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■f- IN MECHANICAL DRAWING

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GRAMMAR GRADE PROBLEMS
IN MECHANICAL DRAWING

CHARLES A. BENNETT

ILLINOIS, AND

THE MANUAL ARTS PRESS
PEORIA. ILLINOIS

Charles A. Benneli

1916

FOREWORD

This collection of simple problems in mechanical drawinj^ has been prepared to
meet an evident need in teaching the fundamentals of this subject in grammar grades.

It ought to be true that the habits formed in the first use of drawing instruments
in the grammar grade classroom or workshop would never have to be unlearned, even
tho the pupil became an architect, an engineer, a designer, or a draftsman, and that
in so far as he learns mechanical drawing at all in these grades, he would learn what
is fundamentally correct; he should learn the elements of correct expression in this
universal language of the industrial world.

It ought to be true, also, that his work in mechanical drawing, while not at first
following 'exactly the same course of models or problems as he follows in woodworking,
would be parallel or closely related to the shopwork, and, in its later stages, occupy the
same relation to the shopwork that the draftsman's work bears to that of the mechanic.

How to accomplish this result is the problem which this little book attempts to help
solve. Alone, the book can do no more than half solve the problem, but when used
under the direction of a trained and efficient teacher, it can help in forming right
habits and in acquiring practical skill in simple drafting.

In the preparation of this little book the author is especially indebted to the students
who have been in his classes at Bradley Polytechnic Institute during the past few years.
They have suggested many of the problems, and their later experiences in teaching
mechanical drawing to grammar grade classes have furnished valuable data which
has been freely used in these pages.

Peoria, Illinois,
July, 1916

2065970

CONTENTS

Foreword

To THE Teacher

To THE PCPIL

Tools and Supplies

Group I

Horizontal and Vertical Lines — Lay-out of Sheet.
(12 Problems.)

Lettering

.Sheet A.

Group II

Horizontal and Vertical Lines — Dash Lines ■
Selection of Views. (12 Problems.)

Lettering
Sheet B.

Group III

Page
S4

Inclined Lines — Foreshortening — Use of Triangles.
(12 Problems.)

Sheet C.

Group IV

4'>

The OctuKon and the Hexagon. (S Proljlems.)

Lettering

Sheet D.

Group V

The Circle -C(

ines — Sections. (12 Problems).

Group \T 04

Tangents. (12 Problems.)

Group VH 00

Working Drawings. Selection of V'iews — Detcr-
minati(m of Scale — .\rrangcment of View.s —
Lines — Lining in — Selection of Dimen.sions —
Placing of Dimensions — Figures — Dimensioning
Circles and Arcs. (5 Problems.)

TO THE TEACHER

It is assumed by the author that in every class in
mechanical drawing there will be marked individual
(lilTerences in ability of pupils. This fact, however,
does not demand that instruction be entirely individ-
ual. On the contrary, it is believed that far better
results can be obtained, especially in the early stages
of the course, if some class instruction be given.
Indeed, class instruction becomes almost a practical
necessity under the conditions in most schools where
grammar grade boys are taught.

In order to provide for class instruction when most
needed and to recognize individual capacities, the
jirohlems in this book have been arranged in groups
according to fundamental stages in the process of
learning to draw, and in each group there have been
placed a rather wide range of problems; some are very
simple, others much more difficult. // is not expected
that any pupil will work out all the problems in any one
group, but it is intended that each shall work enough
to enable him to master the essential processes of the
group and be prepared to proceed successfully with
the problems of the following group.

The notes in each group are not intended to take
the ])lace of instruction, either class or individual,
which should be given by the teacher, but they are

intended to be a valuable supplement to such instruc-
tion. From a study of these notes the teacher will
readily see what principles and processes should be
emphasized in each group. For example, it is easily
seen that in the first group the emphasis is placed on
the proper use of the tools, (a) in making measure-
ments, and (b) ia drawing the several lines constitut-
ing the lay-out of the sheet. Time and effort, on the
part of both teacher and pupil, will be saved by giving
plenty of drill in making lay-outs. The teacher should
be sure that every pupil is forming just the right
habits in this fundamental process in the first grouj).
Teachers Often fail to get satisfactory results in me-
chanical drawing chiefly because they are la.x in this
first step in the use of rule, tee-square, and triangles.
Wrong habits formed here are difficult to eradicate.

After insuring the formation of correct habits of pro-
cedure in the use of instruments, the next most import-
ant concern of the teacher is to lead the pupil to gain
power in visualization. The constructive imagination
of the pupil must be developed. He must be led to
see views of the object not shown on the paper before
him, in order that he may represent them. To assist
in accomplishing this purpose: (1) some of the problems
are given with both the perspective view and the three

GRAM>[.\R C.RADE TROBLEMS IX iMECIIAXICAL DRAWIXG

views of orthographic projection; (2) some are given
with the perspective view only; (3) others present two
views to find a third, which is sometimes a sectional
view; and (4) still others require the student to w-ork
entirely or in part from specifications. No one of these
methods of presenting a problem should be employed
all the time; in order to get surest results in visuaHza-
tion all should be employed during the course.

The question of requiring freehand solutions of the
problems before making the mechanical drawings of the
problems is left entirely open to the teacher. Experi-
ence would seem to indicate that such sketching should
not be a prominent part of the work of the first
six groups, but may well be given emphasis in the
seventh.

There is a third phase of elementary mechanical
drawing which this book emphasizes; namely, lettering
and the use of conventions in dimensioning. Ability
to do good lettering cannot be learned in a few hours;
it comes only with thoughtful and extended practice.
Comparatively short exercises at frequent intervals
are more interesting and more economical of time and

effort than large sheets of lettering. The lettering
problems are, therefore, placed between groups of other
problems instead of together. But the teacher should
feel at liberty to use the lettering sheets out of the
order given in the book.

The teacher who wishes to be most successful in the
use of the problems in this book will consciously and
continuously keep in mind the three points of emphasis
mentioned above; namely:

(1) The correct method of procedure in the use of
instruments, especially in making lay-outs.

(2) The progressive development of the power to
visualize.

(3) Frequent, thoughtful work in lettering, and later,
in dimensioning. No dimensioning is to be done on
finished drawings before Group VII.

All the problems in this book are intended to be
worked out in pencil only. No inking should be done
until the high school is reached, or until a larger portion
of time is given to mechanical drawing than is usual
in the grammar grades, and not then until good work
in pencil has been done.

TO THE PUI'IL

A working drawing is a i)usiness letter to a niccluuiie.
We learn mechanical drawing in order to be aulj to
make good working drawings. Mechanical drawing
is then a kind of language, a means of transmitting
ideas from one person to another. It is a form of
expression that is universally understood by workmen
of all nationalities. A workman in Russia or Italy or
Japan can read your drawing if it is properly made, and
\ou can read the drawings made in these foreign coun-
tries even tho you do not know a word of their spoken
language.

At the present time when nearly every man hopes lo
build a home or a machine or a boat or a factory or
some other structure, and when mechanical ideas are
commonly carried from factory lo customer, some-
times across the ocean, by means of mechanical draw-
ings, it is desirable that every boy study this universal
language of industry. He should at least be able to read
the simpler forms of it, which he can readily do in the
grammar grades, and learn lo use il lo some extent
as a means of expressing his ideas. This Ixjok is, there-
fore, intended lo help you in learning a new language.

TOOLS AND SUPPLIES

Each member of the class should be supplied with the following :-

Drawing Hoard
Tec-Scjuare
45° Triangle
3o''-6o° Triangle

It is desirable tliat these be selected with reference to accuracy and durubilit}'. To ^et the best results
standard tee-S(|uares and triangles are essential. If, however, a lower-priced tool must be purchased
the "Springfield Kit," board 19x13 in., is suggested. This is manufactured by The .Milton Bradley Co.,
Springfield, Mass.

Scale

.■\ny flat foot rule accurately graduated to sixteenths of an inch will do, but it is desirable to have one
that does not have graduations extending to the end. For an inexpensive rule of this type the " Xala
Rule" manufactured by M. B. Bourland, Peoria, lU., is suggested.

Compass

It is very difJiciUt to find an inexpensive pencil compass with a sufficiently firm and durable joint. In
the long run it is best to pay the price of a medium grade instrument of standard design, such as is sold
by all drawing instrument dealers. In case this is impossible the course can be carried on, though not
with the best of results, by using a very inexpensive compass of the type of Eagle No. 376 made by the
Eagle Pencil Co., New York.

Thumb-Tacks

The inexpensive stamped steel tack is satisfactory.

Pencil Eraser

Drawing Paper in
sheets 9x12 in.

Two are needed: a hard pencil, 2H, 3H, or 4H for the lay-outs and an H or F or No. 3 for lining and
lettering. To get the best results, leads or pencils of the same grade of hardness should be provided for
the compass.

I Soft.

< This need not be a high-grade paper.

Trarinc Paner Cfor I et 1 ^'^'^ '"'^y ^^ '■^" ''°"'' paper used in typewriting or the inexpensive tracing paper used by architects.
1 idc o ipci viui c - .p(^^ ^. disadvantage of the latter is in the fact that it comes in rolls and must, therefore, be cut into
tenng) m sheets 6x9 m. smaU sheets.

PROBLEMS

GROUP I
Horizontal and Vertical Lines — Lay-out of Sheet

Problem I A. The first problem in this group is to
draw three views of a block of wood that is 1 " thick,
4" wide and 7 " long. Fig. 1 is a perspective drawing, or
picture of this block. Fig. 2 shows the three views to

Fig. 1

be drawn. By looking at Fig. 2 again, and at Fig. 1 , you
will see that the top view in Fig. 2 represents what you
would see if you were to look down at the block in the
direction indicated by the arrow a, Fig. 1 ; you would
see a rectangle 4" by 7". In a similar way if you were
to look at the front of the block in the direction in-
dicated by the arrow b. Fig. 1, you would see the

rectangle 1 " by 7", shown in the front view in Fig. 2.

You will now see what the end view in Fig. 2 represents.

Be sure to notice how these views are arranged:

The front view is below the top view, and the end

FROHT VIEW

view is at the end of the top view representing the end
of the block where the view was taken. This is the
most natural and convenient way of arranging \dews
of blocks and many other simple objects.

Now that you understand what you are going to
draw, you are ready to take a sheet of drawing paper.
This should be 9" by 12". Fasten it to the drawing

GRA-M.MAR GRADE PROHLEMS IN ^MECHANICAL DRAWING

xjuikI logclhcr with

luiard by placing a thumb-tack in each of the four
corners. In doing this be sure that the lower edge of
your paper is square with the lefl-iiand end of your
drawing board
accomplish this.

'Wnir teacher will show vou how to

t
rig. 3

To have the sheet of drawing look well when it is
completed, a border line should be drawn on the sheet.
It is customary to draw this border line first, and then
arrange the views in the enclosed space. Fig. 3 indi-
cates the position of this border line. The wider space
at the left end of the sheet is allowed for binding the
sheets together in book form at the end of the course.
Three holes can be laid out and punched in the wide

space on each sheet, and all bound together with a cord
or with brass fasteners.

In laying out the border line it is important lliat
you use the instruments in just the right way. If you
are ever going to do accurate and rapid work in mechan-

Fig. 4

ical drawing you must form correct habits in the use
of the tools, and the first lesson is none too early to
begin. Be very particular then to proceed as follows:
(1) With the scale placed vertically on your sheet,
make a short line or mark (not a round point or dot)
Yi" from the bottom of the sheet, and another 8"
above this one. (Habits of accurate work can be
formed better by measuring from one edge of the sheet

GROUP I — HORIZONTAL AND VKRTUAL 1J\ES

than from both edges. Discuss this with your teacher.
What will you do if your sheet does not measure
exactly 9" in width?)

(2) With the head of the tee-square held firmly
against the left end of your drawing board, draw a
light horizontal line thru each of the marks just made.
This line should extend almost the entire length of the
sheet, Fig. 4.

(3) With the scale in a horizontal position on the
sheet make a mark 1 " from the left end of the sheet and
another 1014" to the right of this one.

(4) With the head of the tee-square held firml\-
against the left end of your drawing board and one of
the triangles held firmly against the upper edge of the
tee-square, draw a light vertical line thru each of the
marks just made. Draw the lines long enough to
cross the two horizontal fines, Fig. 4. Probably your
triangle will not be large enough to draw all of the line
at once. If this is the case you will have to extend
the fine after moving your tee-square and triangle to
a new position. Be sure that the second part of the
fine joins accurately to the first part. Allow the
horizontal and vertical lines to extend past each other
at the corners as shown in Fig. 4. Remember thai
these lines are all to be very light.

To test the accuracy of your work, place the scale
on the drawing in a horizontal position and see whether
the vertical lines arc just IOI2" apart. Then put the
scale in a vertical position and see whether tlic iiori-
zontal lines are just 8" apart.

\'ou are now ready to draw the three views of the
block inside of the border just drawn. But before you
can do this j'ou must consider the placing of the views
with reference to each other and to the border. Fig. 5
shows a satisfactory arrangement. The following

facts may be noticed and may serve as a guide in later
problems: —

(1) The space between views is less than between a
vieia and the border. The space between the top view
and the front view, for example, which is 3^", is less
than the space between the front view and the lower
border which is 1 ".

(2 ) The space at the left between the border and a view is
the same as that between the border and a view at the right.

CRAM MAR (IRADl-: PROBLEMS IX iMECHAXICAL DRAWIXG

(3) Space above the mews at the lop of the sheet is
greater than the space below the views at the bottom in
order to provide a place for the title; otherwise to look
well, it would be a little less instead of greater than the
space at the bottom.

Fig. 6

of the main divisions of the rule, the one-inch mark,
for example, on the lower border line. Then measure
upward from this border line, first 1 ", then 1 ", then V2".
then 4", according to the dimensions in Fig. 5, making
a short mark at the end of each distance.

Fig. 7

(4) The title is Ys" high, and is nearer to the top virej
than to the border. In this case it is Yi" from the top
view and 5^" from the border. Fig. 5.

With this arrangement of views and these dimen-
sions in mind you are now ready to complete the
lay-out of the sheet. // is important that you proceed
strictly according to the follounng directions: —

(1) Place the scale vertically on the sheet, with one

(2) Thru these four marks, with tee-square, draw-
horizontal lines about as long as those shown in Fig. 6.
In drawing these lines make the top one first, and then work
downward.

(3) Place the scale horizontally on the sheet with
one of the main divisions on the left border hne, and
measure distances for the four vertical lines as shown
in Fig. 5.

GROUP I -HORIZONTAL AND VKRTRAL I.IXKS

(4) Thru the marks thus made, draw vertical lines
as shown in Fig. 7. Draw the left line firsl, working
toward the right.

(5) Add the guide lines lor the title as shown in
Fig. 5 and Fig. 8, and the lay-out is complete.

the vertical lines, beginning with the left one and
working toward the right. In this way you work on
the sheet as a whole all the time, and not on one view
at a time.

Do not erase any of the light lines left at the corners.

, 1

' '

Fig. 8

Fig. 9

The ne.xt step is to go over the border lines and the
outlines of the three views with a softer pencil, making
a heavier line. The effect will then be as shown in
Fig. 9.

In order to form habits that will lead to speed and
accuracy in this work it is important that you go
over all the horizontal lines first, beginning with the
top one and working down, and then that you go over

These are a sign of good technique. They indicate
that you worked to cross lines instead of trying to work
to points. It is far better at the beginning of the course
to work without using an eraser at all.

The last step in the process of making this sheet is
putting in the letters of the title as in Fig. 9. These
may be put in now, or if your teacher prefers, all titles
to sheets in this group may be put in after the practice

GRAMMAR GRADE PROBLEIMS IN MECHANICAL DRAWING

thai Ihi

in lettering at the end of Group III. No dimensions
are to be placed on drawings in this book until you come
to Group VII.

After the drawing is completed, write your name, or
letter it on a line yg" below the bottom border line, and
at the right-hand corner, Fig. 9.

Problem Ib. This problem is just like the iirst one
e.xcept that one corner is rabbeted out, Fig. 10. (1 ) You
will therefore make the lay-out of the sheet just as

The only difference is that there are two rabbets
instead of one.

Problem Id. This problem is a little more complex
than I B and I c because the rabbet runs all the wav

Fig, 10

you did for the first problem; see page 12 and Figs.
3 to 8. (2) Then draw the lines to represent the
rabbet. If you have made the lay-out as indicated
above you will have no serious difficulty in completing
the front view to correspond with the other two.
(3) The drawing should be finished in the same way as
Problem I A, Fig. 9. No dimensions are to be placed
on the finished drawing.

Problem Ic. If you have worked Problem I b your
teacher may not ask you to work this one. In working
this one follow the directions given for Problem I b. as Problem I A, Fig. 9.

Fig. 11

around the block. In working this problem, (1) Make
the lay-out exactly as required for Problem I A, Fig. 8.

(2) Then add the lines to represent the rabbet, and
you will have the complete lay-out as shown in Fig. 11.

(3) The drawing should be finished in the same way

GRULl' I — llDRIZOM'AL AND VERTICAL LINES

BLOCK

U-[^

RABBETED BLOCK

1-
}

DRAW FRONT VltW

TONGUED BLOCK

■*

OKAW FRONT VIEW

BLOCK WITH LUG

GRAMMAR CIRADK FROBLKMS IN MECHANICAL DRAWING

Problem Ie. Draw lop, fmut antl cud views. In
working this problem, (1) .Mal<c the hiy-out as required
for Problem I a, Fig. 8. (2) Then add such Hnes as
may be needed to represent the fact that parts of the
original block have been cut away. Fig. 12 shows

Fig. 12

how the tenon is used in construction. (3) Finish
the drawing the same way as required in Problem I A,
Fig. 9.

Problem If. Follow the directions given for
Problem I e.

Problem IG. In this problem a new lay-out is
required because the thickness of the block is 2"
instead of 1", the width is 3" instead of 4" and the
length is 5" instead of 7". These facts call for new
figures in marking off the spacings for drawing lines.
The following dimensions are suggested: Vertical
spacings for drawing horizontal line, measuring up
from the lower border hne, 1 ", 2", y/ , 3". Horizontal
spacings for drawing vertical lines, measuring to the
right from the left border line, IJi", 5", 1", 2". This
leaves a distance of 3^" between the front and the top
views, and 1 " between the top and the end views, and
in each case the space between views is less than
between the border and the view. Finish the drawing
in the same way as required in Problem I a, Fig. 9.

Problem IH. A new lay-out will be required for
this problem. Study dimensions and determine each
measurement in the lay-out before you begin to draw.
Finish the drawing in the same way as required in
Problem I a, Fig. 9.

GROLl' 1 — IIORI/OMAL AM) Vl-.RIICAL LINES

TEMOM

r-^

'■^

^~^Ji

L BLOCK

)

•^ DRAW tND VIEW

GRECK CROSS
1 1

i- EMD VIEW

— li-

^1-

[
J

GRAMMAR GRADE PROBLEMS IX iMECHAXIC AL DRAWING

Problem Ii. This is one-half of an end-lap joint;
see Fig. 13. A new lay-out is required for this problem.
The following dimensions are suggested: Vertical
spacings for drawing horizontal lines, measuring up
from the lower border Hne, IH", 1 W, 1", 3". Hori-

Fig. 13

zontal spacings for drawing vertical lines, measuring
to the right from the left border line, IM", 6", %",
l%". This leaves the distance between- a view and
the next one less than the distance between the view and
the border. Finish the drawing in the same way as
required for Problem I A, Fig. 9.

Problem I j. Read the directions for Problem 1 1,
and modify them so that they will apply to this prob-
lem.

Problem Ik. It is not expected that very many
members of the class will be able to work this problem.
It is difficult to see what this block looks like. It is
therefore a good lest of your power to visualize. If
you think you see what it is, don't ask your teacher,
but test yourself by cutting the form out of wood or
clay, and comparing the top and front of it with the
corresponding views in the drawing.

If you have the correct form you can readily draw
the end view. Space the views and finish the sheet
as described under Problem 1 1.

Problem II. This is a good problem to test your
ability to arrange the views so they will look well
on the sheet and to test the accuracy of your
figuring. If you are taking a course in woodworking
along with this course in drawing, it is probable
that you have such a cutting board on your work-
bench.

GROUP 1 -IIORI/OX'IAL AND \KR TIC AL LIXES

)-LAP jOlfST

,0 DRAW
erny VIEW

• '

JlI

NOTCHED BLOCK

PCAW TOP V\t\V
5i

GAI NE.D

3 LOCK

(

J EMD View

1 ;.

1 f

CUTTIHG BOARD
Draw three vie\a/s of a cut-

TlhG BOARD i'THICK , b'wiDE

AiND iz-LONG. Make each di-

MEMSIOM OME-HALF OF THE
ACTUAL SIZE

LETTERING

Sheet A. The simplest Icltcrs to make are the six-
consisting of vertical and horizontal lines only, and the
simplest way to make them is to trace them. Take a
piece of tracing paper 6" by 9" and place it on Letter-
ing Sheet A. Hold it in position, and with the soft lead
pencil, trace and draw letters as directed below:

Lines 1 and 2. In tracing the letters in these two
lines you should learn the proper strokes for each letter.

H LTfif

Fig. a

These are indicated on Fig. a. For example, the letter
I should be made with a down-stroke of the pencil.
H is made by two down strokes and then a hori-
lUIIHII zontal from left to right. The arrows near
[HJHII] each letter in Fig. a indicate the directions
of. the several strokes, and the figures indi-
'°' ' cate the order to be followed in making the
strokes. It is important that you remember the order
and direction of each stroke, and apply this knowledge
in all your lettering.

Lines 3 and J^. In tracing these two lines you should
use the proper strokes, hut you should give special
attention to the proportions of each letter. Fig. b
shows the standard jiroporlions for a letter H. ■ By

counting the squares you will see that it is 6 units
high and 4 units wide, and you will notice that the
horizontal bar is just above the middle guide line.
This is true of the middle bars of E and F also. In
making guide lines for lettering, the toji and boUom
lines are always selected, and sometimes the middle
line and the lines which divide the letter into thirds.
See guide lines for line 7 on Lettering Sheet A. Fig. c

4 Ak 3i 5t

HLTEF

lig. c

gives the correct proportion of each of the six letters
we are now studying. H is 4 units wide; L is a little
less, or 3J4 tinits; T is a little more, or 4)^ units;
E is4 units at the bottom, but onlySJ^'^ at the top; F
is made like an E, but omitting the lower bar. In trac-
ing you should notice the proportions of each letter.
This will help you to remember the proportions of each
for use later.

Lines 5 and 6. After you have learned the strokes
and the proportions of these letters you are ready to
consider spacing of letters. Fig. d shows ditTercnt
spacings from 5 units down to 1 unit. The question
arises, which one is the best for words? It is clear

(rontinucd on page ?4)

HLTEF HILT LIFE FILE
riTLE THEFT UTILE E

i^^

GRAMMAR GRADE PROBLEMS IN MECHANICAL DRAWING

that the S-unit spacing is loo open — in fact, open
enough for the spacing between words; and it is equally
clear that the 1-unit spacing is too close to look well.
We will adopt the 3-unit spacing as our standard be-
cause the -Ir-unit space is more open than the letter
itself, and the 2-unit is a little less
open than the letter. The ideal
spacing is obtained when the space
between letters is just as open as the
letters themselves, so that the eye
readily passes along the word to
the next space between words. But
when we say that we will adopt the
3-unit space as a standard we do not
mean that all spaces between letters
will be 3 units. What we mean is
that the spacing will he made to look
just as open as two lis placed 3 units apart. For ex-
ample in the word HILT, line 3 on Lettering Sheet A,
the spaces belween'H and I, and between I and L are

3 units, but if T were to be placed 3 units away from
L it would be much too far from L to look. well. As a
matter of fact, the vertical line, or stem, of the T is only

4 units away from the vertical line of the L. Con-
sidering the shape of the two letters this distance gives
satisfactory spacing. Notice how this same idea is
applied in the other combinations of letters on the
sheet. Sometimes it becomes necessary to shorten
parts of letters to make the spacing satisfactory.
For example, when two T's come together as in

Fig. d

LITTLE, Line 2, the horizontal parts of the T's should
be less than 4}/^ units.

Trace the w^ord IF, Line 5, then repeat the word IF
in the space between IF and IT. Be especially care-

I H LTEF H I LT LI FE Fl LL
TITLE TH EFT LITTLE E
I H LTEF H I LT Fl FE Fl LE
THIEF FILE LET IF IT
IF IF IT IT LEFT LEFT
HILT HILT HEFT FILE
I F H E LEFT TH E FLEET

Fig. e

f ul that you space the letters and the words to look well.
Next trace the word IT, and then repeat it. Treat
the words LEFT and HILT in the same way. Make
the word FILE at the end of the 6th line.

Line 7. On line 7 space very carefully the phrase
IF HE LEFT THE FLEET. When this has been
done and you have added a border line, the entire sheet
will look like Fig. e.

HORIZONTAT. AND VkRTICAI. LinKS — DasII LiNKS

Problem II a. This grooved block is made to liL
the tongucd block I c. It is supposed that in working
problems in Group I you learned to make an accurate
lay-out for a sheet, and to make the lay-out with very

light lines, so that in your drawings there is a good
contrast between the finish lines and the lay-out lines.
If you did not learn this, you should do so in this group,
for you can never make high-grade mechanical drawings

with reasonable speed and accuracy until you learn
to make a good lay-out. The general lay-out for this
problem is exactly the same as the lay-out for Prob-
lem I A, Fig. 8. The completed lay-out is shown in
Fig. 14. This completed lay-out is shown to let you
see that the lay-out should have very light, full lines
e\en where dash lines are to appear in the finished

As your Icachei
represent hidden

ill tell \'ou, dash lines are used to
ges. Such lines are often called

dotted lines, but really they are not dolled lines at all,
for they consist of short dashes. These dashes, when
[)roperly made, should be a little longer than the
spaces between the dashes. The exact length of the
dashes cannot be definitely stated for all kinds of
drawings, because the lengths of the dashes \-ary accord-
ing to the size of the drawing. For most of the work
in this book a dash that is about ' s" long, followed by
a space that is about jV ", will be satisfactory. Fig. 15

CRA M.MAI
It

. (;rai)E 1'

ilso il

iOIU-KMS IX MKCIIANICAL DKAWIXG

illuslratcs such a dash hue. It also ilkistralcs how a
dotted line should l)fj;in and c-nd. It should begin
with a dash and end with a dash unless it is the con-
tinuation of a full line, in which case it should begin

with a space, Fig. 16. Be sure to remember this;
your drawings will look better if you do. In putting
in the dash lines, the dashes should be made nearly as
heavy as the finish lines of the drawing. These heavy,
pencil, finish lines of the drawing correspond to the ink

lines which are used by draftsmen and in more ad-
vanced school work.

Problem IIb. This stand, Fig. 17, is made of live
pieces of wood — the top and the four k'gs. The
grain of the wood in the legs runs the same way as in
the top, and the legs are glued on. This kind of a joint,
when the leg comes out flush with the edge of the top,
is not usually shown on the drawing. In other words
the drawing is made just the same as it would be if the
stand was cut out of one piece of wood.

In the top view, Page 27, is a good illustration of how
dash lines should join each other — dash meeting dash.
Dash should not meet space nor space meet space.

Problem II c. This problem is similar to Problem
II A, but recjuires a different lay-out.

Problem II d. Draw top, front, and end views.
The problem gives good experience in drawing dasii
Unes.

GROri' 11 IIORI/.OXIAI, AM) \i:Rri(AL LINKS

GROOVED BLOCK

1
t
1

STAMD

[

•t

-1 J

^1-

• 1 ■

DRAW FROMT VIEW

GUIDt BLOC

DRAW
"^ END VI LW

J ,

HOLLOW BLOCK

CIRA.M.MAR CiRAD

iOBl.K.MS IN .MKCHA.MCAL DRAWlNc;

Problem He. Up to this time in arranging views
on the sheet, you have placed them as shown in a, b, c,
Fig. 18; the top view, a, is above the front view, b;
and the end view, c, is at the right of the top view.
But in drawing the dado joint there are other arrange-
ments of views that are better. The placing of views
as in d, e, f, is better because less space is required
for the drawing and because it seems more natural
to see the end view in the position, f, than in the

position c. It often seems desirable lo show the left
end of an object instead of the right end. In such a
case the end view is placed at the left as in g. In other
words a right end view is always placed at the right
of the front view (or at the right of the top view, as
the case may be) and the left view is placed at the left.
Furthermore, it is often true that no more than two
views of an object are needed to tell all we need to know
about it. This is the case with the dado joint. If
you were to omit either the top view, h, or the end
view, g, you would still have all the facts shown that
you would need in making the joint. But you cannot

m.l g.

iw tv

Why? On your sheet
lews only, as shown in j and k.
Problem II f. Read about the selection of views
nder Problem II E. In the forked joint we may
•lect c, Fig. IQ, and any one of the other three views

shown. In this case the views b and d are jusl alike.
Why would you select b or d instead of a? You may
draw c and d on your sheet.

Problem II g. Read about the selection of views
under Problem II e. Draw the two views of the
mortise-and-tenon joint that tell the most about it and

GROUP II -llORl/.OXrAL AND \ 1;R1UAL LINES

DADOJOIMF

FORKED JOINT

MORTISE-AMD-TEMOn JOINT

CROSS-LAP JOIHT
■6

GRAM MAI

lell it in the simplest, clearest way.
ing show the two parts put together.

Problem II h. Read about the selection of views
under Problem II e. Draw the two views of the

I I cross-lap joint that tell

I ~l the most about it in the

simplest way. In your
ri I |I_. p4 U drawing show the two

[J I I U P^'ls put together.

Problem III. The usual

method of laying out a

'■' .'^ cross-lap joint in the shop

^''"' ^ is shown in Fig. 20. This

shows a jiiece of stock somewhat longer than the two

parts of the joint in order to give space for sawing off

the ends square. The lines on the views in the draw-

KADK PROHl.KMS I\ MKCl lAXlC A
In vour draw

\\vi\(;

ffl

ing show the knife and gage lines on the stock when
properly laid out. Make a similar lay-out drawing for
the middle-lap joint.

Problem II J. Draw loj) and front views of the
bench hook.

Problem IIk. \Vc iiave an oilstone i-|" thick, l%"
wide, 5] s^" long, and wish to make a box or case for it
such as is shown in the perspective drawing. The
stock from which the case is made is -fs" in thickness.
The stone projects jV" abo\e the upper edge of the case.
Make a drawing showing the to]) and front views of the
case with the stone in it.

Problem II l. Draw the front and top views of a
bo.x whose inside dimensions are 1^" deep, li?4"
wide, 7' 2" long, and the stock for which is 3^" in
thickness.

-■

■^v ^•^

' ^'

SAW TO L

MES MARK

to S

Fig. 20

GROIT II - llORl/.OXIAl. \X1) XKKMCA!. I.IXl-;

IDDLt

-LAP JOINT

I
~ 1

— li —

— Ij —

BENCH HOOK

OILSTOhE

BOX

Sheet B. This lettering sheet is planned to be used
in the same way as Lettering Sheet A. Take a piece
of tracing paper 6"x9" and place it on the sheet. Hold
it in position, and with the soft pencil, trace and draw
letters as follows: —

Lines I and 2. In tracing the letters of these two

LETTERING

top than at the bottom. In K and X the TiYi units
are measured from the le/l ui)|)cr corner; in the Z from
the right upper corner. Notice that the angular
openings on V, A and W are all different: The V^ is
43^2 units, A is 5, and W, 3J/2-

Lines 5 and 6. These lines constitute an exercise

NMRVAWXYZ

nmRvawxyz

Fig. g

hnes be sure to make strokes in the order indicated
in Fig. f. Learn the order of strokes for each
letter.

Lines 3 and 4. While tracing these tw-o lines make
a study of the proportions of each of the letters. These
proportions are indicated by the numbers in Fig. g,
and are readily shown by the guide lines and spacing
lines on the sheet. Notice that the third stroke in
K is part of a line drawn from the upix-r left corner
of the letter to the lower right corner. Fig. g. Notice
also that the K, the X and the Z are narrower at the

in spacing. Re-read the discussion of spacing under
"Lines 5 and 6" of Lettering Sheet A before begin-
ning to trace line 5. Trace the word MAN and then
repeat it in the space left before the next word, taking
special care to have the letters properly spaced and
the word as a whole placed in the middle of the space
available. The words THE, WET, and MAY should
be treated in the same way.

Line 7. On line 7 space ver\' carefully the sentence
WE MAY WALK AWAY. Add border line to
finish the sheet.

'NMKVAWXYZ I WALK
^LATHE VELVET VAN

VV"^^:

. ..^^

GROUP III

Inclined Lines — Foreshortening — Use of Triangles

Problem III a. This problem would be like some
of the problems in Groups I and II were it not for the
inclined line. This line is drawn with one of the
triangles used as a straight-edge. The only real
difficulty in the problem is in understanding the end
view. The lower part of this view represents a receding
surface; that is, a surface that slopes back; or, as we
usually say, the surface is foreshortened. If you
follow the plan of making the lay-out as you were
instructed to do in the first two groups you should

have no trouble in determining the length of fore-
shortened surfaces. It is readily accomphshcd by
projecting directly across from one view to another.

Problem IIIb. This is an angle block such as is
used by machinists. Draw the top, front and end
views. Give special care to the lay-out.

Problem IIIc. Draw the two views of this angle
block that tell most about it in the simplest way.

Problem IIId. In working this problem be sure to
make a careful lay-out.

rinl.li

mill \

ANGLE BLOCK

■--r

s\<

J-

CKl) LINKS

angle: block

^ ^ ~-7£/^ —

^.^.^

REEL

1 1

____^-^—

-«

-c-

-=-=

" ■==-

zi n

■ — 2 — '

^ 1

rroblcm 111 D

CRA.MMAIi CRAUt; rROliLKMS 1\ .MIXIIAXU- \1

AWIXC

Problem IIIE. This kind of a corner block is ustd by
cabinet-makers to stiffen pieces of furniture. It is
glued into an inside corner. The new feature of this
l)roblcm lies in the fact that the acute angle is 45°
and can therefore be drawn with the 45° triangle
[placed against the U'e-s(|uare.

Problem IIlF. Select and draw two views of the

miter joint. Notice that the acute angle at the corner
must be 45°. Wh>-?

Problem IIIg. Since the acute angle in this frame
is 60° the inclined lines may be drawn with the 30°-60°
triangle held against the tee-scjuare.

Problem IIIh. Draw the top, front and end views
of the cord winder.

c;r(

)i i> 111 p

CORINER BLOCK

^.^,)

XCI.IXKI) LINKS

'rohk

mUi,

RIA

w T(
\

)P VI

JLAR

C.RA.MM \R CRAD

a)liLi:.MS IN .MIXIIAMCAL DRAWING

Problem IIIi. la making ihc lay-oul Inr I Ik- top
view, draw a liorizonlal center line. In iliis wa\- llie
intersection of the lines making the acute angles are
readily found.

Problem III J. Draw the toj) and front views of the
bench stop.

Problem IIIk. This is intended to give some good
experience in the use of the 3()°-00° triangle, as well as

proviile a test of your grasp of the ]irinciplc of fore-
shortening. The drawing should be made to a scale
of 6" = r. That is, each line should be drawn half the
length indicated by the figures. Your teacher will
tell you more about drawing to scale.

Problem IIIl. Using the given molding, draw-
two views of a picture frame for a picture that is
81-2 " by liyy. Make drawing to scale of 6" = 1'.

GROUP iii~i.\ci.im;i) links

HOSE HOZZLE SUPPORT

DRAW PROMT VIE.W

BENCH STOP

PICTURE FRAME

Sheet C. This sheet follows nalunilly after Letter-
ing Sheets A and B, and completes the alphabet. The
plan of procedure is just the same as in the others.

;rinc;

also, that the middle l)ar of the U is al)ovc the middle
guide line while the corresponding bars of P and R
are below that line. The proportions of the letters
Take a piece of tracing paper 6" by 9" and place it on are indicated in Fig. i. Fig. j shows six letters which

oq'cguj'opbrs
oqcguJdpbrs

llic she

I. Hold it firmly in position, and with the soft

ace and draw letters as follows: —

1 and 2. While tracing these two lines you

Fig- J

are expected to learn the strokes of all the curved
letters; see Fig. h.

Lines 3 and 4- In studying the proportions of the
curved letters, notice that the O and Q are each a
little more than 4 units wide. It should be observed,

should be associated together in trying to remember
their proportions. All of these ktters are a half un!t
shorter at the top than at the bottom. The first five
all line up to a vertical on the left, while Z alone lines
up on the right. Remember this.

Lines 5 and 6. The treatment of these lines is tlvj
same as in previous sheets. Repeat the words COGS
in the space following it. Then repeat JUG and
GUDGEON, being especially careful to get good
spacing.

Line 7. For this line select a text, motto, sentence
or phrase that will fit nicely into the space. Estimate
the spacing carefully before you begin to do the
lettering. You can do this by making a trial copy
on an extra sheet of paper.

LKTTKRTNG

OQCGUJDPBRS RUG
GOUGES PROUD UP

?-'s

iAllL-riiit; Sluvl C

GROUP IV
The Octagon and the Hexagon

Problem IV A. In drawing the octagon consult
Fig. 21. Start with the hne a b, which in this case
should be 2' s" long. The entire figure is to be drawn
with the 4.^° triangle and the tee-square. Draw the
linrs ill the order indicated in Fig. 21. The first is

5
N

) -

N /

Fig. 21 Fig. 22

a vertical line thru a, the second a vertical line thru
Ij, the third a line from a, incHned upward to the
right, the fourth a similar line thru b, etc. Notice
that in order to draw the horizontal line 7 you must
mea.sure 2J's"- up from b along the Hne 4. Finish the
drawing as in previous groups.

Problem IV b. The process in drawing this hexagon
is similar in some respects to Problem IV a, except
that the 30°-60° triangle is used. Notice that the
diagonal of the hexagon, 5^", is the only dimension
given for that view. This diagonal is represented by

the line a b in Fig. 22. With the triangle against
the tee-square, draw the lines in the order indicated by
the figures 1, 2, 3, 4, etc. To show the thickness of
the block the lower end of the side view is drawn.
You are to complete this view. Notice how many

Fig. 23 Fig. 24

degrees each line you draw with the triangle makes
with a horizontal line.

Problem IV c. In its method of procedure this
problem is similar to the two previous ones. In this
case, however, one side of the hexagon, instead of its
diagonal, is given. In Fig. 23 this side is represented
by the line a b. Draw the other lines of the figure
as indicated by figures in Fig. 23. To draw the inner
edge of the frame, measure in from the outer hexagon
a distance equal to the thickness of the stock, and draw
the lines of the figure. Be sure to measure perpendicu-

GRorr i\' iiii'. ociAcoM axd riii', iikxac.on

DCTAGOMAL BLOCK

\ /

, -7

\ ..I

HEXAGOMAL BLOCK

HEXAGONAL FRAME

DRAW PROMT VIEW

HEXAGONAL PRISM

DRAW TOP VltW

1 ^/ M/

J\/

\/\

' 1

44 GRAMMAR GRADE PROBLEMS IX MECIIAXICAL DRAWING

lar to the sides, and not on the diagonal lines at the
corners.

Problem IVd. In drawing the hexagonal prism
with the diameter given you have a problem that is
very common in practical drafting. The given distance

view, .\fler you ha\e drawn the outside octagon
representing the outer edge of the tray, measure per-
pendicularly in from each side } g", then J-i " in from
that, as shown in Fig. 25. After this has been done,
draw lines thru all of these points parallel to the cor-

Fig. 2

is represented by the line a b in Fig. 24. Draw the
lines in the order indicated.

Problem IV E. Draw the octagon on a waste piece
of paper so as to be able to locate it in just the right
I)lace on the sheet. See Problem IV a.

Problem IV F. See Problem IVd.

Problem IV G. This problem is a test of your
knowledge of the process of drawing an octagon and
of the accuracy of your work. The drawing is to be
made to a half scale, 6" = !', in order to go on your
sheet conveniently, and even then it will be desirable
to draw the right-hand side view instead of the front

Fig. 26
responding sides of the octagon. These lines should
meet on lines drawn from the corners to the center of
the octagon. Test the accuracy of your work by
drawing hnes, as ON and OP, Fig. 25.

Problem IVh. In working this problem you will
find it desirable to make the front and side views of
the entire pyramid in the lay-out. This is the easiest
way to get the lines representing the sloping sides
drawn at the proper angle. When drawn in this way
the front view in the lay-out will overlap the top view,
Fig. 26. You will readily see, however, that the
truncated part to be lined in does not overlap.

GROUP IV -Till': O-.TAGOX AM) Til!': IIKXAGON

RIM&-TOSS BASE

Zi^

IHote-Base,5- thick.

_SauARE HOLE. THRU BASE

STAR

Mote -THicKnEbS,l;f

OCTAGON/

\L TRAY

\
\

k /

/
/

\ 3

/^'

^Ak-4

-1-

-k

TRUMCATED PYRAMID

ProblLiii IV G

lktikrinh;

Sheet D. The first three lines o( this sheet are all
figures and Ihey arc to be treated as follows: — Trace
the first line to learn the strokes, Fig. k. Trace the
M\()nd to study the form and proportions of tlie figures.

not include figures. Either in this selection or in
practice work following this sheet, before you reach
Group VII, you should work with smaller letters and
figures. Fig. 1 suggests sizes of letters you can readily

1lf7 069 5.3-2«3

\\m will see that there are two styles of 3 given, one
based on the 8 and the oilier on the 5. Either style is
permissible. Trace the third line with special reference
to spacing, repeating each of the two groups.

On the fourth line space carefully, so as to occupy the
full line, the following figures:— 8932490756382910.

On the remaining three Hnes letter such a selection
as may be approved by your teacher. It may or may

make with the guide lines on the present sheet. It
also shows how by the addition of a few intermediate
Hnes it is possible to make guide lines for a variety of
work. Notice especially the spacing for fractions.

A good plan in learning to make the smaller sizes of
letters is (a) to change from the %" to the 14" size,
(b) Next try the rs"; (c) then the Vs".

Here is an extra problem that may interest you.
Draw guide hnes on a sheet of paper and carefully
letter the following: —

•THE LOVING EYE
THE SKILFUL H.\ND
SHALL WORK WITH JOY
AND BLESS THE LAND "

GROUP V
The Circle — Center Lines — Sections

Problem Va. Boforc you draw a circle you must
find Ihe center of the circle. The most common method
of tinding the center is to draw lines intersecting at the
center. Such lines are called center lines. They should
be light Unes.

.Another important thing to remember in drawing
circles is to test the setting of your compass. This is

Fig. 27

readily done by drawing on a scrap piece of paper a
circle, or short arcs on opposite sides of the center, as
a and b in Fig. 27. If the distance from a to b, meas-
ured thru the center o, is the measurement desired,
I lie compass is properly set. If not, change the setting
of the compass, and test again. When the compass is
.set be sure you do not change it in putting the needle-
point into the paper or in drawing the circle. Your
teacher will show you just how to do this without
danger of error. In drawing the target, test the setting
of the compass for each circle; when drawn test all
your circles by laying the scale on the drawing.

Beginning with this group we have a new order in
finishing drawings: —

1. Line in the circles and arcs of circles.

2. Line in all horizontal lines, beginning at the top
of the sheet and working down.

3. Line in all vertical lines, beginning at the left
of the sheet and working toward the right.

4. Line in inclined lines, taking those of the same
angle together.

5. Letter the title.

Be sure to remember this order because it is import-
ant that you form the
habit of working in
this way in order to
acquire speed and ac-
curacy.

Problem Vb. In
making your lay-out
for this and other
problems draw the im-
portant circles first, and project from the circles to
the other views. Never reverse this process.

For example, the circle O, Fig. 28, represents the

(Continued on page 50)

Fig. 2S

GROUP V -Till'. CIRCLE CF.XTER LI N'KS — SECTIONS

Proljk

111 \- A

/ COM
TOP

riE STA

PLETt \
VIEW

X-

^»

•4a> \','^^

=rx

WHEEL

V 1

\j^> \^

i
1
i

U-

CAST

IROn WASHER

{ T

^ ^\

\ \.J

-1

• —

■at

noTE-SuBSTiTwre a

SecTIOMAC VIEW FOR
THE SIDE VIEW

r^ — ^M

GRAMMAR GRADE PROBLIMS 1\ MKCIIAM

AW IXC ;

face view of a circular disc, and the rectangle P repre-
sents the side view. Always draw the circle O first,
and project across to draw the top and bottom lines of
the side view. If the reverse of this process were
attempted any slight error in measuring the length
of the rectangle or in locating the center O or in setting
the compass would prevent the projection lines from
joining the circle at the tangent points. The circle is
therefore drawn first and drawn accurately. Be sure
to test your setting of the compass.

The drawing of the cart wheel shows the face view of
the wheel and a sectional view. The sectional view, or
section, is commonly used in representing round ob-
jects, or objects of revolution, as they are technically
termed, because a section thru the center, or axis of
revolution, usually tells more about the object, or tells
it better, than any other view. A section is repre-
sented by drawing lines at an angle of 45°, sloping either
to the right or to the left, at an even distance apart.
Drawing these hnes is called cross-hatching. The pur-
pose of this cross-hatching is the same as that of tinting
a surface; it enables the eye to readily distinguish the
particular surface cross-hatched.

In describing a section we say that it is "taken"
at a certain line or thru a certain point. This one,
for example, is a vertical section taken thru the
center of the wheel. This section represents what
you would see if the wlieel were cut vertically tliru
the center, and you were looking flirectl\' at the sur-
face cut.

Problem Vc. This ])rol)leni is similar in purpose to
Problem \' li.

Problem Vd. The main purpose of this problem is
to give experience in substituting a sectional view for a
side view.

Problem Ve. This problem is a study of cylinders
at right angles to each other — a cylindrical mallet
head with a cylindrical hole in it.

Fig. 29

Fig. 30

Problem Vf. Just as intersecting center lines
determine the centers of circles, so cross lines determine
the centers of arcs of circles. In this drawing of the
collar the centers of the %" arcs are found beforehand
if the lay-out is made properly.

Problem Vg. In making drawings of the bushings
your teacher will indicate whether you need most to
make sectional views or side views; either will satis-
factorily represent the object. In drawing the octagon
of the second bushing either of the following methods
may be employed because the diameter is the dimen-
sion given: (1) It may be drawn within a square of
the same diameter, Fig. 29. Draw the square, and its

GROUP

V -THI

; ciiuLi-

M/5

vLLET HEAD

-j-

COMPLETE \

K™

VIEW n

■^

CKXTKR LINES — SF.C'IIOXS

roblem \' r.

BUSHIhGS
1

COMPLETE

THIS V1E.W

)l^^

COMPLETE

THIS VIEW

• 4 "

COLLAR

K1I +

I /^

"X \, t

(r\ \

—

._.

•n -

y /

DRAW SECTIONAL
VIEW HERE

— ii

PULLEY

GRAMMAR GRADE PROBLEMS IX MECIIAXICAL DRAWING

diagonals; then, using the corners of the square as
centers, strike arcs with radius equal to half of the
diagonal. (2) It may be drawn outside of, or circum-
scribing a circle of the same diameter as the octagon,
Fig. 30. Draw all four of the diameters as shown in
the figure so as to find the exact points on the circle
thru which to draw the sides of the octagon. These
sides are tangents to the circle at the points where
the diameters intersect the circumference of the
circle.

Problem Vh. This problem requires both the
completion of a front view and the substitution of a
sectional view for a side view.

Problem Vi. Be sure to draw the vertical center
line which determines the centers of the half-circles.

Problem Vj. This problem gives you an oppor-
tunity to work from a "data sheet." Your teacher
will indicate which two sizes of washers you are to
draw or will allow you to select. In this problem the
term "face view" is intended to mean the same as
the term "front view" used in previous problems.

Problem Vk. Consult your teacher concerning
which of these you should draw.

Problem Vl. Read the directions carefully. Notice
that it is the picture, not the frame, that is 3}4" in
diameter.

GROUr V-THK CIRCLE — CEXTKR LIXKS -SECTIONS

ROLLER

WASHERS

c —

•i

EMERY WHEELS

hoTE-DRAW SECTIONAL AND FACE. VIEWS OF ONE

PICTURE FRAME

DRAW PROMT AMD SECTlOMAL VIEWS
OF A FCAMt FOR A CIRCULAR PICTURE
5i" IN DIAMETER. USEOntOFTHt
MOLDINGS 5H0WM BELOW,

L^t,

GROUP VI

Problem VI a. If you wish to avoid difficulties in
drawing tangents, always find the exact point where the
flraight line joins the circle, or in the case of two circles,
just where one circle ends and the other begins. This

Fig. 31

will save you a great deal of trouble. For example in
drawing the line NM, Fig. 31, tangent to the circle
(), it is important to find the point N so that you may
know just where to take up your compass in lining in

the circle and just where to begin lining in the straight
line NM. In this case it is easy to find N becau.se
NM is a horizontal line. N is therefore in a vertical
line drawn thru O, the center of the circle.

In drawing the horseshoe magnet (1) draw the
horizontal center line first, (2) next the vertical center
line, (3) then the two circles, (4) after which it is easy
to draw the horizontal lines, and (5) finally the vertical
lines. In lining in follow the order described in Prob-
lem Va.

Problem VI b. The same general directions given
for Problem VI.\ apply in this one.

Problem VI C. See general directions under Prob-
lem VIA.

Problem VI d. See general directions under Problem
VIA.

GROUP VI — T

H0R5E5H0t MA&hET

-itj

-w

Draw front view

SLOTTED LIMK

) — e

Draw promt view |- in thickm£.5s

AXGKXTS

CHAIN LINK
1 1

>) ("AX

) V:

; :

Probkni W B

ROCKER ARM

^^ ((

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56 GRAMMAR tlRADK I'ROULEMS lx\ MECHANICAL DRAWING

Problem VI e. Sec general directions un;ler Problem

VIA.

Problem VI f. See general directions under I'roblem

VIA.

Problem VI G. In this problem it is more difficult to
find the points of tangency because the straight Hnes
are not horizontal. The method is shown in Fig. 32.
Notice that the 45° triangle, shown in dash lines, is first
placed up against the two circles; then its position is
changed so that a line can be drawn thru the center
and the point of tangency.

Notice also that points of tangency thus found are
used in determining the length of one of the lines in the
front view.

Problem VIh. The drawing of the faceplate pre-
sents another new problem: to find the center of an

arc of given radius that will be tangent

to two straight lines which are at right

angles with each other, or in other

words, to draw an arc in a square corner.

Fig. 33 shows the process: — With the

given radius and a as center, strike

the arc" be. With the same radius and
b and c respectively as centers, strike arcs intersecting
at d. With d as a center, strike the required arc.

C.ROUr VT — TANGENTS

ROCKER ARM

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C.RAMMAR c;RAI)E PROBLEM!^ IX MECHANICAL DRAWING

Problem VIi. This problem is similar to I'niblcni
\lii. It gives experience in spacinj; holes around a
. rrilcr.

Problem VIj. Honor rrobleni. 'I'his gives expe-
rience ill worthing from a table of data. Your teacher
will indicate the size of the bolt for
which you will draw a flange.

To find the center of the arc in the
side view consult Fig. 34. The line
ab corresponds to the left vertical line
in the side view of the flange; the
ine cd corresponds to the sloping line
n the upper part of side view of the
lange. The line ef is perpendicular
to ab at the point p, which corresponds to the left end
of the arc in the flange drawing. It is desired to find
the center of a circle on ab which shall pass thru
p and be tangent to cd. This means that we must
find a point on the line ab which is the same distance
from p that it is from the line cd.

Fig. 34

Todo this bisect the angle between cd and ef. (l)\Vith
ni as a center and any convenient radius draw an arc
cutting the two lines at g and h. This gives us two
points equally distant from m. (2) With these points
as centers and any convenient radius, strike arcs inter-
secting at n. (3) Draw a line thru m and n intersect-
ing the line ab at o. This point o is equally distant
from the point p and the line cd. (4) With o as a center
and op as a radius, draw the required arc.

Problem VI K. Honor Problem. This is the most
difficult in the group because two arcs join each other
at a tangent point. This requires especially accurate
construction work. The problem also requires the find-
ing of dimensions from algebraic formulae. But the
problem is all the more interesting because of these
facts.

Problem VIl. To help you in selecting an object
to draw, the following list is given: — cutting board,
sleeve board, bread board, hand-wheel, section of
molding, hexagonal socket wrench.

GROUl- VI -TAX(,K\TS

COUPLIMf,

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FLAHGE

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OGEE WASHER

nOTE-DRAW WASHER FOft ij BOLT

Diameter of Bolt = d
= 4d-f-4' C=ld+i" E.= 3D
= 2dT:i' D=ld F= D + t

Select

SOr-

E OBJECT THE

DRAW-

IMG OF v\

niCM

irsvOLvEb The

D RAW-

IING OP TAMSEMTS to CI0CUE5. |

DRAW TV

3 THREE VIEWS

AS MAY

BE REQUIRED

TO REPRESENT

THE

OBJEL.T

GROUP VII

Working Drawings

Problem VIIa. A working drawing should he made
fromthestandpoint of the workman. It should give the
views that will help him most in visualizing the object,
and give the dimensions he needs; and these should be
placed where he can most easily find them. In making
the drawing of the nail box you will take the same stcjis
in the process that the draftsman usually lakes in
making a more complex drawing: —

0=^0

□

1. Select Vieivs. In this case you need three views
to show the object most fully and clearly — the top,
front and end views. If this were a simple box without
a handle, the top and front views would be sufficient.
Fig. 35 shows three views, a, b and c, of a notched block
in which the view c may be omitted. It tells nothing
that needs to be known by the v.-orkman which is not
told by the other two views. Fig. 36 shows how one
view, with the thickness given in a note, may sometimes

take the place of two or three views. In the nail box
>ou could omit the top view and transfer the dimen-
sions in this view to the other two; you could omit
some of these dimensions by making a note stating
that the thickness of all stock except the bottom is
}^"; but for an inexperienced workman the three views
as shown are better than two.

2. Determine the Scale. The scale to which a draw-
ing is to be made depends upon the size of the object,
the size of the sheet of paper available, and the use to
be made of the drawing when completed. In the case of
the nail box you have one view 10" long and another
414" to be placed end to end on a sheet of paper that
is 103^" on the border hne. It is obvious that you
must make the drawing to scale. A little figuring will
show you that you can use the scale 6" = 1', often spoken
of as half size.

3. Arrangeincnt of Vird's. In arranging the views,
always place the top view above the front view, and
the end or side view near the end or side where it is
taken; that is, the right end view should be at the
right of the front or top view, and the left end view at
the left, Fig. 18. In spacing for these views remember
that dimensions are to be added. At least ' f " of siiacc

GROLI' MI- WORKIXC; DRAWINGS

is needed for a line of dimensions. Where two lines
of dimensions are to be placed on the drawing as is
usually the case, at least i-j" should be left l)et\veen
views.

4. Lines. The lines used in making pencil drawings
are the same as shown in Fig. 37.

-^— — — ^-^— Full Line

5.. Lay-oiU. Make the lay-out of the sheet as
follows:

(a) Make the border lines as described in
Problem Ia.

(b) Make the lay-out of the views as described
in Problem Ia, or if it contains circles, as described in
Problem Va. It is essential, as a rule, that center lines
lie drawn before circles, and that the circles be drawn
before tangent straight lines, or straight lines projecting
from circles.

6. Lining in. In lining in the drawing follow the
order given in Problem Va, namely, (1) circles and
arcs; (2) horizontal lines, beginning at the top of the
sheet; (3) vertical lines, beginning at the left; (4) in-
clined lines, taking those of the same angle together.

7. Selection of Dimensions. There is one rule to
follow in selecting dimensions: namely, put on the

ilimensions that the workman will need in making the
object. This rule is easy to stafe but difficult to follow.
It is difficult because in order to select just the right
dimension tlie draftsman must know, in general, at
least, how the work is done. Moreover, in factories
a drawing is often used by several different workmen,
each doing a different part of the process of manufac-
ture, and each wanting certain dimensions which may
not be needed by all the others. In general we may
say: (a) The over-all dimensions of the object are
needed. These will show the size of the completed
object, (b) The thickness, breadth and length of each
individual piece of the object must be shown. These
will be needed in getting out stock, (c) The dimen-
sions of the parts of every joint must be shown, (d)
The dimensions necessary to lay out the shape of any
formed, modeled or irregular part must be given, (e)
The location, size and depth of every hole must be
shown.

A common device among draftsmen for meeting
many of these conditions is to give parallel lines of
dimensions, one line consisting of the total or over-all
dimension, and the other the sub-dimensions; see end
of top view in the drawing of the nail box. This device
may be made to serve as a check on the draftsman's
work because the sum of all the sub-dimensions in a
given line must equal the total, or over-all dimension.

8. Placing Dimensions. Figs. 38, 39, 40, 41, 42 show
different ways of placing dimensions. In nearly every
working drawing there is one principal view — one that

AMMAK CRADK I'ROULKMS IN MECHANICAL DRAWING

-tells more about the object than any other view. In
this case it is the top view. The best rule for dimen-
sioning in this particular case is to place the dimen-
sions below and to the right of this main view, in so
far as that is practicable. Fig. 38. — This brings the
dimensions in groups between the views, where they
are most casilv seen, whichever view is the center of

1 s

'-'

attention. Sometimes the rule has been given to place
the dimensions at the bottom and at the right of all
views, Fig. 41, but this takes some of the dimen-
sions too far away from the place where one naturally
looks for them when centering his attention on the
principal view.

In case the space between views is not sufificient to

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II — -

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t
1

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Fig. 41

GROll' \II -\V()KKI.\(. DRAW IXC.

allow of two lines of dimensions the anangemenl in
Fig. 39 has some advantages. If the views are so close
together as to make it impossible to put any dimen-
sions between them without crowding, the method
shown in Fig. 40 is often used. This keeps the dimen-
sions near the principal view, which is desirable, but it
requires that two of the dimensions be placed on the

Fig. 42

view itself, which is not desirable. However, from
the standpoint of the workman, the method shown in
Fig. 40 is more desirable than that shown in Fig. 41.
The method shown in Fig. 42 avoids placing any
dimensions on the views, but scatters them so much
that in general it is not as desirable as that shown in
Fig. 40. From the above discussion it is clear that you
should endeavor to so place your views that it will be
possible to use the method of dimensioning shown in
Fig. 38

ig depend

The placing of the figures in dimension-
)on the space available. Fig. 43 shows

k,4

^-^A"^'-

correct placing of figures. In general all figures are
placed parallel to the dimension line, and so they can be
read from the bottom of the sheet or the right-hand end.

When dimensions are run at odd angles it is sometimes
a question how a dimension should be placed. Fig. 44
shows correct positions of figures at various angles.
Problem VIIb. This problem involves finding the
center of an arc that will pass thru three given points.

GRAMiMAR GRADE PROBLEilS IN MECHAXICAL DRAW! NCI

The construclioii necessary is shown in Fig. 45. Tlie
given points are a, b, and c. Using each point as a

Fig. 45 I'ig. -16

center, strike intersecting arcs as shown. Straight
lines thru the intersection points of these arcs meet at

the required point o which becomes the center for
striking the arc a h c.

Dimensioning Circles and Arcs. Circles should be
dimensioned by their diameters, Fig. 46. Arcs siiould
be dimensioned by their radii, Fig. 47. Circles should
be located by their centers, Fig. 48.

Fig. 48

Problem VII 0. The following are possible objects
to draw: joint, bench-hook, bird house.

Problem VIlD. The following are possible objects
to draw: knife box, bracket shelf, cyHnder head.

GROUP VII — WORKING DRAWINGS

hAIL BOX
1

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Make working drana

ING OF SOME

OBJecT WM.CH MAY B£

BiiPRESEnTED

BY SraAlGHT UIMES

Pn.bl.-n

VII B

Make

WORKinS

DRAWING OF Ad

OBJECT

REQUlRln

& CIRCLES AND

STRAISHT UMEb TO REPRfiSEnT IT

GRAMMAR GRADE PROBLEMS IN MECHANICAL DRAWING

Problem VII E. This problem has been selected
to show how an extra sheet of details may sometimes
be used to advantage. It would have been possible to
have placed all the dimensions of the detail sheet on the
assembly drawing, but in that case the drawing would
have been badly crowded. By adding the sheet of
details greater clearness is obtained. Notice that all

sizes, is given in decimal form. For your convenience
approximate sizes are given in Fig. 50.

These figures include only a few of the most common-
ly used sizes. The slot in the top view is usually drawn
at a ditTcrent angle from that in the front view, that is.

^>-^>

dimensions of the

Ap,,.

top of the stool

.\,>. Dium.

are found on the

5-^8

assembly draw-
ing because the

6— ^f
8-^

top is not shown
on the detail
sheet. Also

9— H

11 — 6-4

notice that the

12—3^
15-M

method of as-

.A]

1-2 D-]

sembling the parts, namely, by screw, is shown in the
assembly drawing. You will see that the screws are
made with light hnes in order not to give them too
much prominence. Fig. 49 shows an approximate, but
very convenient method of drawing screws. The lines
of the threads are at an angle of 60° with the center
line of the screw. The figures 1, 2, 3 and 4 indicate
the stages in the process. The curve of the point is
drawn freehand. Sometimes the last stage in drawing
the threads is omitted, leaving them as in 3. The size
of a screw is indicated by its length L and by its wire
gage number, which means its diameter, D. The
tliameter of a screw, as found in the table of wire gage

■ig. 50

•ig. .■>1

at an angle of 45° to the horizontal. This avoids con-
fusion with other lines in the top view. The front view
of the head is drawn with angles of 45°, tho this is not
the actual angle to which screws are made. It is,
however, the most convenient angle to use in drawing.
Screw 4 in Fig. 49 is called a flat head screw; screw 5
is called an oval head screw; and screw 6 is called a
round head.

Fig. 51 shows easy ways of drawing wire nails and a
bolt such as is used in w-oodwork. The head shown in
1 is that of a casing nail, in 2 that of a finishing nail.

GROUP VII — WORKING DRAWINGS

GRAMMAR

IRADE

PROBLK.MS IN

MECHANICAL

DRAWING

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P-1 AK

THE "PROBLEMS SERIES"

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problems which liave been
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PROE

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100 practieaj problems
p. Kspecin-lly valuable
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PROBLEMS IN FURNITURE MAKING.
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