

FIG. 56.
MACHINE DRAFTING . 25
The pen should never be laid away without cleaning. There
is a trick of creasing the pen wiper with the left hand, passing
it between the nibs of a ruling pen—without its adjustment
being changed—and cleaning the inside and the outside of the
pen with one motion. this can be acquired with practice and
the ordinary ruling pen cleaned as quickly as one with a hinged
joint.
Adjusting screws should not be lubricated with oil, but by
rubbing a lead pencil point over the threads.
If the trouble is with the surface to be drawn upon—if it
is a glazed one, powder and rub it; if unglazed, use a sponge
eraser or art gum. -
47. Blots. Blots may be caused by any one of the follow-
ing conditions:
The ink being too thin for the quality of work being done.
Too much ink in the ruling pen.
Lint or dust in the pen, in the ink, or on the surface.
Rough spots, due to erasing, on drawing paper; small pro-
jecting threads on tracing cloth; or, minute holes in tracing
cloth.
Moisture on the surface.
Ink on the outside of the pen.
The remedies are obvious.
48. Erasing. To erase a blot, if a large one, proceed as
follows:
(a) Absorb superflous ink by absorbent cotton or the
corner of a blotter, being careful not to touch nor disturb the
softened surface of the paper or cloth under the ink.
(b) After the ink is perfectly dry, slip a triangle, or other
hard smooth surface, under the area affected, and erase clean
with a rubber composition ink eraser. -
(c) Brush off loose particles and clean with a soft rubber.
(d) Burnish with a burnisher made for the purpose, or
with the thumb nail.
26 MACHINE DRAFTING
Erasing shields are a help in some cases, but in general, less
time is wasted by erasing too much and inking again than by
taking the pains to erase no more than necessary.
A knife or a steel eraser requires skill and experience in
using. It should be very sharp and care should be taken not to
abrade the surface of the paper or cloth—just barely skim off
the ink. Its use should be restricted to removing “squips,”
that is, over-run lines, and the little trimming up to be done in
places that will not be inked over.
GEOMETRICAL CONSTRUCTION.
49. Machine parts are largely made up of solids bounded
by plane and cylindrical surfaces. The reason for this is that
these surfaces are the easiest to construct and measure.
The chief uses of the planer, shaper, and milling machine
are to construct plane surfaces, while the drill press, boring
mill, and lathe are to construct cylindrical surfaces.
An object, the surfaces of which are planes, has sharp
corners. Sharp corners are avoided in machine construction,
being either rounded off or filled in. The rounded corners
are generally represented on drawings by circular arcs which
are tangent to straight lines. *
If an object is bounded by surfaces other than planes, in
order to avoid sharp corners, the surfaces must be tangent to
each other. For these reasons, methods of passing circles and
lines tangent to each other are important to draftsmen.
The essential steps in drawing a circular arc tangent to two
lines are as follows: (See Prob. 2.)
Determining the radius,
Locating the center,
Locating the starting point of the arc,
Locating the stopping point of the arc.
The starting and stopping points are points of tangency.
MACHINE DRAFTING 27
Tangent problems involving straight lines and circular arcs
are solved by an application of the following general rules:
1. (a) If a circular arc is tangent to a given straight
line, its center must lie on a line parallel to the given line and
at a distance from it equal to the radius of the circle. (See
“Another Way” Prob. 2.)
(b) The point of , tangency must be at the foot of the
perpendicular dropped from the center of the arc to the line.
2. (a) If a circular arc is tangent to a given circle, its
center must lie on one of two circles concentric with the given
circle; its radius being equal to either the radius of the given
circle plus the radius of the arc, or, the radius of the given
circle minus the radius of the arc.
(b) The point of tangency must be at the intersection of
the line joining the two centers, with the given circle.
Solutions to a number of typical problems are here given.
If the student is to enable himself to solve problems that he
meets in practice, he must not follow these solutions blindly
but must grasp the underlying principles and see the reasons
why. -.
These are not the only possible solutions. The merit of a
geometrical solution consists in its fewness of steps and its
avoidance of multiplication of errors.
Compare the two methods of Prob. 10.
50. Checking. Before beginning his work the checker
should have outlined a method of checking that will test every
detail of the design and the drawing for errors and inac-
curacies.
It saves work for the tracer to have the pencil drawings
checked before they are traced.
It is best to begin by broadly criticising the design as a
whole, going more into detail as the work progresses, and
finally considering the most minute details.
Some such outline as the following should be in sight of the
checker while he is at work.
2
MACHINE DRA, FTING
/ f
2, f


** My
$ 7.24, 244, 4 & 62.4%
% & £4
//2 2% ecºnca 44 acc/
/3. & e »azza, a 4.



MACHINE DRAFTING 29
ASSEMBLY DRAWING. 1. Question the general effective-
ness and fitness of the design to accomplish the purpose for
which it is made. -
2. 'Question Strength,
º Rigidity,
Lubrication,
Adjustability to wear,
Adjustability to different kinds of work.
Is the material trimmed to the minimum consistent with cost
of material, cost of labor, and the appearance and quality
desired in the finished machine?
(214.
6
gºs º ºs ºf (7)
- - l: = § -US)
- * *| | -
FIG. 58.
Can a different design serve the purpose and be more cheaply
made? -
In applying these tests make note of the changes and ad-
ditions to the drawings that would make it more legible.
Make note of all errors that are easily discernable, and
everything that is questionable and needs further consideration.
3. See that it is possible to assemble the machine.

30 - MACHINE DRAFTING
4. See that the moving parts will not interfere.
5. Determine from the overall dimensions whether or not
the machine can be placed in the position intended for it.
DETAIL DRAWINGs. 1. Are the different views sufficient
and accurate?
2. See that the details are properly grouped and are to
such scale as will go on the standard size detail sheet without
crowding the title.
3. Sufficiently dimensioned 2
4. Clearly dimensioned 2
5. Over-dimensioned 2
6. Could the dimensions be followed and pieces unlike be
produced 2 (See Plate D–16.)
7. Compare dimensions of parts that join together, and
with the assembly drawing.
8. Are there finish marks where needed ?
9. Are there sufficient notes on material and workmanship?
10. Is the number of pieces wanted designated 2
11. Is the piece number or the pattern number given 2
TRACINGS. 1. Is the tracing to size?
2. Compare with detail drawing by superimposing.
3. Check the title, number of tracing, and date.
4. See that the tracing is signed by the proper persons.
51. Checker’s Notes. Fig. 57 shows the notes made by
the checker in checking the drawing shown in Fig. 58. The
notes should be made on a separate piece of paper and pinned
to the drawing. The numbers on the drawing, unless it is
a blue-print, should be made in pencil so that they may be
easily erased.
The drawing and notes are given back to the person
responsible for the mistakes. When he corrects a mistake he
makes a check mark opposite to the note referring to it.
When all of the mistakes are corrected, the checker checks
the corrections, drawing a line thru his note and erasing the
corresponding number on the drawing as he approves each
one. When all is correct he indicates it on the drawing.
MACHINE DRA FTING 31
KINKS AND SHORT CUTS.
52. The French or Irregular Curve. The French curve
is used as a ruler for drawing non-circular curves. When a
curve is determined by a number of points, a smooth freehand
curve should first be drawn lightly in pencil thru the points.
The French curve is then fit to a part of the curve by trial and
3 SS
FIG. 59.
a line drawn as far as the French curve follows the general
direction of the curve. The French curve is then moved to
another position so that it fits farther along the curve and also
follows the part of the curve just drawn for a short distance.
This operation is repeated until the curve is completed.
The heavy line a, c, b, e, d, f, g, Fig. 59, is being inked.
Position 1 of the curve is drawn in light lines and shows only
a part of the curve. Position 2 in heavy lines shows the entire
curve, and position 3 in light lines shows only a part.

32 MACHINE DRAFTING
In position 1 ab is drawn, in position 2 cd, and, in position
3 ef.
53. Fig. 60 shows an instrument designed by the author.
Its outlines consists of tangent circular arcs of different radii.
The small blackened areas at A, B, C, D, etc., are holes cut
f
6
thru the instrument. The corners of these holes are centers
of the arcs a, b, c, d, etc. Its operation is as follows:
Use the instrument as a French curve to pencil the curve
to be inked, marking the ends of the arcs (1, 2, 3, etc.) passed
over by the pencil, and also their respective centers (A, B, C,
etc.).
After penciling the result is as Fig. 61. The centers and
tangent points being given, the curve can now be inked with
the compass. A trial will convince the experienced that this is
a saver of blots and a preventive of their accompanying losses
of time and temper. This instrument may be made out of

MACHINE DRAFTING 33
cardboard, and by following the solution of Prob. 27, Plate
D–25, its outline may be made to approximate any curve.
54. Templets of Standard Parts. The templet method
is a means of reduplicating small drawings. The drawing to
be reduplicated is made and trans-
ferred to another piece of paper by
pricking thru the essential parts.
Fig. 62 shows a templet devised by
the author. From this a bolt head
or nut can be laid out by pricking
> thru the holes surrounded by the
-7 S. - small circles. The process is as
follows:
The pricker point is placed at A,
Fig. 63. If it is a bolt head to be
FIG. 61. drawn, the notch H of the templet is
slipped against the point; if a nut,
the notch below H is used. The holes are pricked thru as
shown.
Lay out lines and arcs are drawn. Fig. 64.
Lay out lines and
arcs are drawn. Fig. |
64. * O O O O
The finished head.
Fig. 65.
A templet when
made should be filed //E AD
away for future use.
55. A Master FIG. 62.
Templet. Where
there are a number of sizes of standard parts a master templet
can be made from which different sizes can be laid off direct
or from which individual templets can be made. Fig. 66 shows
such a templet of a nut.
In making this templet, the smallest and the largest standard
size nut were accurately laid out to scale from a table of
/2 =/



34. MACHINE DRAFTING
dimensions. Lines were then drawn connecting the principal
points of each.
To lay out a nut of any other size, the process is as follows:


~~|~~~ T
i -
Aft

FIG. 63. FIG. 64. FIG. 65.
From A and B on the line AC lay off the bolt diameter of
the required nut and draw the lines FG and DE. DE marks
the top of the nut, and the intersections of FG with the lines
connecting the corner layout points of the largest and smallest
sizes, locates the corner layout points for this particular one.
C
× !
^k %
|
/r - /T
^ Iz 4. N |W 4. 6
* | * | i
§
S. S ->
+4+
A

FIG. 66.
A vertical line dropped to the line K from the intersection
of FG with the line H locates the center of a small arc. The
center of the large arc can be found by the intersection of a 45°
line, drawn from an outside corner, with the center line. See
Plate D–19.
By laying off the proper height this same templet may be
used for a bolt head.
MACHINE DRAFTING 35
56. Section Lining. In section lining or “cross hatching”
the spacing is generally done by eye. Where a great deal of
hatching is done it saves the eyes to use a mechanical device to
do the spacing. There are a number of section liners on the
market, but most of them have other objectionable features
besides the price.
72: E. Jø0/AAPA-
FIG. 67.
Fig. 67 shows a common and simple device for mechanical
spacing. It consists of a piece of wood or celluloid that will
not quite fill up the space inside of a triangle. With the middle
finger of the left hand on the piece of wood, and the index
finger on the triangle, one is slipped while the other is held,
thus “walking” in steps of equal length.
If a piece of wood is not available, should the draftsman
be so fortunate as to possess a few coins, he can make use of
the same principle and get the right spacing by some such
combination as shown in Fig. 68.

36 * M. H. CHINE DR 4 FTING
57. Fig. 69 shows an adjustable three-piece section liner.
It can easily be whittled out
of hard wood. The author has
used one made by himself for
ten years. To set it to a given
space proceed as follows:
Draw two lines a and b at
the proper distance apart.
Set the triangle on b.
Slip clamp c to the left to
loosen the device, and spread d
and e as far apart as the tri-
angle will permit.
Hold d fast, slip the triangle
to a, move c to the right, and
the liner is set.
5¢
—
FIG. 68.
|sº wºme ammº sºme é,
f*=N /
Problems. Make drawings of the problems named below,
following the steps as given.
1 to 10. See plates marked Problem 1, Problem 2, etc. to
Problem 10.
11. Draw the examples on Plate D-23.


MACHINE DRAFTING 37
12. Draw the examples on Plate D–24.
13. Draw the examples on Plate D–25.
14. Draw to scale Plate D–26.
15. Draw to scale Plate D–27.
16. Draw a light horizontal line AB about 3" long. By
the method shown on Plate D–13 obtain one thirty-second,
GH, of AB. .
Draw another horizontal line EF, transfer GH to EF and
by the reverse of dividing, multiply GH by thirty two. Com-
pare the lengths of AB and EF.
This as a test of a draftsman's skill in sharpening a pencil
and using the instruments.
Before working problems 17 to 26 study carefully pages
40 to 48.
17. Make a drawing of the bolt heads, screws, and nuts as
shown on Plates D–19, D–20, and D–21. The student may
choose the diameters and work out the proportions from the
plates. The diameter of slotted screws should not be greater
than 3”.
18. Make a detail drawing of each piece shown on Plate
D–9. Draw each piece separately to the scale that seems best.
19. Make an assembly drawing of the connecting-rod de-
tailed on Plates D-1, D–2, and D–3.
20. Make a detail drawing of the cross-head casting de-
tailed on Plate D–8. Draw the one piece only.
21. Lay out an assembly of a bearing like that drawn on
Plate D–4. Diameter of shaft 4”. Use about the same
thicknesses of parts as is used in the 34” bearing detailed on
Plates D–5, and D–6. See also Plates D–7a, D–7b, and D–7c.
22. Detail the parts of Prob. 21.
23. Check Plates D–22a, D–22b, and D–22c. These
plates are an assembly drawing of a shaft turning attachment
for a lathe. This attachment carries two tools with separate
feed screws. The regular cross-slide is removed from the lathe
and is replaced by the attachment. There are V blocks which
fit into the yoke to steady the shaft. These are not shown.
38 MACHINE DRAFTING
Place a piece of tracing paper over the drawing and number
the corrections as shown in Fig. 58.
24. Detail pieces No. 1, No. 2, No. 3, No. 4, and No. 5,
shown on Plates D–22a, D–22b, and D–22c. Proportions
may be obtained from D–28, D–29, D–30, and D–31.
25. Detail the pieces on Plates D–22a, D–22b, and D–22c,
that are not detailed in Prob. 24.
26. Make an assembly drawing from Probs. 24 and 25.
For tracing problems, trace the drawings done by some one
else.
THE FOLLOWING ARE ADDED IN THE FORM OF
BRIEF NoTES AND SKETCHES. THEY ARE INTENDED
To ENRICH THE CourSE OF PROBLEMS BY POINTING
OUT A FEW FUNDAMENTAL MECHANICAL PRIN-
CIPLES AND SOME OF THEIR MORE COMMON AP-
PLICATIONS IN MACHINERY.
40 MACHINE DRAFTING
When a machine parf has nor 30fficiemſ
J/renºſh // 'FA/L5.”
Hºi-
©
A rod beſnº broke” by an ÖVERLoA2"
7his piece is subject fo TENS/LA 57RESS"
2^
ø º
42/22
$22.2//A
C & D
A Shorf piece crushed” 7% riveſ/5 &eing
a V/3e Co/wea's SS/ow or 5HEAAE/2"arºſs 50%-
Žoo/*a-E-55/VE 57RE55 year ſo ''SHEAA/V< 57/F553"

MACHINE DRAFTING 41
7%e resisſance of a g/ven piece ſo rºoſ/e
&y ſension or by compression varies a/-
/ec//y 23 ſhe area of ſhe sma//esſ secſion
fhaf can be co/ from ſhe //ece &ºy a p/ame
Azerpend/cu/ar ſo ſhe direcſon of ſhe ///7–
furſ”? force. *
7%e res/s/ance of a 2/ve/7//ece ſo rup/Ure
// Shear/17 varies direcſ/y as ſhe area of
ſhe sec//o/7 50//ec/ ſo Shear &
7e5/5 have been made o/7 2//fere/7/
/77aſer/a/5 ſo deſer/7//7e //e/r/e3/3/a/7ce
Azer 39Jare ſnch fo ſension, com/zress/or.
and shear/ng, respec//Ve/y.
Arom dafa ſhus oºſa/nea/ 3/remºſh of
/77ach/ne 2arfs are compuſed.
42 MACHINE DRAFTING
A/VALYS/5 OF J 7TPE’s SATS
Ż ſom/ressed///ers
* Ş
Nº. No.5ſº
ſº Öfreſched/ff/ers – 7e/75%
A 6AEAM / 04/2Ep/W 7//5 ///ø/ A.
Ny Q
§ —s
º NS:
š s ſº
*S S Sº? Š%NS
§s sº
$ wo S 2== SR 7
% gº *\ S >--> N
Ż2 Żyż e
7%é.3%ze ºffer ſhe §
head//5, com/essed. SS S.
Le §
§
Jeaſ A-A /3/772/75/27 tr. 2” Ş
V 7///TEA/7 Š
Aſo, 7 //EAD
\







MACHINE DRAFTING 43
77+E WE/7&E /*//VC/PLE

W.
%
A fami/ar /08/raſon of ſhe acſion of ſhe Wedge

~~T *
emº sº. 4
º
\ |
! |
| 1
\–L
77e wedge used for bind/m/

%
%
—r- – “tº
(–===biº
A camp /a/ //, on ſhe Wed/e///mcſp/e
*— — —%
4 x ––––– =le
62 — — —z7


7he eage a/c of a wedge shaped"/"ſece
of paper wrapped on a cy/nder/zroa/ces a
/e/x, Wºh /5 ſhe corve of ſhe screw firead
44 MACHINE DRAFTING
77+E WAE/GE PAINC/PLE
Wedgea"&/eler//7”.
©
*—-
aſpe 0.5ed/m b//
am 4700ſ/Jarew
-
O
&nd/yde/ce
=
I
Adjusſing Wedge
Wedge 3%zed &A"fora/s/a/ binding
N-
º AN
—
§
APE 7/-/Are A/75
7his ſhow's ſhe use of ſhe meage/mo/e/7 ma/-
-/ng a figh/Azpejoſmſ.



MACHINE DRAFTING 45
7AE WE/73E Pºr//wc/PLE
g-z
& := * 7. &
§-> Z
º A.4/77/4/ /75 VFLO/~/Máſſy 77
/50L7 A/V/7/YU7' OF O/VA 77//TEA/7
A/ove / ſhow/7 ſhe medºng acſºn of Jarew ſhread;
|W
a tº N
/ EA/7 Ja/TE VV
* F
SNSS slº.
ZATV:///V6 BY
WE/26//VG
Where a greaſ fºrceſ; re/rea//z move an offeº/
3/2/2/2/20/a/e/ ſhe meage 277/7% ſo 0.5ea.
[-
L
7/5 shows ſhe wedge principe of a 2%//a27/27
§SSN
s












46 MACHINE DRAFTING
A5E4/7//V6.5
*---, F---,
% wº-ºº:


J//p/NG 6/ocar


JHAFT AND AEAA/VG
U/yWO/ſ/y Wo/TN
A/ove /5 shown fºe effecſ of wear
Aze/ween rubbing 5urface5.
// /wo pieces A and 8 rub fogeſher,
Aoſh being e2//y haza, a rough 32.2f on
on A roughens à, B/n form abrades A,
and go fºie process goes on Unf/-//re
/he 717/Aemſ,2y Caſs"- ſheby eaf each offier 22
/ſ, 27 ſhe o/her/a/7Z A/S soffer ſham A.
a rough 5poſ on 5 coſs a paſh in A which ſm
furn does noſ affade 5. Arough 2/aces on A
are 3/mooſhed ov/ by A.
MACHINE DRAFTING 47
AEAA/NGS
|
Bear/17//eſa/
A/ove ſs shown a means of faſting Up near
and prov/a/ ///caſion
7/e bearing Show/2 no/ be Go Gma// nor
ſhe pressure so greaf ſhaf ſhe ſubricanſ
/5 570eezed' &//
7%ere show// be no sharp corners ſo
scrape ſhe ///canſ from ſhe mov/nº part
7%e bearing show///e so designed ſhaf
ſhe heaf generafed by ſºc/27 w/ be
conducted and rad/aſed away.

48 MACHINE DRAFTING
//07/0/y of /MAC////YE A24/77.5
&emera/y a pomſ on a mov/, parſ of a ſma-
a/re moves back and forſ/ ſm a straigh/ /me.
/7 a 2/ra/e, o, /7 a./aff ſhaf is a com/maſon
of Cºrzw/zra/ rec//mear moffo/7.
&7 474//r
(2/ec//ſº 4-7 V2 Nº/2/2/4"
/3% of 7° flºº %
4725.5//ead/
A/o reſs 3hown a a/agrama/c zepresemſaffon
of ſhe 5-ſpea &Awar/Mozzow” 7he paths of
ſhree/o/ö, ä"4"a/?”e///a/2; shown
7%e 3/4er cra/7/r/moffo/7/3 Used//n "Aſºc/2-
Aoaſ/wa. Éné/ME5"ſo converſ ſhe expand//77
moſon of a gas ſolo com/wos ſoºr, moſon
/ſa /øy revº/eº U//fºrm/y 2/20/272,73
w//e/0/a/200/ moves Jr.//07// a7227
ſhe axis, every// of ſhe Zody aesarſ/es
a //E//x. -

The Drafting Room Series
By FREDERICK H. EVANS, M. E.
I. READING MACHINE DRAWINGS.
Pamphlet of 20 pages and 17 plates.
Price, in Filing Box, 75 cts.
Without Box, 50 cts.
II. MACHINE DRAFTING.
Pamphlet of 48 pages and 44 plates.
Price, in Filing Box, $1.25
Without Box, 1.00
III. INTERFERENCE OF MOVING PARTS
AND TOOTH GEARS.
Pamphlet of 40 pages and 21 plates.
Price, in Filing Box, 90 cts.
Without Box, 65 cts,
THE SERIES COMPLETE WITHOUT
DUPLICATE PLATES. *
Pamphlet of Parts I, II and III, with 54 plates.
Price, in Filing Box, $2.00
Without Box, $1.75
... º. ººk:
* * : - 3. * * > .
T
* *** * * *
* * x-r -
is ** ...' * - ~ Tº º
* * ~ *, *, r*.*, < **
- - . . . . . ;- - - -º r
+ T " " . . * * *
-, *
*, *
x * . . . .” “* *
* —- *
- * , -" -
... Tº >
* - - * →
+ * * * ,
* } * ,
- -: !
- --- |
i t , &
; & - *- -
É.
~~
x:
--
r–
-
-
# "sº ---.” . 4.
* , i . . "
* , , , - • g - *- º
#-, " -- * – $. * + y " . , º * * § - * , .# = sº. .
“... ... → ~ - - - - * . - t #
*— ; & - - - * * # ...sº
§: - - ~~ - - --- "- , - - - - - - ~ * } h ł żº
gº. 4 # * , - ; " & - ; * *{{ {
* : * , i - * * * . -- -- - z - 3. - ºrs
! I- - - * ~ * - - - s' -- x- - - x * - -- -
#", - X. - - * I - - r -- w - 2% - i ," +
H. * . - - - -- t - { •º ; -
*— T & -- i 4. -: * - , - . ~~ - - . . . -
§ 1 -. - e- ºf
** = - … ~ 23 ºr - - -
* – J. - * -, - . . . . . . . . . . . . . . . . .
p : F r * , * f r * * 3. - * : : , -
º~
§
º
.
-
-
-
-:-
*
-
&
-
--
* * * *- - -> - *Y. -- * & - * * - - - *-
* - - º • 3 - - - - - - --- -
3- ºr t & x -t, - * ** - } - > - -
" * * - - ** * * > - . - - r w -
k - -- 3. -- - - - :
* -- +. > - - g
In . . i - - - - a * * -
; : : - -
* ~. - - • *-* w
rººf º- - - - * 3. -3.
sº. - -: - * - .
. . " 3. -- *ws -
s—k , sº | - º r F &
~ * r - - - * , - * . 3. ..
:
º
:
-
~,
-
* — tº - - - *
1: ... 'T' s.
º
s
º
-
-
i
g•ºr
§
.
*.
-
-
#
g
º
3, ... . . .” - ºr
# *ſ, *ā, sº
*
& - * -- *- ... < *.*
**'. . . * sº º º, sº I 3: Tº...º. ...," " . , it: ; : * * ~ ; *. # * – -- g **
ºt * , , *... ." . . . ºilº. º. - .º ſº . . . . . . 'ºvº. 2 :-.... . . ºf 2: I . . . . . " If..."---. ... -- . . -
* - *::::: - ; - lººkº it, a . +, 4 - > *"... . . . . . . . . . * = . . . . . . * . k. _ " -
* ** * *...* # - * : ~ †
3.
**** * *
s.
sº s—" º
ſ:
§
:
%3
3 * * is * *; c. * *
; ºne g "... -º-º:
; : . # -, *" º
fº "...º.
*. *- *...º.º.
* ..., º
:*. ** - *...
& . tº E.I." 'º jº. . -
- -º “...º.º. tº . ..- : **** Tº 5 * * - E- * * *- * @.,
§§ : º ºt * “t. ‘. . º.º. 5 º', ;
- *.
%
: `-- … #so
s ºf: **** , º, *r- .g. + ... : : - « º —- 3. “ xº~
ºś, źtº ºil
sy ...º.º. - #: * . . . :* .-- º
$3 =&# ºf ... *
..º.º. 7 – ... - ***T*
* - . º-ºº-ºº:: *, *-*...*.*.
- ºg - # , * * -- - & $ • *āº. - * º ºf sº ... *s A ºf:
sº tºº. . . . . ài. ::º-ºº...H. f.º.
sº, $3. T. &. - i; ຠ'º' ſºft. lfº
º: ...” . . - r ºf: i- º:*iº 1 ºr
- º ºg º żºł .#s ºsº. .# 4 tº
.
§





























*sºcº-wº
i.
t
*
2/
THE D RAFT IN G ROOM SERIES
ºj.
*
.*
r)
gº
#.
p-
C
*.
- PART III
Interference of Moving Parts
and Tooth Gears
BY
FREDERICK H. EVANS, M. E.
THE MANUAL ARTS PRESS
PEORIA, ILLINOIs
D R A FT IN G R O O M S E R 1 E. S., P A R T III
Interference of Moving Parts
and Tooth Gears
By FREDERick H. Evans, M. E.
Assistant Professor of Manual Arts, Bradley Polytechnic Institute, Peoria, Ill.
Formerly Draftsman for the Ironton Engine Co., Ironton, O.,
the Link Belt Machinery Co., and Sargent
and Lundy, Chicago
THE MANUAL ARTS PRESS
PEORIA, ILLINOIS

coPYRIGHT, 1913,
FREDERICK H. EVANS.
FOREWORD.
The principal problems of kinematics with which the drafts-
man has to deal are in testing for interference of moving parts,
and in the study of gears.
In the following text the author endeavors to express himself
chiefly by drawings. Mathematical formulae are reduced to a
minimum. Kinks and short cuts demonstrate the use of paper
as a tool in such a way as to render the mechanical work of
solving the problems in this subject much more accurate, less
difficult, and, we hope, more interesting.
In making working drawings of bevel gears (especially when
the axes are not at right angles) the draftsman finds himself
facing a difficult task in computation. A method is here given
that has been tested and found to be the simplest, shortest, and
most accurate known to the author.
INTERFERENCE OF MOVING PARTS.
58. It is necessary in the design of a machine to test for
interference of moving parts. This can be done on the drawing
board. º
Plate G-1 is a diagramatic representation of the principal
moving parts of a steam or gas engine of the reciprocating
type. In this diagram cr represents the connecting rod, c
represents the crank, f represents the frame, and ch represents
the cross-head. A connects ch and cr; B connects cr and c, D
connects c and f, and there is a sliding connection G between
ch and f.
59. Motion is not Absolute but Relative. We can not
think of a moving object without thinking of an object which
it passes over, thru, under, at the side of, toward, from, or,
around. The latter object we regard as being without motion,
and we say it is fixed. Before we can conceive of, or analyze
the motion of a body we must regard some other body as
fixed with which to compare its motion.
What do we regard as fixed in the following?
1. A locomotive runs sixty miles per hour.
2. The conductor moves thru the train.
3. The sun rises and sets.
4. The earth revolves.
On Plate G–1 the frame f of the engine is assumed to be
fixed in the plane of the paper, and c, cr, and ch moving.
Either c, cr, or ch can be assumed fixed and the motion of the
other parts represented.
Problem 1. On a piece of tracing paper trace the heavy
outline ABD as shown on Plate G-1:
When c is fixed in the plane of the paper, show the positions
of f, ch, and cr when brought to occupy the same relative
positions to each other as is shown in ABD, A,B,D, etc.
5
6 INTERFERENCE OF MOVING PARTS
ANALYSIS. If the triangle A,B,D be revolved about D as
a center until B, coincides with B, and the triangle AaBal) be
revolved about D until B, coincides with B, etc., the required
positions are obtained.
CoNSTRUCTION. Place D of the tracing paper on D of
Plate G-1 and pass a needle thru D of both. Revolve B, of
Plate G-1 to coincide with B of the tracing paper and mark the
position of Aa. Proceed in like manner to locate As, A, and
As. The different positions of cr, ch, and f may now be drawn.
However, since motion is only relative, the result can be
most readily obtained by tacking Plate G–1 to the board and
revolving the tracing paper about D to the required positions.
OBSERVE: (a) That D for all positions is a point com-
mon to the tracing paper, the drawing beneath it, Plate G–1,
and the drawing board.
(b) That the result is the same whether the tracing paper
is fixed and the drawing is moved, or the drawing is fixed and
the tracing paper is moved so long as the proper points of one
are made to coincide with the corresponding points of the other.
Problem 2. The same as Problem 1 when cr is fixed.
Problem 3. The same as Problem 1 when ch is fixed.
PRACTICAL APPLICATION. Plate G–2 is a drawing deter-
mining the limits of the frame of an engine in order to clear
the connection rod in all positions. The heavy line in the top
view bounds a section of the frame cut by a plane passing thru
the center of the cross-head pin and the center of the main
shaft. The heavy line in the front view bounds a section of
the frame cut by a plane passing thru the center of the con-
necting rod in different positions.
In each case, the space inclosed by the heavy line is the
space necessary for the moving parts to pass thru, clearance
being allowed.
Another way of looking at it is to regard the heavy lines as
different views of a solid generated by the moving parts into
which no other part of the engine can protrude.
INTERFERENCE OF MOVING PARTS 7
The frame is regarded as fixed to the paper because it is the
part of the machine that is under investigation for interference
of moving parts.
Problems. Detail drawings of parts needed in the follow-
ing problems are given on Plates D–1 to D–12, inclusive. No
clearance to be allowed.
1. Draw the limit lines for the frame of the engine.
2. Draw the limit lines for the connecting-rod.
3. Draw the limit lines for the crank and counter-weight.
INSTRUCTIONS. Draw only the moving parts that are neces-
sary. Make the drawing in pencil and as simple as possible to
obtain the required results.
As a suggestion to the student an explanation of the making
of Plate G–2 follows.
A pencil drawing of the cross-head, connecting-rod and
counter-weights was made, the center lines forming a diagram
similar to the heavy lines of Plate G-1. An outline similar
to the light lines of Plate G-1 was drawn on a piece of tracing
cloth. The tracing cloth was moved so that the light lines
representing the different positions of the connecting-rod came
successively over the center line of the connecting-rod in the
pencil drawing. The connecting-rod was traced in each of
these positions.
The same result could have been obtained by making a
templet of the connecting-rod, placing it in the proper positions
on the tracing cloth, and tracing around it. This is an easier
method when the shape of the moving part is so irregular that
it is less difficult to construct a templet than it is to draw the
different positions of the part by other means.
8 INTERFERENCE OF MOVING PARTS
TRANSMISSION OF MOTION BY MOVING
CONTACT.
60. On Plate G–3 is drawn a lathe attachment that was
devised to finish eccentric castings. A is a finished eccentric,
B is a rough casting, R is a roller, D is a cutting tool, and E
is an arbor between the lathe centers. A and B are fixed on
the arbor E, R is constrained to roll against A, and the point
of the tool D is constrained to move in a plane containing the
axis of the arbor and the axis of the roller.
Problem 1. Find the shape of B after finishing. Otherwise
stated thus: Find the locus of the point of the tool D on the
rough casting B. -
This problem is to be constructed on the drawing board by
the application of the same principles that were used in doing
the problems in interference of moving parts.
Problem 2. Find the shape of A so that B will be a perfect
circle.
The required shape of A could be obtained in the lathe by
substituting a blunt tool to act as guide instead of the cutting
tool D, placing A where B is and B where A is, and sub-
stituting for R a driven grinding wheel of the same diameter.
A will then be ground to the proper shape to act as a cam in
this attachment to turn the eccentric casting B to a circle.
61. Observe. In Problem 1 the different positions of the
connecting-rod was obtained by locating the different positions
of its two centers. Notice that the centers of the bearings are
represented by points on the drawing and are thought of as
points, yet, in reality, they are center lines or axes perpendicular
to the plane of the paper. *
Every point of the engine parts which we have studied
moves in a plane. So do most machine parts. The motion of
a screw is a notable exception. In dealing with machine parts
INTERFERENCE OF MOVING PARTS 9
having plane motion only, we draw the first part of the problem
while regarding the plane of the drawing paper as being parallel
to the plane of motion of any point of the part studied.*
This being true, we may regard the motion of the axes of
the bearings as the motion of points, since they will be so
represented.
From the preceding we may deduce the following rule:
When two views of a body whose points have plane motion,
are given, and one of the views is a motion view, any position
of the body may be completely determined by locating any two
of its points in that position on the motion view.
* A view on a plane so taken will be called a motion view.
10 INTERFERENCE OF MOVING PARTS
TOOTHED GEARS.
62. Spur Gears. It is the purpose of spur gears to trans-
mit rotary motion from one to the other of two parallel axes.
Gear teeth by acting one against another transmit the same
motion as would be transmitted by their respective pitch circles
rolling against each other. See Fig. 70.
Aase Cir(f
Ø
/
© /mo/uſe (ſm
<) Ž i
%N
º:
3.
fº =
arch croſſ
º
$º a; šº s -
Š-(LN&/ tº º *
§ {\ is gºeh acaw)
e of Ac//or (P1) º
/nvo/uſe (//7)
&5e
«Žr (AE)
FIG, 70.
Ordinarily we think of gear wheels as turning about fixed
axes, but in studying the action of teeth against each other it
is sometimes simpler to regard one wheel as fixed and the other
one as moving about it. See Fig. 71b.
Fig. 71 (a) shows teeth of two cycloidal gears in contact.
Fig. 71 (b) shows the relative motion of one tooth of the gear




INTERFERENCE OF MOVING PARTS
§i
4.
2%
º
C.
O
tº
&
;
SQ
N
%
i
M
1.
i


12 INTERFERENCE OF MOVING PARTS
A as it enters and leaves a space between two teeth of gear B.
Fig. 70 shows two involute gears in mesh.
The study of toothed gears is primarily a study of the relative
motion between two bodies revolving about fixed axes and
having a constant angular velocity ratio.
There must be considered: the power to be transmitted,
strength, friction, wear, velocity, available space for the gears
to occupy, noise and vibration in running, and the cost of
manufacturing.

QS
&
N NS &
S 23° i
^sº * N
Sºyº
Ş XX ź
ſº
º
s:
%
FIG. 71 (b).
In Fig. 72, let the circles M and N, with centers A and B
respectively, represent the pitch circles of two gears. Pm is a
point on the circle M that is in contact with the point Pn on
the circle N.
Suppose that N is fixed and that M rolls on N until A
occupies the position A1. A will have traveled in the arc AA,
(the center of which is B) and the point Pm will occupy the
position Prm, in which the rectified arc KPn equals the rectified
arc KPm.
If any body, such as the pattern of a gear tooth be made
fast to the circle M, then, as M rolls on N the locus of any
point of the attached body may be found, for we have the
INTERFERENCE OF MOVING PARTS 13
locus of A and may obtain the locus of Prm. See Art. 61.
This is illustrated in Fig. 73.
The locus of a point Qm on the contact surface of a gear
tooth Trn is shown in Fig. 74. The circle MM to which
Tm is attached is rolled on NN.
FIG. 73.

14 INTERFERENCE OF MOVING PARTS
63. The locus of Qm must be tangent to Tn since each
point of the contact surface of Tm must touch Tn but not
crush into it.
If the locus of each point of the face and flank curve of a
tooth be plotted, the face and flank of its conjugate tooth is
the line tangent to these loci.
FIG. 74.
The conjugate curve of a tooth Tm, Fig. 74, may be
obtained by regarding the disc N on which the conjugate tooth
is to be drawn as fixed and trace the outline of a templet of
the given tooth on M in a number of positions as M rolls on
N. The common tangent to these curves is the outline of the
face and flank of the required conjugate tooth. See Fig. 71b.
The involute and cycloidal teeth are the ones commonly
used in practice.

INTERFERENCE OF MOVING PARTS 15
64. Involute Teeth. Imagine a contrivance as drawn in
Fig. 75. E and F are two discs mounted on the parallel axes
AB and CD and connected by a thin, flexible band K which
is wrapped around each. Trm and Tn are pieces fastened on
AB and CD as shown. PG is a wire of very small diameter
fastened on the band K and long enough to extend beyond Tm
and Tn. M and N are two discs on AB and CD respectively
that roll in contact with each other.
Diam. of E. Diam. of M.
Diam. of F Diam. of N.
It can be proved that if E is turned in the direction of the
arrow, K being kept taut, F will be caused to turn, and the
angular velocity ratio of E and F will be constant and the
same as would be transmitted by M and N rolling together.

16 INTERFERENCE OF MOVING PARTS
If E is turned, K being kept taut, and the end of the wire
fastened to K moves from L to T, the involute curves Im and
In are such that the other end of the wire will be in contact
with each during this movement. That is, Im and In may be
regarded as generated simultaneously by the wire.”
If the diameter of the wire is considered to be so small as
to be negligible, then Im and In will be in contact during the
movement. -
Hence, Im and In by moving in contact will produce the
same constant angular velocity ratio between AB and CD as
is produced by M and N rolling together.
Fig. 70 is a drawing of involute teeth in mesh. The letter-
ing corresponds to Fig. 75. The part of the tooth that is
beneath the base circle in each case does not enter into contact
but is of such shape that it will not interfere with the meshing
teeth.
65. Cycloidal Teeth. M and N, Fig. 71a, are two pitch
circles of meshing gears.
Imagine that a circle Q rolls simultaneously on the outside
of N and the inside of M. In so doing M and N will be
caused to roll together.
Let Po be a point on Q, its locus on N is an epicycloid,t
and its locus on M is an hypocycloid.
Since these curves can be generated simultaneously by one
point while M and N are rolling together, it can be shown
by a line of reasoning similar to that given with involute gears
that they are conjugate curves.
Similarly, if a circle R rolls simultaneously on M and N
a point Pron it will generate an epicycloid on M and an
hypocycloid on N that are conjugate curves.
Fig. 71a shows how these cycloidal curves go to form
cycloidal teeth.
* For a method of plotting the involute see Art. 73.
† For plotting cycloidal curves see Art. 74.
INTERFERENCE OF MOVING PARTS 17
GENERAL PRINCIPLES OF CONJUGATE CURVES.
66. In Fig. 76 M and N are two discs which may be
regarded as pitch circles. 1, 2, 3, and 4 are points fixed to
M. When N is fixed and M is rolled on N each point moves
in a trochoidal curve as drawn in the figure.
The locus of any two points fixed to M, Fig. 77, equi-distant
from A, may be made to coincide by revolving one or the
other about B as a center. The subtended arc on N of the
angle of revolution equals in length the subtended arc on M
of the angle made by lines thru A and the respective points.
Thus the locus of 4" may be made to coincide with the locus
of 4 by revolving it around B thru the angle 8 where Rect.
arc” PK’=Rect. arc PK.
From this it can be seen that a templet of the locus of a
point 3 on the line AB may be revolved about B to coincide
with the locus q, q being the intersection of the circle rr thru
3 and any curve tt attached to M. t
If templets of loci of a number of points on AB are made,
the loci of a number of points of tt may be drawn by thus
revolving the corresponding templet about B thru the proper
angle. The common tangent to the templets thus revolved is
the conjugate curve of tt. See Art. 63.
Any curve fixed to N to which the templets can be thus
revolved tangent may have a conjugate curve on M. Con-
versely, any curve to which the templets can not be thus re-
volved to become tangent can have no conjugate curve on M.
67. The distinctive advantage of involute teeth is that the
distance between centers of meshing gears may vary, and they
will still transmit a constant angular velocity ratio.
This is not true of cycloidal gears. While cycloidal teeth
have advantages, yet, there is no property of the cycloidal
curves that makes them peculiarly fit to form the shape of gear
* The abbreviation “Rect. arc” will be used for rectified arc. The
author believes that by so doing the likelihood of mis-interpretation-
by the student is less than if “arc” or “length of arc” were used
instead.
18 INTERFERENCE OF MOVING PARTS
FIG. 76.


20 - INTERFERENCE OF MOVING PARTS
teeth other than the fact that the cycloid is a geometrical curve,
can be defined, and reduced to commensurate terms.
An approximate cycloidal tooth on one gear and its conjugate
tooth on the other gear, serves the purpose just as well.
68. Bevel Gears. It is the purpose of bevel gears to
transmit rotary motion between non-parallel axes.
Gears that transmit rotary motion between axes which are
non-coplaner are called skew bevel gears. Skew bevel gears
will not be studied in this chapter.
For a comparison of spur and bevel gears, see Figs. 78 to 83.
Two discs, Fig. 78, or the frustrums of two cones, Fig. 79,
will roll together with a constant angular velocity ratio.”
These cannot transmit much power on account of slipping.
If projections are put on one disc (frustrum) and corres-
ponding depressions are cut in the other disc (frustrum),
slipping is prevented.
If projections are put on each disc (frustrum) and corres-
ponding depressions are cut in the other disc (frustrum), the
result is the ordinary spur (bevel) gear.
M and N, Figs. 78 to 83, in spur gears are called pitch
circles, in bevel gears pitch cones.
The part of the tooth added on to the pitch circle (cone)
is called the addendum. The part cut out of the pitch circle
(cone) is called the dedendum.
The surfaces A and B are theoretically spherical surfaces on
which the outlines of teeth are laid out as in spur gears. The
surfaces of the teeth are such that if one end of a line is fixed
at V and the other end is moved along the tooth outlines on
A and B, the line generates the teeth.
In Fig. 84 M and N are frustrums of cones. These cones
have a common vertex V. A and B are spherical bases of M
and N respectively. The spherical bases are a part of the
surface of a sphere with center V. P is a point on the spherical
base extended.
* The vertices of the cones must coincide.
INTERFERENCE OF MOVING PARTS
21

22
INTERFERENCE OF MOVING PARTS
FIG. 80.
FIG. 81,

INTERFERENCE NG PARTS
º
§
^-ºff 2
º

24 INTERFERENCE OF MOVING PARTS
If N is fixed and M rolls on N, the point P describes a
curve on the spherical surface of B extended. This curve is
shown, also the surface generated by the motion of the line VP.
Notice the similarity of the motion of the point P in Fig. 84
to the motion of the point 4 in Fig. 76.
In Fig. 76 two discs, M and N, are rolling together. In
Fig. 84 the frustrums of two cones, M and N, are rolling
together. In Fig. 76 the point 4 moves in a plane, in Fig.
84 the point P moves on a spherical surface.
The discussion of spur gears in Arts. 62–67 may be applied
a-g sºs
A ea s
º
2 …
2
N
FIG. 84.

INTERFERENCE OF MOVING PARTS 25
GAAA’.5
CowVE/VT/owAL /TAPAESENTATION

Javar GaAA's
FIG, 85.
f

/#/7
2
2O 7T y” 3 f
| E.
3.07. gº 3o 7"
6/?-? 3
4. ſº
ÆATV-L 65.4/7's
FIG. 86.
Æzz/; J/?aff Darreſer, and f/7e /Number of
7eefh, /7%mefrzz/ Pººh, aſz/ ſhe ſace of each
gear 2 e //72%zzºa.
26 INTERFERENCE OF MOVING PARTS
to bevel gears by substituting “frustrum of a cone” for “disc,”
and regarding the trochoidal curves as described on spherical
surfaces instead of planes.
In practice the surfaces A and B, Figs. 78–83, are not
spherical but conical. A and B are called back cones and their
elements are perpendicular to the elements of their respective
pitch cones. The tooth outline laid out on the back cone so
nearly coincides with the theoreti-
cally perfect tooth outline laid out
. on the spherical base of a pitch
AT- cone that no appreciable error is
introduced, by this more practical
ser method.
Æ5), * A tooth outline on A will prac-
tically coincide with a spur gear
tooth outline having the same pitch
and a pitch radius equal to the
—A c_ slant height, SH, Fig. 79, of the
/57- back cone A.
FIG. 87. To make a drawing of a bevel
gear that gives a view of the
teeth is an excellent problem in projection but it is a task that
a draftsman in ordinary practice is seldom called upon to do
except for display purposes. Also, it may be said that it is
unnecessary to draw the teeth of spur gears except in cases
where the drawing is to be read by persons who are so
technically illiterate as to be unable to read the conventional
representations of drafting. Where such a drawing is required
a neat approximate method should be used.
69. Gear Trains. When a large reduction or increase of
angular velocity is made between two axes, it is done by con-
necting the axes by a number of gears arranged as represented
in Fig. 87. This arrangement is necessary where much power
is transmitted since gears having less than 12 teeth do not work
well. A number of gears so connected is called a train of gears.

In Fig. 87
3ar
/37.
INTERFERENCE OF MOVING PARTS 27
When axis A makes 1 revolution,
axis B make;-2 revolutions.
When axis B makes 1 revolution,
axis C makes 39–3 revolutions.
13
When axis A makes 1 revolution,
axis C makes;x*-6 revolutions.
Notice in the train of gears that the drivers have 36 and
39 teeth respectively, and the followers have 18 and 13 teeth
respectively.
- 36.7"
A
_A^* 7–

3oz., fº
|a f 6O7"
2.5 7"
/272 Z7 8
/47:
AT
/27–
FIG. 88a.
36 × 39
18×13’
ratio of A to C, we have a fraction the numerator of which is
the continued product of the numbers of teeth of all the drivers,
and the denominator, the continued product of the numbers of
teeth of all the followers, hence, the following rule:
The angular velocity ratio between two axes connected by a
train of gears may be expressed by a fraction the numerator of
which is the continued product of the numbers of teeth in all
the drivers, and the denominator the continued product of the
numbers of teeth in all the followers.
In the quantity which expresses the angular velocity
28 INTERFERENCE OF MOWING PARTS
70. Cut gear teeth are cut by accurately formed cutters.
It is only necessary that the pitch and the number and kind of
teeth on a gear be known in order to select the proper cutter
with which to cut the teeth.
Patterns for cast teeth are generally laid out from either an
accurately constructed templet made especially for that
FIG. 88b.
particular sized gear, or, from a templet odontograph which
is a templet with a curve that can be adapted to various sizes
of teeth. Printed directions accompany the odontograph.
Tables have been compiled from which the radii and centers
of circular arcs can be obtained to approximate various forms
and sizes of teeth.
Each shop has a method and a system of its own for doing
this kind of work. When a young draftsman is required to
lay out gear teeth accurately, he is generally given definite
instructions how to do it according to the system followed by
the concern with which he is working. Should he be left to
take the initiative he should bear in mind that in gears, a
little knowledge is a dangerous thing. If he is able to obtain
the pitch, form of teeth, and pitch diameters the general
methods given in this book can be followed.

INTERFERENCE OF MOVING PARTS 29
71. Working Drawings of Gears. The dimensions that
must be known in order to make a cut gear are shown in the
working drawings in Figs. 89 and 90.
r
ſ
§
M
s's
H
6/~/7 a./-/–4377 a 77-y
(44.7/vvolv7r-Aſ&SJ72
FIG. 89.
e Number of teeth
The Pitch Diameter== in both spur and
Diametral Pitch
bevel gears.
1
By the Browne & Sharpe Standard, Addendum= | H
Diam. Pitch
1. 157
and the Dedendum=
Diam. Pitch
From this: The Diameter of a Spur Gear Blank=
No. of Teeth-H2
Diam. Pitch -
In making a working drawing of a bevel gear; a freehand
sketch, similar to Plate G–6, of the meshing gears should be











30 INTERFERENCE OF MOVING PARTS
made, then a, b, c, d, e, f, etc., of Plate G–5 should be com-
puted and tabulated, after which the dimensions may be filled
in by following Plate G–6.

$
F-
//
#
:
N
t—
º

- -—l
J Al Taºy – /& 7FE-7-/-y
/44"/w VOZ.4/7′
//w. ALZ. Ove/r
FIG. 90.
72. To Rectify an Arc. It is theoretically as well as
practically impossible to lay off the exact length of an arc on a
straight line, or, a straight line on an arc. However, the
degree of accuracy attainable is not limited by theoretical con-
siderations, but, as in all other measurements, by the accura
of instruments and the acuteness of sight and touch. -
INTERFERENCE OF MOVING PARTS 31
The method generally used is that illustrated in Fig. 91, in
which TO is the given arc and TQ a tangent at T.
Starting at O small spaces are stepped off with the dividers
until a point P, less than one step from T, is reached, from
which point the same number of steps are taken on TQ.

C
O > O
| As 'T' & | |
A A3
FIG. 91. FIG. 92.

Theoretically, by this method the error may be made less
than any assignable value by making the steps sufficiently
short, since the shorter the chord the nearer it approaches in
length to the arc which it subtends.
Practically, an error of measurement is made with each step
and the resultant error is the difference between the algebraic
sum of errors made in stepping off the arc, less the algebraic
sum of errors made in stepping off the straight line. Hence,
the probable sum total of errors in measurement varies directly
with the number of steps.
There are a number of approximate methods of rectifying
an arc. The following is a method devised by the author:
73. The Rectifier. On a stiff piece of paper a circle of
some commensurate diameter is drawn, Fig. 92. AB is drawn
tangent to the circle and B is carefully located by an accurate
scale so that AB equals the computed length of the semi-
circumference AC.
AB and AC are divided and subdivided into the same number
of parts. Tangents are drawn to the circle at each division and
32 INTERFERENCE OF MOVING PARTS
FIG. 94.
FIG. 95.


INTERFERENCE OF MOVING PARTS 33
the proper lengths taken from AB and laid off on each to plot
the involute CB.
A templet is cut out as shown in Fig. 92.
The following explains the use of the rectifier.
To rectify on PQ the arc TO.” Fig. 93.
Place the pricker point at K, Fig. 94, and slip the notch of
the templet against it. ;
Turn until R of the templet falls on the
line KL.
Draw AB by ruling along AB of the templet.
Turn the templet about K until R falls on
KO, Fig. 95, and mark where the involute in-
tersects AB at N.
Draw the line KN until it intersects TQ at
Q. TQ is the arc TO rectified as required.
Fig. 96 is an enlarged view of the notch K.

74. Plotting Trochoidal Curves. In Fig. 97, A, B, C,
and D are points fixed to M. Let it be required to plot the
locus of each when M is rolled on N.
These loci may be drawn by plotting the loci of any two
points fixed to M. See Art. 61.
Let the locus of A and D be chosen.
The locus of A is the circle AA’ with E as center.
When A is at A’ D will lie on an arc of a circle with
center A' and radius equal to AD.
D will also lie on the line A^C' extended where Rect. arc
FC’=Rect. arc FC.
Any number of positions of A and D may be thus obtained.
The accuracy of this method depends on the accuracy with
which the locus of C, which is an epicycloid, is plotted.
An easier and more accurate method is to plot the locus of
A and E as follows:
FIG. 96.
* The same method is used when the radius of the arc is less than
the radius of the templet circle.
34. INTERFERENCE OF MOVING PARTS
With E, Fig. 98, as center, draw an arc thru A, and with A
as center draw an arc thru E.
angle AEK AC
Lay off K and L so that—
angle EAL CE
Divide AK and EL into the same number of equal parts
(1, 2, 3, etc., on AK, and 1’, 2’, 3’, etc., on EL).

-T
FIG. 97.
ER RATU’ M
Lay off K and L so that
angle
angle A. E. K.
INTERFERENCE OF MOVING PARTS
35

36 INTERFERENCE OF MOVING PARTS
sº." - ‘o
*0

INTERFERENCE OF MOVING PARTS 37
With 1, 2, 3, etc., as centers strike arcs thru E.
With E as center strike arcs thru 17, 2’, 3’, etc.
The intersections of these arcs at a, b, c, etc., are points on
the locus of E when E is a point on M, and M is rolled on N.
75. The Trochoidal Templet. The last method above
was used in plotting the trochoidal templet, Fig. 99.
The points in the imaginary circle U are in the locus of A
fixed to M when M rolls on N.
V is the imaginary circle described by E fixed to N when
N rolls on M.
W is the locus of E fixed to M when M rolls on N.
X is the locus of A fixed to N when N rolls on M.
Any trochoidal curves of M and N may be plotted as follows:
Place the trochoidal templet over the paper on which the
curves are to be plotted.
Make a templet similar to that shown in Fig. 100 where
FG=AE.
Mark on this templet the points to be plotted.
If M is to roll on N place the pricker point successively at
1, 2, 3, etc., of U in Fig. 99 and slip F of Fig. 100 against it
while the sharp end is at the corresponding point of W.
Prick thru the points on the notched templet in each position.
This will mark points of the required loci on the paper
underneath.
In making Fig. 71b the points on U and the locus of a point
on the circumference of M, Fig. 98, were pricked thru to the
paper on which the drawing was to be made.
A templet shown in Fig. 101 was then made to follow these
points as just described, and with a soft pencil, the tooth
curve on the templet was drawn in each of its positions.
Problems. 1. (a) Construct a trochoidal templet for
pitch circles 6 and 8 inches diameter respectively. See Arts.
74 and 75. (b) Plot a series of trochoidal curves using a
moving templet with points located as in Fig. 100. (c) Make
a templet of a gear tooth for the 6-inch pitch circle and find its
conjugate tooth on the 8-inch circle. See Figs. 101 and 71b.
38 INTERFERENCE OF MOVING PARTS
2. (a) Draw Browne and Sharpe Standard involute teeth -
of two meshing gears. Diam. pitch=2”; 12 and 16 teeth.
See Fig. 70.
For plotting the involute study Arts. 72 and 73. (b) In-

~y-

| FI.J. 101.
&
F1G. 1 ()0.
dicate on the drawing the exact length of wearing surface of
each tooth. -
3. (a) Draw Brown and Sharpe Standard cycloidal teeth
of two meshing gears. Diam. pitch=2, 12 and 16 teeth. (b)
Indicate on the drawing the exact length of wearing surface
of each tooth.* See Figs. 71a and 71b.
* NoTE To TEACHER: In assigning this problem let one student
make the describing circles as large as possible, and another as small.
Compare and discuss the advantages and disadvantages of each.
INTERFERENCE OF MOVING PARTS 39
4. Calculate the angular velocity ratio between the first
and last shaft of Fig. 85. Fig. 86. Fig. 88a.
5. Calculate the different ratios betewen A and E in Fig.
88b. Gear No. 2 and No. 4 are loose on shaft B; and No. 8
and No. 10 are loose on shaft E. M. and N are sliding clutches
on B and E respectively, the purpose of each being to engage
either gear on the shaft with it, constraining the shaft and the
gear to move together.
6. Make a layout drawing, similar to Plate G–4 of the
gears shown in Fig. 88a. Dimension the gears, obtaining the
dimensions by scaling.
7. Compute the dimensions of the gears shown in Fig. 88a
and compare with the dimensions obtained in Prob. 6. See
Art. 71. -
8. Detail the gears in Fig. 88a. *
9. Detail the gears in Fig. 88b. Would axes C and D
lie in the same line?
10. Make a layout drawing of two bevel gears. Diam.
pitch=3, 30 and 38 teeth, axes intersecting at an angle of 75°.
Dimension by scaling.
11. Compute the necessary dimensions of Prob. 10, using
Plates G–5, G–6, and G–7.
JUN 2 1 1918
The Drafting Room Series
By FREDERICK H. EVANS, M. E.
I. READING MACHINE DRAWINGS.
Pamphlet of 20 pages and 17 plates.
Price, in Filing Box, 75 cts.
Without Box, 50 cts.
II. MACHINE DRAFTING.
Pamphlet of 48 pages and 44 plates.
Price, in Filing Box, $1.25
Without Box, 1.00
III. INTERFERENCE OF MOVING PARTS
AND TOOTH GEARS.
Pamphlet of 40 pages and 21 plates.
Price, in Filing Box, 90 cts.
Without Box, 65 cts,
THE SERIES COMPLETE WITHOUT
DUPLICATE PLATES.
Pamphlet of Parts I, II and III, with 54 plates.
Price, in Filing Box, $2.00
& Without Box, $1.75
III, INTERFERENCE OF MOVING PARTS
}
{
2/3/4/2 77ły A/S/^//-/
|
9. . . 8. ） 8
zºzºï1 fãſ/nºži
| 1
|
|


University of Michigan
• * * * * *
#}}// ±||8;“
įAº5ķo}}ºploo2/4
*%/'，# #| ?? ）
§ 14| | | `ĀGOED
5°8
（~//ā2/A3 #4
ºffſ/M3. -77/vº
. --r---+----*4.|-
–{{{ſae}%}-！ «），(\]
||
// S – OAVE
/ 7 *
Ore 5#
One 6 %
7òfa/Zººerſ，
ºņi！ S ſăi
5，5
–ſ）.
TAT№ſo
;ź-||-"7õſa/Zºer
//J-ØVE ?/03 :
/ 9 *
/f7/v/SA/ ALZ (2)/z/?





University of Michigan
GenCral Library
Ann Arbor, Michigan
& e a e º 'º'
e
ſº
& e º & © tº
e e C & ©
º
→r47á• •
4.7
z9 ?
—— 9.ſFeſt&ž+^*, ºs
8|-¿lº »| ##
|- «æ • - • • • - - - - - --→ •-F|####º | ſiji
-– — °'º-i2/2/%%^{f\}
^^)--/#!--∞
{3?||） {
%ò
¿ \
/f7/v 44.4 67VÆA? /5xcae ºr}
/face 5 /M/A/Rare-o “ſī’’’_|_--†}}-， -.• • •-， -
{
••→3/3
3gºre øe ºg+24+?！
rºž-|jº 32
& |-//J – Owae
ȘI-ȘI… w-， -,#
|3.||}/#$2 7
32"|R）'N
SN
§f7/y 44, 4. OVEAT
|/ 7 №
-+-+R& -4 Eſé4
| ||×
\; || ?-
-H+ +
TTEITĘ
(r)• •
ŞI ŞI
№-N
NOEN№7 ……… …）z7 TOET!”—r
N 'Nºploſis|-#47/7// _ºffiwr _ _ _ { //////>—ſ）， Y l.ºººoo _
*N§}bºļ8ș34/7ĒĢEĻŠ
† №§I-I-ſ-ſ ==++j-1
§N|-— /5|-
Ņ§// S – ONE-
ºſºlº DAN/o *
ºſº|[[VI]
uŘSSITÉS






University of IVilchigan
General Library
Ann Arbor, Michiga
* & © e º e
&
© e º & © e
& © e º e
º
© & 6 G &
*
= z*
sº
*S*-s ºr
2-tº-º-º- — — —---
*
* * * * * *
* - - - - - - - - - - - - - - - - - - - - -
|W=====№ſ,
`| || F=#F5
!|
{į+--+--*）（…<!-!===-ſy
\~--ü– – – –] !
→L | \!!！！！
→
A55A://54.x or /M4//Y APE4/p/ſy G.

University of Michigan
General Library
Ann Arbor, Michigan
|+−4 #4- ;
§ ,“–––“/ 6 iJē-T3"|~ļºſ- , Wſpozv&#7° lºronw
|－ /
L
@)$
3ģ----
ºſº;|
–• • • • • → → → → → *
#-##-#7aº
/Ž///Jraggezza
C/ O/yaer C/45， 7 SOL/C 4/WO Co/7
25*



S CI
University of Michigan
General Library
Ann Arbor, Michigan
/-
|×£- ſ ºù><ſ
/á*5wſ|2{
*… ><!--<, ≥37ą2}_~\\!
-nº-Wyw->¿¿ & FTITĂ
FFOEFFH giº
rļāſ， -09_ _ !?
|/2|}\!\,ſqoºt
----• -> --◄ • • • • •!== -1Q`
ÞBaº&#ff –ſ_IĘ~4�||
\\//~}(\;
}ſ
C/. 7Tyya?//. S. /F/ny, 44 ） . o/ae/?– 77/YO
3 #„5 #
|<！—7——
43æ&&/**+é|5.→ +
§, |, ! '}8
–ī--- | ----_ | | | |##~#~#~
ºſſo→ /|--{}
�■！< \，-••••• • • •
!2A^\2!I-I~!@!
• y=--|－-+-iuſ-ſit →
/yo/e-g.ſe/es' fø be ariſed sfaggerea|{
^o/po/«/ ſºſººffff;}
C. /. 7 Tºyº-
į/y/, /， //y, 4 LL OVEF? – 7 WO


University of Michigan
General Library
- - t =
. . . . . ~ i-- * ~
* ... ." . - ! ºf 1 + - - i. i. ºf S
* - . . . . . . Cí * - - - ** *
* e o e º e
tº
• * >
* * * * e e
... • * e s e
&
° tº see
D 7A
lų
/5„ſºs2° 4-
3.* ——.
ĮĖ//J#~[\*
* t）_wrs ， !№rs=|-
}Ņ7-J-}|||Å
ſae !======：：|
2?·N//#// ± ——||ºplºſ:
}r<– /O→<– / O –>+Olg|}}}i\o
N.!1] !
<!,|----8ſæ~||
™-，~lſo•4,1 ſ.• •Ș*-->+---- 8----| • •–|—
^4）| *|?-ß - z4!！!！0! №> !
¡¡¡---#--#----#ffff;|
U.tı.||
/ | <\ ,,- - -------- - - - - - - - - - - - - --- – – – – – *|||ºblęs
7 =●3ſ-Q~ !|
}-2T204.-}}3k Ř|QoA§N
Ķ�}Tāſ ; *-------+--------! SAŅ ņ
N//r|||$%§
//5SŌTŌS\ \ {3\o|6 $<ī ）, (§§Q
|-3, , R^\\&||&|8--— 6;−È.~ |ſ\,
Àaeſae|/||Ş•ºſią,|
ºr- k\，-2ā，\LJſ} \-\>N-----------------|-e， a-， ſ-， º-， ， • • •æ ææ». «-»， «æ æ æ ， -）， ± «）， Tºſſ__（***： *）（.*?）\，\ ！ ， ） （* - * *|--------◄ e-æ ° æ • • • • • • • •!= 4\s*=\-Ětry
ºſº*Ñ````~ !!\r\!QO |-ſoſ
` №§~,}}AºNTĀ "Ķ Ķ ķ
{r;—ſ/|~ ! ）
dá —L'）/O ·/5 j.–|—&5
%7777ZAL ALONG/T4，7744）. ŐEcTººy
Cols
º
2
Ny
N]-
Cu
ful-
... • * • I- y

VZ CI
University of Michigan
General Library
e e º e º &
©
º e C C C &
... • * * * *
D 7B
§ · · · ·.
3.º.3 :�Q
�• ©�3
: $<263T− → +
3ºſ-×}V
/ >}|! W
fºi-geze7zzo||-&-�
į.jſ4 Zºj// Leº）！ºcaN† #---ſja
\ſ/,-}}<！-ā ºrºEſſêā（)!\ĮT-+-
| |º | t–)1{ \
|^–|—Ģ-ll ſ㊖|-
--ii ----：<！--|^ --$}}�
§}u7±}H--→I#
→ģeTā7ºº.§§�-lºy!§
=► • = − • • •=• • • • •=. • • •-， ） •ſł--• • •- -> • •-，•|-}|ºniſº
--+− + №į <!-----ºg-±••--
|`\{\==================$g=====++=ſ~\º}||\!\
%）si}}T;loºpiſ
~||\!†•-6}+|0)N
N• • • • • • • • • • ►► • Tº ）№k|-
• •–łeſſ|،
e）|�«№«S，
^！”[X^{ſ}}）
\，
!bſſTęſº )ſºl L}=-{
w●L^----
|>+<+$}•|-№-
+#--*
7 OP VIEW– X：Z
|№ /|
/2 #
\,

{{/. CI
University of Michigan
Ceriºral Library
T, .
CA Oſ
|}|
|{T}# {
|įį} º {
|| | ||
șĻſ--jºš -†††|
/^}: ||
āT|-«-»{---- «-»ſº ~~į.+---+---+5«-»ºï，
§§§==#~##}S}-）?
§.* —|
LL72I-J
/7#*№.
JSÆz 7.- /f-/Ț
/
！22 #
→
--iff-jºž----4）
----}{+-+-+\
Nº） 4° /
�į
Ņ||
, '$!H—;
[i•-!— \J —+ – –þa
}T!ſ
（, ) –||–|!{
§ || ? }}S
-NRRRRRRRRN
Iſu RT> →
try8N→– 25ÑN
Ł ł§|Ș„^
%| ，
74
«-» -.• ！， --★ → «-»*-----№
NN^
|-— ſo —
JSE， 7 A-/Ț.
ſul-

D 7C
niversity of Michigan
General Library
Ann Arbor, Michigan
#
#
$!
#-
l .
-
$
N)l Ko
$ls
Co
fh
CY
St
[Y
S| $
N) •is,
#RS 32
N)l\© #
Sſo, fºPs
- $
N)
s
i
A5 I
il [-ſ/ ºY-#
5.# |
# N O }
/{N) \ | y
f-Nl . , \
Ri C uº
-+- S'- —Noſ-l





University of Michigan
General Library
Ann Arbor, lºſichigan
2"Across•ş|#--
* （= A ！ } |-
(）+
Å
/*Z J. O/YE- ET4c/-/
30*
））22.#
|+−— /O>++/O
####—º
(ĒĒĒĒĒĒĒĒ
–S –
-@@ĒË
X®،+
|---5%———5 #——
(ſ)|CO#
Țn，-'—'）;
|| || .++oriº# - ºko{
/•|!!! aº}';r., ſ
# Sººn.}Hiſā|&3y-|-6#! "
!|
!!
įC/ 7Tyyolo
│ │ │ſ-32 #|?
2|
ā
JE CZT/4.5

6 CI
liversity of Michigan
General Library
Jnn Arbor, Michigan
* * * - - - - - -
Słł,
D & me - - - - - -
Cºl.
ſ}}ſ@ſDrj//úr,īſā•
;：2<~IQr-rţi
|| || N.|
|||
|||| || || ||
{}\!
−</2#|
#：#e-+- -}
Á№， ſiĪŅ #
8
C. / 7TYYQ
asſº
la
y T.
k
U.
!
|
co
t
6.
/ "A-/-e: Zº


University of Michigan
General Library
Ann Arºor, Michigan
ZJ
ĢºzzzEºzyźZŅ-ZZZZZZZX-r-ZZZZZZ！&ZZZ
A5/Tºº/yza – 77^^2
3 3 **





University of Michigan
General Library
Ann Arbor, Michigan
- - /'e/a>E- 724 º


University of Michigan
ièneral Li brary
Ann A. bor, Michi 33 in
6/TAPA//Ø4./ 60/V57AŤUC-7/O/V
8 #,”
70/7/V/OF A LINE //v70 g）,/24/77,5
7ÆE SQUARTE
Wofe: 7Áe 45°anº 30°×60° fri-
øyſes ſeep ſhe relative posiſjon fo
eách of her Showry, ſr， ſhe consfrvoſjø7
aſºove.
„4q–7|Ar|*N！A5
7ò Ø/ØE A ///ME/V70 %*#;/%/?7，5
7/7e consfrv.cf/or/ show/7 above?
is done enfreſy wiſh ſhe 30% 60°/27，
ang/éon ſhe fee square 7/ijszſivaſes
avý // e /o /h/rºſs, så f^3, †we/%3,4%
Žhis is converwer/ /o /ay off a /'ne İffff;
//ches anº /ee/ ſo any 5cºle.ºs •
º e
�


University of Michigan
General Library
* 6 e e º e
• * * * * *
D 14
**
A/ £7MENS/o/N 3.
F - Hâr F3 - F-4- -º- -2-o'-- -2°4′-
+ = -41 -º- -º-º-º-
7/lesſo” AVO/p 25 J
S 727c//07/7e/e3,5- Aloo ſh;3. —I-II T.
/7– eras the he?/ºr of Sfy/e of 3. — 3 #
//mension” ſhe 7% 7%/707
S/ope of a 77e.
#
J
;
ef 7, 7.
1. !" Q, —º
32 | ? \ SA
o’ Coº/PEC7- Avoſo |
agº Anº cS
º 2 /6 N 1% • s --
2 ”. e
3.2 e t
- |- O ~$.”
{ } <> \
y \º /ſeverve Figures argé.
CoA'A'EC 7 Avo/O

# I CI
niversity of Michigan
General Library
Aſsº- 1-i-º-, - i. - . ,-- . : *** **** -
ºrbor, i...ºnigan
e e s e º &
e e º G &
*
* e < e < *
---- »
|
|-* 2
||-<- 4
&3
ĆORATEĆ7
!ºff-
6øRÆEc7-
|-
/7/ME/VS/o/v/v6
H−−– 9
|
|
–||– –-€Đ--—†to f----
|
{
±|-**8) … |
8●
|----4|
Avo/pCoApºEc7-
3#{|-/33-| |--/g-
}ÓoÆRECT AVO/Z
Avonº
[7]MENS/O/Y/N6AN ：
/FREGULAAT 6:/ºwſ:
�
�©
��


University of Michigan
General Library
Ann Arbor, Michigan
| <
\!\，
fach of the grºw，75
aº^ove /ocaſ? //he &#7//eº/io/º
Ørecâșeſy
►-
4
/#
ſöył
i
7
|-
•¿•
$, il
«） ----
On a roughcasſing,f/75
/70/e js /?ofprecise/y/ozzº/eº.
ØMEWS/O/V/WG
|-<----
|-æ
Coſo,
2.# —-
– —ı
/` IAJ
©ae.
T-À
ĆoATATEC7-
L—º4.
|-ºž
|
>l<ſ
}
/g —-
ºblęſ
|
№
i
|--/4–
H« — 24 ——.
N ISQĻ1/8-
| 3.56°●
8
|
CoÆPA#E-c7-
3 ——.
/ğN
ſ@3 -
ſºlº-8
|wi！
--/4'-
-- /4–
M
2 !
|4.
/
—/4


University of Michigan
General Library
Ann Arbor, Michigan
/57/V/SH MARKS
/F7A7/5/7± =
/F7/V.º | | | | | | | || .
f/ºce/77/775/7ī TÆF7W.#-#→
Izºº (ºggiºA vo/2
/º/，5/7|S-= __-__-__ --★ →→→→
/F7/7. & Aſo//s/?Of/,și ſ---&-- №§./2Țſgºſ，~~~~Fr
f/7e/r-|\|\}|_ . Šį, . ! Șių\!-\!\!\!----şin –- -i \\!--
Şaof fºrce- /\/ar/13-}|___?.?.?.}©|ſºſ}|-§
/F777 82Scrºpe(See 7èxf)Ζ ~|<-- • • •
/F7/2 &- &7/7a/77/5 specifies777/5 affoe.5 /?of
777777→fſhe /ſ/ra/o/f/ff/7/5/7.
6ore~///ø/，/r/
•Ø/r/r：S
//rj//- for||}}，
A3ore/*fo/es|--???--|-24--
/7e/?/77·•• …”，
7/ijs Speziffe5 //e7/775 40e5noț�

(ZEGAȚETE OF Accavar4øy，; :::::


hiversity of Michigan
General Library
Ann Arbor, Michigan
N
7, §; }
Z.
ZZz/
x 9 7272
c5
///ME/MS/o/MS AND FINISH MAAȚArs
/4#Vºyw º&5///////////e /，7 rough\º（~）
firm A// Over–6275e førzſe/7
//º/ſő fº/V/O/Y ÓFANA JHAFT
2-/MACH/AME Ò7EEL
Woº /his represents the masſ ſhoro method of ameňºloming and marſing
: ; 81 GI

University of Michigan
General Library
Ann Arbor, Michigan
Gºa Pawt ca 4. Corws 7-ºuc7/o/v
×6
C/S, ST-ºp. /To u Ga-7 //EX. /VUT
Q
—/#0* #oč? --→=
\[>4，
1|
– 4cross/F/ą/3T
→– A.CrOSS CO/*/7€/35
U →z,
C/. 5. Srºp. APoc/Gay//Ex. BoŁ7°
//E442
C/S, Sºrſo, ffovgº/ SQUAFE
Bo L7- HEAD3 :


6 I CI
University of Michigan
General Library
Ann Arbor, Michigan
D 20
Conv vE/vºr/o/v4 L SCAPETyy //EA PS
JE 7.- Jer/PÆyy-Co/wÆT/Fo//v7-
@|-
-2\\-š，výz
fŤOU/No Fo//vºr/á/7·
Q
~\\}|
¿s#=#=№
còFäövàº，/7
r- º */US//
/7Ņ！ #\\còŽ%"$#@w
NSC27 №.
G ve Scºperyy



0Z CI
University of Michigan
General Library
Ann Arbor, Michigan
D 21
Co/Yveſ/v7-/o/w/º/. JcÆPETyy //EAcºs
pºſá0%-
TE}
|-
TEL
--EL--E-
！=）H==
<■∞）：
//EX. CAPJ^APETWY
F/á0%T
§§
º | §
47—ł—
//EX.C4.A> SCAPET MY
F7/Y/5a/Eo //E/7/7
3
/# D
Ş)
SŲ\,
SJ ſ
ZD
--→
--→
«5ĢUąÆPET//e/4/7 Cąº Jc/TEVY
ł 42
}
A=Tepaevc////€442 /FZ „47”øſtº
Cowry7E/75ų^{ºr
//E42 ; ;:








IZ CI
niversity of Michigan
General Library
Ann Arbor, Michigan
f
à
;
TO

University of Michigan
General Library
Ann Arbor, Michigan
D 22B
‘‘.AM 7/4 -z^/ø：/ /
:9çd'822
w/ ºd ſº ºzzz 69} = （– – – – –
ł
QR)-■
• • • • •
„ ！ №
• Z


8ZZ CI
University of Michigan
General Library
Ann Arbor, Michigan
D 22C
29 dºo
AM 774 767/Q
ģoſ


ſniversity of Michigan
General Library
Ann Arbor, Michigan
s
§
&aſon/E7/r/CAL 62/ws7 Arucz/o/y
&//ſcLE5 A/VD 72/VGA/V7.5
JYMaols
G/very Azo//7/.5 so
G/ve/7 /l/res — — — — — —
Gºver, Aſaa// ºr <- - - ->
Aſeºuſrea/A2/7′s o
Aſeºvirea/ / /nes
Feawſrea Aſaaff o--
Co/75/roc//o/7 /º//7f.5 o
(2/73frvcfforz Lines
Cozzafrvcfjor, Aſaa/ o ––
/. 4.
_^
Cº- - > 2”
2’
3. | 6 _^
2
— —e— —-H -><– — -

University of Michigan
General Library
Ann Arbor, Michigan
:
:
Q1A/39A/w/ a7A/t/ º 5721//o
wo/12724-1SNOO 79.2/4/.42/wo:/0

University of Michigan
General Library
Ann Arbor, Michigan
:
:
GeoME 7/7/a44. Cows7/ru/crony
6//Pclaſs Awa 7A/VGA/V7's

Jniversity of Michigan
General Library
Ann Arbor, Michigan
D 26

9Ż CI
Jniversit
y of Michi
A: º
nnºrbor, Michigan
• e o e º "
• e o 'º

ZZ CI
University of Michigan
General Library
Ann Arbor, Michigan
D 28
/M46/////F SLJDES
CT_ff
*{\ 2//- NË | #
|-> ;Z（ſ）}

8Z CI
University of Michigan
General Library
Ann Arbor, Michigan
D 29
/PÆPoÆPoA7°77o/Y ZZ/4g/ſ4/º?
//4c////YE’.5LJAZE:5


6Z CI
University of Michigan
General Library
Ann Arbor, Michigan
º
.
*—
/Yºr/ Jare
Ze’s 5 77%/7 #*
*
§
JSY §
| S
‘M's Sº
Sº S’ D.
* Y. SA §
ź º, ne. 2 * § *H
-ā- †-2 c., | -\lº
St. N
_x- NJ
3.

University of Michigan
General Library
Ann Arbor, Michig ir
PROPORTION DIAGRAM
Machine Slides
For any value of C, and C. (Plate D-28), determined by previous calculation, a slide
can be laid out to correct proportion as follows:
Draw the line N, N, and an indefinite line RS (Plate D-28).
Place N, of Plate D-29 on N, of the drawing, with the line O, Y, perpendicular to RS, and
prick thru the points marked 1.
Place N, of Plate D-29 on Na of the drawing, with the line O.Y., perpendicular to RS, and
prick thru the point marked 2.
Plate RS of Plate D-29 on RS of the drawing, wth O.Y., passing thru N, of the drawing,
and prick all points marked r.
Place RS of Plate D-29 on RS of the drawing, with O.Y., passing thru N., of the drawing,
and prick all points marked s.
Thru these points draw the proportion diagram in very light lines.
The correct proportions of the slide are determined by a series of intersections between
the lines of the proportion diagram and the extensions of N,Na, RS Etc. of the drawing.
On Plate D-30 the determining points of intersections are lettered with small capitals
with a leading line from the letter to the point and to the line it determines. Each line of the
proportion diagram is lettered with the same lower case letter as the point it determines. The
dimensions refer to the proportion diagram.
Stock parts should be made to the nearest size to the scaled dimensions, and other parts
affected by such a departure from the scaled dimension should be changed accordingly.
Dimensions should not be made to read closer than necessary. Variations from scaled.
dimensions, should be on the side of excess stock. - :
©
:
i
University of Michigan
GCneral Library
Ann Arbor, iiichiºn
:
<$
§§
.S.
t—
FN
Lºs
& N
s
ſº
ſl.
+&
>
.*S$


Jniversity of Michigan
General Library
Ann Arbor, Michigan
:
*/27.2%/0, 442% of /Ceaſo/c22 /ou cy/2/2/
AMog Ziy 2779//b/7/
H- F
\ T
&
H
NS
/2=-||
|
A/O977 Mog77
MOM/ 77av:/779// Moº/ 1st/9
(j) \{-|-&-(9)
S’9/V//-Z/-/. Fel L/
:


2
University of Michigan
General Library
Ann Arbor, Michig.1)
:
AºA'a /*77-77/V65
Co/yve/v7/o/VAZ. AfEPA’aja/v7477ow
—#63+
7op
@ ++ G)
+
S/27% A7amſ Søe /ºro/7/ 5fae /727ſ Jøe
ATLBow - Caro.55
Aſſoffo/77
7FA:
/ra/7/ Jøe º * :
Joe OuTLA-7 7 o’7f Jaſe /72/77 Jøe
A La OVV /*own Way 7FE J/Z25: Oay72.É.7
Caross
. + —H —C)— —so
Jør V/4 × Caross (//wwow. CAEcer MLVE CAA'
A/w/ews are ſhe
Jø/77e
—F. -[3H- —(3)— —HG)—
702 702 7öp 702
AP2/7f /727ſ Jøe /72/ Jae /72/7/
Cocar 647E Wºlver &zosa Wºlve 45°/ſlaow



2
Jniversity of Michigan
General Library
Ann Arbor, ilichigan
*

I SO
University of Michigan
General Library
Ann Arbor, Michigan

University of Michigan
General Library
Ann Arbor, lºſichigan

f
£ €)
niversity of Michigan
General Library
Ann Arbor, Michigan
º
&
Bava/ GAAPrs
Oa72/M/VG 77+E /MACH//VED
/JIME/VS/ows 8 y ZAYocy7-
FEgº/fro: A Mayov/ for coffizº the feeth of ſwo
Æeve/ gears of 3 Pºſch, /2 2.72 /37eeſh respecſ/ve-
/y, /#/ace, Axes perſpera/co/ar
/ºf:/, /7 am ——
//
/Zºderzºom
Aaaendom- .*N Z2,
:
1
- - //2 of 7eef/,
Affº/7/72/77. *Z7727-27.7%
Compare w///, /*ATE


Jniversity of Michigan
General Library
A". *
". j. ł * - ~~~ ; , - -- --
*i. i -
* W. * * : *
º

&
Aſºvaz (Ž4/7 forrazu, AE
AXE s 962°
(90/4/V777-Y
fo/PMULAf
i
/7/27/7727/27/ Affa/7
/V//er of 7eeſ/, /7 627, 1
Y 77%ase are zºº
mºnºz by ſhe
A Mø/// &/-
fo/75 of f/he
C7
* * * * 2 a J gear:
Azaenezum =# (A & 5.5%)
/7272/7270/77 62 =4;? (#&J 57%)
(27.5%/7f f = V/*, 2*
Aºh Am/e of Gear 1 (7= 7am-'4
2 A = 90°-g
• 2 × 2
Adžemº/m Ang/e f =#x360
Zºe/20m Anze ſ = 7× #
Azaze/774/77 //7crease a/
/* = 5: X &
of Čezzr/ f
Azazemzº/77 /7crease — aſ A
/77 = + x
of Gear & f
University of Michigan
General Library
Ann Arbor, Michigan
º
AEVEL GEAR’s
CALcul-A7ED /7/ME/vsſory 5
Az
3% + 24-
| rôear 1
ŠºšS.H."
&
&
&
N º
&
&
\)
\S
§
h

3
University of Michigan
General Library
Ann Arbor, Michigan
&
o
AE-vaz GEAAF.5
CALcu, ATED /7/M&T/vs/o/v.5
///mber of 7eeſh ſm &ear 1 =A \ %
/Vº/7/2/r of Veeſh //7 Gear/5 =Af
Anze of Axes =&
///7/2r of 7ee//, //7 f/he g-sº -* , 47.
/mazmary &ear & - *** * 372
/ºr oſher 20amtſties 50/25//roſe /7/7.47E 6-5

liversity of Michigan
General Library
nn Arbor, Michigan
PROB. 1
L-E731-3=57;:（-1
67/ VÆT^v/2
4./Te QviſtEdi i:...
[ '80 HA


University of Michigan
Gencral Library
* F, -} = sy- , , , ; ' ..…
Ann ArbCr, fictiºn
i

f
Sw \b \\
\ ` J.
Gºverw.
Aſsovºro: A dar/m2
of ſhe fºre fascale.



& in

2$
d7&A5 ſay paraway6 A/Pcs

*
Awoſha Ar WAr
University of Michigan
General Library
Ann Arbor, Michigan
i
º
ºf
H–3 * —- &localN6 &/7
6/VE/v.
Afagº/Fra: A
º of ſhe ſºvre
fo jø/e.
N
V.
V
400A77/NG Alo~477/V6 ſºnv/5
CA/v7E/75 of 72/vee/Vcy A/vo
ATA/V/N6 JMALL AFCŞ.
F//v/.5H.






i
University of Michigan
General Library
Ann Arbor, Michigan
i
º,
{
L–T.
67 ve/v
S/2 45°triary/e
fo Azosition
Aſoled 30%60°
ſo this 205/-
//a/7 Š sº
Pºzzvy 1
FEquared
firzāsh //& V//zes
wifh 754, are 227a.
fr/a/7&ſes, arzaz' ſhe
o//ey//e/rzes A2/ſhe
SE7 7"/"A/V6LE MET/7/a/2
3/?own
}
{\!
+
§


University of Michigan
General Library
Ann Arbor, Michigan
PROB. 5-6


_l/


9-9 *{10}HAI
University of Michigan
*
General Library
Ann Arbor, Michigan
i
/
;
G/very
Aſa'90/TED: A Zºzzw/r27
of ſhe fºure ſo sca/2
/??”.7%z//?r //-
Sec/or /ø A A'.
Æloca/N6 &/7; //wa/va &/y7E/rs
AND 7ANGE/W7 A2///75, A/V2 /2,+Aw/ye AA’z.

i
liversity of Michigan
General Library
nn Arbor, Michigan
i
TJEE
LZ /
V
aſi)
/-ocaſ/N6 CEW7&A's
9–
N-si > −7–
/ OC47/NG 7ANG/v7/?/v7.5
AND /Zeavy/NG SMALL Aags

i
niversity of Michigan
General Library
Ann Arbor, Michigan
:
CN
:
'soayv 77vvvgº onvlaavu/7 awv
gº LAvºy-la/F9ivvZ ow/16/207
'Sºuz LA/22 ow//boo.7
awtz-Zoo ow//boºg
×
2/ex of a/a4, 24, ſo
&Mé2/29/a24/755/


University of Michigan
General Library
Ann Arbor, Michigan
PROB, 10


'N/EA/9

0[ "{10}} &{
liversity of Michigan
General Library
.nº Arbor, Mich.33.r.