ESSENTIALS OF DRAFTING Clas 1^ *vf 4<^ Copyright >N^^ n /^ COFmiGHT DEPOSIT. N ESSENTIALS OF DRAFTING BY THE SAME AUTHOR A HANDBOOK ON PIPING 359 Pages 359 Illustrations 8 Folding Plates Postpaid, $4.00 ESSENTIALS OF DRAFTING A TEXTBOOK ON MECHANICAL DRAWING AND MACHINE DRAWING WITH CHAPTERS AND PROBLEMS ON MATERIALS STRESSES, MACHINE CONSTRUCTION AND WEIGHT ESTIMATING BY CARL L. SVENSEN, B.S. ASSISTANT PROFESSOR OF ENGINEERING DRAWING IN THE OHIO STATE UNIVERSITY, JR. MEM. A.S.M.E., MEM. S.P.E.E., FORMERLY INSTRUCTOR IN MECHANICAL ENGINEERING IN TUFTS COLLEGE AND HEAD OF THE DEPARTMEMT OF MACHINE CONSTRUCTION AT THE FRANKLIN UNION SECOND PRINTING — CORRECTED NEW YORK D. VAN NOSTRAND COMPANY 25 Park Place 1919 T253 COPYRIGHT, I918, 1919, BY D. VAN NOSTRAND COMPANY NOV -5ISI9 THE-PLIMPTON-PRESS NOEWOOD-MASS«U-S-A ^ ^^^ (e)CI.A5Iir>440 'jx''A^''^!ik'Xk ^;i\ ^^:!/yji M !(^^^nr^i^^:^'i s DEDICATED TO THE AUTHORlS FRIEND GARDNEB^CHACE ANTHONY WHOSE INFLUENCE AS AN ENGINEER. AND TEACHER. ON THE DEVELOPMENT OF AMERICAN MECHANICAL DRAWING IS UNIVERSALLY RECOGNIZED ' § / ^ ^>^)^)^^WYf^> &^ )^)^v/^^f ^i^i^i^t rWf PREFACE The evening technical school has been rapidly developing during recent years. From a makeshift it is coming to occupy a field distinctly its own. The ambitious man attending an evening technical school is fully the equal of his brother at the day technical school and his worth is being increasingly realized. The foundation subjects — mathematics, mechanics, and draw- ing — require particular attention in evening courses, where the time may be somewhat limited and the needs of the student varied. This book has been prepared for Ohio Technical Draw- ing School students as part of a technical course. Progress in engineering work of any kind depends upon an intimate knowledge of mechanical drafting as the language of the engineering world. Its possibilities must be understood. The mere drawing of lines and more or less copying of exercises or sketching from a few models is far from the purpose of a draw- ing course. The value of drawing as one of the working tools to be treasured and used during a lifetime in the most useful of professions, engineering, should be realized. It is as an aid in the study, and later use of engineering knowledge, that drawing finds its place. These preliminary remarks may serve to explain the makeup of the book. The actual handling of the instruments can best be taught by careful individual instruction of each student, after which false or awkward motions should be immediately corrected. Inefficiency in this respect is one of the most severe handicaps of many "self-made" draftsmen. The treatment of the various subjects is necessarily somewhat brief, as it is intended that per- sonal instruction should be given in each subject. In the first studies the student is taught to represent each object in strict conformity to the laws of projection. All lines are drawn, all intersections are shown, and invisible surfaces are all vii viii PREFACE indicated by dotted lines. For simple parts such drawings are easily read and they are generally used in the drafting room. When more complicated pieces are met with or where whole machines or constructions are to be represented, such a method would lead to great confusion and often would produce a drawing which it would be almost impossible to read. The time nec- essary would be very great even for an expert. In such cases the full lines representing the visible surfaces are shown, but the intersections and invisible surfaces are not all drawn in. The selection of what lines to draw and what lines to leave out is an important study in itself. Furthermore there are many representations of parts which are or appear to be violations of orthographic projection, which are used because practice has shown that they convey the idea to the workman more completely or easily. Other representa- tions are used to save the draftsman's time, or in the interests of simplicity. Almost anything which will make a drawing more readily intelligible is justified. This statement must be used with caution, as what will seem plain to a man familiar with the work may not be so plain to the workman or other reader. A drawing has one great purpose, and that is to be useful. To this end lines may be added or left out, shading may be used, or notes may be put on. As an expression in the engineering language each drawing should have only one meaning, and should state that meaning with the least possible chance for misinterpretation. Many of these idiomatic expressions of the engineering language will be considered in the later chapters. The chapters on Materials and Stresses, Machine Construc- tion, and Estimation of Weights are brief treatments of subjects which are necessary for the making of intelligent drawings. Con- siderable elementary machine design is included as belonging in a practical treatment of mechanical drafting, for the author does not look with favor upon fine distinctions between ''subjects." It is the "usability" which really counts. The subjects are arranged to suit the author's convenience, but they may be taken in a different order if desired. The problems are placed in one chapter at the end of the book, so that a selection may be easily made. These problems are suggestive, and may be amplified by the teacher, who should make a free use of actual shop blueprints and castings. PREFACE IX The author beheves that the highest grade work can be done by evening school men, and in an experience of many years has always found that they are ever ready to meet the most exacting requirements when satisfied that what they are receiving is really worth while. Appreciation of the helpful criticisms of Prof. Thos. E. French is here expressed. CARL L. SVENSEN Columbus, Ohio, Sept. 1, 1917. CONTENTS PAGE Preface v CHAPTER I Drawing Instruments and Materials 1 Instruments and Materials — Use of the T Square and Triangles — • Use of the Scale — Drawing Pencils — Use of the Compasses — Use of the Dividers — Use of the Ruling Pen — Character of Lines. CHAPTER II Lettering 7 Lettering — Gothic Letters — Proportions and Forms — Letter Spac- ing — Titles — Bill of Material. CHAPTER III Constructions 13 Essential Constructions — Angles — Circles — Plane Figures — To Bisect a Line — To Bisect an Angle — To Divide a Line into any Number of Equal Parts — To Copy an Angle — To Construct a Triangle, having given the Three Sides — To Construct an Equi- lateral Triangle — • To Construct a Regular Hexagon — To Con- struct a Regular Octogon — To Draw an Arc of a Circle, having a Given Radius, and Tangent to Two Given Lines — To Draw a Circle, Passing through any Three Points not in the same Straight Line — To find the Length of an Arc of a Circle — To Draw a Tan- gent to a Circle at any Given Point — To Draw the Arc of a Circle of given Radius, Tangent to an Arc and a Straight Line — The Ellipse — • To Draw an Ellipse by the Concentric Circle Method — To draw an Ellipse by the Trammel Method — To Draw a Curve having the Appearance of an Ellipse by Means of Circular Arcs — The Involute — To Draw the Involute of a Triangle — To Draw the Involute of a Circle — The Parabola — To Draw an Equilateral Hyperbola, CHAPTER IV Projections 23 Purpose of Drawings — Orthographic Projection — The Planes of Projection — Some Rules — Dotted Lines — Auxihary Views — Required Views — The Imaginary Cutting Plane — Representa- tion of Cut Surfaces. xi xii CONTENTS PAGE CHAPTER V Materials and Stresses 31 Materials — Cast Iron — White Iron — Gray Iron — Properties of Cast Iron — Wrought Iron — Properties of Wrought Iron — Steel — Bessemer Process — Open Hearth Process — Properties of Steel — Malleable Iron — Suggestions for Selection of Material — Loads and Stresses — Axial Stresses — Unit Stresses — • Modulus of Elasticity — Ultimate Strength — Factor of Safety — Average Values. CHAPTER VI Screw Threads 40 Uses of Screw Threads — The Helix — Parts of a Screw — Right- and Left-hand Screws — Forms of Screw Threads — Multiple Threads — Split Nut and Square Thread — Conventional Repre- sentation of Screw Threads — Threaded Holes — Strength of Screw Threads. CHAPTER VII Bolts and Screws 48 U. S. Standard Bolts — Bolts — Studs — Threaded Holes — Machine Screws — Cap Screws — Cap Nuts — Set Screws — Locking Devices. CHAPTER VIII Riveting 57 Riveting — Rivet Heads — Lap Joints — Butt Joints — Calking — Miscellaneous Connections — Rolled Steel Shapes. CHAPTER IX Working Drawings 62 Classes of Drawings — Special Detail Drawings — How to Make a Drawing — Tracing — Order for Inking Lines — Assembly Draw- ings — Exceptions to True Projection — Blueprints. CHAPTER X Sections 71 Sectional Views — Broken and Revolved Sections — Location of Sectional Views — Objects not Sectioned — Dotted Lines on Sec- tional Views — Sections of Ribs and Symmetrical Parts. CHAPTER XI Dimensioning 77 Purpose of Dimensions — Dimension Lines — Elements of Dimen- sioning — General Rules — Systems of Dimensioning — Location of Dimensions — Shafting — Tapers — Small Parts — Methods of Finishing — Checking Drawings. CONTENTS xiii i»AGE CHAPTER XII Machine Construction 87 Machine Operations — Drills — The Steam Engine — Pistons — Sliding Bearings — Wear and Pressure — Stuffing Boxes — Use- ful Curves and Their Application — Fillets and Rounds — Arcs and Straight Lines — Flanged Projections — Flange Edges — Flanges and Bolting — Keys. CHAPTER XIII Sketching 98 Uses of Sketching — Materials for Sketching — Making a Sketch — • Taking Measurements — Some Ideas on Sketching. CHAPTER XIV Estimation of Weights 105 Accuracy — Weights of Materials — Weight of Loose Materials — Weight of Castings — Methods of Calculation — Weight of Cylin- der Head — Weight of Plunger Barrel — Weight of Forgings. CHAPTER XV Piping 112 Piping Materials — Pipe Fittings — Standard Pipe — Pipe Threads. CHAPTER XVI Intersections 117 The Line of Intersection — Intersection of a Vertical Prism and a Horizontal Prism — Intersection of a Vertical Prism and an IncHned Prism, Visibility of Points — Intersecting Cylinders — Choice of Cutting Planes — Connecting Rod Intersection. CHAPTER XVII Developments 123 Surfaces — Development of a Prism — Development of a Cylinder — Development of a Pyramid — The Development of a Cone — De- velopment of a Transition Piece. CHAPTER XVIII Picture Drawing 130 Isometric Drawing — Isometric and Non-Isometric Lines — Angles — Positions of the Axes — Construction for Circles — Oblique Drawing. xiv CONTENTS PAGE CHAPTER XIX Shade Line Drawings 136 Shade Lines — System in Common Use — Surface Shading — Shad- ing Screw Threads and Gears — Special Surface Representations — Patent Office Drawing. CHAPTER XX Drawing Questions, Problems and Studies 141 Index 181 ESSENTIALS OF DEAFTING CHAPTER I DRAWING INSTRUMENTS AND MATERIALS Instruments and Materials. — Drawing instruments and materials should be selected with care, and under the guidance of an experienced draftsman or teacher. The really necessary equipment consists of the following: Set of case instruments comprising: 6-inch compasses with fixed needle point leg, removable pencil leg and removable pen leg, 5-inch dividers, 5-inch ruling pen, Bow pencil, bow dividers, bow pen. 24-inch T square. 16 " X 20 " drawing board. 6-inch 45° triangle. 10-inch 30° X 60° triangle. Irregular curve. 12-inch architect's scale. One dozen thumb tacks. 2 H and 4 H or 6 H drawing pencils. Drawing paper. Erasive and cleaning rubbers. Pencil pointer. Black waterproof drawing ink. Lettering pens and pen holder. Pen wiper. Use of the T Square and Triangle. — The T square is used for drawing horizontal Hues, with the head always against the left- hand edge of the board, Fig. 1. The upper edge of the T square blade is always used, and lines are drawn from left to right. The 1 ESSENTIALS OF DRAFTING triangles are used for drawing all other lines. Vertical lines are drawn by placing a triangle against the upper edge of the T square and drawing upward along the vertical edge, which should be placed toward the head of the T square, as shown in Fig. 2. Use of the Scale. — The scale is used for laying off distances. Whenever practicable, drawings should be made full size. If a 1 1 Thumb TacM Fofier fiori^ontal Line Dirvction — t^ ^ T-s Vs, V2, V4, 1, IV2, and 3 inches to the foot. The scale 3 " =1' means that the drawing is one fourth the size of the object, or that each one fourth inch on the drawing represents 1 inch on the object. In this case, the 3 inches is divided up into 12 parts, each of which represents 1 inch. These parts are further divided to represent quarter inches and other fractions. The double mark CO following a figure means inch or inches; the single mark (') means foot or feet. A common scale graduated to V32 of an inch may be used for many reductions. In such cases use the half inch for an inch in drawing one half size; the quarter inch for an inch in drawing one fourth size, etc. For half size one sixteenth becomes one eighth, and similarly for other divisions. DRAWING INSTRUMENTS AND MATERIALS Fig. 3 shows the distance 2 feet, 5V2 inches, laid off with the scale of 3" = 1'. Drawing Pencils. — It is necessary to have pencils of the right degree of hardness and properly sharpened. For lettering, f^ig.^ Fig, 5 Fig. 6 Fig. 7 figuring, laying out, etc., a long conical point should be used. A 2 H pencil will be found satisfactory. For the drawing itself, one 4 H pencil and one 6 H pencil, carefully sharpened, are needed. After removing the wood, Fig. 4, the lead is made slightly conical. Fig. 5, and then formed as in Fig. 6, using fine sandpaper or a file. Fig. 7 shows enlarged side and front views of the lead. start H er^ Fig. 10 Use of the Compasses. — The compasses, Fig. 8, are used for drawing large circles. The needle point should be adjusted with the shoulder downward and so that the point extends about V64 inch beyond the pen point, Fig. 9. A 4 H or 6 H lead should then be sharpened as for the drawing pencil, and placed in the pencil leg. Remove the pen point from the compasses, insert 4 ESSENTIALS OF DRAFTING the pencil leg, and fasten it. Then adjust the lead so that the end of it is about V64 inch above the needle point, Fig. 10. The joints in the legs are for the purpose of keeping the point and pencil perpendicular to the paper. The compasses should be operated with one hand (the right hand). The needle point should be placed in the center, and the marking point revolved clockwise. Once around is enough, starting at the point in- dicated in Fig. 11. The bow instruments are used for small circles and divisions. The method of setting the points and using is the same as for the large compasses and dividers. Use of the Dividers. — The dividers are used for transferring distances and for dividing lines. They should be handled with A ^ J Srxi \ Center / . > Fig. le.' the right hand. When dividing a line, the points should be revolved in alternate directions, as indicated in Fig. 12. To divide a line into three parts, first set the dividers at a distance estimated to be about one third. Try it, and if too short, increase the distance between the divider points by one third of the re- maining distance. If too long, decrease the distance between the divider points by one third of the distance which they extend beyond the end of the line. Repeat the operation if necessary. The Use of the Ruling Pen. — The ruling pen is used for inking the straight lines, after the pencil drawing is finished. Ink is placed between the nibs of the pen by means of a quill which is attached to the ink bottle stopper. Care should be taken to prevent any ink from getting on the outside of the pen. The proper amount of ink is shown in Fig. 13. The pen should be held in a vertical position, and guided by the T square or triangle. It may be inclined slightly in the direction of the line which is DRAWING INSTRUMENTS AND MATERIALS 5 being drawn, but the point must always be kept from the angle formed by the paper and the guide. Do not hold the pen too tightly, or press against the guide. Both nibs of the pen must touch the paper. Frequent cleaning of the pen is necessary to obtain good lines. The same methods apply to the compass and bow pens. Character of Lines. — All pencil lines should be fine, clear, and sharp. For most purposes continuous pencil hues may be used. The character and weight of ink lines for use on drawings, may be found by reference to Fig. 14. A F B -— G C H ^_ D J - E K Fig. /^. A. Full line for representing visible surfaces. B. Dotted line used with A for representing invisible surfaces. Dots about Vi6 inch long and very close together. C. Center line — very fine dot and dash. D. Witness line — short dashes. E. Dimension line — long dashes, or fine full line. D and E are often made the same. F. Fine line for shaded drawings. G. Dotted line for shaded drawings. E. Shade line for shaded drawings, about three times thick- ness of fine line. J . and K. for special purposes, representing conditions not specified above. When shade hnes are not used, a fairly wide Hne should be adopted as wearing better, and giving better blueprints. The width of line will depend somewhat upon the drawing. Large simple drawings require a wide hne, while small intricate draw- 6 ESSENTIALS OF DRAFTING ings necessitate narrower lines. Drawings which are large and still have considerable detail in parts require more than one width of line. An experienced draftsman will use wide lines for the large and simple parts, reducing them for the complicated places in such manner that the different widths of lines are not noticeable. The student is cautioned to proceed slowly and strive for a uniform width of line until experience teaches discre- tion. Center lines are drawn very fine, and are composed of dots and dashes. All symmetrical pieces should have a center line. All circles should have both horizontal and vertical center lines. Much information concerning the many different kinds of drawing devices used by draftsmen for saving time and other purposes can be found in the catalogues of drawing material companies. CHAPTER II LETTERING Lettering. — The subject of lettering in connection with work- ing drawings is of great importance. Neat, legible letters, made free hand and with fair speed, are required. This chapter will deal with such letters. Those who wish to pursue the subject further should procure a good book on lettering, such as French & Meiklejohn's '^Essentials of Lettering," published by McGraw- Hill Company, New York, or Daniels' ''Freehand Lettering,'' published by D. C. Heath & Company, Boston, Mass. Either of these books may be obtained for $L00. Great care and continual practice are necessary to do good lettering, but the appearance of neatness, the greater ease of reading, and lessened liability of mistakes, make up for the extra time and work. Commercial Gothic Letters. — Commercial gothic and lower case letters or small letters are the forms most used by engineers and draftsmen. These are shown in Fig. 15, with the proportions and directions for drawing the various lines. The vertical capi- tals and lower case letters are shown in Fig. 16. The same pro- portions and order of strokes apply to the vertical letters. The inclined letters should have a slope of about 3 to 8, as showTi in Fig. 17. Some draftsmen use the 60° slope, but this does not give as pleasing a letter (Fig. 18). In all cases very hght pencil guide lines should be drawn to limit the tops and bottoms of the letters. The size of the letters is determined to some extent by the character of the work, but for most drawings the capitals should be Vs inch high, and the small letters about two thirds as high (Fig. 17). For penciling use a 2 H pencil, with a well sharpened round point. For inking, a ball point pen may be used for fairly large letters, and Gillotts 404 or 303 for small letters. The pen may be dipped into the ink and the surplus shaken back into the bottle, or the quill may be used as with the ruling pen. For good work, the pen 7 8 ESSENTIALS OF DRAFTING U/v/rs 1^1 '\\l^-- % ,\\m^// /\4i I ly V ' _^ -5d^ U-^i-J k-5i-l \^5p^ V-5^ Ua^ U-J5-4 2, / P' P' )9' ,S' / 2 3 ^ i# :9 S : F 3^ P" B ■ ■ ■ k_^^ U5^ U5-'— j U-5--J abed Gif g h rj \k I m n op q^ r s f u V w x^y z Fig. 15 point must be kept clean, requiring frequent wiping. The pen point should be kept pointed toward the top of the paper. Proportions and Forms. — The proportions and shapes of the various letters should be studied and drawn to a large scale. For purposes of study, the letters are divided into groups. The following points should be observed. Rounded letters, such as LETTERING 9 I LT H F E NM Z YA K V WX O C G U J D B P R S I 2 3 4 5 6 7 8 9 a abed efghij kimnopqrs t u V w X y z rig. 16 C, J, 0, Q, and S, may extend very slightly outside of the hmiting lines. Pointed letters, like A, V, and W, may have the point extending very slightly above or below the guide lines. The horizontal bar in the letters B, E, F, H, and R is very slightly above the middle, and for the letter P it is very slightly below 10 ESSENTIALS OF DRAFTING the middle of the vertical height. For the letter A the bar is placed about one third the height of the letter. The letter W is wider than it is high. The two outside strokes of the M are parallel. Letter Spacing. — The spacing between the letters when combined to form words will vary with different arrangements. The only general rule which can be given is that the area between r/g. /7 F/g. /a the letters should be about equal. A few illustrations will be given, showing the positions of some combinations of letters. When such letters as A and T, or A and F, are used, they should in general be placed close together, as in Fig. 19. A few words are shown in Fig. 20. In the lines marked wrong the letters are equal distances apart. In the lines marked right the letters are spaced so that the areas between them are about equal. The r/g. /9 combination of letters in each word, or the combination of words in a line, will determine the spacing of the letters. Titles. — The matter of titles for drawings is subject to great variation. The titles for detail drawings may or may not con- tain the name and location of the concern. The name of the machine, its size and number, the names of the details, scale, date, and names or initials of the draftsman and engineer, should be given. An example is shown in Fig. 21. Assembly drawings generally have more elaborate titles. Good titles cannot be made by rule, though a few suggestions may be of assistance. It is often advisable to center the lines composing the title. This LETTERING 11 WRONG RIGHT wron; RIGHT Fig. 20 may be done by counting from each end of each line toward the center, and placing the middle letter or space on the center line. The Une can then be completed by working in opposite directions from the center hne. The important facts should be given due 500 GALLON STEAM JACKETED KETTLE SCALE /i=/Foof- DRAWN BY D FA. TRACED BY W. E. CHECKED BY C.S. APPROVED BY-t^s^ DATE Sept /2. /9/7 ORDER NO. B-462 REVISED Jan. 4. 19/ Q Draw. No. 4-C-I45 Fig. 21 12 ESSENTIALS OF DRAFTING prominence. This may be done by using large letters, by using heavier or blacker letters, by wide spacing between letters, or by using extended letters. The element of time should be con- sidered in the selection of letters. In general, the title should be placed in the lower right-hand corner of the drawing, and OHIO TECHNICAL DRAWING SCHOOL CoLi/MBus, Ohio. CYLINDER FOR 4^5 i/ERT ENGINE Full Size Droivn by J. /< Traced by J, /f. Approi'ed by -jy^^.-c/. Dote Sept. /2, 1917 rig. ^2 may or may not be ''boxed in" (Fig. 21). Some concerns use a title extending across the end of the drawing, in which case it forms a ''record strip" (Fig. 22). Bill of Material. — A bill of material is often put upon each detail drawing in connection with the title. Sometimes a separate Part No Name of Part No Want ELD Material Pattern No. / Spindle 1 Steel 2 Spur Cenfer / Steel 3 Cap 3cre^ 4 Steel 4 Cone Sef 3creu\^ 1 Steel 3 Bo^ Pins 2 Steel 6 Thru 5 f- Screv^ 1 Steel 7 Clamp Screi^ 1 Steel S Box 2 Brass K-^5 9 dasher 1 Brass W-/33 /o Thrust Check Nut / Steel r/g. 23 sheet is made containing a Hst of drawings, material, number required, pattern number, location, etc., for the entire machine or construction. Both methods may be used together. The advantages of a separate list are apparent in certain classes of machines where some drawings are used for many different ma- chines. Bolts, pins, keys, and similar small parts are often given a number, which is used to designate them. The applica- tion and uses of lists are so varied that they must be learned for the company where one is employed. A material hst is shown in Fig. 23. CHAPTER III CONSTRUCTIONS Essential Constructions. — Geometry forms the basis of the constructions used in the making of drawings. A knowledge of some of the principles of geometry is therefore essential. A point indicates position in space. When a point is moved it Fbra//e/ Lines F/g.2^ rig. es Fig. 2 6 generates a line, which may be either straight or curved. A surface may be formed by moving a line. A plane surface is one which will contain two intersecting straight lines. Two straight lines are said to be parallel when they are everywhere the same distance apart (Fig. 24). Angles. — When two lines cross they form angles. The size of the angle is determined by the amount of opening between the lines. The angle A, in Fig. 25, is greater than the angle B. If the lines are revolved about their in- tersection, so that the angle A is made equal to the angle 5, then both angles are called ''right" angles (Fig. 26). The angles C and T> are also right angles, so that all four angles are equal. As shown, each angle is one fourth the way around the point of intersection. 13 l^'9-27 When a right 14 ESSENTIALS OF DRAFTING angle is divided into 90 equal small angles, each of these small angles is called a ''degree." Then it takes 4 times 90, or 360, degrees to go all the way around the point where the hnes cross. Circles. — A circle is a curved line formed by moving one point around another point and at a constant distance from it (Fig. 27). The curved line is called the circumference. The constant distance is called the radius, and the fixed point is called Verh. 3 4 £qui lateral- /J II sides equal. Isosceles- Two Sides egual. Scalene -All sides different Fig.ee Right Triangle- One angle is a right angle. the center. Lines drawn from the circumference to the center form angles, which are measured in degrees. Two lines crossing each other at the center of the circle, and making equal angles with each other, form four right angles, so that a circle is said to contain 360 degrees (written 360°). A piece of the circumference is called an arc. Other features of a circle are indicated in Quadn'lafera/ Square ffecfangle F/g. 29 fThombus ffhomdoid Fig. 27. The length of the circumference is equal to the diameter times 3.1416. (3.1416 is called "p?, " and is often written tt.) Plane Figures. — A plane figure made up of three lines is called a triangle. There are several kinds of triangles (Fig. 28). All three angles of any kind of a triangle, when added together, are always equal to 180 degrees. The sides of the right triangle have a very useful relation to each other, which is illustrated in Fig. 28. If the length of each of the two sides is squared and added together, the sum will be equal to the square of the length of the hypotenuse; thus, in the figure, (3)2 + (4)2 = (5)2 or 9+16 =25 CONSTRUCTIONS 15 A plane figure made up of four lines is called a quadrilateral. When the opposite sides are equal and parallel, the figure is called a parallelogram. There are several kinds (Fig. 29.) Other regular plain figures are shown in Fig. 30. Solids may have almost any form. The names and appear- ances of a number of solids are shown in Fig. 31. There are many geometrical constructions which are of use in Pentagon He^Ogon Fig.SO Hepfagon Octagon mechanical drawing. Detailed instructions for the solution of some of these problems follow. These problems should be studied carefully and be fully understood. They should be worked out with a very sharp pencil, fine lines, and extreme accuracy. To bisect a Line. — (To divide a line into two equal parts) : Given the line AB (Fig. 32). Using points A and B as centers, .^i;- Base Right Ob/iqL/e Truncated Hexagonal Frustum of a Rigtit Circular Prism Prism Tr/ongular Prism Pyramict Triangular Pyramid Cone Fig. 31 and a radius greater than one half the length of the fine, draw the arcs 1 and 2. Through the points where these arcs cross each other, draw the line CD^ which will divide the line AB into two equal parts. The Unes CD and AB form right angles, and are said to be perpendicular to each other. The steps used in solving this problem are illustrated in Fig. 32. Any given line is shown at a. At 6 is shown the given line and the arc of a circle having a radius greater than one half the line, and its center at the upper end of the line. At c another arc has been drawn, having the same radius as before, but with its center at the lower end of the line. At d a line has been drawn through the inter- sections of the two arcs, dividing the given line into two equal parts. It is not necessary to draw the whole of the arcs or the 16 ESSENTIALS OF DRAFTING intersecting lines. The usual appearance of the completed problem is shown at e. To bisect an Angle (Fig. 33). — Given the angle AOB. With as a center, and any radius, draw an arc intersecting the sides of the angle in points 1 and 2. With points 1 and 2 as centers, and a constant radius, draw arcs cutting each other at C. The line OC will bisect the angle. To divide a Line into Any Number of Equal Parts (Fig. 34). — A e ^ Fig. 3 2 Given the line h'B. It is required to divide the line into five equal parts. From one end of the line draw another line, making an angle with it, such as 55. On 55, using any convenient setting of the dividers, step off five equal spaces. Join the end of the last space with the end of the given line. Through points 4, 3, 2, and 1 draw lines parallel to 5, 5', intersecting the given Fig. 34 Fig. 35 line at points 4', 3', 2', and 1'. The line h'B will then be divided into five equal parts. Another method of dividing a line is illustrated in Fig. 35. From one end of the given line draw a perpendicular such as ^' A, using the triangle and T square. Next place the scale in such a position that one end of any five equal divisions is at point 5, and the other is on the line W A. Mark opposite each of the divisions, and through each mark draw a vertical line intersecting the given line, which will then be divided into five equal parts. To copy an Angle (Fig. 36). — Given the angle AOB. To con- struct another angle equal to it. Draw a line A'O' . With as a center and any radius, draw an arc cutting the sides of the CONSTRUCTIONS 17 angle at 1 and C. With 0' as a center, and the same radius, draw the arc VC\ With 1' as a center, and a radius equal to the chord IC, draw an arc cutting the arc TC at C. Draw CV. Angle AV'B' will then be equal to the angle AOB. To construct a Triangle, having given the Three Sides (Fig. 37). — Given the three lines A, B^ C. Draw line A', equal to Hne /t ]/ o' fc' A 0C Fig. 38 A. With 1 as a center, and a radius equal to line B, draw an arc. With point 2 as a center, and a radius equal to line C, draw another arc, cutting the first arc at point 3. Join point 3 with points 1 and 2, completing the required triangle. To construct an Equilateral Triangle (Fig. 38). — Given one side of the triangle, A. Draw line 1-2, equal in length to line A. Fig. 39 Fig. ^0 Fig ^1 With 1 and 2 as centers, and radius equal to line A, draw arcs intersecting at 3. Join point 3 with points 1 and 2, completing the required triangle. To construct a Regular Hexagon (Fig. 39). — If the distance across corners is given, draw a circle having a radius equal to one half this distance. Draw the diameter 102. With points 1 and 2 as centers, and the same radius, draw arcs cutting the circle at points 3, 5, 4, and 6. Join these points to complete the required hexagon. It will be noted that the radius used as a chord divides the circumference into six equal parts. The 30 X 60 triangle may be used to construct a hexagon. Explain how. 18 ESSENTIALS OF DRAFTING To construct a Regular Octagon (Fig. 40). — Given the square 1-2-3-4. With the corners of the square as centers, and a radius equal to one half the diagonal, draw arcs cutting the sides of the square. Join the points thus found, completing the required octagon. An octagon may be constructed inside of a circle by using the 45 -degree triangle. Explain how. To draw an Arc of a Circle, having a Given Radius, and tangent to Two Given Lines (Fig 41). — Given the hues AB and BC and Fig.^2 F/g. ^3 '^^^ '^^ thod Fig. ^4 the radius R. Draw DE parallel to BC, and at a distance equal to R from it. Draw FG parallel to AB^ and at a distance equal to R from it. Where DE and EG cross, gives point 0, the center of the required arc. To draw a Circle, Passing through Any Three Points (not in the Same Straight Line) (Fig. 42). — Given points A^ B, and C. Draw lines AB and BC. Bisect lines AB and BC, using the construc- tion of Fig. 32. Where the bisecting lines cross at is the center of the required circle. The radius is the distance from to any of the three points. To find the Length of an Arc of a Circle, and measure it on a Straight Line (Fig. 43). — First method (when angle AOB is less than 60 degrees): Given arc AB with center at 0. From one end of the arc draw the tangent line AC. Draw line AB and extend it to D, making AD equal to one half of line AB. With D as a center, and radius DB, draw arc BC. Then AC will be a straight line equal in length to the arc AB. Second method: Draw tangent AC as before. Set the dividers at a small distance. Start at point B, and space off the points 1, 2, 3, etc., along the arc, until point 5 is reached. (Point 5 may come at any place near the point A.) Do not remove the dividers from the paper. Step back along the line the same number of spaces, as shown. The line AC will then be very close to the length of CONSTRUCTIONS 19 the arc AB. By taking small spaces, the chords may be assumed equal to the arcs. To draw a Tangent to a Circle at a Given Point on the Circle (Fig. 44). — Given point P. Place one triangle with its hypotenuse passing through the given point, and the center of the circle as indicated in first position. Using the other triangle as a base, turn the first triangle over into the second position, and move it until its hypotenuse passes through point P, when the tangent F/g. ^5- AP may be drawn. The base triangle must be held firmly in place in the one position. To draw the Arc of a Circle of Given Radius, tangent to an Arc and a Straight Line (Fig. 45). — Given arc AB, hne CD and radius R. Draw line EF parallel to CD, and at a distance R from it. With radius R2 = Ri+ R and center 0\ draw an arc cutting line EF at 0, the center of the required tangent arc. Note the points of tangency, which are marked T. The point of tangency of any two arcs is always on the line joining their centers. This is further illustrated in Figs. 46 and 47, where the points of tangency are marked T. The Ellipse. — An ellipse (Fig. 48), is a curve formed by a point moving so that the sum of its distances from two fixed points is a constant. Each of the two points Fi and F2 is called a focus. The F/g. ^8 longest line, AB, drawn through the center is called the major axis. The shortest line, CD, is called the minor axis. The con- stant distance is equal to the major axis. A tangent to an ellipse at any point may be constructed by drawing lines from 20 ESSENTIALS OF DRAFTING the point to the foci. Extend the Unes and bisect the angle FiPE, or the angle F2PG. This bisecting line P H is the re- quired tangent. A line through the point P and perpendicular to the tangent is called a normal. The major and minor axes of an ellipse being given, the foci may be located by draw- ing an arc with C or Z) as a center, and a radius equal to one half of the major axis. This arc will cut the major axis at the foci. To draw an Ellipse by the Concentric Circle Method (Fig. 49.) — Given the major and minor axes AB and CD. With as a center, draw cir- ■^' cles having the major and minor axes as diameters. Draw radial Hues OeE, OfF, etc., divid- ing the circles into a number of parts. Where the radial lines cut the large circle, draw perpendicular lines. Where the radial lines cut the small circle, draw horizontal lines. The intersection of a vertical and horizontal line from the same radial line will determine a point on the eUipse, as indicated at 1, 2, 3, and 4. Determine as many points as necessary, and draw the curve through them very lightly free hand. It may then be strengthened, using an ir- regular curve. To draw an Ellipse by the Trammel Method (Fig. 50). — Given the major and minor axes AB and CD. On a small strip of paper mark off one half the minor axis and one half the major axis, as shown in the figure. Place the point 3 on the minor axis and the point 2 on the major axis. Make a mark on the paper opposite the point 1. Move the point 3 along the minor axis, keeping the point 2 on the major axis and moving it as indicated by the arrows. The point 1 will then trace out the required elHpse. The usual method CONSTRUCTIONS 21 is to place the trammel in a number of positions, and make marks on the paper opposite the successive positions of point 1. To draw a Curve having the Appearance of an Ellipse, by means of Circular Arcs (Fig. 51). — Given the major and minor axes AB and CD. On the minor axis lay off 03 and 01, each equal to the difference between the major and the minor axis. On the major axis lay off 02 and 04, each equal to three fourths of 03. With point 1 as a center, and a radius equal to IC, draw the arc ECG. With 3 as a center, and the same radius, draw the arc JDH. With 2 and 4 as centers, and a radius equal to 2B, draw the arcs GBH Siud EAJ. The Involute. — Tie a piece of string about a lead pencil point. Place the triangular scale with its end resting upon a piece of paper. Wind the string about the scale, keeping the pencil point toward the paper. Hold the scale firmly with one hand. Keeping the string tight, and the pencil point on the paper, un- wind from the scale. The curve thus formed is the involute of a triangle. The involute of any other figure may be obtained by unwinding a string from the desired form. To draw the Involute of a Triangle (Fig. 52). — With A as a center, and AC as a radius, draw an arc until it reaches the ex- tension of side AB at point 1. With point J5 as a center, and 1j5 as a radius, draw an arc from 1 until it reaches the extension of side CB at point 2. The curve may be continued by increasing the radius each time that it passes the extension of one of the sides. Compare this curve with the one drawn by means of the triangular scale and string. 22 ESSENTIALS OF DRAFTING To draw the Involute of a Circle (Fig. 53). — Divide the arc of a circle into a number of equal parts. Draw the radial hues OA, OB, etc. At the end of each radial line draw a tangent. Starting at point A, lay off the distance Al on the tangent equal to the arc AG, using the second method of Fig. 43. Starting at B, lay off the distance B2 on the tangent, equal to the arc BAG. Con- tinuing, lay off on each tangent a distance from the point of tangency equal in length to the arc of the circle, measured from the point of tangency to the point G. The Parabola. — A parabola is a curve formed by a point mov- ing so that its distance from a line called the directrix is alw^ays equal to its distance from a point called the focus (Fig. 54) . To draw a parabola, having given the directrix CA D, and the focus F. Draw a line parallel to the directrix, and at any distance from it. Using this distance as a radius, and i^ as a center, draw an arc, cutting the parallel line at point 1. Draw as many lines as may be necessary, parallel to the directrix, and using their distances from the directrix as radii, with i^ as a center, draw arcs cutting them, thus locating points on the required parabola. To draw an Equilateral Hyperbola (Fig. 55). — Given the point P and the axes G and H. Draw horizontal and vertical lines through point P. On each side of point P step off equal distances PF, PA, AB, etc. Draw lines from to each of the points thus determined. Where line OA crosses the vertical line at point a, draw a horizontal line. Through point A draw a vertical line intersecting the horizontal line just drawn at point 1, a point on the required curve. Horizontal and vertical lines drawn from the diagonals will locate other points on the curve, as shown at 2, 3, 4, 5, and 6. CHAPTER IV PROJECTIONS Purpose of Drawings. — The representation' of objects and constructions having three dimensions upon a surface having two dimensions has been accompHshed in many ways, some of which are illustrated in Fig. 56. Drawings have two principal uses which are: I. To tell the shape, 11. To tell the size. A drawing tells the shape by the position of the various lines, Isomefric Perspec/'fi/'e / A / 1/ 1 Orfhographic Ob/ique Fig. ^6 These numbers are called while numbers are used to tell the size, dimensions. Orthographic Projection. — Most engineering drawings are made in '^orthographic projection." By this.means the shape and proportions of a construction may be accurately defined. The number of views depends upon the object or construction to be described. This can be understood by reference to Fig. 57, which shows two views of a cylinder. The upper view shows the circular form and the lower view shows the height of the cylinder. Notice that the diameter of the upper view is the width of the lower view, and that the two views are included between parallel vertical lines. An object requiring three views is shown on P'ig. 58. Note the arrangement of the 23 Front |/?(f>v Height- — Oiamefei — H F/g. 57 24 ESSENTIALS OF DRAFTING views. The top and front views are included between parallel vertical lines, and the front and side views are included between parallel horizontal lines. The Planes of Projection. — The method of obtaining the views and getting them in the correct relative positions will be explained in con- nection with Figs. 59 and 60. Con- sider two glass planes, one hori- zontal and one vertical (Fig. 59), with an object placed in the angle thus formed. By looking through the vertical plane the front of the object may be seen, and if this view is marked out on the glass, it is called the front view, elevation, or vertical projection. If, instead of look- Top ^ Front 5/de Fig. S6 //on'zonf-af P/ane af/er- /^x/s i^rh'ca/ F/dne I, Prq/ecf/o/7 L/ne -^^Frojecf/on Line F/g. S9 ing through the glass, we consider that lines have been drawn from every point in the object perpendicular to the vertical plane, the object is said to be projected out to the vertical plane. The lines are called projection lines. By joining the PROJECTIONS 25 points in which the projection Hnes touch the vertical plane the front view will be obtained. In the same manner the top view, plan, or horizontal projection may be found by projecting up Fig. 60 to the horizontal plane. If the joint between the two planes is now taken as an axis, the horizontal plane may be revolved up about the axis until it is in the same plane with the vertical plane. This brings the top view directly above the front view. By placing a third glass plane at one side of the object, and per- pendicular to the other two planes, as shown in Fig. 60, a side view may be obtained. The plane con- taining this side view can be re- volved about the axis shown until it is in the same plane with the vertical plane. This brings the side view on the same line with the front view, as shown in Fig. 61, where the three views are in their correct positions. Some Rules. — The following points should be thoroughly understood, as projection is the basis for all shop drawings. Left Side Right Side 26 ESSENTIALS OF DRAFTING Note the three views of the point P in Figs. 59, 60, and 61. Locate other points in the same manner until all points on the object are accounted for in each of the three views. Horizontal distances (as L) show the same in the top and front views. Vertical distances (as H) show the same in the front and side views. 1 r I I I I I ii, D O I ... I Vertical distances (as W) in top view are horizontal distances {W) in the side view. The top view is the same length as the front view. The top view is the same width as the side view. The front view is the same height as the side view. The front of the side view is toward the front view. The front of the top view is toward the front view. The arrows (Fig. 61) indicate the relation of the front view to the other views. Note the difference between the left side view and the right side view. Lines which represent visible surfaces are full Hues. Lines which represent invisible surfaces are dotted hues. (See left side view, where it is necessary to look through the object in order to locate the horizontal dotted hne.) The top and front views of any point are always in the same perpendicular line. The front and side views of any point are always in the same horizontal hne. Dotted Lines. — The question of dotted lines is illustrated in Fig. 62, where two views of several objects are shown. A is a square prism with a square hole all the way through; B is a cylinder with a circular hole all the way through; C is a square prism with a square hole extending from the top down to the depth shown in the front view (note that the top views of A and C are the same, and that the front views show the extent PROJECTIONS 27 of the holes); Z) is a cyhnder with a hole extending up part way from the bottom, as shown in the front view, therefore the hole shows dotted in the top view; £^ is a square prism with a cylindrical boss on top; F is a, cylinder with a smaller cylinder extending downward from the under side, thus the small cylinder is dotted in the top view; compare F and D, which show that it is necessary to read both views to determine the object. A large number of all sorts of projection problems should be solved to obtain a thorough understanding of orthographic pro- jection. ^at/s or Cenfer L/ne r/g. 63 Auxiliary Vie'ws. — The three planes just described are per- pendicular to each other, like the boards coming together at the corner of a box. The faces of an object which are parallel to the three planes are projected to these planes in their true size and shape. It is often desirable to show the true shape of a face which is not parallel to any of the three regular planes. In such cases. Fig. 63, an extra plane called an auxiliary plane may be used. This extra plane is placed so as to be parallel to the in- clined face. The inclined face is then projected to the auxiliary plane by perpendicular projecting lines, as shown in Fig. 63. The distances W and iS then show in their true length and the hole shows the true shape in which it cuts the inclined face. Com- pare the auxiliary plane with the side plane. Notice that the distance W shows in its true length in the side plane, but that the vertical dimension is i/, which is shorter than *S. The auxiliary 28 ESSENTIALS OF DRAFTING plane and the side plane may be revolved about the center line or axis until they are parallel to the plane of the paper. This has been done in Fig. 64, where the object is shown by its projec- tions. Note the location of the points 1, 2, 3, and 4. The center line of the auxiUary view is parallel to the inchned face. The width W is the same in the auxiliary view and in the side view. The points 1, 2, 3, and 4 are located in the auxiliary view by projecting lines perpendicular to the in- clined face which cross the center line at right angles. The distances on either side of the center line are then obtained from the side view and measured on the corresponding projection lines of the auxiliary view, as illustrated for point 4. Compare Figs. 63 and 64 carefully. Required Views. — A bracket is shown in pictorial form in Fig. 65, together with its three views in orthographic projection. Note the relation of the views. A picture of an object is shown F/g. 64- o /^/g. 65 F/g. 66 in Fig. 66. Since most of its detail is inclined, a side view and auxiliary view are used. In this way true shapes are shown. Other views are not needed. They would be somewhat difficult to draw and would not add anything to what is already shown. Very good practice is to be had by deciding the number of views PROJECTIONS 29 and proper treatment for such machine parts and constructions as one encounters. The Imaginary Cutting Plane. — It is not always possible to indicate easily and clearly the interior construction of a machine /='/g. ey Fig. 6a t ^ 71 r/g 71 /^/g 70 r/g. 69 or part by means of dotted lines. In such cases resort is had to imaginary cutting planes which reveal the hidden parts. Such an imaginary cutting plane passing through the object of Fig. 67 is shown in Fig. 68. The part in front of the cutting plane is removed in Fig. 69, leaving the object as shown in Fig. 70, where the surfaces cut by the plane are indicated by parallel inclined lines. Such a surface is said to be cross-hatched or section-lined. The view is called a section, or sectional elevation. In orthographic projection the two views are drawn as in Fig. 71, where the section occupies the same position relative to the top view as the front view which it replaces. Note that the top view is shown complete. The top edge of the cutting plane is shown as a center line in the top view. The rules of projection apply to sectional views. The object is imagined to be cut by a plane and the part in front of the plane removed in order to show the cut surfaces and the details beyond the cutting plane. Representation of Cut Surfaces. — The surfaces which lie in the imaginary plane are indicated by a series of parallel lines. Different pieces are shown by changing the direction of the lines. The width of spacing for section lines is determined by the area to be sectioned. Different materials are sometimes indicated by 30 ESSENTIALS OF DRAFTING different forms of section lining. Fig. 72 gives the forms sug- gested by a committee of the American Society of Mechanical Babbitt or White tyieta/ Otass p;. ^:y>;::;;:A:-;:/.;;cS Concrete fiock Origina/ Fitting Elartti /Ituminum Water Sand Rubber, Vutconite or Insutat/on Puddte Astiter Other Ma fen a ts Fig. 72 ,^ Engineers. The character of sectioning should not be depended upon to tell the material. It should always be given in a note if it is not perfectly evident. CHAPTER V MATERIALS AND STRESSES Materials. — Engineering constructions must carry loads and transmit motions. For such purposes various materials are made use of according to their adaptability. The most used material is iron in its different forms — cast iron ; wrought iron ; steel ; and the steel alloys. In addition to iron there are the yellow metals, or brass and bronze compositions, white metals or babbitt, tin, lead, etc., and the various timbers. It is important for the draftsman to know something of the properties of these materials, the methods of forming into ma- chine parts, and the relative expense, so that a proper selection of material may be made for the particular case in hand. Cast Iron. — Cast iron is a hard, brittle, granular substance obtained by burning the impurities from various ores, the most common being Magnetic Oxide, or Magnetite Ferric Oxide, or Red Hematite Brown Hematite Spathic Ore Cast iron contains carbon and various impurities, such as silicon, manganese, phosphorus, sulphur, etc. White Iron. — There are two principal kinds of cast iron : white cast iron, in which the carbon is chemically combined, and gray cast iron, in which the carbon is free or mixed in the form of graphite. White cast iron contains a small amount of carbon, and is very hard and brittle. It is used in the manufacture of wrought iron and steel. White cast iron is very difficult to machine. Gray Iron. — Gray cast iron contains some carbon in chemical combination and a considerable amount in the form of graphite, which is mixed with the iron. Gray iron is softer than white iron and is easily machined. It contains from 0.5 per cent to 1 per cent of combined carbon up to 2 per cent. 31 32 ESSENTIALS OF DRAFTING Properties of Cast Iron. — Cast iron is the most useful of metals, as it can be readily melted and cast into any desired form by first making a mold. For this reason it is adapted for making complicated shapes. Its cheapness renders it available where IH!llll'intiiltiii'li!^U»Hlil Fig. 73 Fig. 74 rigidity and weight are required. Cast iron cannot be welded and has very little elasticity, so that it is not adapted for use where shocks and sudden loads are to be cared for. Cast iron has a crystalline structure, and when cooling the crystals form at right angles to the surface. Where square corners are encountered the arrangement is as indicated in Fig. rig. 75 73, in which fracture is likely to occur along a6, called the plane of fracture. This may be prevented by rounding, as in Fig. 74. Cast iron expands at the moment of solidifying, but shrinks upon cooling. This action sets up cooling strains in the casting, espe- cially if there exists a considerable variation in the thickness of the section in the different parts of the piece. For this reason a uniform cooling arrangement is always desirable, and sudden changes in section should be avoided. MATERIALS AND STRESSES 33 Cast iron is about four times as strong in compression as it is in tension. Wrought Iron. — Wrought iron is almost pure iron, obtained by melting pig iron and squeezing out the impurities while it is in a plastic state. For such purposes a puddhng furnace (Fig. 75) is used. Iron is put into the furnace and melted. When in a plastic state it is taken in the form of a ball on the end of a puddle bar and squeezed or pounded and heated again. This process is jssssissr iA/A >^ UNDER PRESSURE. \ \\'\VM I V'A-s-. Fig. 76 continued until most of the impurities are burned or squeezed out. It is then rolled into bars or billets. These billets are further rolled into rods of various shapes and sizes called merchant bars. This rolling process gives the iron a fibrous structure due to a certain amount of impurities which remain after the puddling. Wrought iron contains a very small amount of carbon. Properties of Wrought Iron. — Wrought iron is malleable and is the best material to withstand shocks. It stretches and so gives warning before breaking. It cannot be cast, but must be rolled or forged into the forms required. For this reason it is not adapted for complicated shapes. It can be welded, punched, bent, etc. Owing to its method of manufacture, it is expensive 34 ESSENTIALS OF DRAFTING and is supplanted to a considerable extent by mild steel, which has a similar composition. Wrought iron is almost equally strong in tension and compression. It is stronger in the direction of the fibers than across them. Steel. — Steel is made by burning carbon and impurities out of pig iron and then adding the desired amount of carbon. An- other method is to add carbon to wrought iron. There are two processes of making steel from pig iron: the Bessemer process and the open-hearth process. Bessemer Process. — In the Bessemer process from five to twenty tons of melted pig iron is put into a converter (Fig. 76). Air under a pressure of about twenty pounds per square inch is caused to pass in streams up through the metal, and the carbon and impurities are burned out. This requires about ten minutes, and leaves practically pure iron, to which the proper carbon content is added by putting in liquid spiegeleisen (white iron) or ferromanganese. This makes it into steel, which is poured into ingots. These ingots are rolled into blooms and other desired shapes. Open-hearth Process. — By this process large amounts of steel are made at one time, generally about fifty tons. Steel, scrap, and pig iron are melted on the hearth of a Siemens regen- erative furnace. The metal is kept in agitation by chemical reac- tions, caused by adding iron scale or scrap iron which furnish the necessary carbon. Properties of Steel. — Steel is composed of iron and carbon in chemical combination. It has a uniform granular structure and may be formed to shape by forging, rolling, or casting. Steel varies greatly in its qualities, depending upon the carbon content. It is sometimes designated as Soft Steel about 0.19 % carbon Medium Steel " 0.30 % Hard Steel " 0.75 % up to 1.8% carbon Steel having less than 0.25 % is frequently called mild steel. Malleable Iron. — Small parts of cast iron can be made less brittle by being surrounded by iron scale or some form of an oxide of iron and kept at a bright red heat for over sixty hours. In this way some of the carbon is removed and the material is made to resemble wrought iron. It is used for small pieces which MATERIALS AND STRESSES 35 cannot be easily forged. Hardware castings, pipe fittings, etc., are often made of malleable iron. Suggestions for Selection of Material. — The best method of learning the proper materials to be used is by observation. The material best adapted cannot always be used, because of cost, method of shaping, etc. Ask why, when a special material is used. The '^ factor of cost" is always present — the ''factor of safety" should always be considered first. Observe broken parts of machines as a valuable means of obtaining sound in- formation. The use of special metals is often one of trial and observation. Some things which influence the selection of ma- terial are given below : Method of Shaping Casting Cost of Pattern Forging — Drop Forging " " Die Pressing — Stamping " " " Extrusion — Drawing " " " Rolling " " '' Number Required Method of Finishing Strength Required Kind of Loads Moving or Stationary Parts Lightness or Weight Wear Where liquids or gases are used the chemical action must be considered. Loads and Stresses. — The materials used in machines are subject to various loadings which must be resisted by these ma- terials. The internal resistance must be equal to the external or applied load, or the part will fail. There are many ways of applying the load, each bringing into play a different form of resistance by the material. This resistance is called stress. Stress is a measure of the strength of the material to resist an external load. There are three kinds of simple stresses : tension, compression, and shear. Axial Stresses. — A bar is a portion of material having a uniform section, such as a cylinder or prism. When a load is applied to a bar so as to be uniformly distributed it is called an 36 ESSENTIALS OF DRAFTING axial load. Such a load produces a direct stress in the bar. The section made by passing a plane at right angles to the axis of the bar is called a cross section. The area of this section is the cross- sectional area and is usually spoken of as the area. It is generally measured in square inches. When a load is apphed to a bar so that it tends to lengthen the bar it produces a tensile stress (Fig. 77). When the applied load tends to shorten or compress the bar it produces a com- I I w^ k^:i )-- ^ p f r/g. 77 ■t r/g. 7$ F'-g 79 pressive stress (Fig. 78). When the applied load acts at right angles to the bar and tends to push one cross-sectional plane by another it produces a shearing stress (Fig. 79). Unit Stresses. — In order that the strength of various materials may be compared, the strength of a bar one inch square is used as a unit. The strength of such a bar is called the unit stress, or stress per square inch of cross-sectional area. The stress is usually given in pounds per square inch. To find the unit stress, divide the applied load by the cross sectional area, or: Let A = area of cross section in square inches. P = total load in pounds. / = stress in pounds per square inch. Then the unit stress is P (load) / = A (area) MATERIALS AND STRESSES 37 Thus, if a rod has an area of 3V2 square inches and is subject to a load of 35,000 pounds, it has a unit stress of f = — = —^ = 10,000 lb. per square inch. •^ A 3.5 Elastic Limit. — From the formula given above it follows that if the load is doubled, the unit stress will also be doubled. This means that the unit stress is proportional to the load. By ex- periment it has been found that this law does not hold for all loads, but only up to a certain load (depending upon the material) . This load or limit is called the elastic limit and is expressed in pounds per square inch. For stresses less than the elastic Umit the increase or decrease in length of the bar is directly propor- tional to the stress. The increase or decrease in length is called the strain, and the total strain divided by the length is called the unit strain. Let I = length in inches e = change in length in inches s = unit strain Then e s = - I Modulus of Elasticity. — Below the elastic limit both the unit stress and the unit strain are proportional to the load, so that they bear a constant relation to each other. This relation is expressed as the quotient obtained by dividing the unit stress by the unit strain, which will give a constant called the modulus of elasticity and represented by E. Then ^ Stress / E = — = — Strain s p Ultimate Strength. — I he formula /= — gives the unit stress A of a material for a given load. If the load is sufficiently large the piece will break or rupture. The value of / when rupture takes place is called the ultimate strength of the material. Factor of Safety. — The ultimate strengths of materials as well as the elastic limits are not constants, although most of them are pretty well known from large numbers of tests. However, 38 ESSENTIALS OF DRAFTING it is not desirable to stress a material too near its elastic limit, as there may be imperfections or lack of uniformity. The manner in which the load is applied also affects the stress which it is safe to impose upon a given material. For this reason various ''factors of safety" are used. A factor of safety is a number obtained by dividing the ultimate strength of a material by the unit stress actually imposed upon it. The actual stress is referred to as the safe working stress. Often the safe working stress is ob- tained by dividing the ultimate strength by a suitable factor of safety, depending upon the nature of the loading. Average Values. — The values given in the following tables are averages and will serve for purposes of computation in the absence of more definite figures. Elastic Limits Material Cast Iron. . . . Wrought Iron Steel Pounds per Square Inch Tension 6000 25,000 35,000 Compression 20,000 25,000 35,000 Moduli of Elasticity Material Pounds per Square Inch Cast Iron 15,000,000 27,000,000 Wrought Iron Steel 30,000,000 Ultimate Strengths Material Pounds per Square Inch Tension Compression Shear Cast Iron 20,000 50,000 60,000 to 100,000 00,000 50,000 60,000 to 150,000 18,000 Wrought Iron Steel 40,000 50,000 to 80,000 MATERIALS AND STRESSES 39 Factors of Safety Dead Load Live Load Material One Kind of Stress Alternate Tension and Compression Varying Loads. Shocks Cast Iron 4 3 6 5 10 8 15 Wrought Iron and Steel. . . 12 CHAPTER VI SCREW THREADS Uses of Screw Threads. — A screw is a cj- lindrical bar having a helical projection. The form of this helical projection varies, according to the uses to which the screw is put. Screws are used for the following purposes: To fasten parts of machines together; to transmit motion; to convert rotation into transla- tion, or vice versa; for the adjustment of parts in their relation to one another. The Helix. — A helix is a curve generated by a point moving equal distances lengthwise of a cylinder while it is moving equal F'/g. eo distances around the cylinder. If a right triangle is wound around a cylinder the hypotenuse will form a helix. The points 1, 2, 3, 4, etc., of Fig. 80 will come at the same numbers on the curve when the triangle is wound around the cylinder. The pitch of a helix is the distance which the point moves parallel to the axis while it goes once around the cylinder. To draw the Projections of a Helix. — In Fig. 80 let T> be the diameter and let the pitch be the distance indicated. Divide the circle shown in the top view into any convenient number of equal parts, and draw vertical lines through each point. Divide the pitch into the same number of equal parts and draw horizontal 40 SCREW THREADS 41 lines. For each space around the cyHnder the point will move one of the spaces along the pitch, thus locating the curve as shown. Parts of a Screw. — A screw is known by its outside diameter, indicated in Fig. 81 by d. The diameter di is called the root diameter. Point b is the top of the thread and point a the bot- tom, or root. The area corresponding to di is called the root area. One half the difference between the outside diameter and the root diameter is called the depth of the thread. Right- and Left-hand Screws. — Screws may be either right - or left-hand. A right-hand screw thread (Fig. 93) requires the screw to be turned in a clockwise direction to enter the nut. A left-hand screw thread (Fig. 99) must be turned counter-clock- wise when entering. The pitch of a screw thread is the distance which the screw will advance for one complete turn for a single threaded screw. Forms of Screw Threads. — The forms of screw threads are shown in the accompanying figures. Fig. 82 shows the Sellers, Franklin Institute, or U. S. Standard thread, as used quite gen- erally in the United States. The proportions are indicated on the figures. The tops and bottoms of the V's are flattened so that the depth of the thread is decreased 0.25 the depth of the 42 ESSENTIALS OF DRAFTING V. The flats make the thread less hable to injury on the sharp Vs and less liable to weakening at the bottom of the grooves than the sharper V thread shown in Fig. 83. This form of thread r/g. 86 F/g. 69 is also in quite general use. It is conveniently formed on a lathe, and does not require a special tool, or regrinding of the tool, as is the case for the U. S. Standard. The angle for both the above forms is 60 degrees. The Whitw^orth thread, or standard of Great Britain, is illus- trated in Fig. 84. In this form the angle is 55 degrees. The threads are rounded off at the top and bottom, making a strong shape. Fig. 90 Fig. 91 The forms described above are the ones most commonly used for fastening parts together. Fig. 86 shows the square thread, a form well adapted for use in transmitting motion. The Acme thread, a modification of the square thread, is shown in Fig. 87. The angle may be either 29 or 30 degrees. This form is used for transmitting motion. The relieving of the thread allows the use of a split nut. A common example is the SCREW THREADS 43 lead screw of a lathe. Fig. 88 shows the buttress or breechlock thread so called from its use in guns to take the recoil. It is designed to take pressure in one direction only. This form has the strength in shear of the V form, but avoids the tendency to Fig. 92 split the nut. Fig. 85 shows the knuckle or rounded screw thread. This form can be cast in a mold.' It is used only for rough work. Fig. 89 shows the common wood screw. An attempt is made to consider the differences in strength of the Fig. 93 Fig. 9a Fig. 95 Fig. 9 6 wood and steel. For adjustment, Figs. 82, 83, 84, 86, and 87 are used. Thrust screws for pillow blocks, crossheads, etc., are familiar examples of adjusting screws. Multiple Threads. — Screws may have either single, double, or other multiple threads. A single-threaded screw consists of a single helical projection (Fig. 90). The pitch is the distance from one thread point to the next thread point. The lead is the 44 ESSENTIALS OF DRAFTING distance which the screw will advance for one turn. When a large pitch is required on a small diameter, the arrangement of Fig. 91 would weaken the screw by reducing the root diameter (Fig. 91) at point A. To avoid this, two parallel hehcal projec- tions may be used, as shown at B (Fig. 91). This is called a double n-p. 9 7 ^^ZZZZ^ Fig. 9S r/g. 99 F/g. 100 thread. Similarly, a triple or quadruple thread may be formed. In this manner a large lead may be obtained without lessening the strength of the screw. Split Nut and Square Thread. — A portion of a square threaded screw, and a section of a nut for use with it are shown in Fig. 92. Fig 101 F/g. 102 F/g. 103 The method of drawing the helix has already been explained. Note the dotted line a-5, which indicates the undercutting of surface ahc, and shows why a split nut cannot be removed from a square threaded screw. The sloping side of the Acme thread does away with this undercutting and allows the removal of a split nut. Conventional Representation of Screw Threads. — It is not often necessary to draw the helix in representing threads, as there are a number of conventional representations in use. Figs. 93 to 100 are common methods. Figs. 93 to 98 are for right- hand threads, Figs. 99 and 100 are for left-hand threads, and Figs. 96 to 98 are for either right- or left-hand threads. It is not SCREW THREADS 45 generally necessary to draw the pitch to scale. The distance between lines may be estimated by eye and arranged to avoid crowding of the lines. The number of threads per inch of other than U. S. Standard should be given by note, as '' 12 threads per Top^ c:>t--3/f^'l-J-J ^^±-> Fig. 104 inch, right handJ^ This may be abbreviated to '^12 Thds. R. HJ' or "12 Thds. L. i7." Sometimes the number is given for U. S. Standard as indicated in Fig. 96, or the Roman numeral may be used, as in Fig. 95. Three representations for square threads are shown in Figs. 101, k F/'g. 105 Fig. /06 102, and 103. The square threads are generally drawn to scale, and if of large diameter the helix may be drawn in, as in Fig. 92. Threaded Holes. — Representations for threaded holes are shown in plan, elevation, and section, in Fig. 104. It will be observed that the lines representing the threads slope in the 46 ESSENTIALS OF DRAFTING r/g.l07 F/g. 108 Fig. 109 opposite direction when the hole is shown in section. The reason for this is that the far side of the thread is seen. As shown, either single or double circles may be used in the plan view. When the last two forms are used they should always be marked ''Tap" as indicated. For small diameters, the V's may be put in free hand. The lines representing the roots of the threads when visible are sometimes made heavier, but when dotted all lines should be of uniform thickness. Strength of Screw Threads. — There are three methods of failure, shearing of threads, tension at the root of threads, and bursting of the nut. Let /s = unit shearing stress in pounds per square inch. ji = unit tensile stress in pounds per square inch, p = pitch in inches I = length in inches The shearing strength of the V thread (Fig. 105) will be Ps = TT di Ifs and for square threads (Fig. 106) having the same outside diameter and pitch „ 77//. Ps = TT d2 V 2 fs which shows that the square thread is much weaker in shear than the V thread. The tensile strength of the V thread (Fig. 105) will be Pt ='/^Trd,^ft and for the square thread. Fig. 106, having the same outside diameter and pitch ^ , , , „ . Pt = 74 TT C?2^ ft The V thread will have a considerable tendency to burst the nut, as shown in Fig. 107. As the angle between the threads decreases, this bursting tendency decreases until the square form is reached, when it becomes zero (Fig. 109). The following tables give some desirable data concerning screw threads. Further information may be found in the handbooks published by Machinery and American Machinist. SCREW THREADS 47 Dimensions of U. S. Standard Threads Threads Diameter Root Root Diameter per Inch of Tap Drill Diameter Area 74 20 V16 .185 .026 Vl6 18 74 .241 .045 Vs 16 V16 .294 .068 Vl6 14 2V64 .345 .093 ■ V2 13 ^732 .400 .126 V16 12 ^32 .454 .162 Vs 11 V32 .507 .202 V4 10 Vs .620 .302 Vs 9 74 .731 .420 1 8 2732 .838 .551 iVs 7 3732 .940 .693 1V4 7 1732 1.065 .889 IVs 6 17l6 1.159 1.054 1V2 6 17l6 1.284 1.293 IVs 5V2 1^732 1.389 1.515 1V4 5 172 1.491 1.744 iVs 5 IVs 1.616 2.049 2 4V2 174 1.711 2.300 Tensile Strength of U. S. Standard Screw Threads Diameter Threads per Inch Total Strength of One Bolt for Unit Stresses of 4000 5000 6000 74 " 78 72 Vs 74 78 iVs 178 174 178 172 178 174 178 2 20 16 13 11 10 9 8 7 7 6 6 572 5 5 472 105 270 500 805 1200 1680 2200 2770 3120 4240 5120 6120 7040 8120 9200 135 340 625 1010 1500 2100 2750 3460 3900 5300 6400 7650 8800 10150 11500 160 405 750 1210 1800 2520 3300 4160 4680 6360 7680 9180 10560 12180 13800 CHAPTER VII BOLTS AND SCREWS The most common fastening for holding parts of machines together is some form of bolt or screw. There is a great variety of forms, many of which are shown in this chapter. U. S. Standard Bolts. — Figs. 110 and HI show the pro- portions of the U. S. Standard hexagonal bolt head and nut. As indicated, there are two general forms, chamf erred (Fig. 110) and rounded (Fig. 111). The same proportions hold for both types. The rounded type is used when the parts to be bolted together are nicely finished. The distance across flats W is made equal to one and one half times the diameter, plus one eighth inch, or W = V/2d+'/s" The thickness of the bolt head is made equal to one half the distance across flats, or T =y,d+ Vie" The thickness of the nut is made equal to the diameter in all cases. These same formulae hold good for both the hexagonal and square forms. Fig. 112 shows the square form. The radii for the various arcs are shown on the figures, and when not given in terms of the diameter are obtained from the construction, as indicated. The distance across corners is gen- erally found by construction, as indicated in Fig. 110, by drawing a line xy at 30 degrees with the base of the head. x-z = one half distance across flats x-y = one half distance across corners It should be noted that the radii R and Ri of Fig. Ill, are both drawn from the same center. The length of the radius Ri is found by construction when drawing the bolt head or nut. When 48 BOLTS AND SCREWS 49 ^c^- 'V d V I Fig. /I2 heads or nuts are finished or machined, the distance across flats is often made Vie inch smaller than standard, in which case W =1V2^+Vl6" 50 ESSENTIALS OF DRAFTING The proportions of bolt heads and nuts are collected in the following list, which also gives some approximate values to be used when drawing to small scale, or where exact size is not important. Exact Approximate Diameter of bolt d W T Cn d Cs d 'Ud +V8" W '/,d+Wu"=- 1.155TF d 1.414TF d V/,d Vzd lV4d+V8 d 2M d Distance across flats Thickness of bolt head (Hex.) distance across corners. . Thickness of nut 2d d (Square) distance across corners Bolts. — A through bolt is one which extends through two pieces, and carries a nut, as shown in Fig. 113. Care must be taken to allow sufficient thread to insure the two pieces being held firmly together. For this reason, the distance from the end of F/g. //3 r/g. //4 r/g.ns the thread at A to the under side of the head B must be less than the thickness of the two flanges. Since the bolt head and nut are standard only three dimensions are necessary when specifying a bolt. These are, diameter, length from under side of head to end of bolt, and length of thread measured from the end of the bolt. A tap bolt is a bolt which makes use of a part of the machine to take the place of a nut, as shown in Fig. 114. To be sure that the two pieces will be held firmly together, the distance AB must be less than the thickness of the flange. BOLTS AND SCREWS 51 Studs. — A stud bolt or stud is a cylindrical bar having threads on both ends (Fig. 115). Studs are used when there is not room enough for through bolts, and where there is danger of a tap bolt rusting in. Cylinder heads for steam or water machinery are familiar examples. In such cases the heads have to be taken off frequently, and if tap bolts were _ _ ..^ used, the threads might rust in, and break when an attempt to remove them was made. If successfully re- moved several times, the thread would be worn so as to become loose and render the keeping of a tight joint difficult. When a stud is put in place it becomes part of the casting, and the wear then comes on the nut and stud, both of which are made of wrought iron. The material will stand the wear much better than cast iron, on the outer end of the stud will prevent the nut from rusting on. Threaded Holes. — Holes for bolts and studs are generally threaded by using taps. Machinist taps come in sets of three, Fig. 116 A small amount of oil Fig. lie F/g //7 Fig. 119 designated as taper, plug, and bottoming taps (Fig. 116). The operation is as follows: First a hole is made with a driU having a diameter about equal to the root diameter of the screw. Such a drill is called a tap drill. The thread is then cut by inserting and turning in the taps illustrated, and in the order given. The use of the bottoming tap is often omitted, as it is seldom neces- sary to have threads to the very bottom of the hole (the reader is referred to catalogs of machinists' tools for further informa- 52 ESSENTIALS OF DRAFTING tion). Unless it is desired to have a stud jam at the bottom of a hole, clearance, CD, should be allowed, as shown in Fig. 117. The depth of the hole is tli.e distance AB, If necessary the *-B- -<4 FJaf Finisher Head HZ?h Oyal Fi/l/sfer Head T /9= 1.64- A-. 009 O C= .66A-.002 Jl D= ./ys/a-.o/s a= i c "^^JlJ^l k B = /.6^/J -.009 i^h Round Head X^g'—-^ E3 3- /.asA-.oos C= .75 A D- ./73A-f:0/5' £= iC +.01 C- .66A-.002 D= .l73Ai-.0/5 e'-. ^F F= . 13^ B -fC F/af Head B = 2/i-.ooa C -(A-.008)-r/.739 P = ./73A i-.OJ5 Fig. I20 thread may be carried to the bottom of the hole and even the drill point may be ground off so that a flat bottom hole may be obtained as in Fig. 118. This will prevent the drill from pointing or breaking through, as indicated by the dotted lines. A better F/g. fe^ D / ^ s 16 3 e 7 /6 / 2 9 /6 S e 3 7 1 H 7 /6 a 9 /6 S & 3 /3 /6 7 e / Is 1? 3 3 e 7- /6 / 9 /6 S e II 16 s 7 8 /i Ik method is to put a boss on the casting opposite the hole, and then use a regular drill and plug tap (Fig. 119). Machine Screws. — Small screws are made with a variety of forms of heads. They are especially adapted for use with small parts of machines. Fig. 120 shows the various forms of heads, and the proportions as recommended by the American Society of Mechanical Engineers. The sizes of machine screws are BOLTS AND SCREWS 53 designated by numbers. Diameters range from .060 inches to .450 inches. Cap Screws. — For many purposes bolts having different dimensions from the U. S. Standard are desirable. Hexagonal and square cap screws are shown in Figs. 121 and 122. The distance across flats is less than the U. S. Standard, and the thickness is greater. Cap screws are also made with heads similar to those shown for machine screws. Cap screws are designated by their diameter in inches. The diameters are in even fractions of an inch, starting at ^U'. Cap Nuts. — Where an especially finished appearance is de- sired, cap nuts may be used to conceal the ends of studs. They are frequently seen on polished cyl- inder heads, and similar places, shown in Figs. 123, 124, and 125. Set Screws. — For holding pulleys on shafts, and otherwise preventing relative motion, set screws may be used. Several forms are illustrated. Any combination of point and head may Fig.iaa F,g 12^ Fig.iaS Several forms of cap nuts are N= US Sfd. No Thds. per inch. KIZ Fig. /26 Fig. /23 rig. /B9 \.m @ Fig. 130 I Fig. 131 be obtained. Some proportions are shown in Figs. 126 to 131. A projecting set screw on a revolving pulley is a source of great danger, and should be avoided. The many forms of headless and hollow set screws on the market render the use of other forms unnecessary in such cases. The relative holding power of the different forms of ends of set screw are given by Professor Lanza in the A. S. M. E. "Trans- actions," Volume 10. Average results of tests on four kinds are as follows: 54 ESSENTIALS OF DRAFTING A. Flat end, ^/le inch diameter, 2064 pounds B. End rounded, V2 inch radius, 2912 pounds C. End rounded, V4 inch radius, 2573 pounds D. Cup shaped end, 2470 pounds The set screws were all ^/g inches in diameter, and were tightened with a pull of 75 pounds on a 12 inch wrench. Locking Devices. — The vibration of machinery often causes nuts to become loose if they are not provided with some form of locking device. The commonest method is to use two nuts. They may be full size, or one of the arrangements shown in Fig. >^ HI spring Coffer >^ \5 -^ Cc7sf/e A/ufs Z^^fK "SI T r/g. /S2 132. The castle nut illustrated forms a good method. Lock washers consisting of a piece of sheet metal are effective. One corner is turned down, and another corner is turned up, as illustrated. The following table gives the dimensions for U. S. Standard bolt heads and nuts. BOLTS AND SCREWS 55 Dimensions of U. S. Standard Bolt Heads and Nuts d w c d T Cs Diameter of Bolt Flats or Short Diameter Corners or Long Diameter Thickness of Nut Thickness of Bolt Head Corners or Long Diameter V4 V2 ^764 74 74 2732 Vie "/32 "/16 7l6 "/64 ==732 Vs V16 "/64 78 V32 3732 Vl6 2V32 2V32 7 16 "/64 1764 V2 Vs 1764 72 7l6 174 V16 ^V32 178 7l6 ^64 178 Vs IV16 1^64 78 ^32 172 V4 IV4 1^764 74 78 174 Vs IV16 l«/64 78 2732 2732 1 IVs 178 1 ^7 16 278 IVs l^Vie 2732 iVs 2732 27l6 1V4 2 27 16 174 1 2^764 IVs 2Vl6 2^732 178 1732 3732 1V2 2V8 23/4 172 17l6 3^764 IVs 2Vl6 217 16 178 1732 378 1V4 2V4 37 16 174 178 3"/64 IVs 2^7 16 31732 178 1^32 47 16 2 SVs 378 2 17l6 4^764 56 ESSENTIALS OF DRAFTING Depth of Tapped Holes and Distance for Screw to Enter Diameter of Screw 74 16 Vs Vl6 V2 Vl6 Vs V4 Vs 1 174 IVs 172 IVs 1V4 17s 2 D Diameter of Tap Drill ^764 ^732 Vl6 Vs 2764 ^764 ^732 ^764 74 ^764 «V64 P/64 P764 1^764 P732 172 178 P732 Depth of Hole 7l6 7l6 ^7l6 74 I7l6 1 174 172 178 174 2 274 272 278 274 3 37s Allowance for Drill Point 7l6 764 732 764 78 764 /l6 32 7 74 V 32 "/16 ^732 7s ^732 7l6 ^32 72 Distance for Screw to Enter 78 7l6 7 16 Vs Vl6 ^7 16 78 1 174 17s 172 174 178 27s 274 278 278 274 CHAPTER VIII RIVETING Riveting. — Since machines and structures cannot be made in one piece some means of fastening the parts together must be used. For many purposes where a permanent fastening is re- quired, rivets are used. A rivet is a bar of metal having a head made on one end and a length sufficient to allow forming a head on the other end after being put into place. The holes for rivets may be either punched or drilled. As punching injures the metal, drilled holes are better for boiler or other pressure work. ^ig. /33 Fig. /^^ Fig- /3S Holes are made Vie inch larger diameter than the rivets used in them. Thus a one-inch rivet is ^Vie inch diameter before driving. The computations for pitch and efficiency of joints, matters relating to design, are beyond the scope of this work, but the following articles will suffice for drawing purposes. Rivet Heads. — The forms of rivet heads are shown in Figs. 133, 134, and 135. The countersunk head and the button head are illustrated in Fig. 133. These forms are used for structural work. For pressure work the cone head or pan head of Fig. 134 may be used, or the common form of Fig. 135. Lap Joints. — When two plates lap over each other and are held by a row of rivets as in Fig. 136 it is called a single riveted lap joint. A double riveted lap joint is shown in Fig. 137. The distance between the centers of two rivets in the same row is 57 58 ESSENTIALS OF DRAFTING called the pitch. The distance from the center hne of the rivets to the edge of the plate is called the lap. The lap is commonly made equal to one and one half times the diameter of the rivet. Fig. /36 r/g. /3 7 The distance from the center of a rivet in one line to the center of a rivet in the next line is called the diagonal pitch and may be found from the formula: p' =y,p + ^ 3 Either chain riveting (Fig. 138) or staggered riveting (Fig. 139) may be used when there are several rows of rivets. f/'g. /3d f/g. /3 9 Butt Joints. — Three forms of butt joints are shown in Figs. 140, 141, and 142. In Fig. 140 a single butt-strap having a thick- ness of about one and one fourth times the thickness of the plates RIVETING 59 may be used. Figs. 141 and 142 show single and double riveted butt joints with two butt-straps. In such cases the butt-straps may be Vie inch thinner than the plates. When three plates come together they must be arranged so ^)=r3:^=P; 4y f/g. /^/ r/g. 14-2 Action A- A r/g. /^3 1 Sect ton 3 -3 as to maintain a tight joint. One method used is shown in Fig. 143. In order to obtain a fit one of the plates must be thinned out. Calking. — For many purposes rivets must make a leak tight joint as well as hold the plates together. To assist in this a 60 ESSENTIALS OF DRAFTING blunt chisel is used to force or pound the edge of the plate down. This is called calking and makes a water or steam tight joint h 'W-'M r 1 ^^^^^^^^" %p |)^^'j^ \\\\^ ^'%^^''''' CP r/g. /^4 fig. /^5 r/g. /'^6 1 r/g. /47 between the plates. The bevel of about 75° shown is to make the calking easier. Miscellaneous Connections. — Some miscellaneous connections are shown in Figs. 144 to 147. Angles may be used as in Figs. rK 7^ M N^ r/g. /^& r/g. J 4-9 144 and 147 or one of the plates may be bent as in Figs. 145 and 146. In this case the radius of curvature (r) may be about two and one half times the thickness of the plate. Also note that a short straight part {x) should be provided to allow easy calking rciiT AngleiX] Channel[Z] Beamij ) Z-Bar{7L) Tee (T) rig. 150 (Fig. 145) . When drawing to a small scale thin sections are some- times blacked in as shown in Figs. 148 and 149, which also il- lustrate methods of closing the ends of cylindrical tanks. With rounded ends the radius of curvature may be taken equal to the diameter of the tank. RIVETING 61 Rolled Steel Shapes. — For many constructions, rolled steel shapes are used. The dimensions and weights as well as other properties can best be obtained from the handbooks issued by C0/^i^£Nr/ONAL . S/SN5 FOR RiyFT/MC Shop Fie/d CountersunM and Fiafiened 7*vo Ful/ Heads o • Inside Ouis/de BofhSides ^ High Q Q CcH/nfersunk dc Chipped /ns/de or Opposite side 1 P/fch 3 Ik /i // £i 2§ 3 The Osborn system of conventional representation for rivets is shown in Fig. 151. CHAPTER IX WORKING DRAWINGS Classes of Drawings. — The origin of a drawing is of interest, and a knowledge of how drawings are produced is essential. Roughly drawings may be divided into two classes; detail draw- ings and assembly drawings. These names are sufficiently de- scriptive in a general way. Drawings are sometimes made from a machine or part by measuring and sketching. The usual source of a detail drawing is the designer's board. Here the whole machine is laid out to scale in a more or less complete manner, the relation of one part to another is shown, and such fixed dimensions as are necessary are determined. The shapes of the various parts as required for strength and motion are worked out and drawn. From such drawings the detail drafts- man works and finishes the drawings of the separate parts. A detail drawing shows each piece separately and completely defines it (Fig. 152). The number of views is determined by what is necessary to show the shape and size of the object. A pin, shaft, or bolt can generally be shown in one view, while a casting may require two, three, or more views together with sectional and auxiliary views. The main views should always be arranged in strict conformity to the rules of projection. The third quadrant is used exclusively for this purpose. Auxiliary views and sections may be placed in other positions but explana- tory notes should always be used to define them as explained in Chapter X. The size of paper and the scales to use have been treated in other chapters. Use a scale that will show the object clearly and that will not require crowding of the dimensions. In general it is better not to use more than one scale on the same sheet. To this end large and small pieces would not be put on the same sheet. There are many concerns where each part is drawn on a sheet by itself. The character of the work will determine the practice in this respect. 62 WORKING DRAWINGS 63 It is generally well to draw large castings separately and to group small parts together as: Small Castings, Bronze and Composition Castings, Forgings, Bolts and Screws. F/g. 152 Special Detail Drawings. — Special detail drawings are some- times made for the different classes of workmen. These might be classed as follows: Pattern Drawings, Forging Drawings, Machinist's Drawings, Stock Drawings. There are many advantages to this system where a large num- ber of parts are made as each workman is given only such in- formation as concerns him. As pattern dimensions are used only when the pattern is made or for alterations they complicate the drawing and can better be left off the machinist's drawing. One method is to put the pattern dimensions and information on the tracing in pencil, make several blueprints, and erase the pencil 64 ESSENTIALS OF DRAFTING — - _ 1 --- r- 1 1 -+ - 1 1 v_. (b - - -> \ - - ! - — r— 1 1 1 C 1 1 1 1 v._. I 1 — ^- 1— [- > > -~ i r 1 1 _u_ 1 1 1 1 1 ~_ L-|— — _J ' - - -— — — 1 J 1 information from the tracing. Gasolene applied with a soft cloth is excellent for this purpose. For forgings two separate drawings will be necessary, one for the blacksmith and one for the machinist. The saving in time will make up for the expense of the extra drawing in most cases. WORKING DRAWINGS 65 How to make a Drawing. — A detail drawing is started by first locating the main center lines as shown in Fig. 153 for the necessary views. Next "block in" the fixed dimensions in all views and from them work out the shape of the object. The small circles, fillets, etc. should be drawn last. Figs. 153 to 158 show the drawing for a slide valve in the various stages of making. After completing the drawing in pencil it is ready to be inked on paper or traced. Tracing. — Most drawings are now inked on tracing cloth. This is a translucent linen cloth. There are many grades, some nearly transparent. One side of the cloth is generally shiny or glazed and the other dull. Either side may be used but the dull side is to be preferred. The cloth is tacked down over the pencil drawing and the lines inked in as though they were on the cloth. The surface of the cloth should be rubbed over with powdered chalk and then the chalk thoroughly removed. A clean blotter will serve the same purpose. The fine thread running at the e^ges of the cloth should be torn off before using to prevent wrinkling. As the cloth is absorbent it should be protected from moisture. Order for inking Lines. — The weight of line to be used has been discussed in the first chapter. First ink the center lines using a fine dot and dash line. The order of inking then is: 1. Sinall circular arcs and circles. 2. Large circular arcs and circles. 3. Irregular curved lines. 4. Straight horizontal lines. 5. Straight vertical lines. 6. Dotted circular arcs. 7. Dotted lines. 8. Witness and dimension lines. 9. Dimensions, notes, title. 10. Section lining. When a large or complicated drawing is to be inked it is ad- visable to ink one view at a time or to start only so much as can be completed on the same day. If a view is left uncompleted it will generally be found very difficult to join the various lines, because the cloth is very sensitive to atmospheric changes which cause it to stretch. 66 ESSENTIALS OF DRAFTING Assembly Drawings. — An assembly drawing shows the parts of a machine in their proper relation to one another. There are many kinds of assembly drawings, some of which will be described. An Outline or Setting drawing is frequently made to show the appearance of the machine, give center distances, and overall dimensions. Such drawings are used to illustrate the machine to prospective customers, to lay out the foundation, and for locat- OUTLINE DRAWING be:nch shears ing the machine in its building. Fig. 159 shows one form of such a drawing. An Assembly Working Drawing is often made when only a few of the machines are to be constructed. Such a drawing might contain a number of part views or sections. It would be com- pletely dimensioned so that no separate or detail drawings would be required. Fig. 175 shows such a drawing. Part Assembly Drawings are sometimes made giving a few pieces in their proper relation to each other and either partly or completely dimensioned. When completely dimensioned no further detail drawings are made. Assembly drawings made to show the sizes, location, and method of fastening pipes and wires are called piping or wiring diagrams or drawings, depending upon how completely they are figured. Erection Drawings are an important class of assembly drawings. They show the proper order of putting the parts together, dimen- WORKING DRAWINGS 67 f^ig. /60 sions, such as center distances, which must be exact, give the location of oil holes, valves, switches, etc., and methods of making adjustments. 68 ESSENTIALS OF DRAFTING Diagram Drawings are used by many concerns. These com- prise a sectional or external view of the whole of the machine upon which the parts can be numbered or named. Such a draw- ing frequently contains a list of the parts, drawing numbers, pattern numbers, materials, weight, and other information. Outline drawings are often used for catalogs, advertising, and similar purposes. Some of the points to be considered are given (^-- F/g./e/ Fig. /62 F/g. 163 in the following list. The one upon which emphasis must be put will depend upon the use to which the drawing is to be put. 1. Get the important points. 2. Sense of proportion. 3. Suggestion. 4. Simplicity (few lines). 5. Record peculiarities in shape or design. 6. Use notes if necessary. 7. Number of machine. 8. Name of manufacturer. 9. Trade names. 10. Use of shading. 11. Not necessarily to scale. &how Drawings are sometimes made. These are often in the nature of a picture in which the center lines and dimensions are left off (Fig. 160). Line shading as explained in a later chapter is often used. A good effect may sometimes be obtained by mass shading with a soft pencil, using the dull side of the tracing cloth. For more particular work on paper, India ink tinting applied with a brush can be used. WORKING DRAWINGS 69 Exceptions to True Projection. — There are many cases where true projection is departed from in the interests of simplicity and clearness. Figs. 161, 162, and 163 show a few cases. The slot in the screw is drawn at 45° in the top view but is not projected -LU. i ! ! Fig. 164 F/g. 165 Fig. 166 to the elevation. The same practice is followed for holes and pins. The location of bolt holes is another illustration. The front view of Fig. 164 shows the true projection of the bolt holes. The front view of Fig. 165 shows the preferable method which Fig 167 F/g. /ee locates the centers of the bolt holes at a distance apart equal to the diameter of the circle of drilling. In such cases the other holes need not be projected as they add nothing to the information conveyed by the drawing. When holes are drilled as in Fig. 165 they are said to be ''Two Up" or off centers, and when located as in Fig. 166 they are said to be ''One Up" or on centers. Pipe flanges on elbows and fittings are usually drilled "Two Up" and 70 ESSENTIALS OF DRAFTING with four, eight, or some multiple of four holes, so that the flanges can be turned at right angles. Other exceptions to true projection are discussed in the chapter on sections. Blueprints. — The object of making tracings is to provide a convenient means for obtaining several copies of the original drawing. The most common method is by the blueprinting process. Blueprint paper is paper which has been coated with iron salts which are sensitive to light. The method of making blueprints is as follow^s: Place the tracing with the right side or inked side next to the glass of a printing frame as shown in Fig. 167. Next place a piece of blueprint paper on the tracing with the coated side down. Follow this with the felt pad and close the frame. Expose to the direct sunlight as indicated in Fig. 168. The length of the exposure varies from 30 seconds in strong sunlight with rapid printing paper to three or four minutes under the same conditions with slow printing paper. The time can best be found by trial, as the age of the paper and the brightness of the light all exert an influence. After exposing, the paper should be removed and thoroughly washed. The excess water may be blotted off and the print hung up to dry. New paper has a yellow color on the coated side. After exposure this changes to a gray-bronze except where the lines of the tracing prevent the light from reaching it. Electric light is very generally used in the larger mechanical factories for making blueprints. Machines for this purpose as well as many other methods of duplication are described in draw- ing supply catalogs to which the reader is referred. CHAPTER X SECTIONS Sectional Views. — Probably the most useful form of con- ventional representation is the sectional view obtained by an rig. 169 imaginary cutting plane described in Chapter IV. Free use of sections often saves much time as well as possibility of mistakes in reading drawmgs for constructions which have compUcated Fig. Jyo Fig. / yi m F,g.l72 cores. The choice of views should be made with care and for a definite purpose, never for appearances. There are many special sections, some of which are described in this chapter. An article 71 72 ESSENTIALS OF DRAFTING by the author, '^ Sections of Ribs and Symmetrical Parts," in ''Machinery," June, 1915, gives further apphcations. Broken and Revolved Sections. — When a long piece of uni- form cross section is to be represented, a larger scale can be used -74 ^I I F/g. 173 by '^ breaking" the piece. The manner of breaking generally indicates the form of cross section and material as in Fig. 169. The break is made free hand but should be carefully done. The two sides should appear to match, that is, if the sectioning comes on the upper side of one half it should come on the lower side of Sechcn A A in d/'rcchon of orrav Fig. 17^ the other. A similar method of "set in" sections is often used for such conditions as are present with wrench handles, pulley arms, brackets, hand wheels, and rods. Figs. 170 to 173 show some examples. Location of Sectional Views. — When conditions permit, sec- tional views should be placed according to the laws of projection SECTIONS 73 as explained in Chapter IV, and are drawn in the same manner as the other views by assuming a part of the machine or parts to have been removed. When many sections are required or other 74 ESSENTIALS OF DRAFTING reasons make it necessary to place the sectional views in another location, arrows and notes should be used to explain them as shown in Fig. 174. Extra sectional views are often very useful in explaining parts of a machine or details of a part. Since the cutting plane is imaginary it need not be continu- ous; thus several sec- tions may be used and the views represented as though occurring on a single plane. This is illustrated in Fig. 175, where the cutting plane is changed as shown in the top view. Thus the front sec- tion is taken on the plane A, B, C, D, E^ F, and the side section on a plane through the center. Objects not Sectioned. — When a full view will serve the same purpose just as well a sectional view should not be used. This is true in the case of shafts, bolts, nuts, screws, rivets, keys, pulley F/g. /77 arms, etc., which are very seldom drawn in section except when the cutting plane is at right angles to the long dimension. This treatment of a section is shown in Fig. 176. SECTIONS 75 Dotted Lines on Sectional Views. — Very often a sectional view contains only the outline of the sectioned surfaces and the full lines which appear. How much of the part behind the plane Fig. 1 79 Fig. 160 Fig. i8l of the section should be represented must be determined for each particular case. When an object is represented by a view made up of one half in section and one half exterior most or all of the F/'g. 162 dotted lines may be omitted from both halves, as was done in Fig. 175. Sections of Ribs and Symmetrical Parts. — Ribs, arms, and gear teeth are not ordinarily sectioned even though they appear 76 ESSENTIALS OF DRAFTING on the plane of the section. Figs. 177 and 178 illustrate such cases. In Fig. 177 the plane M N passes through the ribs, but is not sectioned in the other view as it would give a false impression of solidity. In Fig. 178 the true projection without sectioning the rib is shown at A, while the usual conventional section is shown at B. The representation of a cylinder head in Figs. 179, 180, and 181, shows a similar case. A true section on the plane AB is given in Fig. 179. In Fig. 180 the section is taken on CD and revolved into the position of AB. The bolt holes and lugs are then located at their true distances from the center. By this means one view could be made to represent the cylinder head by adding a note to give the number of lugs. An alternate method is shown in Fig. 181, where the section FE is revolved. The idea in all cases is to avoid a view which might in any way be confusing and to convey the true shape clearly. When a rib occurs on the plane of a section and it is necessary to distinguish it, coarse sectioning may be employed as in the cone pulley of Fig. 182 where the ribs are sectioned but alternate lines are omitted. A note giving the number and thickness of the ribs would allow the end view to be dispensed with. Observe that the half end view is bounded by the center line and not by a full line, as the pulley has not been actually cut in half. CHAPTER XI DIMENSIONING Purpose of Dimensions. — The purpose of dimensions is to give the necessary figures for constructing machine parts and putting them together. A drawing gives the shape of an object, Fig. /as the dimensions tell the size. These are two operations and both should be kept in mind. Dimension Lines. — Dimension lines show where the figures apply to the drawing. They are terminated by arrow heads. The arrow heads should be about twice as long as they are wide. Fig. 18^ Fig. ids Fig. 183 shows the construction of an enlarged arrow head, and its proportions. Fine full red ink lines are sometimes used for dimension, center, and witness lines. The arrow heads and figures are always black. The figures and notes should always be placed so as to read from the lower or right hand side of the 77 78 ESSENTIALS OF DRAFTING drawing. Never use slant fraction lines. In most cases it is considered bad practice to place the figures upright as shown in Fig. 184 where the figures may be easily read with the wrong dimension lines. Fig. 185 shows a better arrangement. The witness and dimension lines should be as fine as possible so as not to conflict with the Hnes of the drawing. In the interest of clearness there should be as few lines as possible crossing each i'Top /6Thd.U.SS ' \^^^ ^ ..-£S^^-1^..- n I Diom- r^ — + — 1^3:^^^ ]L KlVO 0)|^ ^3 3 a ^ \)o 5- Or/// 6 \.J li ^4 u Fig. 186 other. The center lines and object hnes have only one purpose and should never be used as dimension lines. Generally the dimension lines can be kept outside of the views, thus keeping the size and shape of the object separate. In such cases place the larger dimensions outside the smaller ones as in Figs. 186 and 188. Fig. 187 shows a poorly dimensioned drawing of a pump plunger and Fig. 188 the same piece properly dimensioned. Fin- ished surfaces are ordinarily indicated by a letter ''/" placed across the line which represents the surface to be machined. Elements of Dimensioning. — Constructions can be separated into parts and these parts can then be divided into geometrical DIMENSIONING 79 solids. Each of the sohds can then be dimensioned and their relation to each other fixed. Figs. 189 to 193 show a prism, a pyramid, a cone, and a cyhnder with dimensions. Figs. 194, 195, and 196 show combinations. Note that the same location of dimensions is maintained. In dimensioning cylinders give the diameters on the elevation as in Fig. 195. Placing of the five Fig. 187 Fig. 188 diameters on the end view would result in crowding as well as inconvenience in reading figures placed at an angle. Always give a diameter in preference to a radius if the part is a complete cyhnder. For quarter rounds, fillets, and part circles give the radius. General Rules. — To dimension a drawing successfully the construction of the pattern, machining, fitting, and putting to- gether of the machine must be gone over. It is necessary to keep constantly in mind the person to whom the drawing is addressed and the purpose for which it is to be used. 80 ESSENTIALS OF DRAFTING Hints: Do not humjy Give sizes of pieces for the pattern maker, Give sizes and finish for the machinist, Give assembly dimensions. Give -office dimensions, Give notes where needed. Fig./ 89 ATv ■-r- r VVl ; v_ \J T V! Fig. 190 ^ ^rJ ,: Q - 1 -^ " -Q- rig 192 y/////////y/A r?- \ '///////////// Fig. 191 Fig. 193 Fig. /9^ Fig. /95 It is necessary to remember that surfaces and not lines are being located. The dimensions of the piece must be kept in mind. Detail drawings are generally made to serve both pattern maker and machinist, and the figures indicate the size of the finished piece. The pattern maker is left to make required allowances for finish, shrink, and draft. In the case of forgings two drawings are sometimes made, one for the blacksmith giv- ing the rough sizes, and another for the machinist giving the finished sizes. Systems of Dimensioning. — Four general systems of dimen- sioning may be mentioned as follows: 1. All figures outside of the object lines. 2. All figures inside of the object lines. 3; All figures given from two reference lines at right angles to each other. 4. A combination of the preceding three systems. DIMENSIONING 81 The four systems are illustrated in Figs. 197 to 200. The first method is to be favored as the dimension lines and figures are kept separate from the interior and allow details to be easily seen. The size and i L shape are separated. The second method may be used when there is little detail within the view. It preserves the outline of the view but often there is confusion due to the crossing of the lines and crowding of the figures. The third method is particularly adapted to plate work and laying out where holes must be carefully located. The fourth method is the one generally used but making it -* >i ^ >- .^ ., V 1 y ' 1' -* »■ r/g./gy r/g, 196 conform to the first system by placing dimensions outside when- ever it is conveniently possible. • Location of Dimensions. — Facihty in manufacture should be a motto in dimensioning. The figures must be so placed as to be easily found and perfectly clear in their meaning when found. Select that view which most completely defines the object and start with it first. If an assembly drawing, dimension only one piece at a time and finish all views of that one piece before starting another. Put on similar dimensions at the same time, as diame- ters, lengths, etc. Do not jump from one piece to another. Work from the more important dimensions to those of less importance. 82 ESSENTIALS OF DRAFTING See that all center distances are given. Consider the effect of location upon ease of reading the drawing. Similar pieces should be dimensioned in exactly the same way. Fig. 201 shows a gland, -• ^ h \ 1 ' 1 -^ >- r/g. J 99 Fig. BOO Fig. 202 a pump valve, and Fig. 203 a cyUnder head. They are all similar pieces and the dimensions are located in the same places on each. In the three figures the similar dimensions are indicated by the letters A, B, C, etc. By observing such methods a system of dimensioning can be K T 1 '^\^ ^ i 2^^ H rig. 20/ employed which will save a great deal of time and many mistakes and omissions. It is seldom necessary to repeat the same dimen- sion on a drawing. Drilling is generally best located in the view where it shows in plan, that is, in the view where it is laid out. Diameters are always clearer when shown on a section DIMENSIONING 83 or elevation rather than on an end view. The drilHng for flanges is dimensioned by giving the diameter of the bolt circle and the size of bolt holes or bolts. The holes are understood to be equally spaced unless noted otherwise. Shafting. — Shafting should be dimensioned by giving the diameters and lengths together with the sizes of keyways and pins and their location. Shafting is made from various grades of wrought iron and steel. For many purposes cold rolled shafting is generally used. This is shafting which has been cleaned of scale and rolled under pressure. It can be used without the F/g. E>02 necessity for turning and is considerably strengthened by the surface skin which comes from the rolling process. Hot rolled shafting is black and must be turned to size before using. Usual sizes are: Nominal Diameters of Shafting 1V4 2V2 4 1V2 2V4 4V2 1V4 3 5 2 3V4 5V2 2V4 3V2 6 These are nominal sizes and are Vie inch larger than actual diameter. Thus a 2-inch shaft is V-^jv^' actual diameter. Com- mon lengths vary up to 24 feet. Special shafts have to be forged of steel suitable for the particular purpose. A shaft drawing is shown in Fig. 204 with the positions of the dimensions. 84 ESSENTIALS OF DRAFTING Tapers. — Various methods are in use for designating tapers. Figs. 205, 206, and 207 show ways of indicating the two diameters and the length. Sometimes a note is employed giving the taper rig. 303 per foot of length as, "^A'' per jooi.^^ When the slope is con- siderable it may be given as 1:1, indicating a 45° slope. In other cases the angle may be given in degrees. In addition there are Fig. 90^ a number of standard tapers in use such as B & S (Brown & Sharpe), Morse Tapers, Reed Lathe Center Tapers, Jarno Tapers, and Sellers Tapers. In such cases the taper is indicated by a number which fixes the three dimensions, large diameter, small diameter, and length. A machinist's handbook should be con- sulted for complete information. DIMENSIONING 85 Small Parts. — There are many small parts such as shafts, pulleys, etc., which can be defined in one view by using a note to give the missing dimensions. When clearness is not sacrificed it is better to use this method in many cases. Small details which are standardized do not need to be completely dimen- sioned. This is true for holts and screws, standard tapers, piping, wire, sheet metal, rope, chain, pins, rolled steel shapes. Methods of Finishing. — In connection with dimensions the limits of accuracy for all fits should be given. The method of /. /=^/g. 205 Fig. 206 ^ rig.eo? ~T finishing is given in another chapter, and should be indicated by a note and arrow. 1. Rough. 2. Rough turned. 3. Ground. 4. Polished. 5. Reamed. 6. Cored. 7. Running fit. 8. Loose fit. 9. Driving fit. 10. Scraped. 11. Finished. 12. Drilled. 13. Chipped. 14. Spot faced. Checking Drawings. — The checking of a drawing is one of the important duties of most draftsmen. Whenever possible it should be done by someone who has not worked on the drawing. The first thing to do is to see if the drawing can be used without unnecessary difficulty, and to see if the parts are such as will fit and operate successfully. There must be clearance for moving parts. Then observe if sufficient views are given to completely determine the parts, and that all dimensions necessary for machin- ing and erecting are given and that they are properly located. Check the correctness of all figures by use of the scale and by computation. All notes should contain a clear statement and 86 ESSENTIALS OF DRAFTING be carefully located. Standard parts should be used where possible. See that the fewest number of different sizes of bolts and similar small parts are used. Consider the materials of which the parts are made, the construction of the patterns and cores, and the method of machining. A valuable article on ''How Machinery Materials and Supphes are Sized" is given in '* Machinery," February, 1916. CHAPTER XII MACHINE CONSTRUCTION Machine Operations. — The parts of machines which come from the foundry, forge, or rolhng mill generally require finishing, such as machining to size, drilling, tapping of holes, etc., before they can be assembled in the machine of which they are to be a part. A knowledge of what is involved in the processes of ma- chining is important to the machine draftsman. The principal machine operations are turning, drilling, boring, planing, and milling. The machines used are lathes, drills, boring mills, planers, milling machines, shapers, etc. In order to pursue the subject of drawing with profit at least Fig . ^O 8 Fig 209 one book on machine tools should be purchased and studied. The advertising pages as well as the reading pages of such mag- azines as ''American Machinist" and ''Machinery" are further sources of information which should not be neglected. Every opportunity should be availed of to observe and study work as it is carried out in pattern shop, forge, foundry, and machine shop. Such knowledge is invaluable and will often enable the draftsman materially to reduce the expense of production by simplifying or adapting his designs. Drills. — Drills are used for making holes of comparatively small diameter. Two forms of drills are shown in Figs. 208 and 209. The first is a flat drill and the second a twist drill. The latter is the form in general use. Drills are used in different forms of machines. Look up the following in the advertising pages of "American Machinist" or "Machinery": Sensitive Drill, Drill Press, Multiple Drill. 87 88 ESSENTIALS OF DRAFTING The Steam Engine. — It is important for the draftsman to learn the names of the parts of the steam engine. Fig. 210 shows the principal parts. M^S=S± 1. Cylinder head. 2. Piston. 3. Casing or lagging strip. 4. Cylinder. 5. Piston rod. 6. Steam chest cover. 7. Steam port. 8. Slide valve. 9. Exhaust port. 10. Valve rod stuffing box. 11. Valve rod gland. 12. Valve rod. 13. Eccentric rod. 14. Eccentric. MACHINE CONSTRUCTION 89 15. Outer bearing. 21. Frame. 16. Main shaft. 22. Crosshead pin. 17. Fly wheel. 23. Crosshead. 18. Inner bearing. 24. Crosshead guide. 19. Crank. 25. Connecting rod. 20. Crank pin. Steam is admitted to alternate sides of the piston by means of the slide valve which is actuated by the eccentric through the eccentric rod. The piston transmits the pressure of the steam \ ^^ Fi'q. ^/I f^ig. 2/2 through the piston rod, crosshead, and connecting rod to the crank. The crank causes the shaft to revolve, carrying with it the flywheel, from which power may be transmitted by means of a belt. Pistons. — Pistons are used in many forms of machines and vary accordingly. Some forms are shown in Figs. 211 and 212. The names of the parts for the form of steam piston shown in Fig. 212, are ^ p.^^^^ ^^^^ 2. Follower, 3. Follower Bolts, 4. Bull Ring, 5. Packing Rings. To prevent loss of pressure by leakage past the piston some form of packing ring is generally employed. Pistons are most always 90 ESSENTIALS OF DRAFTING made of cast iron as are the rings. The rings are turned to a sHghtly larger diameter than the cyhnder. A piece is then cut out and the ring is then sprung into place. For water pistons Fig. 2/^ F/g. 2/5 a soft packing of hemp, fiber, or leather is used. For large vertical engines steel pistons are sometimes used. Sliding Bearings. — Sliding bearings are of many forms, as shown in the following figures. The general end sought is to have the projected area of slide such that the pressure will not force out the lubricant and allow the metals to come into contact with each other. Smoothness of surfaces is only relative and Fig. 2/6 F/g. 217 Fig. 2 16 surfaces in contact wear rapidly, hence the necessity for efficient lubrication. Fig. 213 shows a form of planer guide. It is self-adjusting for wear and can be easily oiled. There is, however, considerable pressure between the inclined surfaces, which means that the power for operating the table increases as the angle A is de- creased, and also the wear. A is commonly made 90° or less for small planers, while for heavy planers it may be 110° or more. The side pressure of the tool must be considered in selecting the proper value of A since it exerts a tendency to raise the table from the ways. MACHINE CONSTRUCTION 91 Fig. 214 shows the form generally used for lathe ways. It is self-adjusting, does not readily hold chips or dirt, but is not so easily kept oiled as Fig. 213. There are many other forms of such bearing surfaces, some of which are provided with gibs for adjusting, as in Fig. 215. Com- Ftg. p/9 Fig. 2^0 F/g.22l mon forms of crosshead guides for steam engines are shown in Figs. 216, 217, and 218. Fig. 218 is used on all sizes of engines, and is satisfactory, since it allows the crosshead to adjust itself to the crank pin and connecting rod if turned concentric with the (777/////////////:^ \< A wm^m r/g. 223 d. F/g.22^ \ Fig. 22 5 cylinder. Sometimes, however, the guides are turned with centers as in Fig. 219. This prevents turning. For small pressures the form shown in Fig. 220 is often used, sometimes with one rod only. Fig. 221 is another form of sliding bearing. The pressure per square inch of projected area on cross- head guides should not exceed 100 pounds per square inch and may well be kept as low as 40 pounds per square inch. Wear and Pressure. — Where there is much wear care must be used in the design of a sliding bearing and guide. Provision should always be made for running over at the ends of the guide. The same applies to the width of the guide. The effect of guides which are too long is shown much exaggerated by the shoulder 92 ESSENTIALS OF DRAFTING "C^' in Fig. 222. Fig. 223 shows the correct design in which the shde runs over the guide at each end and causes more even wear. If ''A" and "B^^ are made of equal length there will be equal wear. This same principle is involved in the piston and cylinder of a steam engine which accounts for the counterbore over which F/ff. 326 Fig. 2PS the piston runs, ''C" (Fig. 224), and similarly for slide valve seats (Fig. 225). Stuffing Boxes. — Some common forms of gland and screw stuffing boxes used on engines, pumps, etc., for preventing leakage of steam or water around the piston rod where it passes through the end of the cylinder are shown in Figs. 226, 227, and 228. For rods IV4 inch in diameter or less the conunon screw stuffing %'' -y ^ ng. ^ f/g. c-so Fig. 23/ box. Fig. 228, may be used. They are generally made of com- position although they are sometimes made of cast iron for cheap work. The gland stuffing box (Figs. 226 and 227) is used for rods IV2 inch and more in diameter. The box should be deep enough for four strands of packing and the gland so constructed as to be able to compress it to about one half its original size. These glands may have the bottom of the gland and box beveled as shown in Fig. 227. They may be lined with composition in which case the lining should be at least ^/le inch thick, but for rods less than 2^/2 inch diameter it is generally advisable to make the gland entirely of composition. These are the com- mon forms, but the student will do well to investigate some of MACHINE CONSTRUCTION 93 the various types of metallic packings, since they are largely used in good designs. Useful Curves and Their Application. — There are many small details in the actual drafting of a design which often give trouble out of proportion to their apparent importance when first en- Ftg. ^32 countered. The following suggestions are made to facilitate the drafting part of design, and not as rules to be strictly adhered to. Various curves which are commonly used are shown. Fillets and Rounds. — The drawing of fillets and quarter rounds deserves attention, since they are of so frequent occurrence. Fig. 229 shows a portion of a machine. The centers and radii of the various arcs are indicated. All radii are too large, but r/g.33S rig. S36 A Fig. .237 Fig ^30 it Fig. ^39 especially 1 and 2. Radius 1 gives a point at y. Radius 2 is so large that it cannot be used for the complete circumference of the boss as indicated at x. Of course a changing radius of fillet might be used, but this would not allow the use of ready made fillet strips. Fig. 230, in which the limiting radii are used, is an improvement. Fig. 231 shows a much better design. Note that the radii 1 and 2 are less than the thickness of the flange and boss respectively. The effect of a quarter circle is obtained by this method in which the flange and boss each start with a straight line. The straight line also produces a better appearance after finishing off the surface of the boss. This is shown in Figs. 232, 233, and 234, where the effect of different fillets is indicated at B 94 ESSENTIALS OF DRAFTING in each of the views. In the first case there is an undercutting, in the second view B shows the irregular outhne produced, while the third case shows the correct design. Arcs and Straight Lines. — When arcs are used in connection with straight lines the fault shown at a in Figs. 235 and 237 should be avoided. Do not run the arc past the tangent point ''a", and notice that the line a-h is a straight line in Figs. 236 and 238. F/g.^^o r/g. 2^/ rig. ^^3 Fig. 2^3 At A in Fig. 239 is shown the effect of not changing the radius when two parallel lines are continued by arcs. At B the thick- ness of material has been kept by maintaining the same center and changing the radius by the distance i. Flanged Projections. — When flanged projections are used with bolts or nuts they may take^a variety of shapes, some of Fig. 2^^ Fig. 2^ 7 Fig. 2^& which are shown in Figs. 240 to 243. After locating the centers of the bolt holes the extent of the flange may be found by adding twice the bolt diameter to the distance between bolt centers. Frequently the outline is obtained as in Fig. 240 in which an arc is drawn from the center of the bolt hole with a radius equal to the diameter of the bolt. A much better appearance is obtained by using a larger radius whose center is at the intersection of the bolt hole and the center hne, as shown in Fig. 241. Either straight or curved lines may MACHINE CONSTRUCTION 95 be used to join the small and large arcs. Sometimes an ellipse may be used. A gland is used for illustration, but similar cases occur in pipe connections, the bolted feet of machines, etc. Flange Edges. — Flanges are often finished with curves so as to avoid machining. Several forms are shown in Figs. 244 to 248. The radius R may be taken equal to the thickness T. The centers for the various radii are indicated. Flanges and Bolting. — A method of finding the diameter of bolt circle and diameter of flange is illustrated in Figs. 249, 250, and 251. For through bolts consider Figs. 249 and 250. Draw D^ Fig. 2^9 Ci ^^ Fig. 2S/ /) in a proper fillet at n. For a trial the radius Tx may be taken as one fourth of the thickness of the cylinder wall t. Then lay off X, equal to one half the distance across flats of bolt head, and 7, equal to one half the distance across corners of nut. The diameter of the bolt circle, Ds, may now be found by laying a scale on the drawing and selecting a dimension. This will be equal to, or greater than, c? + 2(^ + n + X), and may be taken at the nearest Vsth inch. The flange diameter may then be obtained by laying out the distance F, as in Fig. 249, and using the scale to find an even dimension equal to, or greater than, Dfi + 2( F+ r2). The radius r^ may be taken at Vsth to Vieth the thickness of the flange. When studs are used the diameters I>B and Dp may be greatly decreased as shown in Fig. 251. The distance C should be about equal to i, although if necessary it can be made equal to one half the diameter of the bolt. Keys. — Keys of various forms are used to prevent relative motion between shafts and pufleys, gears, crank arms, etc. The common forms are here shown. Fig. 252 is called a saddle key and may be used where only a small force is to be transmitted 96 ESSENTIALS OF DRAFTING and where close or frequent adjustment is required. Fig. 253 is called a flat key, and requires a flat spot upon the shaft. Its holding power is a little greater than the preceding form. Set screws are sometimes used with Figs. 252 and 253 to secure a closer contact. Fig. 254 is the most common form, and may be either square or rectangular in section. The sides of the key should fit closely in the hub and shaft. Various proportions are given for keys. Square keys are often made with 4 ng. 253 r/g. 255 Other proportions are Unwin gives r/g. 256 4 6 4 T = VsZ) + Vs" F/g. 257 The taper for keys may be from Vieth to ^/leths of an inch per foot of length. One eighth inch is often used. The key should MACHINE CONSTRUCTION 97 be half in the shaft and half in the hub. When the force to be transmitted is very large two keys may be used. In such cases they are generally placed 90° apart. The length of keys C J n F/g. e5e F/g. e:^9 r/g. ^eo should be one and one half or more times the diameter of the shaft. Fig. 256 shows the Lewis key, invented by Wilfred Lewis. The direction of rotation for the driving shaft is indicated. It will be noted that this form is wholly under compression. Fig. 255 is a different way of locating a square key. The side iS may be taken as one fourth the diameter of the shaft. Fig. 257 shows a round key. It is a desira- ble form when it can be used, as when located at the end of a shaft. Fig. 258 shows the ordinary plain key; Fig. 259, a key provided with a gib to make its removal easier. Fig. 260 shows a round end ^ 1 \ -h- rfg. ^e/ key which may be fitted into a shaft. Such keys are often used when it is desired to arrange for a part to slide on the shaft. When a long key is secured in a shaft and used for this purpose it is called a feather or feather key. Square end keys may be used in the same way. Fig. 261 shows the Woodruff Key, which con- sists of a part of a circular disc. They are made in a variety of sizes with dimensions suiting them to different purposes. The circular seating allows the key to assume the proper taper when a piece is put onto the shaft. CHAPTER XIII SKETCHING Uses of Sketching. — Freehand sketching is of particular importance in connection with drafting and will be briefly con- sidered in this chapter. All that has been said in the previous chapters concerning the theory and practice of drafting applies to freehand sketching. The term sketching must not be con- sidered as indicating incompleteness, for if anything a sketch must be more complete than a mechanically executed drawing. Sketching is the engineering language of the trained executive as well as a convenient and quick method of representation. Sketches are used to give information from which parts are to be made; they are used for repair parts; new parts; as an aid to reading drawings; as an aid to design; as a means of recording ideas, and for many other purposes. Accuracy of thought, observation, representation, and pro- portion are essential. The four '^P's" of sketching are practice, patience, proportion, and proficiency. Too much emphasis can- not be put upon the necessity of accuracy in proportion and detail. A most interesting example is shown in Fig. 262 which is a reproduction of a sketch for the first steam hammer as drawn by James Nasmith. Quoting from Nasmith's autobiography by Samuel Smiles: * ''I got out my 'scheme book,' on the pages of which I generally thought out, with the aid of pen and pencil, such mechanical adaptations as I had conceived in my mind, and was thereby enabled to render them visible. I then rapidly sketched out my steam hammer, having it all clearly before me in my mind's eye. In a little more than half an hour after re- ceiving Mr. Humphrie's letter, narrating his unlooked-for diffi- culty, I had the whole contrivance in all its executant details, before me in a page of my scheme book. The date of this first drawing was November 24, 1839." * Published by Harper and Bros., New York. 98 SKETCHING 99 Materials for Sketching. — The materials necessary for sketch- ing are a 2H drawing pencil, pencil eraser, art gum, and paper. Either plain or squared paper may be used, but it is better to use the plain paper at first so as not to be dependent upon the aid FiQ. 262. — First Drawing of Steam Hammer, November 24, 1839. which the squares give. The pencil should be kept well sharpened with a long round point. It is desirable to have a small board on which the paper may be tacked, or clip boards such as are used by bookkeepers will be found very convenient as a means of holding the paper. Every sketch should have a title, the date, and the name of the person who made it. 100 ESSENTIALS OF DRAFTING Making a Sketch. — To make a sketch the following order may be pm'sued. First examine the object, determine the num- ber of views necessary completely to define it, and observe the proportions. Then proceed to sketch very lightly, locating center lines and blocking in the limits for all views. Sketch in the details and then go over and brighten up wherever necessary in order to make all parts clear and definite. Straight lines may be drawn by making a succession of short straight lines or by F/g. 263 Fig. 2 6^ F/g.26S marking points and drawing from one point to another. Views should be blocked in completely with straight lines regardless of the number of curves and circle arcs. To sketch a circle draw center lines at right angles (Fig. 263), space off radii, as shown in Fig. 264, on the center lines and in between them. Another method is to block in a square made up of four smaller squares (Fig. 265), then sketch in one fourth of the required circle at a time. Taking Measurements. — There are a great many tools used for determining the sizes of machine parts and constructions. The names of some of the tools should be learned together with the methods of using them and the conditions under which they are used. For this purpose the reader is advised to secure a catalog of machinist's tools. Some of the tools used for various purposes are: The two foot rule for comparatively rough work. The standard steel rule for more accurate work. It should have both binary and decimal divisions. Steel tapes used for measuring rather long distances. Straight edge, used for extending surfaces. The square, used in a variety of forms; fixed, adjustable, com- bination. SKETCHING 101 Calipers, used for obtaining distances. There are many forms; outside, inside, spring, transfer. Surface plate and surface gage. Depth gage and hook gage or scale. Plurnb boh. Micrometer. Vernier caliper. Plug and ring gages. Wire and sheet metal gages. Screw thread gages. Radius gages. The surfaces to be measured are flat surfaces and curved sur- faces. These will appear in many combinations and will require separate consideration in each case. Cylinders may be measured directly with the calipers or scale. A steel tape may be used to measure the circum- ference of a large cyl- inder and the diameter calculated. Angular measurements are made with some form O D O /^/^. ^^e of protractor. The bevel pi'otractor and center square are useful for this purpose. The use of chalk or a marking solution is often necessary or convenient. Curved outlines may be obtained by offset measurements, by rubbing an outline on paper, or by making a template by such means as the conditions permit. Center distances may be found by measuring from the edge of one hole to the corresponding edge of the next hole as indicated in Fig. 266. The question of accuracy in taking measurements will arise frequently. The finished or machined parts should be measured as accurately as the means at hand will allow. Shafts or sliding blocks, or wherever a fit is involved, should* be measured with the micrometer or similar accurate means. Rough castings of small or medium size may be measured to the nearest Vieth inch, while larger ones may be near enough when measured to Vs or even \/4th inch. In all cases judgment must be exercised, and when- ever in doubt take measurements as closely as possible under the conditions. 102 ESSENTIALS OF DRAFTING Where the parts being sketched are for repairs or replacement, very accurate measurements are often required, and in the case of a fit allowance for wear must be made. If a whole new machine or construction is to be built much time can often be saved by- less accurate measurements, as the parts will be dimensioned to go together when the final drawing is made. Ingenuity and common sense are the primary requisites. In connection with measurements it will be necessary to know something of standard nomenclature. For instance, the three Cam Grooi^e - file. Chip or Scratch Not a/ike m^^^z^mMm. Note center punch rrrorAs Fig. 269 rig. 2(5 7 dimensions of a taper are indicated by a single number and a name. Some Ideas on Sketching. — The difficulties which are to be met and overcome when making sketches under trying circum- stances with limited time, inaccessability, with a machine in operation in close quarters, etc. — is little understood or appre- ciated by those accustomed to the conveniences of the drafting room. Many times sketches are made only for one's own use and so can perhaps be made a little less presentable than when made to take the place of a drawing. However, there is a warning which must be sounded, and that is the unvarying rule "to pre- serve definiteness under all circumstances." A sketch may be hastily made, but a careless sketch is worse than useless. Be sure that what is given is right and of certain meaning. The steps which must be followed in making a sketch are: SKETCHING 103 Drill 3 Lugs jEquQ /ly 3p a ced Sketch the parts. Put on diinension lines and notes. Measure the parts and fill in the figures. Some considerations to be kept in mind are : — Use part views to show special features or details. Use notes freely but not as a substitute for necessary views. Show hexagons, octagons, etc., across flats using a note to tell the number of sides or insert a revolved section. Note identification marks, and mark parts to facilitate putting them together and for fixing relative \\ V_i\ positions. Note finished surfaces and kinds of finish. Use templates whenever in doubt as to curves, loca- tion of drilling, etc. Note materials of which machine or parts are made. Measure sizes of holes as well as of bolts, shafts, etc. '^' A small amount of surface shading is often of value. Note the location of the machine in reference to other machines or to building features if such information has any possibility of being useful. Rods, bolts, bars, and long pieces of uniform section can gen- erally be shown in one view. Most machines and some parts of machines will carry the manufacturer's name and identification, sometimes stamped into the machine, and sometimes on a name plate. The information given in this manner should ahvays be noted in connection with the sketch. Sometimes parts are either right or left hand, and this fact should be noted. It is a good plan to examine all parts very carefully for identification marks. When parts bear a definite relation to one another, prick punch marks or a filed groove will often be of great assistance in re- 104 ESSENTIALS OF DRAFTING assembling (Figs. 267 and 268). Oftentimes the top or bottom of a part should be marked. Where a number of bolts are used with reamed holes they are often numbered or otherwise marked (both bolt holes and bolts, Fig. 269) . Very often part views may be used to save time by adding a note : For instance, a circular object with lugs, j ^ — I 4 ^^^ ~V as shown in Fig. 270. In the case of cyhndrical objects the word '' diameter" will often save a view. A washer in Fig. 271. Sections are rather freely It is ^^ TZ^ Fig. 27 1 would be sketched as used in sketching as they give prominence to the sketch, often desirable to make a separate outline sketch without dotted Unes in connection with a sectional drawing of a part, especially when the sketches must be hastily made, as the two sketches result in less confusion than when combined in one view. When sketches are made in connection with diagrams for the transmission of power, or a mechanism of any sort, the com- putations should be included with the sketch, and existing pulleys or other parts should be clearly dimensioned and indi- cated to distinguish them from proposed additions. In the case of foundations where bolts are to be located, differences in level Corbel Tb/r?p/at& of Corbe/ is U5efu/ to /ocafe F/g. 272 must be considered as well as center line distances. When locat- ing shaft hangers, or constructions to be fastened to a wall or ceiling, the surroundings such as parts of the permanent struc- ture, like beams or corbeling of the brick wall (Fig. 272), should be measured and sketched with the part to be installed. The principal point to be brought out in connec'ion with sketch- ing of any kind is to leave nothing to guess — to have too much rather than too little information, and to make every Une and note absolutely definite. CHAPTER XIV ESTIMATION OF WEIGHTS Accuracy. — It is often necessary to compute the weight of machine parts or of piles of materials; for instance, to estimate the amount of coal on hand. The annual stock taking of many companies requires much of this work which must be accom- plished accurately and expeditiously. Some of the methods used should be known together with the degree of accuracy required. For some purposes a result within 5 % or even 10 % may be suf- ficiently close, while in other cases an accurate result may be desirable, as when figuring a large number of pieces of expensive material. The weights of many standard parts are well known and are given in manufacturers' catalogs. The weights of steel shapes are known and tabulated in pounds per linear foot, the weight of bolts per 100, and similarly for other pieces. Weights of Materials. — The following weights are average values for various materials and may be used for ordinary cal- culations. Material Cast Iron . . . Wrought iron Steel Brass Copper Lead Aluminum . . . Granite Brick Concrete .... Water Spruce White pine . . Yellow pine . . Maple Lignum vitae Oak Pounds per Cubic Inch .26 .28 .29 .30 .32 .41 .036 Pounds per Cubic Foot 450 480 490 530 550 710 160 170 120 145 62.5 30 30 41 45 83 50 105 106 ESSENTIALS OF DRAFTING Weight of Loose Materials. — In estimating the amount of material in a pile, its shape may be approximated to one or more geometrical forms and its volume computed. This is best done by making a sketch with dimension lines which are filled in with measurements. Such sketches should be preserved for checking purposes and as a record. The weight per cubic foot or yard is then obtained by loading a car of measured volume and weighing it or by filling a box containing a cubic foot or yard and finding the net weight. The material should of course be disposed as /^ Thick Fig. ^73 near the density of the pile as possible. By careful judgment and some experience a very close approximation of weight may be obtained in this manner. For more accurate work, the surveyor's transit may be used. Weight of Castings. — The computation of the weight of cast- ings most frequently occurs either in connection with the cost or where a machine must come within certain limits of weight. The weight may be calculated from the drawings. For simple objects this is not difficult, but for many shapes much loss of time may be saved by systematic methods and proper division into elementary forms. Two sets of weights must be considered; one the object in the rough, and the other the finished piece. Allowances for finish must be made. It is necessary to know what holes or openings are to be cored and what ones are to be machined. Cylindrical pieces are readily figured by dividing ESTIMATION OF WEIGHTS 107 into separate cylinders. Limits as to weight are very important when machines must be assembled in out of the way places, or where transportation is by pack mules or other primitive means. Methods of Calculation. — The general method of finding the weight of a piece is to compute its total volume in cubic inches and then multiply this volume by the weight of a cubic inch of the material. Most pieces may be divided into flat plates, cylin- ders, and flanges, each of which should be lettered and tabulated. Sometimes fillets may be balanced against bolt holes or against rounded corners. In other cases the fillets may be considered as a certain per cent of the whole. The weight as figured should also be increased to allow for rapping the pattern in the mold. The allowance for finish may be ^1%' for general work but this varies with different classes of work and with the degree of accuracy required in the finished piece. When a piece has a uniform thickness but irregular outline it may be broken up into plane figures and the area of each found separately (Fig. 273). After adding them together multiply by the thickness to obtain the volume and then by the unit weight to find the total weight, as illustrated. The dash lines divide the flat surface into seven parts, each of which is lettered. These may be listed in tabular form. Designation Part Dimensions Inches Area Square Inches A Rectangle 4 xV4 3. B << IV4 X 1 1.75 C « 5V2 X IV4 6.875 D « 4V2 X 1 4.5 E Triangle V2(2V2 X 41/2) 5.625 F 1/4(86 - 28.27) 1.93 G Circle 74(3.1416) .785 Total area square inches . . . Volume = area x thickness = 24.47 X 1.25 = 30.59 cubic inches 24.465 The area of part G is one fourth the area of a circle having the radius indicated. The area of part F is found by subtracting one 108 ESSENTIALS OF DRAFTING fourth the area of a circle having the radius given from the area of a square, one side of which is equal to the radius of the arc. With irregular shapes the area is sometimes divided approxi- mately into regu- lar figures, the dimensions for which are ob- tained by apply- ing the scale to the drawing. This is illustrated in Fig. 274 where the dash line x-x is drawn so that the area B appears to be equal to the area A + A. The distance H is then measured and multiphed by L to find the area. In the case of hollow pieces, find the volume as though the piece was soHd, then subtract the volume of the spaces. /^/ff. 2Z^ ^0 f^ A C B Fig. 2 y5 In Fig. 275 the volume would be found as tabulated, in which the A and B are called plus (+) volumes and C is called a minus ( — ) volume. Designation Part Dimension Volume in Cubic Inches + - A Square prism 3 X 3 X 27-2 22.5 B Rectangular plate 5x6x1 30. C Cylinder 1 X 3.1416 x3 9.42 Totals 52.5 9.42 {A ^B) -C = Net volume 52.5 - 9.42 = 43 + cubic inches ESTIMATION OF WEIGHTS 109 For the ring shown in Fig. 276 find the area of the cross section A and multiply by the circumference of the mean diameter. This method is often a convenient one. Weight of Cylinder Head. — To find the approximate weight of the small cy Under head of Fig. 277 it may be divided into A' Mean Diamefer- Fig. S76 three cylinders, two positive and one negative. The round at X may be balanced against the fillet at y for approximation pur- poses. Allow say ^jx^Xh inch on each of the finished surfaces. The calculations will be as tabulated. Designation Part Dimensions Inches Volume Cubic Inches + - A B C Cylinder << 28.27 X ^^6 9.62 x^8 4.91 X Vs 15.90 3.61 1.84 Total 19.51 1.84 {A + B) - C = net volume 19.51 - 1.84 = 17.67 cu. in. Vol. X wt. per cu. in. = total weight 17.67 X .26 = 4.60 pounds no ESSENTIALS OF DRAFTING ""If =:-=r^ ^ I I I CM Weight of Plunger Barrel. — To approximate the weight of the pump barrel shown in Fig. 278. First divide it into parts as indicated in the figure. The plus volume treats it as a solid. The minus volume consists of the interior cylindrical spaces ESTIMATION OF WEIGHTS 111 H, G, F, and /. The calculations for its cost at ten cents per pound follow. For any other price multiply by the required cents per pound and divide by ten. Since both ends are alike only one half is figured and the result is then multiplied by two. Design tion A B C D E F G H Part Flange Stuff box Main cylinder Port flange Foot flange Cylinder Throat Stuff box Port Dimensions Inches 12 X 12 X IV4 ^^^^X3V. X 14V2 4 7r(6.5) 7 X 7 X IV4 4 x8 X IV4 7r(5)2 4 7r(4)2 4 7r(6)2 4 7r(3)2 X 14 XV4 x4 xlVi Total volumes Volume Cubic Inches + 180 154 481 G2 80 957 274 116 11 410 Multiplied by 2 for two ends 1914 820 1094 cu. in. net volume 1094 X .26 = 285, pounds weight 285 X .10 = $28.50, cost of casting at 10 cents per pound Weight of Forgings. — Steel and wrought iron shafts may be readily figured, especially when turned from stock bars or rods. Forgings, however, require careful consideration as the rough forging may weigh from 25 % to 50 % more than the finished piece, especially if the shape is at all complicated. CHAPTER XV PIPING Piping Materials. — Pipe made of various materials is used for conveying liquids and gases. For a complete treatment of the subject of piping and its uses, piping drawings, etc., see the author's ''Handbook on Piping," D. Van Nostrand Company, N. Y. The illustrations for this chapter are from the above book. Tee Cross £:/t>oi^ Y- Branch f?/ght ^ /v m JjrJ>'J''J(>i7J5 ^ 45 £/boyv J "2^ Reducing Coup/ing 3"R%LCoap//nff j'G/obe A^/«^9^ U-/?/a.-M Plane 4 -\- / \ \ L / \ \ > D/a. J Be sure to pass planes through the contour or outside elements of both cyUnders in order to obtain the extreme limits of the curve. This is very important, especially when the axes of the cylinders do not intersect. Choice of Cutting Planes. — Whenever possible planes should be passed so as to cut straight lines from both surfaces. The hues (not parallel) on the same plane intersect in points which are common to both surfaces and are therefore points in the curve of intersection. The intersection between surfaces can very often be found by horizontal cutting planes, as indicated INTERSECTIONS 121 in Fig. 293, which would be employed for the cases presented in Fig. 294 and similar conditions. Considering Fig. 293 it will be observed that horizontal cutting planes are used. Each plane cuts a straight line from the prism and a circle from the cone. r/g. ^95 as shown in the top view. Where the line and the circle cross is a point common to the prism and the cone. Other points found in the same way will complete the curve of intersection. Connecting Rod Intersection. — Fig. 295 shows a portion of a connecting rod of circular cross section with a rectangular end. 122 ESSENTIALS OF DRAFTING The circular section is increased where it joins the rectangular portion. The curves of intersection are found as described. Notice that the centers for the radii RiRi are in the same per- pendicular line. Di is the diameter of the rod. There are certain "critical points" and these will be mentioned first. Where i^i cuts the width of the rectangular part in the top view gives point a^ and this point will fall on the center line in the side view and so is projected to a^. In a similar manner point b^ may be pro- jected to the top view at point 6^. The end view is needed to obtain the other points. With as a center and the corner distance OC as a radius, draw the arc CCi. Continue the radius Ri in the side view. A horizontal line through Ci will intersect radius i^i at C2 from which C^ and C^ may be projected. The radius OC gives the largest circle which will touch the rectangular section and so determines one end of the curve, as shown. A plane passed through C^ or to left of point (T and perpendicular to the axis will give a rectangular section. A plane to the right of point C^ will give other sections which will be described. To determine the curve in top view. Two points b and c are already determined. For any other point d in end view, draw an arc ddi, with od as a radius. From di project horizontally to c?2 and then as shown to d^ in the top view. To determine the curve in the side view. Two points a and c are already determined. Take any point e in the end view and with a radius oe draw arc eei; project horizontally from ei to 62. The intersection of a vertical line through 62 with a horizontal line through e will give point e^, sl point on the desired curve. Point / and other points are found in the same manner. It will be observed that a plane through e and perpendicular to the axis would give the section indicated by section lines in the end view. CHAPTER XVII DEVELOPMENTS Surfaces. — Surfaces may be divided into two classes, plane surfaces and curved surfaces. Plane surfaces show in their true size and shape when they are parallel to one of the planes of projection, so that an object bounded by plane surfaces can have each of its faces brought into contact with a piece of paper, either by wrapping the paper about the object or placing the r/g. ^96 object on the paper and then turning it until each face has touched the paper. This is shown in Fig. 296 where the paper has been cut so it will exactly cover the object when it is folded about it. Such an outline is called a development. A curved surface does not show in its true size no matter how it is placed with regard to the planes of projection. Some kinds of curved surfaces can be developed by rolling them on a plane as illustrated in Fig. 297. The distance L is equal to the distance around the cylinder and the height R of course remains equal to the length of the cylinder. Other surfaces, such as the surface of a sphere, cannot be exactly developed, but there are approximate methods which are generally accurate enough. 123 124 ESSENTIALS OF DRAFTING Development of a Prism. — The prism of Fig. 296 is developed by laying out in a straight hne and in the proper order the distances 1-4, 4-3, 3-2, and 2-1, which added together are equal to the Fi 9^297 distance around the prism. At each of the points a line is drawn equal to the long edge of the prism and the ends joined together. Then the two ends of the prism are measured out as shown. The development of the lateral surface of a hexagonal prism is shown in Fig. 298. First lay off in a straight line and in proper order the edges 1-2, 2-3, etc., all the way around the prism as shown at the right. At points 1,2,3, etc., draw the perpendiculars equal in length to the edges of the prism, thus obtaining the true size and shape of each face of the prism and in such order that DEVELOPMENTS 125 they might be folded to the form of the prism. Note that a square prism intersects the hexagonal prism which has been cut along the curve of intersection. To find the cut-out on the de- 8 9/0 II 12 2 3^567 velopment draw the vertical hnes A, 5, and C on the faces of the hexagonal prism and locate them on the development by measur- ing their distances from the edges 2 and S. The points of inter- Fig- 300 section may then be located by drawing horizontal lines as shown or by measuring up or down the lines on the front view of the hexagonal prism and measuring the same distances on the same hnes of the development. The development of the top and 126 ESSENTIALS OF DRAFTING r/g. 30/ bottom of the prism may be obtained from the top view and added to the lateral surface. Development of a Cylinder. — The development of a cylinder was illustrated in Fig. 297. One half of a square elbow is de- veloped in Fig. 299. First divide the top view into a number of equal parts. Through each point draw an elemen of the cylinder. By taking the elements close enough together the arcs may be considered as straight lines. The problem is then the same as developing a prism with a large nima- ber of sides. Lay off the distances between the ele- ments along a straight line. At each point draw the element in its true length. Through the ends of the elements draw a smooth curve, very lightly free- hand, and then brighten it up using the irregular curve. The lengths of the elements may be conveniently found by drawing horizontal lines from the front view as illustrated. The develop- ment of the bases may be found by an auxiliary view and from the top view. Development of a Pyramid. — The development of a pyramid with a part cut away is shown in Fig. 300. Assume the pyramid to be complete. There are six equal faces, each one a triangle. The development consists in laying out all the faces in their true size and proper order. The short edges are shown in their true length in the top view as 1-2, 2-3, etc. The long edges are all of the same length and are equal to the distance 0^-1^ shown in the front view. Observe that 0^-1^ is horizontal in the top view. The faces may be constructed in their true size by drawing an arc, with Oi as a center and 0^1^ as a radius. Starting at li, space off the chords li-2i, 2i-3i, etc., equal to l'^-2'', 2^-S^, etc. Draw lines Oi li, Oi 2i, etc., representing edges of the pyramid. Construct the development of the base so that it may be folded into the proper position. Note carefully that the numbers on the base will match the numbers on the edges when the develop- ment is folded to form the pyramid. To show the part which DEVELOPMENTS 127 has been cut away measure the distance OiCi on the edge Oi4i equal to the distance O'^C'^. Measure distances oiBi and 3iAi on the development of the faces and of the base equal to the distances 6^B^ and 5" A^ obtained from the top view. Join points AiCi 128 ESSENTIALS OF DRAFTING and Bi on the development of the faces. On the development of the base construct the triangle AiBiCi obtaining distances BiCi and AiCi from the development of the faces. The com- pleted development is shown by the heavy lines. The Development of a Cone. — The development of a cone is shown in Fig. 301. Divide the base into a number of parts and draw elements of the cone. By taking the small arcs as straight lines the solution is the same as for a pyramid. The surface is thus considered to be divided into a number of equal triangles. This method is sufficiently accurate for most pur- poses. With the radius R draw an arc of a circle. On the arc space off the circumference of the base of the cone. The base need not be developed as it shows in its true size in the top view. Development of a Transition Piece. — A transition piece is shown in Fig. 302 connecting a circular pipe with a rectangular one. The development of such a piece should present no diffi- culties if the previous figures have been carefully studied. Com- paring the two views as given in Fig. 303 with the picture of Fig. 302, it will be seen that the transition piece may be ''broken up" into triangles and parts of cones. The triangles are ABl, BC5f CD9, and DAW, The parts of cones are the curved surfaces between the triangles. Consider the apex of one cone as located at B. Divide the portion of the base 1-5 into a number of parts and draw the elements B-1, B-2, B-3, B-4, and B-5. The triangles thus formed will approximate the surface of the cone. The lines AB, BC, etc. show in their true length in the top view. The true length of the elements may be found as follows: Con- sider a line to be dropped from point B perpendicular to the base of the cone. A line may then be drawn on the base of the cone from point 1 to the perpendicular line, thus forming a right triangle with the element B-1 as the hypotenuse. By constructing this right triangle in its true size the true length of B-1 may be found. This has been done in Diagram I. The length of the perpendicular line is shown at BX and is found by drawing the horizontal lines shown. The base of the triangle is equal to the length of the horizontal projection of B-1. Point 1 in Diagram I is found by making x-1 equal to B-1. In the same way find the lengths of the other elements by laying off x-2 equal to B-2 x-3 equal to B-3 DEVELOPMENTS 129 etc., obtained from the top view. Then draw B-2, B-3, etc. the true lengths of the elements which are used in the construc- tion described below. In the same manner construct Diagram II for the other cone. Having found all the true lengths proceed as follows: Construct the triangle ABl, in its true size. With 5 as a center and B2 as a radius, draw an arc. With i as a center and a radius equal to 1-2 obtained from the top view de- scribe another arc cutting the first arc. This will locate point 2. With B as a center and B-3 as a radius describe an arc. With ^ as a center and a radius equal to 2-3 obtained from the top view describe another arc, thus locating point 3. Proceed until the four triangles forming the conical surface are properly located, then draw a smooth curve through the points 1,2, 3, etc. Con- struct triangle CBo, using the element55 as a starting side. Then develop the conical surface having C as an apex and 6, 6, 7, 8, 9, as part of the base. Construct the triangle CD9 in its true size. Since the piece is symmetrical the remaining parts are the same as those already developed. All kinds of surfaces can be developed approximately by divid- ing them into triangles, then finding the true size of each triangle and arranging them in the proper relation to each other. CHAPTER XVIII PICTURE DRAWING Isometric Drawing. — By means of an isometric projection three faces of an object can be shown in a single view. This is possible by considering the object to be placed in the position of a cube standing on one corner and having another corner exactly F/ff. 304- F/g. SOS in the center of the view. In Fig. 304 the cube is resting upon point A in such a position that point B is located in the center of -1 -* — / — J\ *-2 ■*• i ^ 1 1 N^ \ F/g. 306 r/g.S07 the view obtained by projecting onto a vertical plane. The orthographic projection of this front view is shown in Fig. 305, which is called the isometric projection of a cube. In this view 130 PICTURE DRAWING 131 the line A 5 is vertical and the Unes BC and BD make angles of 30° with the horizontal. All the edges of the cube show equal to each other in length. This length however is shorter than /=~/^. 306 Fig. 309 on the actual cube. For drawing purposes the lines 51), 5(7, and BA^ etc. are made the same length as on the actual cube. The angles formed by the three lines which meet at point B are equal to 120° each. The three lines are called the isometric axes and form the basis for isometric drawing. rig. 3/0. Fig. 31/ Isometric and Non-isometric Lines. — All measurements for isometric drawings are taken along or parallel to the isometric axes. Lines parallel to the isometric axes are called isometric lines. All other lines are non-isometric lines and cannot be measured directly. To make an Isometric Drawing of the Object shown in Fig. 306. — Draw the isometric axes, BC, BA, and BD (Fig. 307). 132 ESSENTIALS OF DRAFTING From B measure V/i' toward D, 1" toward C, and "^/s' toward A. From the points thus located draw lines parallel to the isometric axes and lay off distances corresponding to the figures given in /^/g. 3/ a Fig. 306. Note that lines which are parallel in Fig. 306 are parallel in Fig. 307. To make an Isometric Drawing of the Object shown in Fig. 308. — Draw the isometric axes (Fig. 309) as in the preceding case. Locate the point F by measuring along BC. Locate point ^ by measuring along BC and then down parallel to BA T T Ffg. S/3 Fig. 3/^ as indicated in the figure. Join F and E. Line FE is a non- isometric line. In Fig. 310 point E is located as before. Point T is located by measuring along BC to point & and then parallel to line BD. It is often convenient to think of the object as being placed in a box. This box can be put into isometric and the points in which the object touches it located. Other points can be located by taking measurements parallel to the axes. Angles. — Angles do not show in their true size in isometric drawings. This is evident from an inspection of Fig. 305 where PICTURE DRAWING 133 the angle at B is 120° and that at C is 60° although on the cube they are both 90°. The method of constructing for angles is shown in Fig. 31 L First make the orthographic projection, then transfer by taking distances parallel to the axes, as/^ and L. Fig. S/S Positions of the Axes. — The axes may be placed in any posi- tion provided the angles between them are kept equal to 120° as illustrated in Fig. 312. Construction for Circles. — When circles occur they appear as elhpses and may be drawn by plotting points from the ortho- graphic projection as in Fig. 313 or by the more usual approxima- tion shown in Fig. 314, where the hues are drawn perpendicular to the points of tangency of the circumscribing square. The 134 ESSENTIALS OF DRAFTING intersections of these perpendiculars locate the centers for circular arcs which will approximate the eUipse sufficiently close for most purposes. In the figure TiTiT^T^, = tangent points Ci = center for arc T1T2 and TzT\ CiTi = radius for arc T1T2 and T3T4 C2 = center for arc T1T4 and T2T3 C2T1 = radius for arc TiT^ and T2T3 Oblique Projection Or/hograph/c Project/on VL. F/g. 3/e The same construction is used for arcs of circles as shown in Fig. 315. The interior of objects may be shown by means of isometric sectional views, Fig. 316 and Fig. 317, which are constructed by Fig. 3/9 the methods already described for exterior views. As shown, the sectioned surfaces are taken on isometric planes. PICTURE DRAWING 135 Oblique Drawing. — Another method of picture drawing often useful is obhque drawing or projection, in which the view is obtained by using projection lines oblique to the plane upon which the object is to be represented. In Fig. 318 the orthographic projection of a cube is shown and, on the same plane, the oblique projection of the same cube. The three hues which meet at point B are called oblique axes. Lines BC and AB are always at right angles but the line BD may make any convenient angle /="/^. 320 with the horizontal. It follows that if one face of an object is parallel to the vertical plane, it will show in its true size and shape. After locating the axes the methods of construction given for isometric drawing apply to the making of oblique drawings. Many examples of oblique drawing are given throughout this book. The axes may be located in a variety of ways as shown in Fig. 319. The appearance of an object can often be imprgved by reducing the measurements along the oblique axis, using one half or three fourths of the full dimension. Measurements on the two per- pendicular axes remain unchanged. Two such treatments of a cube are shown in Fig. 320. Such views are called cabinet projection. CHAPTER XIX SHADE LINE DRAWINGS Shade Lines. — The use of shade hnes is a much discussed question. Each drawing has a purpose and if that purpose is better served by the use of shade hnes they should be employed. In many lines of work detail drawings are never shaded and this seems to be the best practice. Outline drawings or assembly drawings which serve partly, at least, as picture drawings are often improved by shading. 136 SHADE LINE DRAWINGS 137 System in Common Use. — In the United States a conven- tional system of shading is generally employed, in which the rays of light are assumed to be parallel, to come from the upper Q z ^- M /^/p'. :^^s ^/ff 324 /='/g. 325 rig 326 rig. 32 7 rig 32a /^/>. s^9 r/g. 330 Fig. 331 r/g. 3S2 and left hand corner of the sheet at an angle of 45°, and to he in the plane of the paper. The lower and right hand edges where the light passes over them are made heavy Hues called shade lines. When two surfaces are in the same plane the line of division between them is not shaded, Fig. 321. Circles follow the same 138 ESSENTIALS OF DRAFTING rules as shown, where A is a hole and 5 is a solid cylinder. In all cases the extra thickness of line is without the surface which rig. 335 it bounds (C, Fig. 321). Most all conditions of shading are illustrated in the figures given in this chapter, which should be carefully studied. SHADE LINE DRAWINGS 139 Surface Shading. — Various methods of hne shading on surfaces are used to show the shape of machine parts. Personal judgment is an important element in the matter of successful surface shad- ing. Fig. 322 shows a cylinder shaded by using fine lines and varying the distances between them. These change approxi- mately as the projections of equally spaced elements of a cyhnder. Fig. 336 Another method is to space the shade lines about equally but to vary the width of the lines as in Fig. 323. The air chambers (Figs. 324 to 328) show a number of different ways of shading conical, spherical, and cylindrical surfaces. As shown, either fine lines near together or varying lines may be used with any of the methods illustrated. Shading Screw Threads and Gears. — On elaborate drawings # r/g.337 F/g. 33S it is sometimes desirable to shade screw threads. Five ways are shown in Figs. 329 to 332. When gears are to be shown without drawing in the teeth the exterior is frequently represented by alternating heavy and fine lines as in Figs. 333 and 334 which show a pair of bevel gears and a pair of spur gears. The rest of the drawing may or may not be shaded. A pair of bevel gears are shown in section in Fig. 335. Special Surface Representations. — Other surfaces may be represented as in Figs. 336 to 338. Three ways of indicating a knurled surface are given in Fig. 336. For a scraped surface Fig. 337 may be used, and for a polished surface. Fig. 338. Patent Office Drawing. — Probably the most general use of shaded drawings is for Patent Office work. Such drawings must 140 ESSENTIALS OF DRAFTING be made on pure white paper of a thickness equal to two or three ply Bristol board, using black ink. The outside dimensions of the sheet are 10 by 15 inches. Inside of this is a one inch margin. At the top of each sheet a clear space of one and one quarter inches must be left for a title which is printed in by the Patent Fig. 339 Office. Fig. 339 shows the layout of a patent drawing. The fewest number of lines should be used; all dimension and center lines should be left off. The plane upon which a section is taken should be indicated. All parts are lettered or numbered. As these drawings are reproduced by the photo zinc process, all lines must be absolutely black and not too fine. If lines are too close together they will run together when printed. The '' Rules of Practice " of the United States Patent Office may be had for the asking and should be consulted by those interested. CHAPTER XX DRAWING QUESTIONS, PROBLEMS, AND STUDIES Most of the drawing studies included in this chapter can be worked in an 11'' X 14'' space or in a division of the space as indicated in Figs. 340 to 343. The layout with dimensions for a regular size sheet is shown in Fig. 340. In some cases a large scale may be advisable in which case the full sheet may be used. An inspection of the problem will indicate the proper space where it is not given in connection with the problem. The order in (3 TACK *^l '"-* '-h^ ' -C / ■^ L .1 . / *-/^-* ^ 1 "-t / -7 " < /-;»■ a * // -^ 1 1 yvoRHiNG space: " ^ ^ 1 ^ 1 ^ ^ E f \ ' 1 =4 - \ which the problems are given can be varied to suit the needs of the class. The question of inking is left for the instructor to de- cide. The author advises that it be delayed until the student has attained considerable proficiency in making pencil drawings. A variety of problems is included to allow a selection to be made and so that the course may be varied from year to year. A number of answers to questions should be neatly written or 141 • 142 ESSENTIALS OF DRAFTING lettered and numerical problems should be carefully worked out to create a coordination between drawing and other subjects, as well as to impress the student with the fact that the mere drawing of lines is not the aim of a drawing course. It is thought 1 7'-^//" - 1 1 ^i"^7" - (■^pprox) r/g 3-^/ Fig. 3^2 /^'9- 34-3 that such problems may create an interest and stir the student with the ambition to seek an engineering education. 1. Describe the proper use of the T square. 2. Show by a sketch the proper method of sharpening a lead pencil. 3. How are horizontal lines drawn? 4. How are vertical lines drawn? 5. Show by sketches the proper adjustment of the pen, pencil, and needle points for a compass. 6. Draw a straight line. Draw short lines crossing this line, and 2^/\q" apart. Draw another short line crossing the original line, and V/i&" from the last line drawn. From this lay off further distances of V /%" and '^^/\&". Add the four distances and check the total length by scaling the line. In measuring a line, place the zero of the scale opposite one end of the line and read the scale opposite the other end of the line. 7. Draw a straight line. Set the dividers at ^/i%" and step off 10 spaces. Scale the distance thus found and check with the calculated length. 8. What is the purpose of the knee joints in the compasses? 9. Examine a drawing material catalog and list five tools in addition to those which you already have, that you would consider convenient for your work. 10. What kinds of pens are used for freehand lettering? 11. What kind of ink is used? 12. What is the slope for slant letters? 13. In what direction should the pen point? 14. How is the amount of ink on the pen regulated? QUESTIONS, PROBLEMS, AND STUDIES 143 15. What hardness of pencil should be used for lettering'' 16. How is the distance between letters regulated? 17. 11" X 14" space. Starting V2" from top border line draw horizontal guide lines ^/s" apart. Use very light pencil lines. Make each capital letter of Fig. 15 or 16 five times. Re- peat the letters which cause most trouble. Use 2 H pencil. 18. 5V2'' X 1" space. Starting V2'' from top border line draw horizontal guide lines Vs'' apart. Make each of the lower case letters of Fig. 15 or 16 five times. Height of letters a, c, e, etc. to be ^/i'. Height of letter 6, k, etc. to be ^/s". Use 2 H pencil. 19. 5V2'' X 7" space. Same as problem 18, but use ball pointed pen. 20. 5V2'' X 7" space. Starting V2'' from top border Une draw horizontal guide lines ^/^" apart. Make each capital letter of Fig. 15 or 16 five times. Use 2H pencil. 21. 5V2'' X 7" space. Same as problem 20, but use ball pointed pen. 22. 5V2'' X 7" space. Starting V2" from top of space draw horizontal guide lines Vs'' apart. Letter the following words, using Si 2H pencil: hill, late, lathe, bolt, quench, wrench, EQUIPMENT, TOOLS, CALIPERS 23. 5V 2'' X 7 space. Same as problem 22, but using pen and ink as directed. 24. 5V2'' X 7" space. Draw horizontal guide lines near the middle of the space for letters having ^/s' caps. Letter the following, using a 2 H pencil. Use caps and lower case of Fig. 15 or 16. "Drawing is the education of the eye, it is more interesting than words. It is the graphic language." "Mechanical drawing is the alphabet of the engineer; with- out this the workman is merely a hand, with it he indicates the possession of a head." 25. Prepare a title and material list for the step bearing shown in Fig. 175. 26. Same as problem 24, but using pen and ink as directed by the instructor. 27. Name and illustrate three kinds of triangles. 28. Name and illustrate three kinds of quadrilaterals. 29. What is a right angle? 144 I ESSENTIALS OF DRAFTING 30. In order that the sills of a house may be square 6 feet has been measured off along one sill and 8 feet along the other. Nails are driven as in Fig. 344 at these points. What will be the dis- tance AC measured along a steel tape when the angle ABC is a right angle? 31. A circle has a diameter of 2 inches. What is its circum- ference? Compare this distance with the sum of the sides of an inscribed hexagon. 32. What is an elhpse? 33. Can a true ellipse be drawn with circular arcs? /=-/g.^^^ 34. Space 478^' wide, h^W high. Draw a hne 2^716" long and bisect it. See Fig. 32. 35. Space as for problem 34. Draw an angle and bisect it. See Fig. 33. 36. Space as for problem 34. Draw a line 2^716'' long and divide it into five equal parts, by method of Fig. 34. 37. Space as for problem 34. Same as problem 36, but use method of Fig. 35. 38. Space as for problem 34. Draw any angle and construct another angle equal to it. See Fig. 36. 39. Space as for problem 34. Construct a triangle, having sides as follows: 278^'; 378^; and 2". See Fig. 37. 40. Space as for problem 34. Construct an equilateral tri- angle, one side 27i6" long. See Fig. 38. QUESTIONS, PROBLEMS, AND STUDIES 145 41. Space as for problem 34. Draw an isosceles triangle having a base of T j^' . Sides make 75° with the base. See Fig. 28. 42. Space as for problem 34. Draw a right triangle. Hy- potenuse 3V2'' long. One angle is 30°. 43. Space as for problem 34. Mark three points (+) not in a straight hne, and draw a circle passing through them. See Fig. 42. 44. Space as for problem 34. Draw an arc of a circle. Radius 2'', with center V2'' from upper and left hand edges of space. Make the angle AOB (Fig. 43) equal to 45°. Find length of the arc. Use first method of Fig. 43. 45. Space as for problem 34. Same as problem 44, but use second method of Fig. 43. 46. Space as for problem 34. Draw a circle 2^1^' diameter. Draw a tangent at any point on the circumference. See Fig. 44. 47. Space as for problem 34. Draw an arc with a radius of V-U'. Draw a straight line intersecting this arc. Draw an arc tangent to the arc and straight Hne just drawn, radius ^/s". See Fig. 45. 48. Space as for problem 34. Draw a hexagon in a circle having a diameter of 2'^ 1^' . See Fig. 39. 49. Space as for problem 34. Draw a hexagon having a measurement across flats (Fig. 39) of 2V4''. 50. Space as for problem 34. Draw a regular octagon inside of a Z^l^' square, See Fig. 40. 51. Space as for problem 34. Draw a regular octagon inside of a 31/8'' circle. 52. Space as for problem 34. Draw a right triangle having a hypotenuse Z" long, and one side 2" long. Draw a circle pass- ing through the points of the triangle. 53. Space as for problem 34. Draw a line Z^!%' long and divide it into parts proportional to 2, 3, and 5. Use a method similar to Fig. 35. 54. Space as for problem 34. Use 30° x 60° triangle and T square to draw a regular hexagon measuring ?P l\^' across corners. 55. Space as for problem 34. Using the 45° triangle and T square draw a regular octagon that will just contain a circle SVie'' diameter. 146 ESSENTIALS OF DRAFTING 56. Space 5V2'' X 1". Draw an ellipse by concentric circle method (Fig. 49). Major axis b" . Minor axis 2". Find 24 points. 57. Space b'^/2" X 1". Draw an ellipse by trammel method (Fig. 50). Major axis b^^". Minor axis 2^/s". 58. Space b'^/i" x 1". Draw a figm^e having the appearance of an ellipse by circular arcs, Fig. 51. AB == h" , CD = 2^/^". 59. Space 5^/2" X 7'^ Draw a ^/a" square in the center of the space. Draw an involute of this square. 60. Space 5^/2' X 7". Draw a semi-circle having its center V4'' from the left edge of the space and 3V4'' down from the top /=~/^. 3^S ri'g. S^z F'/g. S^a of the space. Radius of circle P/4''. Draw the involute of the semi-circle. See Fig. 53. 61. Space b'^/2" X 1". Draw a parabola, Fig. 54. Distance AF = "^/s". Directrix perpendicular. 62. Space 5V2" X 7'\ Draw a parabola, Fig. 54. Directrix horizontal. Distance AF = ^U'. 63. Space 5V2'' X 7". Draw an equilateral hyperbola, Fig. 56. Point P is \" from line OG and 2\U' from OR. Make distances PA^ AB, etc. V4''. 64. Space 5V2" X 7". Draw the two views given and the side view of the prism. Fig. 345. QUESTIONS, PROBLEMS, AND STUDIES 147 65. Space 5V2" X 1". Draw the two views given and the top view of Fig. 346. 1 -^ TT L 3 -a 1 • [*■■/ oZ .^ . /' .1 1 "5 T 'a \ VIEW Fig. 3^0 1 ! 1 yiEVi/ 1 , 1 _i v-li--\ t — // — 1 J" 1 1 1 > 1 / \^^ ^/^r. ^^/ /^/5^. 35a 66. Space 5V2" X 1" . Draw the two views given and the top view of Fig. 347. 67. Space 5V2" X 7''. Draw the top, front, and side views of a regular hexagonal prism, Fig. 348. Corners of hex 2V2''. Height of prism V2''. 68. Space 5V2'' X T' . Draw three views of the object shown in Fig. 349. 69. Space 5 V2" X 1" . Draw three views of the object shown in Fig. 350. 70. Space 5V2'' X T' . Draw three views of the object shown in Fig. 351. 71. Space 5V2'' X V . Draw three views of the object shown in Fig. 352. 72. Space 5V2" X 7". Draw three views of the object shown in Fig. 353. Fig. 353 148 ESSENTIALS OF DRAFTING -*J^|^ r/g.3S^ r/g. SSS y/£w —si y A ■ i -IM n'g. 3S6 fig. 357 VIEW r/g.sse rig. 3S9 A y/r^ F/g. 360 y'EiV r\ 1 7 i. ' ^•^ ; 1 F/g. 36/ QUESTIONS, PROBLEMS, AND STUDIES 149 73. Space 5V2" X 1". Draw three views of the object shown in Fig. 354. 74. Space b'^/2" X 7". Draw three views of the object shown in Fig. 355. 75. Space 5V2'' X 1". Draw three views of the object shown in Fig. 356. 76. Space b'/^" X 1". Draw three views of the object shown in Fig. 357. 77. Space b^^" X 1". Draw three views of the object shown /^fg- 363 in Fig. 358. 78. Space 5V2" X 7''. Draw three views of the object shown in Fig. 359. Fig. 363 Fig. 36^ 79. Space 5V2" X 1" . Draw three views of the object shown in Fig. 360. 80. Space 5V2'' X 7''. Draw three views of the object shown in Fig. 361. 150 ESSENTIALS OF DRAFTING '^- '^- - Draw object Draw object Draw object Draw object 81. Space5V2''x three views of the shown in Fig. 362. 82. Space 57/' X 7' three views of the shown in Fig. 363. 83. Space 51/2'' X 7^ three views of the shown in Fig. 364. 84. Space 51/2'' X 7". three views of the shown in Fig. 365. The drawing of objects in other than their natural posi- tions furnishes excellent prac- tice in the study of projections. It is a useful test of one's knowledge of the theor}^ of drawing, and every student should have some experience with such problems. The method of solution for such problems calls for the loca- tion of each point in its three views and particular attention to relations of the lines. Three views of a hopper are shown in Fig. 366. When the bopper is revolved to 30° about shaft A A, the front view will QUESTIONS, PROBLEMS, AND STUDIES 151 show as in Fig. 367. The top view is obtained by projecting horizontally from the top view of Fig. 366 and vertically from the front view of Fig. 367. The front view of Fig. 367 is changed only in the position of the hopper. In the top view the distances parallel to the shaft A A have not been changed, as the revolu- tion has been about this axis. The side view of Fig. 367 is then obtained in the usual manner from the top and front views. With the apparatus in the position of Fig. 367, it may be re- volved about the shaft BB forward or backward. In this case f^/'g.369 r/'g. 370 -TT- ng.37/ rig. 372 the side view of Fig. 367 will be unchanged except for its position as shown in Fig. 368. After drawing the side view the front view may be drawn by projecting across from the side view and down from the front and top views of Fig. 367. This is possible because the horizontal distances in the front view are parallel to the shaft or axis of revolution. The top view is obtained from the other two views in the usual way. 85. Space 5V2'' X T' . Draw three views of the hexagonal pyramid in the position shown in Fig. 369. 86. Space 5V2" X 1" . Draw three views of the pyramid of Problem 85 after it has been revolved as shown in Fig. 370. 87. Space 5V2'' X 1" . Draw three views of the rectangular prism in the position shown in Fig. 371. 152 ESSENTIALS OF DRAFTING 88. Space h^/^' X 1" . Draw three views of the rectangular prism after it has been revolved from the position of Fig. 371 about a vertical axis. Top view is shown in Fig. 372. 89. Space 5V2'' X 1" . Draw three views and a complete auxihary view of the square prism shown in Fig. 373, after it has been cut by plane A- A and the part above the plane removed. 90. Space 5V2'' X 1" . Draw two views and a complete auxiliary view of the hexagonal prism shown in Fig. 374, after it has been cut by plane A- A. < f}^'i^ Fig. 373 -//- Fig. 374 Fig. 3 75 Fig. 376 91. Space h^l 2' X 7". Draw the two views given and a complete auxihary view, Fig. 375. 92. Space 5V2" X 7'\ Draw the two views given and a com- plete auxiliary view, Fig. 376. 93. Space 5V2'' X 7". Draw a complete auxihary view. Fig. 377. 94. Space 5V2'' X 1" . Draw a complete auxiliary view. Fig. 378. 95. Space 11" x 14''. Draw the two views shown and an auxihary view of the foot pedal shown in Fig. 379. 96. Space 11" x 14". Complete the views and draw an aux- iliary view of the molding, Fig. 380. 97. Why are sectional views used? 98. What is the relation of a sectional view to the other views? QUESTIONS, PROBLEMS AND STUDIES 153 99. Space 5V2'' X 1". Draw a sectional view of Fig. 381 on a plane through the axis. 100. Space 5V2'' X 1". Draw a sectional view of Fig. 382 on a plane through the axis. 154 ESSENTIALS OF DRAFTING End y/e^v >W— ^ — \ ^ Complete Front Vie^ Here ■ICM Fig. 360 101. Space 6V2'' X 1". Draw a sectional view of Fig. 383 on a plane through the axis. 102. Space 5V2'' x 7". Draw three views of Fig. 381, chang- ing the proper view to a section on plane A- A. 103. Space hy^' x 1" . Draw two views of Fig. 385, chang- ing the proper view to a section on plane A-A. QUESTIONS, PROBLEMS, AND STUDIES 155 I "II* — /i- Hg. 361 <^ > t '4 1 Fig. 362 A- T :-i- T _L Ffg. 363 ^3 -* '-4 1 .1 1 7 1 ■ 1 'C e I' 1 1 < r <9 i 1 Fig. 3ea /— » 'P' -i- /^/g)- 365 ^t. 1 A r— ' fe 1 1 1 _ 1 '^i* 1 •^i-^ 1 /^/•g*'. J'6'<5 >.Vi '3 A 1 Fig. 387 1 1 III' ^_L 1 i_J__, 1 ' 1 1 1 1 1 1 1 1 , L 1_J 1 1 -- 1 1 -~1 1 1 104. Space 5V2'' X 1" . Draw three views of Fig. 386, chang- ing the proper view to a section on plane A- A. 105. Space 5V2'' X 1" . Draw three views of Fig. 387, chang- ing the proper view to a section on plane A- A. 106. Space \\" x 14''. Draw three views of the sHde valve. Fig. 388. The missing view to be a section on plane A- A. 107. Draw three views of the shackle, Fig. 186. 156 ESSENTIALS OF DRAFTING >' " "%. i" 1 1 /■ i A 1 '^ -Tr 1 1 1 1 ^ 1 1 ?' 1 ^1 ^vii^ i ' . -r •» 6J — >■ l^/^vw A r/g. 366 108. Space 11'' X 14''. Draw a plan view and a sectional ele- vation for the elliptical cover plate shown in Fig. 389. Out- side dimensions 7" X 9". Six ^Vie inch holes for bolts. The rise in the center is elliptical in plan. The bolts are to be spaced equal distances apart. Draw full size. 109. 11" X 14" space. Draw two views of the crank shown in Fig. 390. This drawing is excellent as an inking or tracing exercise. rig. 369 «J /^iffa/fr /^ ^. Fig. 390 QUESTIONS, PROBLEMS, AND STUDIES 157 110. Compare briefly wrought iron and cast iron. 111. What is cast iron? Name some of its properties. Com- pare its strength in tension and compression. 112. What is wrought iron? How is it made? Name some of its properties. 113. What is steel? How is it made? Name some of its properties. 114. What material is used for bolts and nuts? 115. How is malleable iron made and what is it used for? 116. Of what material would you make the following and why? a. Steam Engine Cylinder. b. Water Pump Plunger. c. Piston-rod. d. Comphcated form of Lever. e. Shaft. 117. What is meant by unit stress? Axial stress? Compres- sion? Tension? Shear? 118. A tie-bar has a diameter of ''/s' and supports a load of 8000 pounds. What is the unit stress? 119. What load will a rectangular tension member measuring ^/s' X I" carry safely if it is made of wrought iron? (Live load.) 120. A hollow cast iron cylinder has diameters of 4'' and 3''. What safe compressive load will it carry if the load is steady? 121. Compute the number of ^/i" bolts for a cylinder head 15'' effective diameter. Steam pressure is 150 pounds per square inch. Allowable working stress on bolts is 5000 pounds per square inch. The effective root area of a ^/^^ bolt is .302 square inches. 122. A wrought iron bolt V/2' diameter has a head V/a" long. Its effective diameter is 1.284. When a tension of 14000 pounds is applied to the bolt, find the unit stress. 123. What are some of the uses of screw threads? 124. What advantage has the acme thread over the square thread? 125. A triple threaded screw has a pitch of Vs inch. How many turns must it make to move a nut 6 inches? 126. Express the following in terms of the diameter of the bolt; distance across flats of hex, thickness 0/ bolt head, and thickness of nut. 158 ESSENTIALS OF DRAFTING 127. In what way does a bolt head differ from a nut? 128. Draw a 1" hex nut across flats and a 1" square nut across corners. Compare them. 129. Space 5V2'' X 1". Draw one turn each of two heUces as started in Fig. 391. 130. Space 5V2" X 1". Draw the exterior of a square threaded screw 3" long which enters V into the section of a square threaded nut. Pitch v. Other dimensions as in Fig. 392. r/g.39i PJTCH I" 3 ^ vmy//yy//A VT^ F-ig.392 V//////////A T Y'^ '\ I I "1 lU[ ^1 I BCD r/g. 393 131. Space 5V^2'' X 1" . Draw four forms of screw threads in section as directed by the instructor. \" pitch. Fig. 393. 132. Space 5V2'' X T' . Fig. 394. At ^, B, and C, draw three different plan views of threaded holes. At D and E draw two different representations of threaded holes in elevation. At F draw a threaded hole in section. At G, E, and /, draw three conventional representations of threaded bolt ends. Diam- eter for all representations to be 1 inch. 133. Space 5V2" X T' . On axis A-B, Fig. 395, draw a ^W through bolt, hex head across corners and hex nut across flats. On axis C-T) draw a V-,!^' bolt, hex head across flats and hex nut across corners. Indicate required dimensions. 134. Space 5V2" X 1" . On axis A-B, Fig. 396, draw a "^ W bolt, square head across corners and square nut across flats. QUESTIONS, PROBLEMS, AND STUDIES 159 On axis C-D draw a Vs" cap screw, head across flats. On axis E-F draw a Vs'' cap screw, head across corners. 135. Space b'^/2" X 7''. Draw the two views of collar and ^ l-n ^ r/g. 395 A -//- ■/J- Tc — 1^- /^ig- 396 F shaft, Fig. 397. On axis A-B draw a ^1%' set screw, head across flats. On axis C-D draw same set screw, head across corners. 136. Space 5V2'' X 7". Draw the gland and stuffing box of Fig. 398. On axis A-B draw a V2" stud and nut. Show nut across flats. Make provision for the gland to enter one half the depth of the stuffing box when nut is screwed onto stud. Show required dimensions. 137. Draw a plan and sec- tion for a double riveted lap joint as directed by the in- structor. 138. Make a scale drawing of two plates joined together at right angles. 139. Space 5V2'' X 7''. Draw sections on planes X and Y and a development of the riveted joint of Fig. 399. See Chapter VIII. Vie'' plates; ^Vie'' rivets; pitch 1^U^'\ lap IV2"; scale Z" = 1 foot. 140. How many views should a drawing contain? Fig. 399 160 ESSENTIALS OF DRAFTING 141. What scales are in general use for working drawings? 142. What are the first lines inked on a working drawing? 143. Is true projection always used? Explain. 144. Sketch and describe one form of stuffing box. 145. Space 11'' X 14''. Make a working drawing showing three views of the slide valve shown in Fig. 400. One view may be a sec- tion. Completely dimension. 146. Space 11" X 14". Make a working drawing of the bearing cap of Fig. 401. Show three views. ^ ^^^ Completely dimension. One view Fig. ^00 1 4.- a 1 may be a section. Supply any missing dimensions. See Chapter XV for size of ^1^' pipe. rig, 40I QUESTIONS, PROBLEMS, AND STUDIES 161 6^ Centers 147. Make detail working drawings for the parts of the eccen- tric shown in Fig. 402. Supply any missing dimensions. Draw- ing should include a properly dimensioned bolt and set screw. Completely dimension the drawing. 148. Make detail working drawings for the parts of the step bearing shown in Fig. 175. Scale 6" = 1 foot. Use two sheets, 11'' X 14'' space. Completely dimension. 162 ESSENTIALS OF DRAFTING 149. Draw two views of Fig. 403. Each view should show true distances. Completely dimension. Submit a preliminary sketch to the instructor. 150. Make a working drawing for the piece shown in Fig. 404. Submit a preliminary sketch to the instructor. F'i'g, 4oa 151. Space h^l^' X 7''. Make a detail working drawing of the construction shown in Fig. 405, using one full view and such parts of other views as are necessary to define its true shape. rig. ^05 152. Space 5V2'' X 1" . Make a working drawing of the sleeve, Fig. 406. One half view to be in section. 153. Make a working drawing of the valve shown in Fig. 407. Show a proper treatment for a section on plane ABC. 154. Draw a sectional view of Fig. 408. 155. Make a detail drawing of the valve body of Fig. 409. One view in section. 156. Make an assembly drawing of the 2" check valv^shown in Fig. 409. Draw a sectional elevation and an exterior end view. This drawing may or may not be dimensioned. QUESTIONS, PROBLEMS, AND STUDIES 163 157. The filling-in piece, Fig. 410, is shown one half size. Scale the iSgure, draw full size, and completely dimension. 158. The guide, Fig. 411, is shown one half size. Scale the figure, draw full size, and completely dimension. n'g.^07 Scale the Draw 159. The bracket. Fig. 412, is shown one half size, figure, draw full size, and completely dimension. 160. The flywheel. Fig. 413, is shown one fourth size. to a scale of 6" = 1 foot, and completely dimension. 161. The bearing, Fig. 414, is shown one half size. Scale the figure, draw full size, complete the views, and completely dimension. 162. Draw a half end view and a sectional elevation of the pump centerpiece. Fig. 415. Choose a proper scale and completely dimen- sion. 163. Space 5V2" X 1". Draw two views of the lever shown in Fig. 416. Both views are to show the true size of the lever. 164. Make detail drawings of each part of the screw stuffing box of Fig. 417. Note that dotted sectioning is used here to indicate the separate pieces. This method is sometimes used to show the exterior and section in the same view. 165. Make an assembly working drawing of the steam jacketed kettle shown in Fig. 418. Draw a half top view and a sectional i /fo/es F/g. ^06 164 ESSENTIALS OF DRAFTING QUESTIONS, PROBLEMS, AND STUDIES 165 -f-^ 1 — r ^s rig. eom Pipt 'i *1^ /l_ Tap for/ sfu^) -($'- •%------- f.. t? ,ff>. 3: ■4i I < L iJEZ^jEhd j|^^ ._a,| -^ ^\—^^-A Tap for g afif^s >>>>>>' •^> 777^7777. —-"-I'M L_: 5i- ^^ 1 Fig. ^2/ t Cap ca — r /^/^. ^22 190. Space 5V2'' X 7''. Find the line of intersection between the cone and hexagonal prism of Fig. 427. 191. Space h^W X 1". Find the Hne of intersection between the sphere and hexagonal prism of Fig. 428. QUESTIONS, PROBLEMS, AND STUDIES 171 ^ -^4- 3' *i "J^ /=-/g.^23^. "^ ^—2i- ■^i "7' JJ ■^^<* rig.'^SS ^ dJ_JL I I Fig.^27 f^ig. ^26 172 ESSENTIALS OF DRAFTING { / A ^5i^ t JJ \ A 1 / ^ / / A J 1 Spr/nff Co/fTcr Pin ^/J^^ H F'/g. a30 192. Find the line of intersection between the cone and cyKnder of Fig. 429. 193. Make a working drawing of the joint shown in Fig. 430. Find curves accurately. 194. Make a drawing for a connecting rod end (Fig. 295) with dimensions as follows. Instructor will assign dimensions. QUESTIONS, PROBLEMS, AND STUDIES 173 I. w = 2V2'' H =4" A = IV2" 11. W = 3'' H =3" A = 2'' II. W = H = £>i = r/^. / rig. ^^i 9 Dimensions will be furnished by instructor. For forms of rivets see Figs. 133, 134, and 135. 217. Space 5V2'' X 7". Make an isometric drawing of the object shown in Fig. 152. Scale 6" = 1 foot. 218. Space 5V2" X 7". Make a cabinet projection from Fig. 152. Scale 6'' = 1 foot. 219. Space 5V2'' X 7'\ For scale of 6'' = 1 foot. Space 11'' X 14" for full size. Make an isometric drawing of the bear- ing cap shown in Fig. 174. 220. Space 5V2'' X 7". Make an isometric drawing of Fig. 275. Scale 6" = 1 foot. 221. Space 5V2" X 7". Make an oblique drawing of Fig. 275. Scale 6" = 1 foot. 222. Make an oblique drawing of Fig. 273. 223. Make an oblique drawing in section of Fig. 276. diameter = 4V2". Width = 1 inch. Outside 178 ESSENTIALS OF DRAFTING ■Knurled CJT" 224. Space 5V2'' X 1" . Make an oblique drawing in section of Fig. 277. Scale 6" = 1 foot. 225. Space 5V2'' X 7". Make an isometric drawing in section of Fig. 277. Shade lines may be used on most any of the problems at the discretion of the instructor. 226. Where should the extra thickness of a shade line be allowed for? 227. About how wide should the shade hues be compared with the fine lines on a shaded drawing. 228. Make a drawing of Fig. 449, half in section, and half ex- terior. 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