MECHANICAL DRAWING FOR CRAWS HAW AND PHILLIPS BooL CQEYRIGHT DEPOSHi Mechanical Drawing FOR Secondary Schools BY FRED D. CRAWSHAW, B.S., M.E. PROFESSOR OF MANUAL ARTS, THE UNIVERSITY OF WISCONSIN AND JAMES D. PHILLIPS, B.S. PROFESSOR OF DRAWING AND ASSISTANT DEAN COLLEGE OF ENGINEERING, THE UNIVERSITY OF WISCONSIN SCOTT, FORESMAN AND COMPANY CHICAGO NEW YORK Copyright 1916 SCOTT, FOEESMAN AND COMPANY II.A4B8385- PREFACE Mechanical Drawing is recognized today as an important part of a secondary education. For all classes of pupils it serves as an important means of developing visualization, strengthen- ing the imagination, and forming habits of careful observation and perception. For those who will make use of it commercially, mechanical drawing is the accepted means of creating a con- ventional picture of objects. This book analyzes mechanical drawing upon the basis of its elements, or natural divisions, such as Perspective Sketch- ing, Orthographic Sketching, Pencil Mechanical Drawing, Ink- ing, Tracing, and Reproducing. Each one of these divisions is treated separately in a chapter. Each chapter organizes the division of drawing which it represents. Hence in each chap- ter there is presented a progressive series of problems in one of the natural divisions of the subject. The book contains six chapters and covers the first two years of mechanical drawing in Secondary Schools. The first four chapters are designed to occupy the time of a class for the first year of the two years' course. As there is a large element of flexibility in the selection of problems, no one individ- ual is expected to solve all problems. The course may be easily extended over a period of more than two years, even to three or four years, depending upon the number of problems solved, whether a part or all of the chapters are included in tlie course, and the time devoted to the subject during each year. The chapters are arranged in the order in which the divisions of drawing are dealt with in commercial draAving room practice. Problems, arranged in groups in each chapter, progress in the order of their difficulty. Each group of problems is chosen to 3 4 MECHANICAL DRAWING emphasize the construction of a certain type of line, the use of particular instruments, and the application of commonly used conventions. It is believed that such a treatment both retains and extends all possible educational values attributed to mechan- ical drawing. In those branches of vocational education which deal with industry, mechanical drawing is the means of showing the plan of construction or the method of assembling constructed parts. Therefore the authors of this book have taken the view that all problems presented must represent commercial industrial prac- tice. They have selected problems which represent several com- mon industrial materials, and the solutions required represent the best commercial drawing room practice. Consequently all abstract problems have been eliminated except in so far as they relate directly to practical problems. This feature, when coupled with the one of dwelling upon one division of drawing until a complete series of problems in it has been solved, makes the book unique in its presentation of unit courses. All of these units, when taken together, complete the field of mechanical drawing, and each one prepares the student for efficient serv- ice in a particular division of the w^hole field of drawing. The course presented in this book has the following subject matter features: 1. Every problem represents typical industrial material, commercial construction, and the best drawing room practice. 2. Every chapter presents a complete course in one of the natural divisions of drawing. 3. All problems are arranged in groups depending upon the elements in drawing which are involved. The student may select or the instructor may assign any one or more of several problems in each group, depending upon student ability and community interest. This feature of flexibility makes it easy to adapt the course at any time to any student in a class and to any class in a community by any one or all of three means : (a) A selection of problems within a group. (b) The addition of problems to any group. (e) The elimination of any section of subject matter or of any group of problems within a section. PREFACE 5 4. All chapters, when completed in the order in which they are arranged, furnish a complete course, both in the subject of mechanical drawing and in the field of industry covered in secondary education, in which mechanical drawing plays a part. The course presented in this book has the following method features : 1. A type problem showing typical conventions and solu- tions is furnished for each group of problems. 2. Numerous data problems, given in the form of freehand sketches and finished mechanical drawings, present a standard in technique. 3. Each division in mechanical drawing is analyzed into its several elements which are presented in a series of well graded, practical problems, involving essential theory and its application. 4 Each division in drawing requires the concentration of the student upon one thing at a time until he has a fair mastery of both theory and practice. The next division reviews this theory and practice in related problems. 5. Each group of problems in each division in drawing is accompanied by explicit instruction and illuminating reading for the student, and suggestive demonstration i^aterial for the instructor. 6. Each chapter in the first year's course closes with a series of review problems and review questions. In order to cover fully the field of mechanical drawing for secondary schools and to prepare students for commercial draw- ing room practice in the several divisions of the subject, the authors have given special attention in the second year of the two-year course to such subjects as Sheet Metal Drawing, Archi- tectural Drawing, and Machine Drawing. The student who com- pletes the work as outlined for the first year will therefore be able to devote his attention to. any one of these subjects or to all of them depending upon his needs. This element of latitude of choice of subject matter makes the book particularly valuable in schools where diafting is taught for early vocational use. A Teacher's Manual and an Outline of the Course of Study are furnished free to teachers using the text. The Manual 6 PREFACE gives brief but pertinent suggestions to assist the instructor. The Outline of the Course of Study shows clearly the plan of the text and indicates possibilities of modifying it to meet local conditions. The authors wish to express their appreciation of the co- operation of H, D. Orth, Assistant Professor of Drawing and Descriptive Geometry, the University of Wisconsin. From the very beginning to the end of the book, he has been a co-author in its production. THE AUTHORS. TABLE OF CONTENTS CHAPTER ONE Page Perspective Sketching 9 CHAPTER TWO Orthographic Sketching 66 CHAPTER THREE Pencil Mechanical Drawing 110 CHAPTER FOUR Tracing and Blueprinting 159 CHAPTER FIVE Advanced Drawing 189 a. Sheet Metal Drawing Problems. b. Furniture and Cabinet Drawing Problems. c. Machine Drawing Problems. d. Architectural Drawing Problems. CHAPTER SIX Isometric and Cabinet Drawing 305 CHAPTER SEVEN Geometrical Constructions 319 CHAPTER I PERSPECTIVE SKETCHING Prospectus It is the aim of this chapter to develop in a condensed but thorough manner the essential principles upon which perspective sketching is based. Furthermore, the presentation is intended to assist the student to develop a fair degree of skill in drawing perspectives of rectangular, angular, and cylindrical objects. Upon completion of the work of this chapter, he should be able to draw objects composed of a combination of these elementary- forms. It is hoped that the student will have gained confidence in his ability to visualize and represent an object pictorially. If this has been accomplished he will find a use for perspective as an interpretation of orthographic drawing which will be treated in the succeeding chapters. Fig. 1. Shaded Perspective of Try-Square General Principles A perspective drawing of an object shows it as it appears when viewed from a given position. Fig. 1 is an example of a perspective drawing. This drawing gives the observer a correct idea of the form and proportion of the object. 9 10 MECHANICAL DRAWING The shading of the drawing, Fig. 1, while adding somewhat to its appearance, does not aid greatly in giving the correct impression of the form and proportion of the object. The shad- ing may, therefore, be omitted, leaving the simplest kind of drawing — the outline drawing as shown in Fig. 2. Such draw- ings will he referred to in this course as perspective sketches. Perspective sketches are valuable as a means of conveying information about the forms of objects to those who are not familiar with the more conventional means of representation used in mechanical drawing. The student will find the per- spective sketch an aid in interpreting mechanical drawing. Fig. 2. Perspective of Tey-Square In this course all objects to be drawn in perspective will be represented as resting on a horizontal plane directly in front of the observer and below the level of the eye. The try-square is shown in Fig. 2 as an observer would see it when standing directly in front of A B with his eye on the same level as S. In Fig. 2 the line marked horizon represents a line in space at an infinite distance in front of the observer. The eye of the observer is on a level with this line and is, consequently, above the level of the try-square, which rests on a horizontal plane. The horizon or horizon line is therefore an imaginary horizon- tal line on a level with the eye of the observer and at an infinite distance in front of him. The apparent meeting of sky and water when one looks over a large body of water is an example of a horizon. Since the horizon is always on a level with the eye of the observer, it follows that, as the eye is raised or lowered to PERSPECTIVE SKETCHING 11 secure a different view of the object, the horizon will be raised or lowered the same distance. Direction of Lines in Perspective. Referring again to Fig. 2, we note that : 1. In a perspective drawing all of the vertical edges of the object are represented by vertical lines in the perspective. Example : Lines A B and C D. 2. In a perspective drawing all of the horizontal edges of the object which are at right angles with the direction of sight of the observer are represented by horizontal lines in the perspective. Example: While not an edge of the object, the horizon line. Fig. 2, is an example of this case. 3. In a perspective drawing all of the horizontal edges which are parallel to each other, but not at right angles to the direction of sight of the observer, are represented by lines which converge to a point on the horizon. Example : Lines A C and B D. 4. Horizontal lines receding to right and left in a perspective, which make equal angles with the horizon line, meet the horizon line at points equally distant from the point on the line directly in front of the observer. Example : In Fig. 2, S is a point on the horizon line directly in front of the observer. The distance from S to Vr is equal to the distance from S to Vl. 45° Perspective. The angle between the beam and blade of the try-square is 90°. The try-square is so placed that the angles which the receding edges to the right and to the left make with the horizon are equal and must therefore be 45° angles. Because of this fact the try-square is said to be drawn in 45° perspective. All of the rectangular objects drawn in this course will be placed in a similar position to that of the try-square, i.e., in 45° perspective. This will insure comparative ease in the construc- tion of perspective sketches, as will, appear later. The points Vl and Vr on the horizon toward which the hori- zontal receding edges of the try- square converge are called vanishing points. A vanishing point is the common intersection of two or more converging lines which represent parallel receding edges of an object. All parallel horizontal receding lines must converge to the 12 MECHANICAL DRAWING same point on the horizon. Example : The horizontal lines of the try-square converging to the right in its perspective meet in Vr. Likewise all the horizontal lines converging to the left meet in Vl. Vertical Lengths in Perspective. 1. Equal distances on the same vertical edge of an object are represented by equal lengths in perspective. Example : In Fig. 2 the try-square blade is represented as entering the beam mid- way between the upper and lower surfaces. The distance from A to the blade is equal to the distance from B to the blade. 2. Equal distances on vertical edges of an object which are at unequal distances from the observer are represented by unequal lengths in perspective. Example : A B and C D represent equal lengths on the object but are unequal in the perspective. 3. Of two equal vertical distances on an object the one nearest the observer is represented by the greater length in perspective. Example : A B and C D which represent equal vertical lengths on the object are both included between two lines of the drawing which converge toward Vr. On account of the convergence of the two receding lines C D is shorter than A B. Horizontal Lengths in Perspective. 1. Equal distances on a horizontal receding edge of an object are represented by unequal lengths in perspective. Example : The spaces between the lines representing the one-inch marks on the try-square blade, Pig. 2, are unequal. 2. Of the equal distances on a horizontal receding edge of an object, those farthest from the observer are represented by shorter lengths. Example : In Fig. 2 the spaces between the lines representing the one-inch marks grow shorter as they are farther away from the observer. 3 Equal distances on a horizontal receding edge of an object are represented by lengths which appear equal. Example : The spaces between the lines representing the one-inch marks on the try-square blade. Fig. 2, are made to appear equal. PERSPECTIVE SKETCHING 13 The varying of the lengths of lines representing equal distances on the object as described above is known as fore- shortening. Foreshortening is the process of shortening parts of a perspec- tive of an object so as to give the impression of true form and proportion. The Cube in Perspective. Thus far only a general considera- tion of perspective has been given. The following is an applica- tion of the principles thus far developed to the representation of a one-inch cube. In this course the cube will be regarded as the hasic form for all perspective drawing. The one-inch cube will be used as the unit of measure and therefore it is essential that its proportions and position with reference to the eye be well in mind. In Fig. 3 the eye of the observer is directly in front of the point S. The vertical faces of the cube make 45° with the horizon and, also, with the direction in which the observer is looking. This agrees with the position of the try-square in Fig. 2 and is said to be in 45° perspective as defined on page 11. In 45° perspective the distances from the point on the horizon directly above the nearest point of the object to the vanishing points and to the eye must be equal. In this course the vanishing points are taken 14" to the right and left of the point above the nearest corner of the object. The edges of the cube are one inch long. The front vertical edge of the cube will be the longest line in the perspective of the cube (See 3 under Vertical Lengths in Perspective). It will be drawn in its true length, one inch. The principles already developed are applied in the follow- ing analysis of the perspective of the cube. Since the side faces are equally inclined to the direction in which the observer is looking : 1. Angle D A E = angle D'A E' 2. Angle F B H = angle F'B H'. Such angles will hereafter be referred to as the angles of inclination. 14 MECHANICAL DRAWING The perspective of the corner G is directly above A. Due to the convergence of A D with B F and A D' with B F' : Angles F B H and F'B H' are greater than angles DAE and D'A E'. tpVl toVl toVr toVr Fig. 3. Perspective of One-Inch Cube Lines D F and D'F' are shorter than A B. D F = D'F'. Due to the convergence of A D with D'G and A D' with D G : 1. G D and G D' are shorter than A D and A D' ; 2. G C is shorter than C A. Due to foreshortening: A D and A D' are shorter than A B, PERSPECTIVE SKETCHING 15 Rectangular Objects PREPARATORY INSTRUCTION FOR DRAWING PLATE 1 The following is a list of the materials needed to make the perspective sketches : 1. Drawing board. 2, High-grade drawing paper similar to Universal — 9''xl2'' sheets. i3H 3. High-grade pencils ^5H 4. Pencil pointer. 5. Erasers — Ruby and Flexible gray. 6. Thumb tacks. 7. A straightedge — ruler or triangle. 1 3 C :: & u I ll. ;o Id •a Q u y^ BORDER line: ^ o ;: 4 2 Fig. 4. Position of Sheet on Drawing Board The drawing 'board should be made of well-seasoned, straight- grained, soft wood, free from knots and cracks. When in use the drawing board should be placed on the desk with the longer edges parallel to the front edge of the drawing table. It may be tilted to any convenient angle. Drawing Paper. In selecting a drawing paper the draftsman should have in mind the purpose for which it is to be used. For 16 MECHANICAL DRAWING freehand drawing, where it is desired to produce a porous, uni- form line with a soft pencil, a slightly grained surface is satis- factory. It should stand erasing without injury. In preparing to make a drawing, a sheet of paper should be tacked near the upper left hand corner of the board with the longer edges parallel to the longer edges of the board. Fig. 4. To fasten the sheet insert a tack in the upper left hand corner ; _^ li ■ - >> •1 \l < 1 >t 'J 1 CORRECT AVOID Fig. 5. Position of Thumb Tacks square the paper with the board, and, stretching it diagonally, insert a tack in the lower right hand corner. Insert a tack in the upper right hand corner, stretch the sheet in the direction of the lower left hand corner, and insert a fourth tack. Press each tack down vertically until the head is firmly in contact with the paper. Fig. 5. Pencils. The lead of the drawing pencil should be of firm, even grain. To secure the .desired effect in the drawing, the hardness of the pencil must be considered in connection with the surface of the paper. For freehand drawing a medium soft pencil should be used on a slightly grained surface. A soft pencil PERSPECTIVE SKETCHING 17 is more easily controlled, and consequently there is more freedom in drawing lines with it than can be secured with a hard pencil. To sharpen the pencil, grasp it in the left hand as illustrated in Fig. 6, and with the knife in the right hand, cut the shavings by drawing the knife toward the body and through the wood Fig 6. Sharpening the Pencil. Whittling Away the Wood Fig 7. Sharpening the Pencil. Pointing the Lead only. About one-quarter inch of lead should be exposed, and the wood tapered back about one inch from the lead. Sharpen the lead on the surface of a sandpaper pad or file, rotating the pencil so as to produce a conical point. Fig. 7. The sharpened lead should be slightly rounded on the end in order that soft lines as shown in Fig. 8 may be produced. This figure also shows the sketching pencil properly sharpened. 18 MECHANICAL DRAWING The Constructive Stage. In making a freehand sketch all of the straight lines will first be drawn very lightly with the aid of a straightedge such as the edge of a triangle or ruler, using the 5H pencil. Fig. 12. 1. When two points on a line are known the edge of the tri- angle or ruler should be placed so that its edge passes through both points. The line may then be ruled lightly. 2. Sometimes only one point on the line and its general direc- tion will be known. In this case the edge of the rule should be made to pass through the point with the edge adjusted to the proper direction. 1 INCH ^- 1 INCH [ i FINISHING line; MEDIUM PENCIL k CONSTRUCTION LINE HARD PENCIL Pig. 8. Sketching Pencil Properly Sharpened Ruling a Line. In ruling a line along a straightedge the pencil is held in the hand as indicated in Fig. 13. The line is drawn with a continuous motion from left to right with the tip of the fourth finger touching the ruler to steady the hand. The forearm should always he at right angles with the line teing drawn. The rule should preferahly he hetween the draftsman and the line being drawn. The Finishing Stage. When the constructive stage has been completed all lines which will not appear in the finished drawing should be erased. The 3H pencil should then be properly sharp- ened and the lines of the drawing traced over freehand. They must be uniform in width and grayness of tone. The Position of the Hand and Pencil in Sketching. In draw- ing a freehand line the pencil is held firmly, but not rigidly, between the first two fingers and the thumb as in writing. In six-etching a horizontal line the ends of the third and fourth fingers should rest upon the board to help support and steady PERSPECTIVE SKETCHING 19 the hand. Fig. 9. With the forearm resting on the drawing board, the hand should be moved from left to right, hinging at Fig. 9. Sketching a Horizontal Line the wrist. This will permit only short strokes, about one inch long, to be taken. To sketch a long line, therefore, one must join together a series of one-inch lines. The position for each Fig. 10. Sketching a Vertical Line stroke should be obtained by moving the hand and forearm in the direction of the line. Each section should be joined to the pre- ceding one, but not lapped upon it, as the lapping of sections produces an undesirable sketchy effect. 20 MECHANICAL DRAWING In sketching a vertical line the hand is placed in the position shown in Fig. 10. The hand rests upon its side instead of upon the ends of the third and fourth fingers. The pencil is moved downward. The strokes are made with a finger movement while the hand remains stationary. In sketching a vertical line the forearm should remain approximately in the position of a vertical line on the sheet. The Border Rectangle. Before starting the drawing of the object on the sheet, draw a border line approximately one-half inch from each edge of the sheet. This may be done in the con- structive stage by placing the straightedge parallel to each edge of the sheet at a distance estimated to be one-half inch in from the edge, and ruling a line lightly. This border rectangle should be traced over freehand in the finishing stage as are the lines of the sketch. DATA FOE DRAWING PLATE 1 Given: The perspective of a cube, Fig. 11. Required: To make a perspective sketch similar to that shown in Fig. 11, on a 9'' x 12" sheet as explained below. Instructions: 1. Draw lightly the border rectangle y from the edge of the sheet. 2. To locate the perspective of the cube use the 5H pencil with the ruler as a straightedge. a. Draw two very light horizontal lines XVr and YZ dividing the space between the upper and lower bor- der lines into three equal parts. b. Draw a vertical line, VW, through the center of the sheet and SU midway between VW and the left border line. c. From B estimate one inch up on S IT, thus locating A, the upper front corner of the cube. 3. Vr is about ^'^ from the right border line. 4. Draw lightly a horizontal line through A and connect A with Vr. PERSPECTIVE SKETCHING 21 5. Get the direction of A D' by drawing the angle of inclina- tion D'A E' equal to angle DAE. This may be accomplished by placing the ruler so that the edge passes through point A and adjusting its direction until the angles appear equal. Fig. 12. 6. To obtain the Mddth of a vertical face of the cube, draw D F so that the figure A D F B appears as a square. Fig. 13 shows the process of locating D F. A ruler or triangle is placed Fig 11. Perspective of Cube with an edge in a vertical position parallel to the line AB. It is then moved back and forth to right and left until, in the judg- ment of the draftsman, the figure A D F B appears as a square. 7. Draw D'F' making AE'=AE. Complete the perspective of the cube by drawing D'Vr and D G. Fig. 11. This completes the constnictive stage. 8. All lines not shown in Fig. 11 should now be erased. The cube and the border rectangle should be traced over freehand with a well sharpened 3H pencil to produce a line of even weight and uniform shade. The remaining lines of the drawing should 22 MECHANICAL DRAWING be allowed to remain light, as drawn in the constructive stage. Omit all reference letters. 9. Write the plate number and name in the lower right hand corner of the sheet as in Fig. 11. Remove the sheet from the board, turn it over and, with a knife or other sharp instrument, press the paper back into the thumb tack holes. The Method of Developing Lettering in the Course. One of the most difficult steps in making a drawing is the lettering of the notes, dimensions, and title. In this course lettering will be omitted from all drawings until the student has had considerable practice in forming and spacing the letters and figures. This practice will be had on small lettering plates. Each drawing plate should he followed hy the lettering plate of the same number. Fig. 12. Sketching the Angles op Inclination Lettering Modern practice demands that the lettering done on working drawings be simple, legible, and capable of easy and rapid ren- dition. The simple Gothic style fulfils these requirements and is therefore quite generally used. Form and Proportion. A careful study of the form and proportion of each letter must be made before the student can hope to make any considerable progress in lettering. Practice PERSPECTIVE SKETCHING 23 in drawing the letters will add something to his control of the media with which he works, but first of all he must have a dis- tinct knowledge of what he is trying to accomplish. Strokes. For convenience in- forming letters they are divided into strokes. In most cases the strokes are natural divisions of the outline of the letter. Three things should be remembered about the strokes for each letter: (1) the number of strokes, (2) the order in which they are made, (3) the direction in which each stroke is drawn. The advantage in knowing and using a system of strokes lies in the fact that drawing the letters repeat- edly in the same manner makes the forming of each letter more Fig. 13. Determining the Width of the Face of the Cube nearly automatic. Hence it adds to the ease with which letters can be produced and aids in securing uniform results. Spacing. Second only in importance to the forms of the let- ters is their relation to each other. The best effect is obtained when the areas included between the letters in a word appear equal. For the capital letters the area of these spaces should be equal to the area of a rectangle one-half the normal width of the H. The space between words should be about three times that between letters. Words set off by a comma should be spaced from one to one and one-half times the usual distance. The space between sentences should be about twice the space between words. The final test of good spacing is legibility. The letters must be far enough apart to avoid a crowded effect and yet the spaces must not be so great that the letters appear scattered. In like 24 MECHANICAL DRAWING manner words must be separated enough to stand out individ- ually, but not enough to make reading difficult. Lettering in Pencil. The pencil used for the freehand work on a drawing should be softer than the pencil used for the mechanical work. It should be of such grade that when prop- erly sharpened a clear gray line can be produced with a single stroke. It should not be hard enough to cut into the surface of Fig. 14. Correct Position of the Hand and Pen for Lettering the paper, as difficulty is then experienced in controlling the direction of the line. The lead should be sharpened to a long taper, conical in form and rather blunt at the end. With one-quarter inch of lead exposed, and this tapered back to the wood, the section of the lead will be so nearly uniform near the end that it will stand considerable use without resharpening. The pencil should be held in the hand in the same position as the pen shown in Fig. 14, with the foreann nearly in the direction of the vertical stems of letters or, in the case of the inclined letters, nearly in the direction of the slant. The strokes should be drawn with a finger movement. The pencil should be turned about its axis PERSPECTIVE SKETCHING 25 frequently to keep the point round so as to prodrce a line of uniform weight. All strokes should be made with the hand held in the same position Shifting the arm to obtain advantageous positions for drawing strokes in different directions is a habit which will prevent the acquirement of commercial speed and at the same time will prevent the development of the professional type of lettering as distinct from the labored effect produced by the average novice. Lettering in Ink. The beginner will find it more difficult to produce satisfactory results with pen and ink than with the pencil because of the complications which arise from the nature of the media. To secure a black line of uniform weight with a quick drying fluid such as India ink, and with an ordinary writing pen, presents a problem which usually requires a careful study of the methods of using these materials and considerable intelligent practice. The pen should be held in the hand as shown in Fig. 14. In drawing a line the points of the pen should be side by side so that the width of the line can be controlled by the pressure applied to spread the nibs. The position of the pen in the hand should not be changed for strokes of different direction, but rather the weight of line should be kept uniform by varying the pressure on the pen. In lettering in ink as in lettering with the pencil, the hand should be held in the same position for all strokes. This will give a better general effect and will make it easier to develop commercial speed in forming the letters. The pen should be filled by applying the quill attached to the stopper of the ink bottle to the under side of the pen. Enough ink should be put on the pen to last a reasonable length of time and to produce a wet line so that when it is dry, enough carbon will have been deposited to make it black. Overloading the pen, on the other hand, will cause the corners to fill at intersecting lines. The pen should be wiped frequently to remove the dry ink from the surfaces of the pen and between the nibs. Fresh ink and a clean pen are necessary to produce sharp clean-cut lines. Titles. The title contains information by which the drawing can be identified, such as the name of the part or parts of the 26 MECHANICAL DRAWING machine or structure, name of the complete machine or structure, manufacturer's firm name and address, drawing number, date, scale, and initials of draftsman, tracer, and checker. The usual position of the title is in the lower right-hand comer of the sheet where it does not interfere with the drawing and at the same time may be read without taking the sheet from its place in a drawer or file. The relative importance of the items in the title is shown by varying heights and widths of the letters or the weight of their stems, or both. The lines should be balanced, i.e., the middle point of each line should fall on the same vertical line. To give the best effect Q/vwiuoL dxAdnt/ d=^U: ^jJpoAhnmJj Ukrf/ DAAnAicnv Fig. 15. Title Material Divided into Groups of Words the lines should vary in length. The general contour of the title is very commonly oval or pyramidal in form. The arrangement of the lines of the title and the determina- tion of the height of each line present a problem in design for the solution of which the contour of the title should be kept in mind. The space between the lines of letters for the single stroke capitals should be from three-fourths to one and three-fourths the height of the smallest adjacent letters. The style of letter used for the title should be dignified. For this reason the capital letters are generally used. The steps in designing a title should be taken in about the following order: 1. Assuming that the wording or at least the substance of the title is stated, write out the complete title and divide the words into logical groups for the different lines. Fig. 15. 3^ PERSPECTIVE SKETCHING 27 2. Eewrite, tentatively arranging the lines as they will be in the printed title. Fig. 16. 3. Decide upon the relative importance of the lines and select heights of letters accordingly. It may now appear that a re- arrangement of the lines will give a better outline without affect- ing the meaning. Om/muxl dxmlnt ii E^^OAtrrumi/ a| TTLo/nuai/ (Mis/ WJlAmMJtwuWM^(mMm/ i" Fig. 16. Tentative Akeaxgement of Lines of the Title 4. The title may be balanced by printing each line lightly in its proper space to obtain the spacing of the letters. Any adjustment necessary to make the middle point of each line fall on the center line of the title should be made. The letters should then be drawn in full weight. This method may be used with ANNUAL EXHIBIT WEST DIVISION HIGH SCHOOL DEPARTMENT OF MANUAL ARTS MILWAUKEE WISCONSIN Fig. 17. Finished Title success by those who have had considerable experience in letter- ing. The beginner will obtain better results with but little more work by lettering the lines first on a trial sheet to get the spacing and then by using these lines as a guide in balancing the lines and spacing the letters on the drawing, as described on page 140. Fig. 17 shows a balanced title. In drafting offices or business firms where large numbers of drawings similar in general character are made, the items com- 28 MECHANICAL DRAWING mon to all titles are very often printed on the pencil drawing with a rubber stamp and on the tracing in type. Uniformity in treatment is thus secured and much time in lettering is saved. Fig. 144 illustrates commercial titles. These title forms are printed on the under side of the tracing cloth. Errors may thus be corrected and changes made in the lettering done by the draftsman without erasing the printed lines and letters. EDGE OF CARD^ _ | BORDER LINE -ICO V -l!fi ioi£ K "^-T J_ Fig. 18. Lettering Card PEEPARATORY INSTRUCTIONS FOR LETTERING PLATE 1 TJie Plate. The first ten lettering plates will be in pencil. Three by five cards of the regular drawing paper, ruled as shown in Fig. 18, will be used. The Lettering Pencil. Use the 3H pencil for lettering, sharp- ened to a conical point as for freehand sketching. Fig. 8. Number, Order, and Direction of Strokes. Each letter or numeral is made by one or more strokes. In general, vertical and inclined strokes are made downward and horizontal strokes PERSPECTIVE SKETCHING 29 to the right. Fig. 19 shows the number, order, and direction of strokes for the numerals 1, 4, 7, and the symbols used for the foot, inch, and dash. The relative width of numerals is shown in column 4. Fig. 19. Order, Number, and Direction of Strokes The Scale of Heights. For convenience in estimating ver- tical distances the space between the guide lines is divided into four equal parts. Fig, 19. A Scale of Widths. The width of the H is taken as the unit of width. The total letter distance is divided into four equal parts. Horizontal distances may be estimated by observing their relation to these divisions, Fiff. 19. 30 MECHANICAL DRAWING Drawing the Strokes. Before starting a stroke, carefully plan its position and direction. Make each line with one move- ment of the pencil. A vertical stroke is made by drawing a line from one point to another directly 'below it. In case a stroke or letter is unsatisfactory it should be erased and redrawn. Foot and Inch Marks. A short dash placed to the upper right of a numeral indicates feet. Two such dashes similarly placed indicate inches. A horizontal dash is placed between numerals representing feet and inches. See Fig. 19. Fig. 20. LETTEPaxG Plate 1. 1, 4, 7 DATA FOR LETTERING PLATE 1 Given: Plate 1 to reduced size, Fig. 20. Required: To make the plate to an enlarged scale. Instructions: 1. Fasten the card to the board either with thumb tacks or by inserting its comers in diagonal slits cut in a larger piece of paper which is tacked to the board. Fig. 18. 2. Draw the numerals and symbols, using the number, order, and direction of strokes shown in Fig. 19. 3. Write in the plate number, followed by the name at the top of the sheet as indicated in Fig. 20. PERSPECTIVE SKETCHING 31 PEEPARATORY INSTRUCTIONS FOR DRAWING PLATE 2 Plate 1, page 21, gave practice iii making a perspective of the unit of measure and basic form in perspective — the cube. The one-inch cube will be used in the following plates as a means of constructing and proportioning the perspective sketches of more complex objects. A Scale of Levels. Fig, 21 shows a horizontal square at dif- ferent levels in perspective. At the left in Fig. 22 the horizontal square is used as the top of a cube, represented at levels one-half inch apart. It will be noticed that in each of these figures the Fig. 21. Vafjation op Area with Level area of the figure representing the square and the angle of inclination increase with the distance below the level of the eye. The distance below the level of the eye of the front corner of each square, Fig. 22, is indicated by the numerals at the left of the figure. In this course the student will be aided in determin- ing the level for the perspective of an object by referring to this scale. To the right of the scale is shown its application in repre- senting a cube at different levels. Vertical Measurements. Under, ''Vertical Lengths in Per- spective," page 12, the general facts regarding these measure- ments are given. In making vertical measurements in per- spective the following rule must be observed. All vertical distances on an object must be measured in per- spective on the line representing the front vertical edge of the object. This is true for the following reasons : 32 MECHANICAL DRAWING 1. The front vertical edge is drawn full length. In Fig. 23, A B is greater than the vertical line through I. To secure this length, one would determine A B and draw tlie vanishing lines. HORIZON 4i-' Fig. 22. Scale of Levels 2. In general, equal vertical distances are equal in perspective only when measured on the same vertical edge. Example : AB = BK = KL. PERSPECTIVE SKETCHING 33 34 MECHANICAL DRAWING Horizontal Measurements. Under, "Horizontal Lengths in Perspective," page 12, the general facts regarding horizontal measurements are given. In making horizontal measurements in perspective the following method should be used: Whenever possible, horizontal distances on an object should be measured in perspective by drawing the faces of a series of receding one-inch cubes so that they appear to be squares. In Fig. 23, lengths A D, D E, E G, G H, and H 1, representing equal horizontal distances, are measured by making faces 1, 2, 3, 4, and 5 appear as squares. Fig. 24. Enclosing Solid The Enclosing Solid. In using the methods of making hori- zontal and vertical measurements given above, one of the impor- tant steps in the construction of the perspective sketch will be the drawing of a rectilinear solid the edges and surfaces of which, so far as possible, are coincident with the edges and surfaces of the object. Fig. 24. This solid will be called the enclosing solid. This solid should be drawn completely before any attempt is made to construct the details of the object in perspective. The Pleasure Cube. The first step in drawing the enclosing solid is to draw a one-inch cube with its upper front corner at the level required for the perspective of the object to be drawn. This one-inch cube will be at the upper front corner of the enclos- PERSPECTIVE SKETCHING 35 ing solid. The front vertical edge of the cube serves as the ver- tical unit of measure and the width of the side faces as the hori- zontal unit of measure. This cube is therefore called the measure cube. The Table Line. When an object rests on a horizontal sur- face its position with reference to that surface is shown by a horizontal line called the table line. The position of this line as shown in Fig. 27 is taken arbitrarily. In its relation to the perspective it should represent the object as resting in a pleasing position on a horizontal plane. The table line should be drawn freehand. DATA FOR DRAWING PLATE 2 Given: The dimensioned perspective of a sandpaper block, Fig. 27. Required: To make a sketch of the sandpaper block, full size in perspective, omitting all dimensions and lettering, or any similar problem assigned by the instructor. Instructions: 1. Draw the border rectangle as in Plate 1, page 21. Here and throughout the constructive stage use the 5H pencil. 2. To locate the center of the sheet proceed as follows : Place the ruler on the sheet with one edge in the position of one of the diagonals of the border rectangle. Rule a light, short line through the approximate center of the sheet. In like manner draw a part of the other diagonal. The intersecting lines will locate the center of the sheet. 3. With the aid of the ruler draw the measure cube with its upper front corner A at the center of the sheet and 3^" below the level of the eye. Fig. 25. Refer to the angle of inclination in Fig. 22 for the required level. Reproduce this angle as illustrated in Fig. 12. 4. Complete the enclosing solid by drawing the lines in the order indicated by the numerals. Fig. 25. Measure vertically and to the right and left as previously described under, ' ' Vertical Measurements" and, "Horizontal Measurements" respectively, pages 31 and 34. 36 MECHANICAL DRAWING 5. To sketch the open space through the sandpaper block which is to be occupied when the block is in use by a block of the Fig. 25. Constructive Stage. Enclosing Solid same dimensions as the open space which holds the edges of the sandpaper, locate B, y.^' below A, and draw line 10 converging Fig. 26. Constructive Stage. Complete with line 3, Fig. 26. Lay off from A on line 3 a distance repre- senting y^' ' The principle of foreshortening applied here will make this distance slightly greater than one-half of the width PERSPECTIVE SKETCHING 37 of the face of the cube. Draw line 11. lu the same manner lo- cate and draw line 12. Draw lines 13, 14, and 15 converging with lines 2 and 6. Draw line 16 vertically from the intersection of lines 7 and 13. Draw line 17 converging with lines 3 and 7. This completes the constructive stage. 6. Erase all lines except the outline of the figure and trace over the sketch freehand with a carefully sharpened 3H pencil. Draw a table line as in Fig. 27. Fig. 27. Sand Paper Block 7. Write the plate number and name in the lower right hand corner of the sheet and press the paper back into the thumb tack holes as directed in Plate 1, page 21. PREPARATORY INSTRUCTIONS FOR LETTERING PLATE 2 Curved Strokes. In making the curved strokes of the 5 and the 2 the student should have in mind the form of the complete oval. The Dimension Form. The dimension form consists of the numerals designating feet and inches, the foot and inch marks, the dash, the dimension and extension lines, and the arrowheads as arranged in Fig. 77. It will be seen that the arrowheads are placed on the dimen- sion lines with their points touching the extension lines. They 38 MECHANICAL DRAWING are composed of two slightly curved lines symmetrical with respect to the dimension line. The length of the arrowhead should be about i'' and the width iV"- Fig. 77. Fig. 28 shows strokes for arrowheads pointing in different directions. STROKES :Y/. -AV 3: WIDTH ■""i r\"" Uli "■ ..J 1 1 '■ ...JJjTT- Fig. 28. Lettering Plate DATA FOE LETTERING PLATE 2 Given: Plate 2 to reduced size, Fig. 29. Required: To make the plate to an enlarged scale. Instructions: Proceed as in Plate 1, page 30, following care- fully the number, order, and direction of strokes. PERSPECTIVE SKETCHING 39 DATA FOR EXTEA DRAWING PLATE Given: A dimensioned perspective sketch of a clamping plate for lathe tail-stock. 5 5 5 5 5 1475 545 75457f 2 22 22 425 5272 27527z liilliiiii TTTTTTTTTT- H Z |- 122'- 5"- V — 475'-2"— J 2"- Fig. 29. Lettering Plate 2 Required: To make a sketch of the clamping plate full size, omitting all dimensions. Fig. 30. Clamp for Tail Stock The upper front corner of the enclosing solid is in the center of the sheet and 3^" below the level of the eye. 40 MECHANICAL DRAWING Angular Objects PREPARATORY INSTRUCTIONS FOR DRAWING PLATE 3 To Center a Perspective Sketch on a Sheet. For the pre- ceding plates definite instructions have been given to center the sketch on the sheet. For the sake of appearance a sketch should be centrally located. The student should use considerable care, therefore, in locating the upper front corner of the enclosing solid. It cannot always be located at the center of the sheet. The following suggestions will be of value in locating the upper front corner of the enclosing solid. A close approximation can be made to the correct position of the front vertical edge of the enclosing solid to right or left of the center of the sheet by referring to Fig. 23. Fig. 31. Enclosing Solid 1. On this figure the distance to be measured to the right and to the left of the front vertical edge of the enclosing solid may be marked off. If the horizontal distance between the extreme points is divided into two equal parts the division will come at the point in the perspective which should be at the center of the sheet. 2. The distance from A B, Fig. 32, to this middle point is the distance which the front vertical edge of the enclosing solid must be to the right or left of the center of the sheet. In locating the upper front corner of the measure cube after the position of the front edge is determined, the length of the front edge of the enclosing solid and the distance of the back corner of the upper surface above the front comer of the enclos- PERSPECTIVE SKETCHING 41 ing solid must be estimated. Half the sum of these two distances should fall above and half below the center of the sheet. DATA FOE DRAWING PLATE 3 Given: The dimensioned perspective sketch of a cord-wind with the upper surface 3" below the level of the eye. Fig. 33. Required: One of the two solutions as stated below. 1. To draw the cord-wind, full size, with the upper surfaces 5" below the level of the eye. Omit all dimensions and letters from the finished sketch. Fig. 32. Constructive Stage Complete 2. To draw the cord-wdnd full size with the upper surface 5" below the level of the eye, and turned so that the longer edges vanish toward the left instead of toward the right. 3. To draw any similar object assigned by the instructor. Fig. Cord-Wind Instructions: 1. Locate the upper front corner of the measure cube A a3 directed under, "To Center a Perspective Sketch on a Sheet," page 40. 42 MECHANICAL DRAWING 2. Complete the enclosing solid as in Plate 2, page 35, taking care to secure the necessary convergence. As it is the aim that the student should learn to make perspective sketches entirely freehand he should now draw as many as possible of the lines of the constructive stage without the use of a straightedge. 3. To locate the lines representing the cut in the near end of the cord-wind lay off A F and D E, Fig. 32, to represent one Fig. 34. Lettering Plate inch and H F and E I to represent one-half inch. From H and I draw lines converging with A N and D M to the right. Lay off A K to represent two inches and draw a line from K converging with A D. This line meets the lines from H and I in L and respectively. Connect E and F L. From draw a vertical line and from P a line converging with K 0. These lines inter- sect ni Q. Draw R Q. By a similar method make the construction for the cut at the farther end of the cord wind. 4. Erase unnecessary lines and finish the sketch in the usual manner. PERSPECTIVE SKETCHING 43 PREPARATORY INSTRUCTIONS FOR LETTERING PLATE 3 Curved Strokes. The oval of the numeral is the basic form for the 6 and 9. In making the outline strokes of these numerals the student should have in mind the form of the complete oval. Whole Numbers and Fractions. The whole number in a dimension will be made ^" high. The total height of the fraction should be twice the height of the whole number with a clear space between each numeral and the division line. Fig. 141. To check these heights mark off an eighth inch and a quarter inch space on the edge of a card and use it as a scale. Fig. 78. 104 520 500 214: 6 6 6 6 6 460 506 672 276: 9 9 9 9 9 690 269 795 926: •4 ? 64 16 64 16 ^2 ^16 '^2 ^^16 16" .7" ^^. ^1" . ,o' r^^ ■14-10;^ H 62-92 -^ — 16-0^- FiG. 35. Lettering Plate 3. 0, 6, 9 DATA FOR LETTERING PLATE 3 Given: Plate 3 to reduced size. Fig. 85. Required: To make the plate to an enlarged scale. 44 MECHANICAL DRAWING DATA FOR EXTRA DRAWING PLATE Given: The dimensioned sketch of a wall bracket, Fig. 36, with the upper surface of the enclosing solid 3^'' below the level of the eye. Required: To draw the wall bracket full size, with the surface as shown 3^'' below the level of the eye, but with the longer horizontal edges receding toward the left instead of toward the right. Fig. 36. Wall Bracket Cylindrical Objects PREPARATORY INSTRUCTIONS FOR DRAWING PLATE 4 The Veriical Measure Cylinder. As stated before, the cube is the basic form for the perspective sketching in this course. To secure a measure unit for cylindrical objects a cylinder is in- scribed in a measure cube as shown in Fig. 37. The cylinder is therefore one inch in diameter and one inch long. The principle PERSPECTIVE SKETCHING 45 of foreshortening makes the axis of the cylinder and the major axis of each of the ellipses representing its bases slightly less than one inch. In sketching, these differences may be ignored. In Fig. 38 these distances are one inch in length. The following is an analysis of a cylinder which will be referred to as the vertical measure cylinder: 1. The distance between the centers of the ellipses is equal to their major axes or one inch. AB = CC' = DD'. Fig. 38. 2. The major axes C C and D D' of the ellipses are at right angles with the axis of the cylinder. These lines do not eon- FiG. 37. Vertical Cylinder, In- scribed IN A Measure Cube Fig. 38. Vertical Measure Cylinder verge, since they represent lines at right angles to the direction of sight of the observer. See, "Direction of Lines in Perspec- tive," page 11. 3. The minor axes E E' and F F' are coincident with the line representing the axis of the cylinder. 4. Due to the difference in level of the upper and lower bases the minor axis F F' of the lower base is greater than the minor axis E E' of the upper base. The minor axis of the upper base may be determined for any level from the scale of levels discussed in the following paragraph. The half length of the minor axis of the lower ellipse may be determined by drawing F H' through D', converging with E H. A Scale of Levels. The left half of Fig. 39 is a scale of levels showing the upper base of a measure cylinder at levels one-half 46 MECHANICAL DRAWING inch apart. It is evident that the area and minor axis of the ellipse increase with the distance of the ellipse below the level of the eye. The distance below the level of the eye of the center of HORIZON fc: Fig. 39. Scale of Levels each circle, Fig. 39, is indicated by the numerals at the left of the figure. In this course the student will be aided in determining the level for the perspective of a cylindrical object by referring PERSPECTIVE SKETCHING 47 to this scale. To the right of the scale is shown its application in representing a cylinder at different levels. To Draw and Test an Ellipse Representing a One-Inch Circle. 1. Draw light indefinite lines at right angles to each other to represent the axes of the ellipse. B T A ^3 . J Fig. 40. Testing an Ellipse 2. On the line representing the major axis lay off on either side of the intersection of the axes one-half the diameter of the circle. 3. Refer to the scale of levels ; estimate and lay off the minor axis. 4. Sketch the ellipse lightly and freely, drawing correspond- ing parts in consecutive order, i.e., draw the long sides of the Fig. 41. Concentric Circles in Perspective ellipse and then the ends. Compare the form thus secured with the corresponding ellipse in the scale of levels. Care should be taken to avoid sharp or blunt ends. 5. Ordinary defects in the form of the ellipse should be de- tected by examining it as follows : a. Turn the sheet to the right, to the left, and upside down, and view the form carefully when the sheet is in each of these positions. 48 MECHANICAL DRAWING b. Locate two points as A and B, Fig. 40, on the axis equidistant from 0. The vertical distances from these points to the ellipse should be equal. Compare these dis- FiQ. 42. Split Core Bos — Axis Vertical tances and make the necessary corrections. Likewise lo- cate C and D equidistant from and compare the vertical distances from these points to the ellipse. Make the nec- essary corrections as before. Concentric Circles in Perspective The problem of drawing two concentric ellipses is more diffi- cult than that of drawing a single ellipse. PERSPECTIVE SKETCHING 49 Fig. 41 shows two concentric ellipses inscribed in concentric squares shown in perspective. The ellipses therefore represent circles. On account of foreshortening, the axes of the ellipses do not coincide with the line representing the diameter of the circles or with each other. In most cases the difference is so slight that it may be ignored. For very large ellipses, however, the construc- tion shown in Fig. 41, where the major axis of the larger ellipse is Fig. 43. Split Core Bos — Axis Horizontal slightly in front of the major axis of the smaller ellipse, must be used. In Figs. 42 and 43 the major axis C F is laid off equal to the diameter of the circle, as in the case of the ellipse representing a one-inch circle. Fig. 38. A one-inch ellipse should be drawn first and tested. In cases where the major axes of the ellipses are made to coincide, the half length of the minor axis of a larger or smaller ellipse may be determined as shown in Figs. 42 and 43. C D is drawn through C parallel to A B. In cases where the axes do not coincide the line corresponding to C D should be made to converge slightly with A B. 50 MECHANICAL DRAWING DATA FOR DRAWING PLATE 4 Given: The dimensions of a split core box for standard one-inch cores, which consists of a hollow cylinder split into halves ; outside diameter 2", inside diameter 1", length 3". Required: A perspective sketch of the split core box with its axis vertical and the upper base 3" below the level of the eye, Fig. 42, or any similar object assigned by the instructor. Fig, 4-i. Lettering Plate 4 Instructions : 1. Draw through the center of the sheet a vertical line to represent the axis of the cylinder. All lines should now be draw7i freehand. 2. Through points 1^"* above and below the center of the sheet draw horizontal lines as the major axes of the ellipses represent- ing the ends of the bushing. The minor axes will coincide wIlIi the axis of the cylinder. Care should be taken to make the angle between these axes a right angle. 3. Draw the ellipse representing the smaller circle in the upper end of the core box at the required level. Refer to the scale of levels to estimate the major and minor axes of the ellipse. Draw the ellipse with these axes and test it as described under, "To Draw and Test an Ellipse," page 47, 4. Lay off the major axis and determine the length of the minor axis of the larger ellipse as described under, "Concentric Circles in Perspective," page 48. PERSPECTIVE SKETCHING 51 5. Only one-half of the larger ellipse representing the lower end of the bushing will be seen. The length of the minor axis of this ellipse may be found by the method illustrated in Fig. 42. H G is drawn through G converging with E F. While only the lower half of the ellipse will be needed, the complete ellipse should be drawn as construction. 6. Complete the constructive stage of the sketch by drawing the vertical contour elements of the cylinder which join the ends of the major axes of the large ellipses. 7. Erase all construction lines and complete the sketch in the usual manner. _Qia^4- JoAn/Bcz^^ z8 8 8 8 8 418 698 785 829 z z3 3 3 3 3 136 983 568 3921 z Z 1^36-8"— ^ 1— 23'-9|— >| _ ^^8-10 >\ Y '^'-32 n 00 CO oo — D — Z 1— l3'-2^'— H |^I69'-0|'^ _ — 1 Fig. 45. Lettering Plate 4. 8, 3 PREPARATORY INSTRUCTIONS FOR LETTERING PLATE 4 The combination of ovals in the 8 serves as a basic form for the 3. In making the curved strokes of these numerals the stu- dent should have in mind the form of the complete oval. DATA FOR LETTERING PLATE 4 Given: Plate 4 to reduced size. Fig. 45. Required: To make the plate to an enlarged scale. 52 MECHANICAL DRAWING DATA FOR EXTRA DRAWING PLATE Given: The dimensions of a picture frame as shown in Fig. 46. Required: To draw the picture frame as though it were lying on a table, with its upper surface 4'' below the level of the eye. At this level a portion of the bottom of the hole will be visible. h- 4 DIAM. s'diam. '-i i ^ #r-i5 t cf -i- ""7K A [ Fig. 46. Picture Frame Section PREPARATORY INSTRUCTIONS FOR DRAWING PLATE 5 The Horizontal Measure Cylinder, Fig. 47 shows a horizontal cylinder inscribed in a measure cube. This cylinder is therefore one inch in diameter and one inch long. Due to foreshortening, Fig. 47. Horizontal Cylinder In- scribed IN A Measure Cube Fig. 48. Horizontal Measure Cylinder the major axis of the nearer base is slightly less than one inch, and the axis of the cylinder is shorter than the line representing the horizontal edge of the measure cube. These differences are so slight that they will be disregarded in the following analysis of the cylinder, which will hereafter be referred to as the horizontal measiire cylinder. Fig. 48. PERSPECTIVE SKETCHING 53 Figs. 49 and 50 are similar to Figs. 47 and 48, respectively, but show a horizontal cylinder at a different level, with its axis receding to the right instead of to the left. 1. Since the axis of a horizontal cylinder in 45° perspective always extends toward a vanishing point, the inclination of the axis indicates the level at which the cylinder is drawn. Figs. 48 and 50. 2. The major axis of the bases are perpendicular to and the minor axis coincident ivith, the axis of the cylinder as in the vertical measure cvlinder. Fig. 49. Horizontal Cylinder Inscribed in a Measure Cube Fig. 50. Horizontal Measure Cylinder 3. The major axis of the nearer base is equal in length to the diameter of the cylinder, or one inch. The major axis of the far- ther base is shorter, on account of the convergence of the contour elements of the cylinder. 4. The distance between the centers of the bases is equal to the horizontal receding edge of the measure cube, which is ap- proximately three-fourths of the front vertical edge of the cube. Since the major axis of the near base is drawn equal to the front vertical edge of the measure cube, or one inch, the distance between the centers of the bases may be taken as three-fourths the length of the major axis of the near base. This ratio remains constant for all ordinary levels. 5. It will be noticed in Figs. 48 and 50 that the minor axes of the nearer bases are practically equal to the distance between the centers of the bases or three-fourths of the major. axis of the 54 MECHANICAL DRAWING nearer base. When the nearer ellipse is drawn, the half length of the minor axis of the farther ellipse may be determined by drawing a line CD through D, converging with AB. Fig. 48. These lines do not converge toward a point on the horizon line, DATA FOR DRAWING PLATE 5 Given : The Split Core Box represented in Plate 4. Fig. 43. Required: To draw the Core Box in a horizontal position with its axis 4^" below the level of the eye, or any similar object assigned by the instructor. Instructions: 1. Draw through the center of the sheet a line in the direction of one of the vanishing points, to represent the axis of the cyl- inder at the required level. The angle of inclination may be obtained from Fig. 22. 2. Refer to Fig. 23, estimate, and lay off three foreshortened inches on the axis. One-half of this length should fall on either side of the center of the sheet to locate the drawing centrally on the sheet. 3. Draw through the points thus determined the major axes of the bases at right angles to the axis of the cylinder. 4. Draw the ellipse representing the nearer end of the Core Box as shown in Fig. 43. C F is made equal in length to the outside diameter of the Core Box, 2". D is determined by draw- ing C D through C parallel to AB. Test each ellipse as described under, "To Draw and Test an Ellipse," page 47. 5. From the ends of the major axis of the larger ellipse draw contour elements converging with the axis of the cylinder to determine the ends of the major axis of the farther base. 6. The half length of the minor axis of the farther base may be determined as shown in Fig. 43. HG is drawn through G converging with E F. E F and H G do not converge toward a point on the horizon line. While only one-half of the farther ellipse will show in the finished drawing, a better result will be obtained by drawing the complete ellipse as construction. 7. Erase all construction lines, including the axes of the ellipses, and finish the sketch in the usual manner. PERSPECTIVE SKETCHING 55, PREPARATORY INSTRUCTIONS FOR LETTERING PLATE 5 Horizontal and Vertical Strokes. As stated under Plate 1 vertical strokes are usually made downward and horizontal strokes to the right. HIT Fig. 51. Spacing op Adjacent Vertical Stems The direction of horizontal and vertical strokes must be exact. The relative width of the letters is shown in column 4. Fig. 52. STROKES 1 2 3 1 1 — .... i hn HIM 1 1 WIDTH III III 1 1 ■ riT — illli Fig. 52. Lettering Plate Spacing. In this and the following plates practice in mak- ing individual letters will be followed by practice in making 56 MECHANICAL DRAWING words. In order that the lettering may present a good appear- ance, it is as important that the letters be well spaced as that they be properly formed. Correct spacing depends more on the judgment of the drafts- man than on any rule which might be given. However, it may be said that as a rule the letters should appear to be equally spaced. Fig. 53. Lettering Plate 5. I, L, T, H For this style of letters adjacent vertical strokes should be a distance apart equal to one-half the width of the H. Example : H and I, Fig. 51. Letters of irregular form should be placed at such a distance that the space appears equal to that between the H and I. Example : I and T, Fig. 51. When spacing a letter the beginning of the first stroke should be carefully located. DATA FOR LETTERING PLATE 5 Given: Plate 5 to reduced size. Fig. 53. Required : To make the plate to an enlarged scale. PERSPECTIVE SKETCHING DATA FOR EXTRA DRAWING PLATE 57 Given: The dimension of a picture frame as shown in Fig. 46. Required: To draw the picture frame as though it were hanging flat against a vertical wall, with its center 3" below the level of the eye. Extension op Perspective Theory PREPARATORY INSTRUCTIONS FOR EXTRA DRAWING PLATES The Measure Cube in New Positions. In the preceding plates the measure cube was drawn at different levels, but always with its side faces at 45° with the horizon. Fig. 54. Drawing a Cube at Any Angle If the measure cube is turned with its side faces making other angles with the horizon, the number of positions in which an object may be drawn will be increased. Fig. 54 shows a method of constructing a measure cube at any level and with its side faces at any desired angle. The steps in the construction are as follows : 1. Draw an ellipse representing a two-inch circle at the required level. 58 MECHANICAL DKAWING 2. Draw a semi-circle of the same diameter as the circle represented by the ellipse, with its center at the center of the ellipse. 3. Mark off on the semi-circle the angles which the faces of the cube are to make with the horizon. These angles should be 90° apart. 4. Vertical lines through these points intercept the ellipse in the ends of the nearer edges of the upper face of the cube. These edges meet at the center of the ellipse which is the upper front corner of the cube. Fig. 55. Cylinder Inscribed in a Measure Cube Fig. 56. Measure Cyi.indkr. 5. Make the front vertical edge one inch long as in 45° perspective. 6. Complete the cube by drawing the remaining edges con- verging so as to give the faces of the cube the appearance of squares. It will be noted that the farther edges of the upper face intersect on the line making 45° with each of the side faces. The Measure Cylinder in New Positions. Fig. 55 shows a horizontal cylinder inscribed in a measure cube with its side faces at other than 45° to the horizon. This cylinder is there- fore one inch in diameter and one inch long. Due to foreshort- ening, the major axis of the nearer base is slightly less than one inch and the axis of the cylinder is shorter than the line rep- resenting the horizontal edge of the measure cube. These differ- ences are so slight that they will be disregarded in the following analysis of the measure cylinder. Fig. 56. PERSPECTIVE SKETCHING 59 1. The distance between the centers of the bases is equal to the horizontal receding edge of the measure cube. This distance will be shorter as the angle of the axis of the cylinder to the horizon increases. 2. The major axes of the bases are perpendicular to, and the minor axis coincident with, the axis of the cylinder. 3. The major axis of the nearer base is equal in length to the diameter of the cylinder, or one inch. The major axis of the farther base is shorter on account of the convergence of the contour elements of the cylinder. Fig. 57. Cylinder Inscribed in a Measure Cube Fig. 58. Measure Cylinder 4. The length of the minor axis of the nearer base will depend upon the angle that the axis of the cylinder makes with the horizon. Fig. 56 illustrates the case in which the minor axis is lengthened, due to the axis of the cylinder making an angle greater than 45° with the horizon. Fig. 58 illustrates the case in which the minor axis is shortened, due to the axis of the cylin- der making an angle less than 45° with the horizon. The length of the minor axis for other positions may be estimated by using Figs. 56 and 58 as guides. For any angle the axis of the cylinder makes with the horizon the length of the minor axis will remain the same for all levels. When the nearer ellipse is drawn, the half length of the minor axis of the farther base may be deter- mined by drawing a line C D through. D, converging with A B. Figs. 56 and 58. 60 MECHANICAL DRAWING DATA FOR EXTRA DRAWING PLATE Given: The objects shown in Figs. 59, 60, 61, and 62. Fig. 59. Concrete Block Required: To draw one or more of the above objects in positions selected from the following table by the instructor. Fig. 60. Nail Box The level at which the object is drawn may be assumed by the student. PERSPECTIVE SKETCHING 61 The right vertical face of tlie enclosing solid makes one of the following angles with the horizon : 1. 15°. 2. 30^ 3. 60^ 4. 11 The objects should be centered on the sheet as in previous problems. Fig. 61. Broom Holder Review Questions 1. (a) What is the horizon? (b) How is it represented? (c) What is its relation to the eye? 2. (a) What is a vanishing point? (b) Where is it located? 3. Where do parallel horizontal lines appear to meet in per- spective ? 4. Do vertical lines appear to converge in perspective? 5. (a) What is meant by foreshortening? (b) Are the per- spectives of equal lengths on the same vertical edge equal? (c) On the same horizontal edge? (d) Are the perspectives of equal vertical lengths at different distances from the observer equal ? 6. (a) What is the angle of inclination? (b) How does it vary? 62 MECHANICAL DRAWING 7. (a) In what position on the drawing board is the paper fastened? (b) How is it fastened? 8. Describe in detail how the pencil should be sharpened for sketching. 9. (a) What is the position of the hand and pencil in sketch- ing horizontal lines? (b) Vertical lines? (c) What is the Pig. 62, Bird House (Dimensioned Perspective) essential difference? (d) What movements are made to produce the line ? 10. (a) What is meant by constructive stage? (b) Finish- ing stage ? 11 In what way does a scale of levels assist in making a perspective of a rectangular object ? 12. (a) Where are all vertical measurements laid off in per- spective? (b) Why? PERSPECTIVE SKETCHING 13. How are horizontal measurements made ? 14. Explain what is meant by enclosing solid. 6S Fig. 63. Book Eack (Dimensioned Perspective) 15. (a) What is a measure cube? (b) Why is it called a measure cube ? Fig. 64. Form for Testing Concrete Prisms 16. Of what use is the table line ? 17. (a) How do you proceed to locate the drawing centrally on the sheet? 64 MECHANICAL DRAWING 18. How are the perspectives of the inclined lines located? Fig. G6. Pen Eack 19. (a) Give the proportions of the vertical measure cylinder, (b) The major axes of the bases are at what angle with the axis of the cylinder? PEESPECTIVE SKETCHING 65 20. How does the difference in level affect the appearance of a horizontal circle in perspective? 21. Of what assistance is a scale of levels in drawing a vertical cylinder ? 22. How is the ratio of the minor axes of two ellipses repre- senting concentric circles determined ? 23. (a) Give the proportions of a horizontal measure cylin- der, (b) The major axes of the bases are at what angle with the axis of the cylinder? (e) What is the relative length of the major and minor axes of the nearer base ? DATA FOR REVIEW DRAWING PROBLEMS Given: The objects shown in Figs. 63, 64, 65, 66. Required: To draw one or more of the above objects in 45* perspective. The level at which the object is drawn may be assumed by the student. CHAPTER II ORTHOGRAPHIC SKETCHING Prospectus In this chapter the work of the preceding chapter will be continued in order that the value of the perspective sketch as an aid in interpreting orthographic views may be apparent. At the same time more general application will be made of perspective principles and additional skill acquired in representing objects pictorially. It is the chief aim of this chapter to familiarize the student with the method of representation generally used in working drawings. By the time the work of this chapter is finished the student should be able to read drawings of ordinary complexity as well as to make freehand orthographic sketches with a con- siderable degree of skill and confidence. PREPARATOEY INSTRUCTION FOR DRAWING PLATE 6 Views. ^ In perspective sketching the object is viewed from one position, so chosen as to show its three general dimensions in one view. Such a means of representation does not show the prin- cipal surfaces of an object in their true form and proportion or the principal edges in their true lengths. In order to represent the principal surfaces of an object in their true form and proportion and the principal edges in their true length, the object is usually viewed in two or more direc- tions, viz. : from directly in front, directly above, or directly from the right or left. Each view thus secured will give the exact form and proportion of the surfaces and the true lengths of the edges toward which one is looking perpendicularly. Views thus secured are known as orthographic. In mechanical drawing orthographic views are generally used. 66 ORTHOGRAPHIC SKETCHING 67 Pig, 69 shows two views of a bench stop. The view marked TOP represents orthographically what is seen from directly above the object and the view marked front represents what is seen from directly in front of the object. The top view shows two general dimensions in horizontal directions, viz. : the dimen- sion from left to right and the one from front to back. The front Fig. 67. Type Problem. Perspective of Bench Stop view shows the horizontal dimension from left to right and the vertical dimension. Thus the three general dimensions are given in the two views and the proportions of the object are determined. Relation of Top and Front Views. It should be clear from the above statement that one of the general dimensions, viz. : the horizontal dimension from left to right, is common to the front and the top views. For this reason as a matter of con- venience in making and interpreting the drawing it is essential that the top view always be placed directly above the front view. 68 MECHANICAL DRAWING Under this condition all distances from left to right may be projected from one view to the other. '^Beading" the Drawing. To form a mental image of an object the relation of its surfaces, edges, and comers as repre- sented must be studied. This process is called reading the draw- ing and is illustrated under the four following headings: (The present discussion is confined to rectangular solids.) Fig. 68. Type Problem. Constructive Stage of the Okthogkaphic Sketch Plane Surfaces. Fig. 69 represents an object having plane surfaces. 1. When the observer is looking perpendicularly at a surface it appears in its true form and proportion. Example : The rectangular top surface A B C D of the bench stop, Fig. 69, is represented in its true form and proportion in the top view. 2. When the observer is looking edgewise at a plane surface it appears as a straight line. Example : Line E F is the front view of the top surface A B C D. Fig. 69. ORTHOGRAPHIC SKETCHING^ 69 Straight Edges. 1. A straight edge viewed at right angles to its length shows as a line in its true length. Examples The front edge of the top surface of the bench stop shows in its true length in line A B in the top view and in line E F in the front view. 2. A straight edge viewed endwise appears as a point. Exam- ple : Point F is the front view of the edge B C. Fig. 69. J_ -JG -d-^ k' 1^ B H SCREWS d '"2 TOP ,.. I FRONT 4 -tt p: :£: c^^jzz^^i^rf^ib^t. FiG. G9. Type Pkoelem. Finished Sketch of Bench Stop Curners. A corner appears as a point when viewed from any direction. Example : The upper front corners at the left of the bench stop are represented by A in the top view and E in the front view. Invisible Edges. Hidden edges or hidden surfaces viewed edgewise are represented by dotted lines to distinguish them from visible edges or surfaces. Example : 6 H in the top view. Fig. 69. 70 MECHANICAL DRAWING Problems and Questions on Orthographic Principles The student should test his knowledge of the orthographic principles just stated by answering the following questions : See Fig. 70. 1. (a) Where is the front view of the horizontal surface 9, 10,15,16? (b) Of 10, 12, 13, 15? (c) Of 9, 11, 14, 16? 2. (a) Where is the top view of the horizontal surface 5, 4? (b) Of 8,1? 2 Fig. 70. Review Problem 3. (a) Where is the top view of the front vertical surface 1, 2, 3, 4, 5, 6, 7, 8? (b) Of the rear vertical surface 1, 2, 3, 4,5,6,7,8? 4. (a) Where is the top view of the vertical surface 7, 8? (b) Of 3, 4? (c) Of 5, 6? 5. (a) Where is the top view of the front horizontal edge 2,3? (b) Of 7, 6? 6. (a) Where is the front view of the rear horizontal edge 15,13? (b) Of 16, 14? ORTHOGRAPHIC SKETCHING 71 7. (a) Where is the front view of the upper horizontal edge 10, 15? (b) Of 12, 13? 8. (a) Where is the top view of the edge 5? (b) Of 6? 9. (a) Where is the front view of the upper front corner 12 ? (b) Of 9? (c) Of the upper back corner 15? 10. (a) Where is the top view of the front corner 2? (b) Of 5? The Type Problem. In each of the following problems pre- sented for solution the methods to be employed and the results to be obtained will be illustrated by a type problem. This type problem will consist of two parts : 1. A drawing of an object similar to, and represented in the same manner as, the one given for solution. 2. A solution of the problem corresponding to that required of the student. Example: Fig. 69 is the type problem for the first ortho- graphic sketch. Fig. 67 is the perspective of the bench hook shown in Fig. 69 and corresponds to the kind of a drawing the student will make from Fig. 71, 72^ or 73. Materials. The materials used for the plates in this chapter are the same as those used in perspective sketching (see page 15; except that in this case the 5H pencil will be used for both the constructive and finishing stages. Perspective STcetcTies. In this chapter perspective sketches will be drawn preceding the orthographic sketches as a means of interpreting the orthographic views and at the same time to continue the practice necessary to develop skill in representing objects in perspective. DATA FOR DRAWING PLATE 6 Given: An orthographic sketch, Fig. 71, 72, or 73. Required: To draw a 45° perspective sketch of the object shown in Fig. 71, 72, or 73 as assigned by the instructor, with the upper front corner of the enclosing solid 3|'' below the level of the eye or any similar object assigned by the instructor. T~ jL_ 'T7i~ I iniCD ^AiC/. J^^Bc Fig. 71. Gain Joint - - -s — 3' — >j ,— TIN BOX ^^ __J ■ 1 --IM 1 12" =1 -Jf-J ■i' y >. -■c^ "tZ-^-JtrA-vty i£l> -d^ (72) Tig. 72. Scouring. Board ORTHOGRAPHIC SKETCHING 73 Instructions: Use the comer marked A as the upper front corner of the object. All lines of this drawing are to be made freehand, includ- ing the light lines in the constructive stage. Omit all dimensions. Pig. 73. Cement Fern Jar PREPARATORY INSTRUCTIONS FOR LETTERING PLATE 6 Inclined Strokes. Before starting an inclined stroke, the stu- dent should sense its direction, moving the pencil between its two ends without touching the paper. DATA FOR LETTERING PLATE 6 Given: Plate 6 to reduced size. Fig. 75. Required: To make the plate to an enlarged scale. 74 MECHANICAL DRAWING PREPARATORY INSTRUCTIONS FOR DRAWING PLATE 7 The Constructive Stage. This stage in orthographic sketch- ing is similar to the constructive stage in Perspective Sketching described on page 18. It consists of drawing all lines of the sketch lightly and full. No attempt should be made to make the lines exactly the right length in this stage. When drawing STROKES 1 2 3 4 _ zir- — I .=1^ ... i ...L— ... ...I i 1 ^ 1 l^= M Vi WIDTH .... lilt" N ill "'"■ Fig. 74. Lettering Plate each line it should be made long enough to give all necessary intersections with other lines. By this time the student should have gained such facility in drawing freehand lines that he will not need the rule to draw straight lines. If a straightedge is used at all in this chapter it should be necessary only in ruling long lines in the constructive stage and in locating one view directly opposite another. ORTHOGRAPHIC SKETCHING 75 In laying out the views of an orthographic sketch on the sheet, proceed in the following manner : 1. Referring to Fig. 68, mark off tentatively the position of the extreme right and left of each view. Shift both marks to the right or left, if necessary, to make A equal B. 2. In like manner mark off the vertical dimensions of each view, leaving a space between the two views proportional to that which is shown in the figure. This distance should be from f _QU^6 fl^i^An/ Q/7^ _ =FFFFF LIFT FIFTH FIT IF f =EEEEE FILLET FILE TELL = zNNNNN FIN NINETEEN FIN f zMMMMM ELEMENT LIMIT = fpEElT TENTH MILE NINE LIME FILM |Z Fig. 75. Lettering Plate 6 to 1". Shift all marks up or down if necessary to make C equal D. 3. Make any necessary adjustments in the general propor- tions of the views. 4. In proportioning the details of the views, a comparison of the dimensions of each detail with the dimensions of the views in which it appears will aid in securing good results. Example: In the front view, Fig. 69, the width of the cleats is about one- sixth of the total length of the bench hook and their thickness is twice that of the board to which they are fastened. 76 MECHANICAL DRAWING Finishing Stage. As in Perspective Sketching, the finishing stage consists in erasing unnecessary lines made in the construct- ive stage, tracing over the outline of the drawing, and otherwise giving it a finished appearance. The student should proceed as follows : 1. Erase all construction lines and retrace the lines of the drawing, using a 5H pencil. 2. Represent all invisible edges by dotted lines which are composed of i" dashes with ^j" spaces between them. The ends of the dashes should be made definite by placing the pencil on the Fig. 76. Dotted Lines paper, moving it the required length, and then removing it as nearly as possible vertically from the paper. Fig. 76 shows the correct method of joining dotted lines to full lines. 3. Place the dimensions on the sketch as described below under, ''Arrangement of Dimensions." Arrangement of Dimensions. Dimensions are placed on a drawing as shown in Figs. 71 and 72 to show the size of the object represented Only those dimensions are given which are necessary to determine completely the size of the object. An over-all dimension is one which shows the distance from one extreme point to another. Example : The five inch dimen- sion in Fig. 71. A detail dimension is one which shows the dis- tance between two points on some part or detail of the object. Example : The three and one-half or one inch dimension. Fig. 73. ORTHOGRAPHIC SKETCHING 77 When detail dimensions and a dimension representing their sum are given, they should be grouped in parallel lines. The shorter dimension should be near the outline of the object to avoid the confusion arising from the crossing of lines. Example : Those below the front view, Fig. 69, are properly arranged. The Dimension Form. Fig. 77 shows what is known as the dimension form. It includes all of the elements of the convention used in indicating linear dimensions on a drawing. The following points should be noted : Fig. 77. Dimension Form 1. Horizontal dimensions read from left to right. 2. Vertical dimensions read from the bottom toward the top of the sheet. 3. Extension lines begin about sV from the outline of the object and continue |'' beyond the arrowhead. 4. The space between the outline of the object and the nearest dimension line or between two parallel consecutive dimension lines is about \". 5. Arrowheads are placed on the dimension lines at their extreme ends. 6. Arrowheads are composed of two slightly curved lines sym- metrical with respect to the dimension line. The length of the arrowhead should be about ^" and the width ■}^'\ Fig. 77. The 78 MECHANICAL DRAWING strokes for arrowheads pointing in different directions are shown in Fig. 28. 7. The whole number in the dimension figure will be made ¥' high. 8. The total height of the fraction in the dimension figure is twice that of the whole number with a clear space between each numeral and the division line. 5^ ^8 Fig. 78. Showing Actual Heights of Whole Number and FuAdTioN To check these heights of numerals in a dimension figure, mark off an eighth-inch and a quarter-inch space on the edge of a card and use it as a scale. Fig. 78. 9. The dimension figure is generally located centrally in the dimension line, which is broken sufficiently to admit it. DATA FOR DRAWING PLATE 7 " Given: Orthographic sketches, Figs. 71, 72, and 73. Required: To make an orthographic sketch of the object shown in Fig. 71, 72, or 73 ; or any similar object as assigned by the instructor, on a 9"x 12'' sheet. Instructions: 1. Draw a border line as in perspective sketching. 2. The rectangles shown about the drawing in Figs. 71, 72, and 73 are proportional to the size of the 9''x 12" sheet and the border rectangle. The over-all lengths of the view of the sketch ORTHOGRAPHIC SKETCHING 79 " STROKES WIDTH Mil illli 1 1 1 1 1 Ik Hill 1 2 3 1 = ' 7 IK S ... ) 1 // / \ Fig. 79. Lettering Plate Fig. 80. Letteri.\g Plate 7. K, Y, Z, A 80 MECHANICAL DRAWING should bear the same ratio to the dimensions of the sheet as the corresponding dimensions in the figure bear to the size of the rec- tangle representing the sheet. With this in mind proportion the views and locate them centrally on the sheet as previously explained. 3. Draw in the details and finish the drawing of the views, as usual. 4. Draw in the extension lines, dimension lines, arrowheads, and numerals following the directions given under, "Arrange- ment of Dimensions," page 76. PREPARATORY INSTRUCTIONS FOR LETTERING PLATE 7 As stated under Plate 6, the student should sense the direc- tion of an inclined stroke before drawing it. The spacing between irregular letters should ap]>ear equal to the area of one-half the H. Fig. 81. KEY Fig, 81. Spacing of Irregular Forms DATA FOR LETTERING PLATE 7 Given: Plate 7 to reduced size. Fig, 80. Required: To make the plate to an enlarged scale. PREPARATORY INSTRUCTIONS FOR DRAWING PLATE 8 It is customary to draw the top and front views of an object when these views will show the form and proportions satisfac- torily and when only two views are needed. Some objects are of such a form, however, that a front view and a view from one side are needed to determine completely the form of the object. The particular side view is selected which will represent the object by the use of the least number of dotted lines. Fig. 82 represents an object which would be well defined by the use % ORTHOGRAPHIC SKETCHING 81 of a front view and one side view. The right side view would be the one chosen in this case. Since the two side views contain the same information, if one is given the other may be drawn. As previously explained, an observer sees all vertical dimensions and the horizontal dimension from left to right in the front view. All vertical dimensions and the horizontal dimensions from front to back are seen in the side view. A right side view is always placed directly to the right and a left side view directly to the left of the front view. This is done both for the sake of convenience in making and reading a draw- fRONT Tig. 82. Beveler RI6HT sioe ing and because an observer, when viewing an object, would, after obtaining the front view, naturally step to the right for a right side view or to the left for a left side view. To secure the front view after the side view is drawn, or to secure the side view after the front is drawn, all vertical distances may be projected from the first of the two views drawn. Fig. 82 shows the front view and the two side views of an object in their proper relative positions. Inclined Surfaces. Any surface which is at right angles to the line of sight, when an object is being viewed, will show in its ti*ue form and size. A surface which makes other than a right angle with the line of sight is called an incliried surface. Such surfaces do not show in their true form and size. Fig. 82 represents an object having inclined surfaces. If one surface is 82 MECHANICAL DRAWING rectangular and two of its edges are at right angles to the direc- tion in which it is inclined, as in the ease of the surface C D E F, Fig. 82, the vertical dimension of the rectangle representing the surface in the front view is less than the actual width of the surface. The inclined surface C D E F is represented by the inclined line G H in the left side view. G H is equal to the true width of the surface, G'H', representing the same surface in the right side view, is also equal to the true width of the surface. It must be evident from a study of Fig. 82 that in representing any rec- tangular inclined surface which has two of its edges at right angles to the line of sight, the dimension represented by these Fig. 83. Construction for Angles and Hidden Corners (Perspective) edges will show in its true length. C D and E F, perpendicular to the direction of sight in the front view, show the true length. of the rectangle in this view. The end edges, G H and G'H' of the surface C D E F, are perpendicular to the direction of sight in the side views and therefore show the true width of the surface in these views. Inclined Edges. A straight edge which is not at right angles to the direction in which it is viewed is represented by a line shorter than the actual length of the edge. Example : The end edges of the surface C D E F are represented in the front view, Fig. 82, by lines C E and D F. These lines are shorter than the actual lengths of the edges, as shown by lines GH and G'H' in the side views. In sketching an angle where the direction of the edge is given by dimensions locating two points on the edge, the line represent- ORTHOGRAPHIC SKETCHING 83 ing the edge should be determined by laying off the dimensions given to locate the points on the line. Where the dimension is given in degrees the ends of the inclined lines should be located by estimating the lengths of the legs of the right triangle of which the inclined line is the hypotenuse. Example : The length of the lines A B and A C, Fig. 83, are laid off to determine the direction of B C. For a 45° angle A B and A C represent equal distances. For a 60° angle AB is roughly -j^ of AC. In determining the position of a line passing through an invisible corner, such as E F, Fig. 83, make a construction for the invisible corner by drawing lines B E and E G. The student should test his knowledge of the orthographic principles just stated by answering the following questions: I a 3 4 Fig. 84. Review Problem Problems and Questions in Orthographic Principles Refer to Fig. 84. 1. Where is the side view of the inclined surface 1, 2, 7, 8? 2. (a) Is line 1, 2 equal to the true width of the inclined surface? (b) Where is its true length shown? (c) Why? 3. Where is the inclined edge 1, 8 shown in its true length? Why? 4. (a) Is the vertical surface 11, 15 on the front or back of the object ? (b) Why ? (c) Where is it shown in the front view ? 5. Where is the vertical surface 14, 13 shown in the front view ? 84 MECHANICAL DRAWING 6, Where is the horizontal surface 13, 16 shown in the front view? 7, Where is the horizontal surface 6, 7 shown in the side view ? 8, Where is the vertical surface 4, 9 shown in the side view ? f 'I-'- -^ — . RIGHT END (P/cCtD f.J,rlLu ».rt- Fig. 85. Type Problem. Hardie. Given Views DATA FOR DRAWING PLATE 8 Given: Orthographic sketches, Figs. 88 and 89, 90 and 91. Required: To draw a 45° perspective sketch of the object shown in Fig. 88, 89, 90, or 91, or any similar object as assigned by the instructor. The upper front corner of the enclosing solid is 2^" below the level of the eye. Use the point marked A as the upper front corner of the measure cube. All lines of this sketch including the constructive stage should be made entirely freehand. Omit all dimensions. Fig. 86. Type Problem. Hardie. Perspective Sketch Fig. 87. Type Problem. Hardie. Required Views A A -A A t \ / J \ / \ / j V \ / 1 I -KM t \ ^ *i'4. ^2"^ ^r^ -!= — 4"- — * ^<- — 4- — — ^ — 6" ^5?^lX f. J-rr^ Qo Fig. 88. Sheet Metal Hopper (86) Fig. 89. Knife and Fork Box Fig. 90. Bench Fig. 91. Book Eack STROKES 1 2 3 4 v\ \// \ \ / / \\ \// \A^ w :$::: T \ \ / / X^ Tt LJl LJ =ll — - 1 J WIDTH iiiii M iiiiiii IIIM iiiii :bt Fig. 92. Lettering Plate Fig. 93. Lettering Plate 8. V, W, X, U, J ORTHOGRAPHIC SKETCHING 89 DATA FOR LETTERING PLATE 8 Given: Plate 8 to a reduced size. Fig. 93. Required: To make the plate to an enlarged scale. PREPARATORY INSTRUCTIONS FOR DRAWING PLATE 9 Dimensioning Angles. The inclination of an edge or surface is commonly determined by giving dimensions which fix two points on the line, usually its ends. Example : The wedge end of the hardie. Fig. 85. In some cases it is desirable to give the inclination of an edge or surface in degrees. In this case the dimension line is an arc with its center at the intersection of the two lines forming the angle. Example : The 45° angle in the end of the bench. Fig. 90. Solution of the Problem. Attention is called to the fact that in the following problems the student is required to draw dif- ferent views from those given. Read the statement of the problem carefully before starting to draw. DATA FOR DRAWING PLATE 9 Given: Orthographic sketches, Figs. 88, 89, 90, and 91, showing the front and left side of each of the objects. Required: To draw the front and right side views of the object shown in Fig. 88, 89, 90, or 91, or any similar object as assigned by the instructor. Instructions : 1. Block in the views of the object as described on page 75 and as carried out in Plate 7, so that they are in the center of the sheet. 2. Complete the details of the views in light lines. 3. Trace over the lines as explained on page 76, making them the proper weight. 4. Draw in the dimension lines and put in the arrowheads and figures in the order given on page 77. 90 ' MECHANICAL DRAWING 5. Write in the plate number and name as usual. Press the paper back into the tack holes. Sb Fig. 94. Spacing of Curved Forms STROKES L [J 2 3 a n g: WIDTH n: Fig. 95. Lettering Plate PREPARATORY INSTRUCTIONS FOR LETTERING PLATE 9 The letter is wider than the numeral 0. The forms of the Q, C, and G are based on the oval of the 0. ORTHOGRAPHIC SKETCHING 91 Spacing Curved Stroke Letters. As stated in the instruc- tions for Plate 5, the area included between the contour of two adjacent letters should appear equal to the area of one-half of the H, "When a vertical stroke and a curved stroke are properly- spaced the clear distance between them is slightly less than one- half the width of the H. Example : The I and 0. Fig. 94. The clear distance between two curved strokes will be less than that between vertical and curved strokes. Example : The and in Fig. 94. _(Mi^f ^^r7d^^(r5^_ =00000 ONYX AVIATION |z f QOOOO QUAIL ANTIQUITY z zCCCCC CHEQUE CONNECTION z zGGGGG ENGINE GAUGE r-5^"z zDDDDD LADLE HEAD FLOAT Z Fig. 96. Lettering Plate 9. 0, Q, C, G, D When spacing a letter having a curved outline the begin- ning of the first stroke should be carefully located. In planning the letter, the clear space between it and the previous letter should be held in mind. DATA FOR LETTERING PLATE 9 Given: Plate 9 to reduced size. Fig. 96. Eequired: To make the plate to an enlarged scale. PREPARATORY INSTRUCTIONS FOR DRAWING PLATE 10 Objects thus far sketched for which orthographic views were drawn have had plane surfaces. In Plate 10 an object having cylindrical surfaces is to be represented orthographically. 92 MECHANICAL DRAWING Cylindrical Surfaces. In Fig. 97 an object having cylin- drical surfaces is represented by orthographic views. 1. The outline of the front view represents cylindrical sur- faces when viewed at right angles to their axes. 2. A simple cylinder, when viewed in this direction, appears as a rectangle. ( ,t