Mechanical drawing : a manual for teachers and students

Front matter

X^^a

NATIONAL DRAWING COURSE.

TEXT-BOOKS.

Preface

The following notes are intended for students, and for teachers of elementary work, particularly for public school teachers. There are many books on the subjects of projection and working drawings, but none which present the principles in ways suited to the needs of the large number of teachers who are required to give instruction in these subjects in the public schools. Most of these teachers have had little instruction in the subjects and frequently do not understand problems which they are expected to explain. This occurs because too difficult work is often planned for their grades, and also because the instruction which many public school teachers have received has been so advanced and theoretical that the simple principles which alone are necessary for elementary work have been lost in the attempt to understand descriptive geometry and the drawings of machine and other details, whose nature and use are often not known.

To understand descriptive geometry certain qualities of mind are absolutely necessary, and many find it impossible to comprehend even the simpler problems of this subject. The draughtsman or drawing teacher of advanced work who is without practical knowledge of the subject of descriptive geometry is very poorly equipped for his duties ; but this knowledge is not necessary for the public school teacher, who will find it best to treat the subject of working drawings in a much simpler way.

This book presents principles and not a graded course of lessons. It covers more than many teachers may require,

IV PREFACE.

though special students or classes of the high school may study work as advanced as any of that presented. Teachers of drawing in the high school should understand all the problems of the book.

It is hoped that the book may assist teachers of both grammar and high schools so to understand the subject that they may give to classes instruction suited to their capacity and needs.

Anson K. Cross.

Contents

PAGE

CHAPTER I. — Materials and their Uses i Paper . . . . . . i

Drawing Boards . . .2

Pencils , , , , 3

T-Square = . . 4

Compasses 5

Dividers 7

Needle , . 7

Scales 8

French Curves 9

Penciling . 10

CHAPTER II. — Geometrical Problems 12 CHAPTER HI. — Working Drawings 28

Nature and Use of Working Drawings 28

Study of Principles 32

Making Working Drawings 35

Views of a Circular Plinth 36

Views of an Hexagonal Plinth ^7

Views of a Plinth and Disc • 39

Views of a Box and Pyramid 40

Dimensioning • . . 43

Lettering 45

CHAPTER VIII. — Orthographic Projection 67 Projection Principles 70

Axes of Projection 71

Views of a Point 71

Position of a Point 72

Views of a Straight Line 74

Views of a Plane Surface . 75

Views of a Solid 76

Views of a Rectangular Card 77

Views of a Pyramid 78

True Length and Position of a Straight Line ... 81

Statements of Principles 83

Projection Problems . ^ 86

Chapter I. Materials And Their Uses

1. Good work cannot be done without good instruments. The best work cannot be done without steel T-squares and triangles, steel-edged drawing boards, and drawing instruments of the best make. Students of art and technical schools should provide themselves with the best instruments.

In the public schools, no more can be done than to give a little knowledge of the principles of instrumental drawing, which will be valuabk to all. To do the best work technically is impossible, because the pupils are too young, because they do not have the time necessary for practice, and because they do not have the materials necessary to produce the best work. Any one of these reasons is sufficient to prevent the making of first-class drawings, and together they make it impossible for us to expect that perfect results can be obtained.

Although pupils of the public schools labor under the above-mentioned disadvantages, it will not do for the teacher to expect bad work, or to be satisfied with work which at first glance is seen to be inaccurate ; for even with the imperfect materials provided it is possible, by careful work, to obtain drawings which are neat and sufficiently accurate for the requirements of simple working drawings.

2. Paper. — The paper must be tough and should have a surface which is not easily changed or roughened by erasing lines drawn upon it. This is most important when drawings are to be inked. For free-hand sketching a soft paper is best ; but for all mechanical work, the paper should be hard and strong.

For pencil drawings a paper which is not smoothly calendered is best, because the pencil marks more readily upon an unpolished paper, and because its surface will not show erasures as quickly as that of a smooth paper. For public school use, several kinds of cheap paper, which are good enough for the work, may be obtained both in sheets, in block form, and also made up in blank books.

Whatman's paper is the best for drawings which are to be inked. There are two grades, hot and cold pressed, suitable for this use ; the cold-pressed having the rougher surface. If the paper is not to be stretched, the cold-pressed is preferable, as its surface show^s erasures less than that of the hot-pressed. The side from which the water-marked name is read is the right side, but there is little difference between the two sides of hot and cold pressed papers. Stretching the paper is unnecessary except when colors are to be applied by the brush, or when the most perfect inked drawing is desired.

The use, in the public schools below the high, of sheets of blank paper instead of blank or other drawing books has its advantages and its disadvantages. If a drawing upon a sheet of paper is spoiled, it may be thrown away and another begun upon a new sheet ; but this fact tends to careless work. To the teacher loose sheets of paper are a source of great care, even if kept in portfolios or large envelopes and retained by the pupils, for the drawings must be examined, and it is not easy to keep them arranged in the order in which they are made.

Blank books cost little more than paper ; and their use tends to neatness and care on the part of the pupils, each of whom is interested to produce the best book. Drawings in the books are always arranged in order and ready for examination. The chief objection to their use is that they cannot be handled as a block for free-hand purposes, or be used with a T-square for instrumental work. This difficulty is avoided by fastening the book, by means of two rubber bands, to a drawing board made to receive it. When fastened to this board the book may be used for instrumental drawing as advantageously as paper upon a board. Used in this way a book is preferable to sheets of paper ; therefore a board should be provided whenever books are used, whether the books are blank books or those of any system.

3. Drawing Boards. — Drawing boards should be made of clear white pine, and should not be painted or varnished; they should have cleats upon the back, so that upon the whole working surface

MATERIALS AND THEIR USES.

of the board the grain of the wood runs in one direction ; for when paper is stretched upon cleats which are fastened at the ends of the board, it is often spoiled by the swelling of the board, which moves back and forth upon the cleats.

The cleats should not be glued or otherwise firmly secured to the board, since the board must change its width with the weather, and if the cleats are firmly secured to it, the board will split or warp. The cleats should be fastened by means of screws and washers, the screws being placed in slots, which allow the board to move. This construction is not necessary for small boards required in the grammar schools.

The best board for use with a drawing book is one provided with a groove to receive the head of the T-square, which should be thick enough to remain in the groove when the book is between the square and the board.

4. Pencils. — To do good instrumental work two grades of pencils should be used, a hard one for the fine working lines and a softer one for the result lines. The hard pencil should be sharpened to the wedge-shaped point illustrated, which is as thin as possible one way, and about one-half the width of the lead the other.

The softer pencil should have a point of the same shape but thicker, so as to give the width required for the result line.

To sharpen the pencil a knife should be used to give the wood the flattened form required in the lead. The lead should then be worked down by the use of a fine file. A substitute for the file, which may be used in the public schools, is given by gluing a straight-edged piece of sandpaper to a strip of wood. A point with which good work can be done cannot be obtained by the use of the knife alone.

A pencil with a round point should be used for all free-hand lettering and figuring, and for other work of a free-hand nature, such as the drawing of irregular curves.

The hard pencil should be used very lightly, as much pressure will indent the paper so that its marks cannot be removed.

All lines should be drawn with the pencil slightly inclined in the direction in which it is moved. The pencil should not be moved in the opposite direction, as it will then act as a plough to tear the surface of the paper.

Any and all lines not needed in the finished drawing should be erased at one time after the final lines have been determined, for the surface of the paper is soiled very quickly when worked upon, after erasures have been made. The Avorking lines and other lines that are to be removed, should be erased when the drawing is ready to finish and before its outlines have been strengthened, in order that the final lines may be left in perfect condition, and may not require retouching on account of use of the eraser.

5. T-Square. — A T-square is an instrument used in connection with a drawing board, for drawing straight lines ; it consists of two parts, a blade and a head, which are secured at right angles to each other. The blade of the T-square should be placed upon the head, which should never be cut to receive it, and should be secured to it by means of screws. This construction allows the parts to be separated for straightening, and the triangles to be moved across the head, which is often desirable, but cannot be done when the blade is set into the head.

The T-square should be used for drawing horizontal lines only. Its head should always be placed upon the left edge of the board. Vertical lines should be drawn by the use of a triangle placed upon the T-square and not by means of the T-square only ; because the edges of the board are seldom exactly at right angles to each other, and the blade of the T-square is often not at right angles to the head, so that lines at right angles to each other will not result from the use of the T-square upon all the edges of the board. Only the upper edge of the T-square should be used, as the edges are often not quite straight or parallel.

6. Triangles. — The usual forms are illustrated. The 45° triangle has two angles of 45° and one of 90°. The 30° and 60° triangle has an angle of 30°, one of 60°, and one of 90°. By placing these triangles upon the T-square, lines at any of these angles with a vertical or horizontal line mav be drawn.

MATERIALS AND THEIR USES.

Lines parallel to any given line, AB, may be drawn by first placing together two triangles (C and D), so that a side of one (C) coincides with AB, and then sliding triangle C upon triangle D, being careful not to allow D to move.

Any parallel lines are most conveniently drawn by sliding one triangle upon the other, or upon the T-square.

Lines perpendicular to AB may be drawn by placing either triangle upon the other, so that its hypotenuse coincides with AB, and then revolving the triangle through an angle of 90°, into the position illustrated by the dot and dash lines.

Lines at 30°, 45°, and 60° with AB, may be drawn by placing one triangle upon the other, so that an edge coincides with AB, and then reversing the triangle, as will be shown by experiments.

When paper is to be cut by the use of a knife and straight edge, the T-square or triangle should not serve as the straight edge, for its edges would soon be nicked and spoiled by the knife.

7. Compasses. — Compasses suitable for any use should have jointed legs, which will allow the points to be placed at right angles to the paper, whatever the size of the circle to be drawn. Compasses should not be used for circles which are too large to allow the points to be thus placed. A lengthening bar is generally provided, which greatly increases the diameters of circles which may be drawn.

The joint at the head of the compasses is the most important feature. It should hold the legs firmly in any position, so that in going over a circle several times, only one line will result. It should allow the legs to move smoothly and evenly, and should be capable of adjustment, as the parts soon wear, and the joint then becomes too loose. The joint should never be so tight that much pressure is required to move the legs.

One leg of compasses is usually provided with a socket to which are fitted three points ; a divider point, a pencil point, and a point carrying a special pen for the inking of circles. Each of these points is generally provided with a joint, so that it may be placed at right angles to the paper.

The other leg should be jointed ; it is often provided with a socket which receives two points, one a divider point, and the other carrying a needle point. Such an instrument may be used as dividers for spacing, or as compasses for penciling or inking circles, and will be all that is needed for public school work. The pen point is not necessary for grammar school use, as inking should not be attempted before the high school.

The cheaper grades of compasses are provided with sharp, pointed, solid legs, and are very objectionable, because these points work into the paper as the compasses revolve and make large holes which spoil the drawing. Even for public school work, compasses should have a needle point with a shoulder which prevents the making of holes in the paper. It may not be possible to provide for the grammar schools compasses with jointed legs ; but the needle point with the shoulder must be insisted upon, if even fair work is desired.

The compasses should be held very lightly between the thumb and forefinger, and should be inclined slightly in the direction in which the line is drawn. No more pressure should be applied than is necessary to obtain the line. In inking, little more than the weight of the compasses is needed ; but in penciling more pressure will be required for result lines. Two grades of pencils are more necessary for use in the compasses than for straight line work ; they should be sharpened as shown on page 3, and so that the wide side of the point is at right angles to a line extending from the pencil point to the needle point. As this is difficult to do, pupils below the high school may use a sharp conical point.

MATERIALS AND THEIR USES. 7

The legs of the compasses should be moved, to give, any desired radius, by taking hold of each leg. The needle point may be placed on one point of the drawing while this is done ; but if the strain due to changing the radius is brought upon the needle point, it will tear the paper and spoil the drawing.

8. Dividers. — The compasses are changed into dividers as already explained. To set off equal spaces on any line, hold the dividers lightly between the thumb and forefinger and place one divider point at any desired point in the line to be spaced ; then revolve the dividers about this point as centre until the other divider point comes to the line, when the dividers are to be revolved about it as about the first point. Revolve the divider points first on one side and then on the other of the line to be spaced, and never lift both points from the paper at the same time. Continue thus until the line is spaced.

To divide a line of given length into any number of equal parts, by use of the dividers, it will be necessary to use so little pressure that visible punctures are not made until the correct space has been obtained; if this is not done in two or three trials a second line should be drawn and the spacing continued upon it. If one line is gone over many times, the divider points will fall into the punctures previously made, and accurate work will not be obtained. When the correct space is found the points must be marked in the line so that they can be readily seen. To do this the line should be gone over several times, each time more pressure being applied to the dividers, until the punctures become visible. If the pressure required to place the points is applied at once, equal spaces will not be given, as the dividers will spring and move while marking the points.

To do work of this nature easily, a pair of spring dividers should be used. This instrument has one point attached to a spring, which is regulated by a screw, so that very slight changes in the space may be made with ease.

9, Needle.. — The needle may be used by the draughtsman and by advanced pupils with great advantage as regards both accuracy and speed. It should not, however, be used by young pupils, or below the high school.

8 MECHANICAL DRAJVIXG.

The needle may be used to set off distances from the scale and to mark the intersections of lines ; it may also be used when lines are to be drawn through two points, to hold the triangle so that only one point requires the attention of the draughtsman. This is done by placing the needle in one point, holding the triangle against it, and revolving the triangle until it comes to the second point.

Points should never be marked by holes in or through the paper, but by the smallest punctures which can be seen. These are much more definite than pencil marks, and have the advantage of locating points so that they are not lost by erasures. When a point is marked in this way a small pencil circle should be drawn about it free-hand, in order that its position may be readily seen.

The needle point may be placed in a handle of soft wood, and should project just far enough to be used, but no farther, as accidents will happen if it is not carefully handled. The best place for the needle point is at the unsharpened end of a pencil. A double- €nded pencil holder for round leads may have the pencil in one end and the needle in the other. This holder should be about 4+" long, so that it may be reversed readily.

10. Scales. — When objects are small they may be represented full size ; but when large, the drawings must be smaller. Common scales for mechanical drawings are \. \, -J, and ^j. full size. These scales are often written 6"=i ft.; 3"=! ft.; ii-"=i ft. and f "= i ft.

Large objects are often drawn to very small scales ; in maps an inch often represents many miles.

Instead of selecting one of the scales named or one found upon the ordinary scales used by draughtsmen, drawings may be made to any scale whatever. Thus, if any object is to be represented in a certain space, a scale should be constructed which will cause the drawing to fill the space in the best way.

To determine the scale by which the drawing of any object may be made of any desired size, divide the length of the object by the length of the drawing desired. Thus, suppose an object 21" long is to be represented in a space which will allow the drawing to be i o^" long. The drawing must be half size, and may be made by measuring the lines of the object and making those of the drawing half as long. If the drawing can be but 7" long, it will be one-third

MATERIALS AND THEIR USES. 9

size. To make the scale for this drawing, draw a Hne 4'' long and divide it into twelve equal parts, which represent inches. Divide one of these spaces into eight equal parts to represent eighths of inches. By means of this scale, the drawing may be readily made by taking from it the dimensions of the different parts.

If views are to be made of a mallet, the length of the front view to be 6", while the actual length of the object is 15", a scale from which the sizes of the different parts can be taken may be made by drawing a line six inches long and dividing it into fifteen equal parts, each part representing one inch. One space may be divided into eight equal parts, and by means of this any part of an inch may be obtained.

The triangular scale (architects') has upon it the following scales : ^V 8"? Tfi-j i? f> i» 4? ^j ^2" ^^<i 3 inches. These are not provided and are not necessary in the grammar schools, w^here a cheap foot rule having three or four scales ranging from :|- to f full size will generally be all that is required. If a drawing cannot be made full or half size, or by one of these scales, a scale can be constructed by the pupils, as explained.

When views of objects are to be made, they should be of such size and so arranged as to produce a pleasing effect upon the sheet or the page, and when none of the scales provided will give the best size to the drawing, a special scale should be constructed.

II. Irregular or French Curves. — These curves are not required below the advanced work of the high school. They are used for curves which cannot be drawn with the compasses. To draw an ellipse or other curved line by their use, care must be taken to have the French curve exactly cover as many points in the line as possible, and then only the central points should be connected. If the line is drawn to all the points covered by the French curve, it will generally fail to continue smoothly through the points in the line beyond the curve.

When French curves are to be used the lines should be very lightly sketched free-hand through the determined points, before the curve is applied to the drawing to obtain the final lines.

lO MECHANICAL DRAWING.

12. Penciling. — Penciling is generally done to prepare for inking or for the making of tracings on tracing cloth, but sometimes practical shop drawings are finished in pencil lines. In this case the drawing is generally little more than a rough diagram, hastily made, and not intended for continued use.

Drawings finished in ink are much more effective and desirable than pencil drawings ; but, as a good inked drawing cannot be made except upon an accurate pencil drawing, pupils should begin with the pencil, and should not be allowed to use ink until they can produce satisfactory results in pencil.

The aim in pencil work should be to approach as nearly as possible the accuracy and decision which are only attainable in an ink drawing. Care in selecting and using pencils, paper, and instruments will produce pencil drawings which have firm, even, black lines, that are very effective, if they are not quite so strong as those made with ink.

It is customary to represent all visible edges by full lines, and all invisible edges by dotted lines. These dotted lines should be as strong as the full lines ; they should be regular and composed not of dots, but of very short dashes, whose lengths are uniform and greater than the spaces between them. Dotted lines are often very poorly drawn, and spoil the effect of drawings otherwise good. The wadth of the line and the length of the dash depend upon the size of the drawing and its purpose. For the drawings which pupils should make, the line given may serve as a copy.

Care must be taken to have all lines stop just where they are intended to end. If lines do not quite meet, or if they pass by each other, as illustrated, when this is not intended, the drawing is spoiled.

The perfect union of lines which should be tangent to each other is also necessary to good work. Straight lines should run into arcs, and arcs into each other, without the slightest suggestion of a break, or of two lines instead of one.

Centre lines are necessary in working drawings. In the study of projection, it is not necessary to show them unless dimensions are

MATERIALS AND THEIR USES. II

to be given. They are represented by dot and dash lines, as illustrated, and extend some slight distance outside the drawing, to show that they are centre lines. Dimensions are placed as explained in Art. 44.

Different materials may be conventionally shown in pencil drawings by using different kinds of section lines. The materials most commonly used are often represented as illustrated in Art. 76.

An accurate and neat drawing is very pleasing and effective ; every draughtsman and advanced student should be able to produce such a drawing with ease. Neatness and accuracy, the results of care and long practice, are essential to good work ; and pupils should understand that without the exercise of much patience, work of real value cannot be obtained.

CHAPTER 11.

GEOMETRICAL PROBLEMS.

The following problems are those most likely to prove valuable to grammar and high school pupils. They are given in order that pupils may be able to apply them in the study of design and working drawings, and that they may learn to make accurate drawings. They are not given with the intention of teaching geometry.

The illustrations represent the working lines by light lines, the given lines by lines of medium strength, and the result lines by heavy lines. In finishing pencil drawings the best effects are obtained by using dotted lines for the working lines ; but if time necessary to obtain perfectly regular lines cannot be given, it is better to use fine, light lines. When drawings are inked the working lines may be red, the given lines blue, and the result lines black.

In working all problems, to obtain accurate results, arcs described as working lines should be of large radii.

Problem i . — To bisect a straight line AB, or an arc of a circle ACB.

With A and B as centres and any radius greater than half AB, describe arcs which intersect at I and 2, Join i and 2 by a straight line, and 1-2 is perpendicular to AB^ and bisects it in j, and the arc in C

Problem 2. — To erect a perpendicular to a given lifie at a given point A in the line.

With A as centre and any radius, set off equal distances A i and A 2 from A. From points i and 2 as centres, and with a radius greater than half 7-2, describe arcs which intersect in j and 4. Join j and ^, and j-4. is the required perpendicular.

1^

GEOMETRICAL PROBLEMS.

Problem 3. — To draw a perpeitdicular to a given line BC^from a point A oictside the line.

With A as centre and any radius, intersect the given line in points i and 2. With points i and 2 as centres and any radius describe arcs intersecting in J. Join A and j ; ^ j is the required perpendicular.

Problem 4. — To erect a perpendicular to a given line AB, from Q, point B, at or near its end.

With B as centre and any radius, draw an arc "t of a circle 1-2-j, With i as centre and the same

radius, cut this arc in 2, and with 2 as centre and the same radius, describe the arc j-4. With j as centre and the same radius, intersect j-4 in 4, Join 4 B ; this is the required perpendicular.

Problem 5. — To draw a line^ EF^ pa^^allel to a given line^ ABy and the distance CD from it.

From any two points, A and ^, in the line as centres, with radius CZ>, describe arcs E and F, Erect perpendiculars at A and B, which intersect the arcs in E and F, Join E and F\ this is the required parallel. In practice, it is not necessary to draw the perpendiculars.

Problem 6. — To construct an equilateral triangle on a give?t base, A B.