Mechanical Drafting REVISED IN 1915 By THE DEPARTMENT OF GENERAL ENGINEERING DRAWING H. W. MILLER, M.E. *. K. STEWARD, C.E. F. M. PORTER, M.S. H. H. JORDAN, B.S. H. O. RUGG, C.E. R. CRANE, S.B. C. A. ATWELL, B.S. In the University of Illinois Urbana, Illinois (Original edition by H. W. MILLER) The Manual Arts Press Peoria. Illinois Copyright, 1912 H. W. Miller and R. K. Steward Copyright. Revised Edition, 1916 H. W. Miller Third Edition, 1917 PRE LIBRARY STATE NORMAL SCHOOL MANUAL ARTS *NO HOME ECONOMICS SANTA BARBARA, CALIFORNIA ACE !*_ In writing the original edition of this text it seemed wise to the author to base its arrangement and content upon two principles which considerable experience proved sound. These principles are : first, that the stu- dent can just as well and perhaps better, be taught the use of instruments on work that will at the same time haVe educational value; second, that for greatest effi- ciency in teaching drawing the text should be made so complete and follow the class room work so closely that lecturing is unnecessary. The above principles were followed by first design- ing a very flexible course in drafting, substituting draw- ings of machine parts for the conventional geometrical figures. The work was arranged into definite groups, according to subject, each group being scheduled for a definite amount of time. Second, the text was so ar- ranged that section, lesson or chapter one, gave all information necessary for the work included in group one, etc. After three years ' very satisfactory trial of the text, ^ the department of drawing has undertaken a complete 09 revision with the desire that the work shall be not only CT> a text, more complete than the first, but also a book of reference that will be of service after the student has "^completed the course. TT TTT n-r o H. W. MILLER. 2 October, 1915. CONTENTS PAGE Chapter 1. Lettering, Freehand and Mechanical 7 Chapter 2. Use of Instruments 29 Chapter 3. Orthographic Projection 52 Chapter 4. Working Drawings 65 Chapter 5. Fasteners, Threads, Bolts and Nuts, etc 88 Chapter 6. Shop Terms, Tools, Machines, etc 106 Chapter 7. Isometric and Oblique Projection 125 Chapter 8. Machine Sketching 147 Chapter 9. Perspective 151 Appendix 161 MECHANICAL DRAFTING CHAPTER 1 LETTERING FREEHAND (1) Freehand or offhand lettering is so much a part of every engineer's daily routine that to be unable to letter with speed and grace is considered an inexcusable discredit. The results of practice show that no one need be embarrassed long because of the lack of this skill, for anyone can learn to letter. However, the acquisition of proficiency demands what skill in any manual perform- ance requires, more or less experience and careful study of principles. It is fortunate for the beginner in lettering that there are very few elements that must be mastered. Most engineers use extremely simplified styles of freehand letters. The Reinhardt alphabet (slant or vertical) is especially noted for its simplicity as it has been stripped of all superfluous appendages. that made formed styles both complicated and time-consuming in their use. In the practice of either type the beginner will find that all of the letters are made up of but two or three charac- teristic elements or strokes, each of which is easily constructed. The first style or type presented is the Reinhardt slant. It should be mastered thoroly because it is in use in most drafting rooms and colleges. It is probable that its use in over eighty per cent of the large drafting rooms MECHANICAL DRAFTING. of the country is due to its legibility and ease and rapidity of construction. EQUIPMENT (2) Selection of Lettering Pens. For a pure type of either Eeinhardt or vertical letter, such a pen should be used as will give a stroke of uniform width, weight, or heaviness, when it is moved up, down, right, left, or diag- onally on the paper; otherwise the letter will have a shading, which does not belong to the types mentioned. Fig. 1 Some pens which have proven satisfactory for letters of a uniform weight are the Sheppard lettering pen, Paysant pen, Moore's Non-Leaking fountain pen, and any of the steel points known as ball pointed pens. Inking of Pens. Apparently a great part of the trouble experienced in the use of the above pens is due to improper inking. No lettering pen should ever be dipped into the ink bottle. The proper method is to transfer by means of the quill attached to the cork a small amount of ink to the inside of the ball pointed pen or between the nibs of the Sheppard or Paysant pens. LETTERING. 9 It is well to hold the pen point over the bottle so that any superfluous ink may not be spilled on the drawing or desk. The word of warning that must be heeded is to use only enough ink and no more. One may be sure of not having too much ink on the ball pointed pen if he will always stroke off the pen upon the quill before trying any letters. Slope Guide. Immediately on beginning practice on inclmed freehand letters it will be well to provide oneself with a sheet of heavy drawing paper, about three by eight inches, across which have been ruled a series of heavy parallel lines at from 70 to 75 to the long edge as shown in Fig. 1. These lines should be at equal inter- vals and from one-eighth to one-quarter inch apart. An angle of approximately 72 may easily be constructed by laying off a right triangle whose base is 2 and altitude 6, Fig. 2. If this sheet, which may be termed a slope guide, be laid just below the line on which the freehand letters are to be made, it will not be difficult to make all first element strokes parallel to each other. It is likewise well to make use of such a guide continually until this slope has become perfectly natural, for nothing so detracts from the good appearance of inclined letters as a difference in slope of the stems. Paper. A good quality of ledger paper will be found best for lettering, inasmuch as it has a smooth, hard surface that takes ink evenly. It is likewise well to adopt a standard letter size sheet, 8y 2 xll, which will be found in stock in any printing office or stationery store, and to 10 MECHANICAL DRAFTING. which all modern office files are adapted in case one wishes to file the finished work. PRACTICE ON ELEMENTS (3) Guide Lines. Unless especially printed practice sheets have been prepared, the beginner should rule on the blank sheet a series of six light parallel pencil lines (preferably parallel to the short edge of the sheet) at intervals of one inch and six at intervals of one-half inch. Element Number I. nannnn Element Number . Fig. 3 First element, Stems. Element one is simply a straight line of varying length, Fig. 3, and making an angle with the vertical equal to the slope adopted for the inclined alphabet. In practice this slope can easily be secured by placing the slope guide just beneath the guide line on which one is working. Several lines of stems should be made on the practice sheet, using the half -inch guide lines, each with a single downward stroke of the pen and at equal intervals. When finished the stems should all have the same slope, be evenly spaced and each have the same weight or thickness thruout its length and all stems of the same weight. LETTERING. 11 Second element, Ovals. The second element is a per- fect ellipse, inscribed in a parallelogram, two of whose sides are parallel to element one and whose base is, for normal letters, a little less than the vertical height, Fig. 3. This element can be made with one stroke of the pen, after some little practice; however, it is advisable for the beginner to form it ill with two strokes, as shown in Fig. 4, making slightly r _^_^_^_^ more than half each time l 7 7 J~ / and letting the ends of the Fi s- 4 strokes overlap. This will in general insure a better joint, as the overlapping tends to smooth out the juncture. Fig. 5 In order that one may learn the shape of element number two in the least possible time, it is suggested that a beginning be made as shown in Fig. 5, with the height of the character one inch. Using the one-inch spaced guide lines already on the practice sheet, rule a series of parallelograms, bases one inch and sides inclined at the slope angle. Then sketch in long sweeping arcs tangent to the inclined sides at their middle points, a, Fig. 5 ; next follow the arcs tangent to the horizontal sides, b, Fig. 5. The completed shape now suggests itself, c, Fig. 5, and a few smoothing up strokes will complete the ellipse, d, Fig. 5. It should be remembered that the 12 MECHANICAL DRAFTING. ellipse is tangent to the sides of the parallelogram at their middle points; this gives the necessary tip that is essential to a graceful appearance of the alphabet. '(a) fr) ' J fcj 6/ ' Compressed Normal Extended. Fig. 6 An excellent variation of this exercise is that of making ellipses of varying widths. It is evident, Fig. 6, that this process will yield alphabets of widely differing general effect, altho the elements entering into their construction are identical. The types of letters produced by the varying widths are as indicated, compressed, nor- mal, and extended. The sketch exercise just outlined should be repeated with diminishing heights of three-fourths, one-half, one- fourth, and finally one-eighth of an inch, the size ordi- narily used in drafting. oadqbpcey Fig. 7 FORMATION OF LETTERS (4) In Fig. 7 it is seen that the lower case letters o, a, d, q, b, p, c, e, and y, and capitals C, G, 0, Q, Fig. 10, are simple elements or combinations of elements one and LETTERING. 13 two. Element one and a portion of element two make up lower case letters g, y, j, f , n, h, m, r, s, and u, Fig. 8, and X S I J Fig. 8 capitals B, D, J, P, R, S, and U, Fig. 10. The remaining straight stroke letters, i, k, 1, t, v, w, x, and z, Fig. 9, and A, E, F, H, I, K, L, M, N, T, V, W, X, Y, and Z, Fig. 10, iklTvwxz Pig. 9 are perhaps easiest to construct. It should be noted that the lower case letters a, c, e, etc., are two-thirds the height of the capitals. The letter t is five-sixths height and abcdefghijklmnopqrstu 12.345 vwxyyz 6739O ABCDEFG H IJ KLM N OPQFISTUVWXYZ Fig. 10 b, d, h, etc., are full height. The tails of the letters g, j, p, q, etc., extend below the base line one-third their height. Numerals are the full stem height except when used in fractions when they should be shortened slightly. See Fig. 10 for complete slant alphabet and numerals. 14 MECHANICAL DRAFTING. VERTICAL LETTERS (5) In Fig. 11 is given an alphabet of vertical let- ters. The principles of construction are of course iden- tical with those of inclined letters. Practice should begin on the two elements, stems and ovals, as directed in Art. 3. No vertical guide will be necessary in this abcdefghijklmnopqrstu 12345 vwxyz 6789 ABCDEFGHIJKLMN OPQRSTUVWXYZ& Fig. 11 case, inasmuch as everyone has a well developed sense of appreciation of the vertical. It may be well to mention that when using vertical letters, an extended style, similar to c or d, Fig. 6, is always easiest of execution and has an excellent appearance. MECHANICAL LETTERS (6) The need for letters made entirely with instru- ments will be only occasional, and space will be given here for only the general methods for laying out such work. In the appendix will be found alphabets of vari- ous styles for use in the construction of titles, signs, name plates, etc. These may be constructed either mechanically or freehand, as desired. LETTERING. 15 Unit Space. If any given height which may be assigned to a letter be divided into six equal parts (for methods see Fig. 12) each of these parts is termed a \ \ chosen distance \ \ A 1 2 3 45 Fig. 12 unit space. It will be noticed in Fig. 13, which is of the mechanical vertical Gothic alphabet most commonly used by engineers, that all stems are of equal width, that is, 16 MECHANICAL DRAFTING. LETTERING. 17 one unit. Either an extended or compressed style of letter may be obtained by arbitrarily increasing or decreasing the unit. CONSTRUCTION OF LETTERS (7) In constructing a word or series of words, the rectangles which will enclose the individual letters can be laid out most rapidly by the method shown in Fig. 14. The vertical distance at the left extremity of the line is Fig. 14 first divided into six units. Any desired number of units, e. g., 5 for the letter H, may then be carried any distance to the right, by means of the T-square, to the left side of the H rectangle, and then by means of the 45 triangle to the upper guide line, thereby obtaining the location of the right side of the rectangle. The unit width of letter stems and other necessary construction may also be secured thru the proper use of the 45 triangle as shown in Fig. 14. For letters involving arcs of circles, after the enclos- ing rectangles have been drawn, the centers may easily be located as shown in Fig. 14 and as indicated for other similar letters in the Gothic alphabet, Fig. 13. In the construction of the letters B, E, F, H, R, and S, it should be noted that the intermediate horizontal stroke is slightly above the center; for A, G, and P it is MECHANICAL DRAFTING. is below. The letters B, E, R, S, X, and Z, and the nu- merals 2, 3, 5, 6, 8, and 9, Fig. 15, will have a more pleas- ing appearance if the width of the top section is less than that of the bottom. The distance d Fig. 15 SPACING (8) Having learned the correct shapes of the indi- vidual letters, it becomes necessary to direct particular attention to their combination into words and sentences LETTERING. 19 in headings, signatures, titles, name plates, etc. While it may be aptly said that beautifully formed letters can result only by a process of designing each stroke as it is executed, this is more especially true of the completed title page or other group of letters, taken as a whole, where as much judgment is employed in the determi- nation of the areas to be left white as those to be made black. Methods of Areas. As a help in securing good spacing by eye alone, a rule that has proven very good is that of making the total areas between successive letters appear equal. It is well to adopt a specific area for this unit. The best unit area is about one-third of the area of the letter M; this is equivalent to a linear spacing of 2 units. KEY TO TABLE, PICK 16. To obtain the space, in units, to be allowed between any letter, e. g., A, and any letter of the alphabet which may follow it in a word, it is seen in the table, Fig. 16, that between A and BDEF, etc., one unit space should be left and between A and CGO, etc., one half unit. In every case the spacing given is that to be allowed between the letter given in the first column and any letter of the alphabet which may follow it in a word. 20 MECHANICAL DRAFTING. 2 1% 1V4 1V4 % % tt Neg. A Ki^'R D CGOQSZ AX JTW VY B BDEFHI KLMNPR CGOQSC 2 X AJTWT \ C BDEFHI KLMNPff COOQSC Z X AJTWT V D BDEFH1 KLMNPR COOQSC 2 X AJTWT V E BDEFHI KLMNPR COOQSD 2 X AJTWT V t BDEFHI KLMNPR COOQST vwxVz AJ C, r BDEFHl KLMNPR COOQSC Z X AJTWT V I, BDEFH1 KLMNPR C COOQSZ X AJTWT V I HPKFI11 KLMNPR C COOQSZ X AJTWV V J BDEFH1 KLMNPR COOQSZ X AJTWT V K BDEFHI KLMNPrf D COOQSZ X AJTWT V I, BDEFHI KLMNPR C ACOOQS J TVWT M BDEFHJ KLMNPR t COOQSZ X AJTWT V N BDEFHI KLMNPR D COOQSZ X A.ITWT V BDEFHJ KLMNPR COOQSD Z X AJTWT V I' BDEFHI KLMNPR U COOQSZ TVWXT AJ q ItliKKIII KLMNPR COOQRli Z X AJTWT V R BDEFHI KLMNPR COOQSU 2 X AJTWT V S BDEFHT KLMTfPR COOQSU 2 X AJTWT V T RDEFHI KLMNPR D COOQSZ TVWXT A J U BDEFH1 KLMNPR I) COOQS* X AJTWY V V BDEFHI KLMNPR COOQST VWXYZ AJ w RDEFHI KLMNPR D COOQSZ TVWXT A J X BDEFHI KLMNPR OOOQSZ X AJTVW T Y HHFF1I! KLMNPR C COOQSZ TV W X V AJ 7, JDEFHI KLMNPR r (XKlQSZ X ATVWT J Fig. 16 LETTERING. Special Cases. The method of areas just suggested can be easily applied in spacing the complete rectangular letters, H, M, etc.; and after some practice will not be found difficult for the curved letters. There are, how- ever, letters which require attention in almost every LAFAYETTE Fig. 17 arrangement in which they occur. In Fig. 17 is shown a word involving A, F, L, T, and Y, all of which, together with J, P, and V, are difficult to combine with other letters and maintain good spacing because they differ so greatly in width at the top and bottom. When L comes before A it is wise to decrease its width one-quar- ter unit. So, also, when T follows F, P, T, V, W, or Y, its width should be reduced one-quarter unit. A after F and before or after T, V, W, or Y, should be set much closer than when used with other letters, in some cases the spacing being even negative, i. e., the F overlapping the A, Fig. 17. Other changes will suggest themselves. Crowding Letters. One of the common errors made by beginners is that of crowding the straight stroke MINING MINI NO Approved Spacing Incorrect Spacing Fig. 18 letters too close together and separating the oval letters too far; this always results in making the inking look heavier in some places than in others, Fig. 18. 22 MECHANICAL DRAFTING. Spacing of Compressed and Extended Letters. In the latter part of Art. 3 it was shown that wide variation in the resulting appearance of an alphabet may be secured by modifying the proportions of the oval element. It should be kept in mind, when performing an exercise in any altered style, that good appearance, i. e., uniformity of shapes, equality of spacing, smoothness of effect, can be produced in only one way: All letters and spaces must be reduced or enlarged in the same proportion. That is, if the letters are decreased one-third their normal widths then the values given in Fig. 16 must be decreased one-third also, in order to give the proper spacing to be used. Thus, suppose the word shown in Fig. 19 (a) , if con- structed of normal letters, is found to be either too long or too short for the space available for it. In (b) and (c) of this figure are shown the same word constructed TERMINAL STATION TERMINAL STATION TEIRK/IIMAL. STVVTIOM (e) Fig. 19 in compressed and extended styles respectively. In each form, however, it will be seen that the distance between straight stroke letters, as that between M and I, conforms to that prescribed in Art. 8; that is, it is one-third the width of the letter M. The values given in the table, Fig. 16, may be used directly by simply taking as the unit for spacing one-sixth the width of the M in the particular style used. The stems of compressed and extended let- ters have the same width as the stems of normal letters, i. e., one- sixth of the height. The method here outlined is applicable to both vertical and slant styles. LETTERING. Mechanical Spacing. In the table, Fig. 16, is given in terms of a sub-division of the standard unit space, the spacing that is approximately correct, according to good design, for any combination of letters. If this table be given some careful study in connection with the principle explained in the paragraph, " Method of Areas," it will be possible after some little practice to design rapidly without constant reference to the table for the correct spacing. NAME PLATES (9) Definition, A name plate is a small metal plate fastened to machine or structure and should contain the following information : Name of the machine (unless it is so common as to be perfectly familiar to everyone), name of the manufacturing company, and address or location of the company's works or factories. DRAWING TITLES (10) Definition. A working drawing title is a con- densed statement of the following information: Name of the piece of machinery drawn, name and address of the manufacturing company, initials of the draftsman, checker, and tracer, scale, drawing number, and other necessary filing data. GENERAL ORDER OF WORK IN CONSTRUCTION OF WORKING DRAWING TITLE (11) Given data. In making up a working drawing title the draftsman ordinarily has given him a certain amount of data as follows: "Details of Horizontal Mill- ing Machine, manufactured by the Landis Tool Company, Waynesboro, Penna. ; drawn by (B. C. S.), checked by ( ) f traced by ( ), scale V 2 "=l", draw- 24 MECHANICAL DRAFTING. ing finished April 2nd, 1915." The above material, con- densed, must be placed within a given title space, per- haps 3"x5". Elimination of unnecessary material and arrange- ment into groups. In order that the given material may be placed within the given title space, every unnecessary word must be eliminated. Eunning thru the given data it is seen that the words italicized can be omitted without the least danger of misunderstanding the remainder. With these words omitted the remaining data seems to group itself naturally as follows: (1st prom.) Horizontal Milling Machine. Details (2nd prom.) Landis Tool Co. (3rd prom.) Waynesboro, Pa. Drawn by ( ), Checked by ( ), Traced by ( ), (4th prom.) Date ( ), Scale ( ). Order of prominence. In a drawing title as well as in a name plate, certain groups of words are more impor- tant than others. In the drawing title the name of the piece of machinery is, of course, given most prominence ; while, in the case of the name plate the name of the manu- facturing company should be given first prominence. In the drawing title the name of the manufacturing com- pany will be given second prominence, address of the company third, and the remaining information, being about equally important, should be given least prom- inence and arranged as desired. The word "Detail" or "Assembly", which may be either included or omitted as desired, will not figure in the order of prominence. LETTERING. 25 Methods of securing prominence. In both advertis- ing and drafting there are in nse two methods for secur- ing prominence of any one group of words over another. The one most generally used is variation in height of the letters of the various groups, to correspond in general to the order of prominence established; if this is not possible thru lack of space, a distorted letter, either of odd construction or of the compressed or expanded style, may be used. One may then depend on the odd appear- ance of the letters to give to that group of words the desired prominence. In the case of drawing titles and name plates the first method, i.e., variation in height of letters is preferable. Margins and margin lines. Before sketching in the guide lines for the various groups of words, margin spaces should be determined and light margin lines ruled in Fig. 20. In doing this certain rules of design must be adhered to ; the upper and lower margins may be of any desired width; however, for best appearance they must be equal. The right and left margins, tho not necessarily equal to the upper and lower, must be equal to each other. In a rectangular space whose width is greater than the height, better effect is obtained if the right and left mar- gins are made slightly greater than the upper and lower; if the reverse is true of the rectangle then the right and left margins should be less than the upper and lower. Guide lines. To obtain the guide lines for the various groups of words, produce the lower margin line to the left until it intersects the border of the title space at A, Fig. 20, and from this point draw up and toward the right a line at an angle of about 60 degrees with the horizontal. Selecting any desired distance as the rela- MECHANICAL DRAFTING. ! h 1 1 ! -iJ zj id o a p 1 1 ^ Zi Z N ; i u [ i s ni 1 1 1 1 1 p R 1 O ^-1 1 1 d Zj U' J 1 1 1 1 1 1 1 p b P V.WAYMEBBDHO: __ i I .urawn: Y_~_~_~. r_u_njc. . QJ 13 O LETTERING. 27 tive height of the letters of the lower group, lay off this distance from A along the 60 degree line; then a relative distance for the space between this line and the line next above; next a relative space for the letters of the next group and so on until all of the groups have been accounted for along the 60 degree line. From the last point, B, draw a line, B C, as shown in figure and from the various points along the line A B draw lines parallel to B C until they intersect the border line, A C; the re- quired guide lines will then be found the same relative distances apart as the points plotted on the line A B. W ' A y N " f ' ' s ' ' a ' Scratch 1 ' ' R Paper 1 ' o ' 1 P " Guide Lines e s B o Scratch Paper Fig. 21 Spacing of letters. Before attempting to place in any of the letters the value of the unit spaces of the various groups of letters must be determined. Tho the various lines of letters may not require all of the horizontal space allotted to them, for best appearance they must be placed centrally ; i.e., with equal margins at their right and left. To accomplish this, rule in a vertical center line of the title space and use the following method : Scratch paper method. Select any point close to the left end of the straight edge of a sheet of scratch paper, 28 MECHANICAL DRAFTING. Fig. 21, and from this point step off with the large and small dividers the proper number of unit spaces in suc- cession, for the various letters and spaces between letters, marking with the divider points the location of the beginning and end of each letter. Placing the scratch paper centrally along the lower guide line of the space into which this group of letters is to go, mark with the needle point the position of the beginning and end of each of the letters. This method has the advantage of centrally placing the entire group and of locating the various letters at the same time. If the letters are to be free hand the above method will be found equally useful. Instead of laying off the spaces in units, the letters themselves should be sketched on the scratch paper and the group placed centrally as before. The style of letters to be used, i.e., normal, com- pressed or extended, will be readily suggested by this procedure. Bill of material. On detail drawings where numerous pieces are shown, a bill of material should be placed above, and usually joined to the title. In general it should contain in tabular form such information as the number of pieces required, material made of, pat- tern numbers, part numbers, name of pieces, and other information. Examples of typical bill of material will be found in the Appendix. GUMMED LETTERS (12) For those who have an appreciable amount of work on titles, signs, etc., the gummed letters sold by the Ticket and Tablet Company, of Chicago, and which are shown in their exact sizes and styles in the appendix, will be found a great convenience. The many uses which such letters serve need not be enumerated. They are made in red, white, and black. USE OF INSTRUMENTS. 29 CHAPTER 2 USE OF INSTRUMENTS DRAWING-BOARD (13) Construction. Drawing-boards are made of either poplar or white pine, the right and left edges, Fig. 1, being reinforced by cleats of some harder wood. These hard wood cleat DRAFTING ONLY Fig. 1 cleats serve both as stiffeners and as runners for the easy sliding of the T-square. The better grades of small Maple or celluloid strip Fig. 2 boards are reinforced on the back by two battens, Fig. 2, and ordinarily, have inserted in their right and left edges a wearing strip of either hard maple or celluloid, instead of the cleats of Fig. 1. It will be noticed in Fig. 2 that 30 MECHANICAL DRAFTING. the right and left edges of the second class of board are broken at intervals by saw cuts which prevent the inserted strip of hard wood from expanding and split- ting the wood. Use. The two sides of the type of board shown in Fig. 1 have very definite uses if the board is to be kept in shape for good drafting. The one side for drafting 1 Head of T-square ALWA\ S to LEFT | Paper o Tacks about %" from edges of sheet Position when not in use I Fig. 3 only, the other for any necessary rough work,- trimming paper, etc. Never trim paper on the drafting side. PAPER (14) Quality. A novice cannot obtain good work from poor material, hence it is imperative that the begin- ner in drawing use the best quality of paper obtainable. A heavy, hard surface paper of the quality of Keuffel & Esser's Normal, or E. Dietzgen's Napoleon is recom- mended. Position of paper on board. In tacking the paper to the board, Fig. 3, keep the sheet well toward the top and USE OF INSTRUMENTS. 31 to the left; about two and one-half inches from the upper and left edges. This should be done in order that the draftsman may work to advantage on the bottom of the sheet, and that it may not be necessary to work to any great extent on the end of the T-square blade, which cannot be prevented from springing slightly. Tacking sheet. Place upper left corner of sheet in approximately correct position and tack to the board, Fig. 3, placing tacks close to the corners of the paper. Then after lining up the upper edge with the upper edge of the T-square blade, stretch sheet and tack upper right corner. The lower edges may be tacked down in any order; or, after some experience, may be left untacked, as these tacks have a tendency to interfere with the T-square and triangles. BORDER LINES (15) The border lines as well as all other construc- tion work done by the draftsman should be placed in by measurements from center lines and not from the edges of the sheet. In the case of the border lines, the measurements are made from the horizontal and vertical center lines of the sheet, Fig. 4. Fig 4 T-SQUARE (16) Construction. Both the blade and the head of the T-square, Fig. 5, are of hard wood, hence the glue 1-4 - e( \ \ \ f '* \ \ L 32 MECHANICAL DRAFTING. Walnut or Ebony Head joint Fig. 5 cannot cement them very tightly together ; neither do the short screws hold very firmly; a fall, even to the floor, may break the joint and damage the T-square. Keep the T-square out of danger of any such fall. In case the joint breaks, take out screws, rough both head and blade with coarse sandpaper, coat well with Denni- son's glue, place blade at 90 with head with triangle, tighten screws and let stand a day. Then take out screws and put in round-headed wood screws long enough to run through and project an eighth of an inch or more. File off screws carefully. Be sure screws are tight. It may be advisable to bore small holes entirely through head and blade for these large screws, to prevent splitting of the wood. Position on board. In drafting, a right-handed man should keep the head of the T-square to the left, Fig. 6, in order that he may handle it with his left hand, leaving the right free for drafting. Never place the T-square in any other position on the board, as the edges of the board seldom form a rectangle nor is the head of the T-square likely to make exactly 90 degrees with the blade. Use of blade. The upper edge of the blade should be used for drafting only; and the draftsman will do well to take excellent care of this edge, for once nicked or USE OF INSTRUMENTS. 33 dented the instrument is practically ruined for good work. The lower edge may be used as a cutting ruler but never for drafting. ALWAYS to LEFT o! Fig. 6 Position when not in use. Any draftsman profits by keeping his drawing instruments in certain definite places, so that as far as possible he may keep his atten- tion entirely on his work, handling his instruments sub- consciously. It is found most convenient to slip the T-square to the bottom of the board, when not in use ; it is here out of danger, out of the way, yet easily accessible. To keep clean. A drawing may easily be smudged by a dirty T-square, so it will be well to give the blade a thoro cleaning with a damp cloth or piece of art gum at frequent intervals. 84 MECHANICAL DRAFTING. SCALE (17) Care. The scale should never be used as a ruler because, as a drafting instrument its efficiency depends upon the condition of its edges, and these edges can easily be defaced by misuse and the instrument badly damaged. Furthermore, the boxwood of which the scale is made warps quite easily; hence, the edges of a tri- angular scale will seldom be found perfectly straight. Fig- 7 Use. On inspection, Fig. 7, it is seen that the numer- als are all placed on the scale so as to appear upright only when one works over the top of the scale or on the edge away from the draftsman and not toward him. All dimensions should be taken directly from the scale as it lies on the drawing and not by means of the dividers. The needle point is the best aid in obtaining dimensions with perfect accuracy. The pencil point is a poor sub- stitute for the needle point. NEEDLE POINT (18) From Richter type of instruments. An excel- lent needle point for obtaining dimensions may be made USE OF INSTRUMENTS. 35 up by inserting into the long knurled barrel furnished with every set of Bichter type of instruments, the small point which is provided for converting the large compass into a set of dividers, Fig. 8. To make in shop. A needle point may be easily made from a strip of white pine i4 // x 1 / 4' / x2 // and a medium size sewing needle. Fig. 9 Construction: Fig. 9. Insert the needle in a vise, point down, with about %" of the point in the vise, and 36 MECHANICAL DRAFTING. carefully drive the strip of pine over the exposed part of the needle; the wood may then be shaved round and pointed slightly at the needle end. TRIANGLES (19) In drawing vertical lines with triangles the ver- tical edge should always be to the left or toward the head of the T-square, Fig. 10. To clean. The surface of the celluloid tri- angles quickly becomes smudged from era- sings and pencil dirt that may be on the drawing; hence, they must be cleaned A Fig. 10 Fig. 11 frequently with soap if the drawings are to be kept in good shape. Letter guide lines. For the easy ruling of letter guide lines without the use of the scale and needle point, it is suggested that along the edges of the 30x60 triangle light lines be scratched with the needle point as follows : Along the hypothenuse and 1/8" from the edge scratch carefully a fine line; also a second line 3/16" from the 38 MECHANICAL DRAFTING. about one inch from the ends, leaving about 1,4" of the lead exposed, Fig. 15. One end is to be sharpened to a round point, the other to a wedge. In shaping up both of these points, use the pencil point file provided in the kit. Fig. 13 Fig. 14 Round point. In shaping up the round point, hold the pencil at an angle of about 45 degrees with the axis of the file. As the lead travels over the file, Fig. 16, revolve the pencil slowly between the thumb and fingers, USE OF INSTRUMENTS. 39 attempting to give it a complete revolution with each stroke. The lead may thus be easily sharpened to a per- fect .cone. In this sharpening be careful that the point extends the full length of the lead exposed. Fig. 15 Fig. 16 Wedge point. In sharpening the wedge point hold the pencil perpendicular to the axis of the file, Fig. 17, Bound point Fig. 17 and so inclined to the plane of the file that the lead may be sharpened the full quarter inch exposed. 40 MECHANICAL DRAFTING. Use of points. The round point should be used for drawing short lines and lettering, the wedge point for long lines; the round point dulls rapidly in drawing a long line and will make a line of varying weight. ERASERS (21) If an eraser becomes apparently greasy and smudges instead of cleans a drawing, it may easily be cleaned by rubbing it with another eraser or by rubbing it on the rough surface of the drawing-board itself. Fig. 18 CLEANING PADS AND BLOTTERS (22) Chamois roll or block. Inasmuch as water proof drawing ink dries so rapidly the pen should be cleaned thoroly with cloth or chamois before each refill- ing. In addition to this cleaning it will be found possi- ble to obtain more clear cut work if after each three or four lines the point of the pen is scraped over a piece of chamois. A convenient cleaner may be made by roll- USE OF INSTRUMENTS. 41 ing up a 2"x4" piece of chamois and binding it with a rubber band, Fig. 18, or by pasting a 2"x 2" piece on a small block of wood. Blotters., Never attempt to blot drawing ink. The ink is too heavy to be absorbed by blotting paper. Always permit the ink to dry. A puddle of ink may, however, be removed by the careful use of the corner of a blotter. LARGE DIVIDERS (23) Adjustment of the points. With the Richter type of instrument, it will always be found possible to ad- just the points of the various tools to any desired length; so, before attempting to use the large dividers be sure that the points are adjusted to exactly the same length and that they are in perfect shape. In case the points of the Gem Union instruments are not of the same length, it will be necessary to grind the long point down on a small carborundum stone. Keep points always in perfect shape for good work. Opening and setting. It is desirable always to handle each instrument with the right hand unaided by the left; this permits of much more rapid work and the habit is not difficult to acquire. To open the divider, insert the thumb between the legs, prying them apart a short dis- tance until the fingers may be inserted and the one leg grasped between the first and second fingers, the other between the third finger and the thumb; the head of the instrument should rest against the knuckle of the first finger. Holding the instrument in this position it is found easily possible to adjust the points to any desired distance. 42 MECHANICAL DRAFTING. To place point. To place the one point of the divider at any point on the sheet, rest the wrist at a convenient distance from the point ; it will then be found easily pos- sible to place the point of the leg between the third finger and the thumb in any desired position. Raising the wrist and keeping the little finger on the paper, the other leg can now be adjusted for any desired distance. It is perhaps as good practice and may be found easier for some to steady the hand thruout the operation by merely resting the little finger on the paper, instead of the wrist. Stepping off distances. After the points have been placed as desired, to step off a certain distance a num- ber of times, raise the first finger to the top of the head, then, releasing the other leg, grasp the head between the first finger and the thumb and step off the distance by swinging the dividers alternately over and under. Hand- ling the instrument in this way it will not be necessary to take a new grip on the head thruout the operation. LARGE COMPASS (24) Adjustment. To adjust the needle point of a compass to both the pen- cil and pen, remove the pencil point and insert pen; after adjusting the needle point so that its shoulder, not the point, is flush with the end of the pen, remove pen and in- serting pencil, adjust lead until it is even with the shoulder of the needle point. Wedge point Fig. 19 USE OF INSTRUMENTS. 43 Use. For adjustment of leads to any desired radius, and placing needle point at any desired center, see Large Dividers, Art. 23. For describing arcs with the large compass the legs should be adjusted as shown in Fig. 19. IRREGULAR CURVE (25) The irregular curves are those which cannot be drawn readily and accurately with the compass. The gen- eral directions of the different portions of such curves are first determined roughly by a number of plotted points at as small intervals as possible (the positions of these points are obtained either by mathematical coordinates or mechanically from other projections or views of the same curve). Before drawing the curve mechanically it is best to draw lightly a freehand curve thru the plotted points, then carefully piece by piece the mechanical curve may be drawn. In drawing the mechanical curve two things must be kept in mind; first, that the final curve must coincide as absolutely as possible with the freehand curve; second, that the curve must be "smooth," i. e., it must have no sudden glaring changes of curvature or "humps." The failure of a novice to obtain a good irregular curve is due to perhaps two causes: first, that he starts with the assumption that it is too easy to require any attention, and second, that he is too easily satisfied with a very indifferent job. Curves having curious "humps" may be termed freaks and are seldom, if ever, encountered in Mechanics. It is difficult to recommend any curve or even several curves as being even approximately universal, so no such advice will be attempted. A great number of such curves are listed in all instrument catalogs and special require- ments will have to be depended upon in any selection. MECHANICAL DRAFTING. However, two curves have found much favor among stu- dents and are recommended for general use. One of these has obtained the name of "Banana" curve, Fig. 20, and the other is the Gr. E. D. Special, Fig. 21. Fig. 20 Fig. 21 BOW DIVIDERS (26) Adjustment. (See Adjustment for Large Dividers.) Placing at center. (See same for Large Dividers.) Opening and closing points. With the center adjust- ment instrument, which is always preferable to the side USE OF INSTRUMENTS. 45 adjustment, after placing the one point at a given point on the sheet, raise the first finger to the head and turn the adjustment screw between the second finger and thumb until the points are apart as desired. Stepping off distances. (See same for Large Dividers.) BOW PENCIL (27) Hard lead. To obtain satisfactory work from the bow pencil the lead should be extremely hard, at least 6H. Ordinarily, the lead supplied with instruments is not more than 2H or 3H, and wears down too rapidly. Try the lead before using it on a drawing, and if found soft, substitute for it a piece of lead from a 6H pencil. Sharpening lead. Since the bow pencil is, like the bow dividers, an instrument of precision, for small arcs the round point will be found more convenient than the wedge. Inas- much as the total amount of use is small compared with that of the large compasses, the need of a wedge point to diminish the number of times required to shape it up, is not great enough to overbalance the inaccuracy and awkwardness of the latter in drafting. It is well to Fig . 22 shape the point as long as the con- struction of the instrument and the strength of the lead will permit. Fig. 22. Adjustment to any radius. In adjusting thepowte to any desired radius, instead of obtaining the dimension directly 46 MECHANICAL DRAFTING. from the scale, it will be better to transfer this radius to the paper by means of the scale and needle point, and set the bow pencil from this as explained under Large Di- viders. Describing arcs. In describing an arc with either the compass, bow pencil or pen, the direction of mo- tion of the lead should be clockwise and thru the total length of the de- sired arc before taking the point from the paper, Fig. 23. RULING PEN (28) Manner of holding. The ruling pen should be held between the first and second fingers and thumb as shown in Fig. 24. In ruling lines, the adjusting screw should be turned from the user. Fig. 23 Position of pen. Unless care is taken to keep the pen in a vertical plane thru the edge of the T-square blade or edge of the triangle, Fig. 25, trouble may be ex- perienced in the ink running under the T-square blade, Fig. 26, or in a badly broken line, Fig. 27. Tilted in the direction of motion. For best results the pen should be tilted slightly in the direction of the motion, Fig. 24; this permits one to inspect the work of USE OF INSTRUMENTS. 47 the pen as it travels. A greater angle than 10 or 15 degrees may however permit the ink to run down and cause a blot. \ 7 *\ I 3 I \\ 1 \\ VA v x \ c/ / // ?'/ VA // T\i yf 'fVf ty 1 // *1W////////1 \ Fig. 24 Fig. 25 Effect of Position 2 Effect of Position 3 Ink ran under T squar Fig. 26 Pen riding on one nib Fig. 27 To fill pen. To fill the pen, always use the quill sup- plied on the stopper of the ink bottle. Never dip the pen into the ink. If by chance any ink has gotten on the out- side of the pen, wipe it off carefully before using; it may save a serious blot. MECHANICAL DRAFTING. Direction of motion in ruling lines. In ruling lines, either with the pen or pen- cil, the direction of motion should be from left to right or from bottom to top of the sheet, Fig. 28. Ruling lines thus, it is always possible to see what the pen or pencil is doing. Never rule lines down the sheet unless they are oblique and are being put in with the triangle. Fig. 29 INK BOTTLES (29) Holder. A convenient holder for the ink bot- tle may be made from two sheets of blotting paper and a rubber band as shown in Fig. 29. A holder of some USE OF INSTRUMENTS. 49 50 MECHANICAL DRAFTING. Fig. 30 kind is advisable and one such as this answers a double purpose. A holder of the style shown in Fig. 30 may be purchased from any of the instrument companies. Closed when not in use. India ink is very heavy and dries quite rapidly; hence, if the stopper is left out of the bottle even for several hours the ink may be- come so heavy as to make it impossible to obtain good work from it. Be sure to close the bottle carefully after each refill- ing of the pen. With proper treatment the ink will remain in good condition for several years. To open bottle and fill pen. To open the bottle without danger of upsetting, grasp the neck between the third and little fin- gers, Fig. 31, and the stopper between the first finger and thumb of the same hand; af- ter removing the stopper, place the quill between the nibs of the pen, and fill as desired. If too much ink is placed in -the pen ragged lines and perhaps serious blots will be the result. Fig. 31 LIBRARY STATE NORMAL SCHOOL l< (30) The protractor in most general use is a semi- of celluloid, horn or metal whose circumference is ^divided into degrees and perhaps half degrees. On the Fig. 32 Line-0-Graph, Fig. 32, is shown a 90 protractor which j\ without any handicap can be substituted for the usual ^180 instrument. To measure any desired angle, the j center of the circle is placed at the vertex, and on one *"" side of the given angle. The value of the angle may ^ then be read directly from the quadrant. 52 MECHANICAL DRAFTING. CHAPTER 3 ORTHOGRAPHIC PROJECTION (31) Definition. An orthographic projection of any object is such a representation on a given plane (usually vertical or horizontal) as will show in true proportion the contours of the object as seen in a direction perpen- dicular to the plane; i. e., as though viewed from an in- finite distance, when all the lines of sight would be paral- lel to each other and perpendicular to the plane of pro- jection. PRINCIPLES OF ORTHOGRAPHIC PROJECTION (32) It is seen from Fig. 1, which is a representation of a machine part that, tho the object is represented as we are accustomed to see it, the picture gives us abso- lutely no conception of the ratio of the several parts of the object to each other; i. e., tho the sides of the square hole in the top may appear to be equal to the thick- ness of the object, one has no means of knowing exactly what the relation is; hence, unless actual dimensions were given for every detail of such a drawing, and these dimensions could be depended upon to be absolutely accurate, one would have no means of making, except approximately, the object which the drawing represents. Hence, it will be appreciated that in making drawings for the use of ORTHOGRAPHIC PROJECTION workmen in shops, such an application of Descriptive Geometry should be employed as will represent each line of the object at least once, in its true mathematical ratio to other lines; i.e., such a representation, that if no dimensions were given, one could compare lines by means of a scale or dividers and be certain of their exact ratio to each other. This branch of Descriptive Geometry is known as Orthographic or Proportional Measurement Projection. Orthographic projection. To obtain such a projec- tion of the machine part represented in Fig. 1, let us im- agine that we have suspended it in space with the face containing the square hole horizontal; then, see Fig. 2, let us imagine that four planes be drawn about this machine part in the positions shown, one, a horizontal plane, a second a vertical plane parallel to the face A, and two other planes perpendicular to both the vertical and horizontal planes just drawn. Pig. 2 Coordinate planes and coordi- nate angles. The three planes just constructed about the machine part in Fig. 2 are known in orthographic pro- jection as coordinate planes and are named individually, the Horizontal or H plane, Vertical or V plane, Profile or End plane; see Fig. 3. The four dihedral angles formed by the H and V planes are known as 1st, 2nd, 3rd, and 4th and are numbered in the order shown. 54 MECHANICAL DRAFTING. Projections or orthographic representations. In ex- plaining the method used in obtaining the orthographic representations of the machine part, the corner A, Fig. 4, will be taken as typical of all significant points of First Angle /' / Ground Fourth Angle Pig. 8 the object. It is desired to represent this point on each of the three coordinate planes, the second End plane be- ing for the time eliminated. From point A are dropped three perpendiculars, one to each of the coordinate planes; the points in which these perpendiculars pierce ORTHOGRAPHIC PROJECTION 55 these coordinate planes are known as the projections of point A, and are called, V or Vertical projection or Front View (always lettered a' if lettered at all), H or Horizontal projection or Top View (always lettered a if lettered at all), and Profile, End Projection, End or Side View (always lettered a" if lettered at all) ; if then from all of the points of the object perpendiculars were dropped to the Vertical plane and lines drawn connecting the piercing points of these perpendiculars in regular FIRST ANGLE PROJECTION Fig. 4 order, Fig. 4, we would have on the Vertical plane a drawing or projection representing perfectly the appear- ance of the front of the machine part; a similar process would give us on the Horizontal plane a correct repre- sentation of the top of the object and on the End plane a representation of the side of the object. 1st and 3rd angle projections. If the object be placed in the 1st angle, as in Fig. 4, the projections referred to above are known as first angle projections. If the object 56 MECHANICAL DRAFTING. is placed in the 3rd angle, as in Fig. 6, the projections are known as third angle projections; i. e., the projections of an object are known as First or Third Angle projec- tions according to the angle in which the object is placed. It should be noted that Figs. 4 and 6 show only those - \ \ \ V Plan* / a ' f a - I"] 1~| Elevation s \ 1 C " End View P Plane Revolved i 7 \ / i / L f / s ^' s* ' ^.-^ D\ ,. H Phmc Revolved x -^ Fig. 5 parts of the coordinate planes that enclose the angle of projection under consideration. No mention is made of the Second or Fourth Angle projections because it would be impracticable to use either as working drawings. Revolution of coordinate planes. Already an appar- ent difficulty has arisen in the question of how to repre- sent all of these projections, e.g., of point A, Fig. 4, on a single sheet of paper when in fact the three projections, a, a' and a" , are found on three planes at right angles to ORTHOGRAPHIC PROJECTION 57 each other. The line of intersection of the Horizontal and Vertical planes is known as the Ground Line or G L; the intersection of the Vertical and End planes is Cr l L lt This difficulty can now be solved as follows : Using G L as an axis, Fig. 5, let us imagine that the portion of the H plane in front of V is revolved down until it coincides with the V plane. It should be remembered that the por- tion of the H plane behind (not shown in the Fig.) re- THIRD ANGLE PROJECTION Fig. 6 volves up till it coincides with the V plane above G. L. In this revolution, a revolves into the new position, a, on the continuation of the perpendicular dropped, from a' to G L; for, if thru the two lines Aa and Aa', Fig, 4, a plane be passed, it will cut from the V plane a line thru a' perpendicular to G L; as a revolves about G L down, it revolves in the plane of Aa, and when it reaches the V plane, must lie on the perpendicular to G L thru a', the line cut from the V plane by the plane of Aa. Since a is before G L the distance Aa', a will be found below G L the same distance ; a' is above G L the distance A a; hence, the distance from G L to the points a and of repre- 58 MECHANICAL DRAFTING. sents the exact distances which the point, of which these are the projections, is from the V and H planes. If then, G t L, be used as an axis and the portion of the Profile plane in front of V be revolved to the right, a" comes into the new position a", a distance to the right of G a L a equal to Aa' and a distance above G L equal to Aa, or on the horizontal line thru a'. Projections of objects. Advancing from the point A just discussed, to all other elemental points of the object and projecting them in turn in the same manner as was A, Fig. 7 we find the representation of the machine part in the first angle, when the several points are properly joined by lines, to be as shown in Fig. 5. Proceeding in the same manner with the object in the third angle we obtain the views as shown in Figs. 6 and 7. It should be noted that ORTHOGRAPHIC PROJECTION t_i_ __i__i ! I 1 Fig. 8 the views are identical in character but appear in differ- ent positions in respect to each other. In practice it is the universal custom to omit both ground lines together with the boundary lines of the three planes. The resulting projections of the object appear as in Fig. 8. Elimination of the first angle. From Fig. 1, it is noted that as we ordinarily see objects the top appears above the front and the right end to the right of the front or the left end to the left of the front, according to the position from which the object is seen. When the object is placed in the first angle and the projections revolved into the positions shown in Fig. 5, it is seen that the left end projection comes in a position to the right of the front and that the top is under the front, an arrangement by no means natural. While, when the object is placed in the third angle, Fig. 6, and projections revolved as shown in Fig. 7, the views assume a group- ing identical with their order on the object itself; i.e., the right end to the right of the front, and the top above the front. Merely for the sake of this natural arrange- ment the third angle will be selected in preference to the first in making working drawings; i. e., all working draw- ings will be third angle orthographic projections. 60 MECHANICAL DRAFTING. SUMMARY OF PRINCIPLES (33) It may be well to summarize a number of prin- ciples brought out in this discussion, likewise to mention several violations of pure orthographic projection. The top view, Fig. 8, represents the exact appearance, with lines in true proportions, of the top of the object; the front vieiv represents the same of the front of the object, and the side view the same of the side of the object. The top and front views must be directly above and below each other and the front and end views must be on the same horizontal lines as shown in Fig. 7, if the group is to represent the true orthographic projection of the object; a violation of this renders the whole draw- ing incorrect. PERMISSIBLE VIOLATIONS (34) In Fig. 5, it is shown that the portion of the End or Profile plane in front of V is revolved to the right; this of course means that the portion of the Profile plane behind V revolves to the left; while, in Fig. 7, the portion of the Profile plane behind V is represented as being re- volved to the right. This revolution to the right of the portion of the Profile plane behind V is ortho graphically incorrect; however, in the case of the third angle projec- tions it is tolerated for the natural order of projections which it produces. PROJECTIONS OF HIDDEN LINES (35) In Figs. 5 and 7 certain lines of the projections are shown dotted lines. This is the custom always fol- lowed for showing hidden or invisible lines. For ex- ample in the projection on the V plane, the two dotted ORTHOGRAPHIC PROJECTION 61 lines show that the hole thru the object is invisible when viewed in a direction perpendicular to the V plane. A simple rule for determining the visibility of a line is to always consider the H projection a view from the top and the V projection a view from the front. This ap- plies equally to first and third angle projection. The Fig. 10 projection on the P plane is considered a view from the corresponding side of the object, that is, looking perpen- dicularly thru the P plane at the object. AUXILIARY PLANES OF PROJECTION (36) Frequently an object is so shaped that it can- not be placed in an entirely simple position with respect to the planes of projection. The face K on the corner brace shown in Fig. 9 will not be shown in its true size 62 MECHANICAL DRAFTING. on either the H, V, or P planes when the object is placed in its simplest position with respect to these planes. Fig. 11 The use of a fourth plane, which is perpendicular to H but parallel to face K, will give an additional view which will show K in its true size. Fig. 10. Fig. 11 shows the correct arrangement of the four views of the object after the V, P, and auxiliary planes have been revolved into the H plane. ORTHOGRAPHIC PROJECTION POSITIONS OF THE THIRD AND FOURTH VIEWS OF AN OBJECT (37) In Fig. 12 is shown the correct arrangement, orthographically, of the three views of an object-box. However, occasions may arise in which it will be in- Fig. 12 convenient to place the side view directly opposite the front; in this case we may imagine that the line of inter- section of the end plane and the horizontal plane becomes an axis about which the end plane is revolved, Fig. 13, until it coincides with the horizontal plane. This entire horizontal plane is then revolved about its line of inter- section with V as an axis, until it coincides with V. The side view will now be found opposite the top instead of the front. If two side views are necessary to show the construction they may be placed on either side of the MECHANICAL DRAFTING. front view, Fig. 14, or on either side of the top view, Fig. 15. No other arrangement is permissible. Fig. 14 In constructing a three view drawing it is best always to construct the top and front views from dimensions and by projection; then, to obtain the side views from these two, entirely by con- struction and not by the use of dimensions. For the sake of con- struction the two ground lines, Fig. 12, may be drawn in lightly; however, they should be erased when no longer needed. Fig. 15 WORKING DRAWINGS. 65 CHAPTER 4 WORKING DRAWINGS WORKING DRAWING (38) Definition. A working drawing of a piece of machinery is such a group of correctly and completely dimensioned orthographic views of that object as will give all the information necessary in constructing a duplicate of the same. Fig. 1. * I Ka* H L E ^zzzzZi^zfiii: 1-1 i i Sr T L 1 1 Fig. 1 DETAIL DRAWING (39) Definition. A detail drawing is a working drawing of one piece of any machine. A group of detail drawings of all of the parts of a machine or any collection of parts is termed a set of details. 66 MECHANICAL DRAFTING. ASSEMBLY DRAWING (40) Definition. An assembly drawing of a machine is a one, two or three view orthographic projection of a machine completely assembled; i. e., all parts in their proper working place. Figs. 2. Uses. Assembly drawings have three important uses. (1) As an index to a working drawing; i. e., an assembly of a machine is ordinarily given with the set of detail working drawings to explain the use of each of these de- tails in the machine; (2) For purposes of advertisement or magazine illustration; (3) As a construction guide in assembling machines which may be sent out from shops in sections. Characteristics. Some characteristics which may be noted of assembly drawings when used for any of the above purposes are: (a) All dimensions are ordinarily omitted; (b) The several views are elaborately sectioned to explain clearly all inside constructions; (c) When given with a set of details the assembly will ordinarily occupy a fixed relative place on the sheet, i. e., the lower left corner or whole left side if necessary. DETAIL WORKING DRAWINGS (41) Arrangement of set of details. In making a set of details a certain order of arrangement should be fol- lowed, both for appearances and ease in reading the draw- ing. As mentioned under assembly drawings, the assem- bly should occupy the left portion of the sheet. In gen- eral, the arrangement of the details on the sheet should be such as to suggest their direct relation in the machine itself; i. e., such an arrangement as is suggested by the relation of these parts in the assembly. It may not always WORKING DRAWINGS. 67 Fig. 2 MECHANICAL DRAFTING. WORKING DRAWINGS. 69 70 MECHANICAL DRAFTING. WORKING DRAWINGS. 71 be possible to carry out this scheme completely; however, in general it will be found possible so to arrange the main details. For further ex- planation see Fig. 3. The assembly is here shown to the left, followed along the bottom of the sheet by the main detail, the remaining details being arranged about the sheet properly with relation to each other if not to the main details. Fig. 3a shows an arrangement with the as- sembly omitted. Fig. 4 r Fig. 5 72 MECHANICAL DRAFTING. Order of work in a set of details. In making a set of details, e. g., of the bell crank, Fig. 4, the following order Fig. 6 of work will be found to lend to the greatest speed: (a) Make list of details to be drawn and number of views required of each, (b) Select scale, (c) Draw on pieces of scrap paper rectangles or rectangular figures of the proper size to enclose the desired number of views of each detail. ' (d) Cut out these rectangles and arrange them on the sheet of drawing paper on which the details are to be drawn, (e) After the rectangles are arranged mark their positions, Fig. 5. (f ) Divide the rectangles on the sheet of drawing paper into smaller rectangles to contain the separate views of each detail, Fig. 6. The rectangles mentioned in (e) WORKING DRAWINGS. and (f) should, of course, be put in only lightly and may be erased when no longer needed. Fig. 7. Fig. 7 Detail signature. Accompanying each detail draw- ing, whether the detail drawing be by itself or one of a set, should be given a characteristic signature containing the following information: Name of the machine part, material of which it is made, number of parts required, and some arbitrary number for the pattern if the object Valve Crank C. I. Reqd 1. Pattern No. A-3. is to be cast. This information should be given in the manner shown above. 74 MECHANICAL DRAFTING. The letter A in the pattern number refers to the sheet A of the Details of the Corliss engine of which this valve crank is a part ; the number A-3, indicates that the valve crank is detail number 3 on sheet A. ORDER OF PENCIL WORK (42) The most rapid progress can be gained in the pencil work of a working drawing by following the order given in Fig. 8. Caution. It is by no means wise to attempt to fin- ish one of several views be- fore doing any work on the others. Fewer mistakes will be made and more rapid progress gained by working on all views at the same time; i.e., when a line is placed on one view, its pro- jections in the other views should be obtained before proceeding with other lines. All views will thus be fin- ished at practically the same time. When one projection of a line is obtained from a given dimension, the other views of this same line should be obtained by the prin- ciple of projection rather than by making use of the scale a second time. This practise, tho it may permit a mistake to remain undetected, has the advantage of pro- ducing drawings which are true orthographic projections. Pig. 8 WORKING DRAWINGS. 75 ORDER OF PENCIL WORK 1 Border Lines 2 Title Space 3 Selection of Scale 4 View Spaces 5 Center Lines 6 Outlines 7 Auxiliary and Dimension Lines, and Dimensions 8 Section Lines and Notes DIMENSIONING (43) In dimensioning the following rules or sugges- tions should be observed : (a) Dimensions should read from left to right or up, and in the direction of the dimension line. Fig. 9. (b) The auxiliary lines used in dimensioning should not quite connect with the lines from which they lead. Fig. 10. (c) Series. A series of dimensions should be given on one continuous dimension line, as in Fig. 11, and not as in Fig. 12. (d) An overall dimension should always accompany a series, both as a check and for the convenience of the workman. Fig. 11. (e) Diameters. Diameters should be placed on a linear diameter of the circle as in Fig. 13 whenever possible; when necessary to indicate the diameter on a straight line projection of a circle, the dimension should be accompanied by the letter D. (f ) Eadii of arcs should be marked R. Fig. 14. 76 MECHANICAL DRAFTING. Fig. 15 Pig. 16 WORKING DRAWINGS. 77 (g) Inasmuch as the meaning of hidden lines is not always clear, it is bad practice to place dimensions on such lines. (h) Place dimensions between views unless clear- ness will be gained by placing them otherwise. (i) Do not repeat dimensions on adjacent views. (j) Dimensions should not be crowded. (k) Dimensions always indicate the size of the fin- ished object. (1) Do not place dimensions on or along Center Lines. Fig. 15. Jm) In general dimension from the center lines and not from the outlines of the object. (n) Fractions should be made with a dividing line in the same line with, but not a part of the dimension line. Fig. 11. (o) The arrows of dimension lines contain two barbs, while those of leaders, Figs. 13 and 16, but one. (p) Arrows should be so placed that there may be no confusion as to which line they point to. (q) Leaders, All leaders, Fig. 16, should be made mechanically and not freehand. (r) Notes. For explanatory notes the leader should end so that the notes may read either horizontally or vertically as the dimensions, but not diagonally. Fig. 16. (s) Dimensions up to two feet should be stated in inches; e. g., 12", 18", etc. Two feet may be written either as 24" or 2'-0". Except for sheet metal, dimensions above two feet should be expressed as follows : 2'-3", 6'-4", 7'-0", etc. The dimensions for sheet metal should be given in inches and in the order of thickness, width, length; 78 MECHANICAL DRAFTING. WORKING DRAWINGS. 79 SECTIONING (44) The primary function of orthographic projec- tion is, of course, to represent the portions of an object visible to the eye. Any constructions hidden by the sur- faces in view may be represented by conventional lines known as hidden lines, Fig. 17. The dotted lines in this figure represent the three recesses in the top, front, and side of the cube. It may be satisfactory to represent in this way the interior construction of so simple an affair as the object shown; however, if the interior construction is in the least elaborate this method is by no means satis- factory. If an interior construction be represented by a number of hidden lines which cross each other, the draw- ing becomes so vague as to be almost unintelligible. For this reason a substitute method has been devised for showing any interior or hidden construction. According to this method it may at any time be imagined that a cutting plane, parallel to one of the coordinate planes, can be drawn in any position, cutting away such portions of the object as will expose any other parts one may wish to see. Ordinarily these planes will be found to pass thru some axial line of the object, Fig. 18 ; however, if desired, they may be imagined drawn elsewhere, Fig. 19. This process of sectioning is purely imaginary and may be represented on only one view of a two or three view working drawing, the other views representing the ob- ject unsectioned by any such plane. The process of sec- tioning is strictly utilitarian ; i.e., one should section only objects whose construction can be more clearly explained by this process than otherwise. Certain terms applying to sections are sometimes confused from the fact that they may apply either to the 80 MECHANICAL DRAFTING. drawing or the object. These terms are quarter section, half section, and full section. The confusion ordinarily comes between the terms quarter and half section. From Fig. 20, it is seen that when one-quarter of the object is removed one-half of the drawing will be found sectioned. Likewise if the entire front or half of the object were removed the drawing would be full sec- tioned. Hence the term quarter section will then, of course, be entirely discarded, as it can refer only to the object. Solid cylinders. The drafts- man should keep in mind the fact that there is but one thing to be gained in sectioning, i. e., to show more clearly the interior construc- tion of any piece of machinery; if the section does not accomplish this purpose it is just so much wasted labor. This point refers particularly to solid cylinders, e. g., shafts, Fig. 21, bolts, screws, etc., which should never be sec- tioned. Fig. 21 Interpolated or Revolved Sections. In such cases as are shown in Fig. 22, with respect to rims and spokes of wheels, standard construction iron, etc., sections known as interpolated or revolved sections are given to show the cross-section of the material at certain places. These sections are obtained by passing planes perpendicular WORKING DRAWINGS. to the axis of the piece to be sectioned and revolving this plane 90 about the center line of the section thus cut. Fig. 22 Section thru spokes. Whenever the cutting plane passes thru spokes of wheels as is the case shown in Fig. 22, the cross hatching is put in as if the plane had been passed on the line AB. Section lines. Indication of material by variation in section lines. It is the custom in many shops to indicate the material of which a piece of machinery is to be made by using a characteristic section line for any parts of that piece which have been sectioned, Fig. 23. There are some apparent disadvantages in this, however, for there is at present no universal standard system of sec- tion lining. Some shops use one characteristic for brass, wrought iron, etc., and others a radically different char- acteristic. Furthermore, unless one uses these section 82 MECHANICAL DRAFTING. Fig. 23 lines constantly or has a chart of them with him always, he may find it quite difficult to remem- ber some of them. A third objection is that it requires an excessive amount of time to draw some of these section lines. Indication of materials by abbreviations and univer- sal section lines. For greatest convenience and ease, both in making and reading a drawing, the writers approve the universal section lining with material abbre- viations as a sub- stitute for the above system, i. e., the use of the standard section line now used for cast iron as the standard for all materials and the particular material of which the piece is to be made indi- cated' by its char- acteristic abbrevia- tion as shown in Fig. 24. These ab- breviations are easy to remember and the section lines can be drawn rapidly. Where necessary a variation in space between section lines may be substituted for a change in direction of lines Fig. 24 WORKING DRAWINGS. 83 TRACING (45) Tracing cloth is a fine quality of cotton coated with a preparation which gives it a smooth hard surface and renders it transparent. Of the various grades of cloth on the market, the imported brand "Imperial" gives by far the greatest satisfaction and is recom- mended for general use. Always before making use of any piece of cloth be sure to rip off about y s " of the selvage edge; it may prevent a bad buckling of the tracing. Tacking to the board. It is best always to have the sheet of tracing cloth slightly larger than the sheet of paper so that the tacks used in pinning down the cloth may be placed outside the sheet. In tacking down the cloth, preferably with the dull side up, be sure to stretch very rig 25 tight and tack firmly. See Fig. 25 for best order of tacking. Preparation of the surface of the cloth. Unless pre- pared in some way, the surface of the tracing cloth will likely take the ink very poorly, giving ragged and faded out lines. The cloth may be dusted or rubbed with chalk or preferably magnesium carbonate, which may be pur- chased at any drug store in 5-cent blocks, and then rubbed with a piece of linen. Order of work. Unless one is sure of being able to finish the tracing of several views of a drawing before it 84 MECHANICAL DRAFTING. is necessary to stop work, it will be found best always to trace one view at a time, finishing that view before leav- ing work. Tracing cloth has a decided tendency to stretch and warp, and it may be found most difficult to make old lines check with new if the tracing has been left standing for a day or more. Erasing. In erasing, use the pencil eraser always in preference to the ink eraser or knife. It may require more time to erase a mistake; however, the cloth will be found in good condition after such erasing ; while the ink era- Scrape out /with knitV ser or knife quite easily rough- ens the surface and causes blots on application of new ink. A knife may be used to advantage in scraping out slight accidental extensions of lines, Fig. 26. Caution. If necessary to rule across ink lines, be sure to move the pen rapidly. If the pen is moving slowly the ink will likely follow down the old ink line to the T-square or triangle and cause a bad blot. Weights of lines. The visible and hidden outlines are the heaviest lines on the drawing and should be slightly less than 1/32" in width. This weight may be obtained by using a number 3 line on the adjustable graduated detail pen. All other lines on the drawing, i.e., dimen- sion, auxiliary, center, and section lines, should have a weight of number one. Fig. 27. Order of inking in tracing. In tracing, the following order should be observed for most rapid and accurate work. WORKING DRAWINGS. 85 Visible Outline Hidden Outlines Dimension, Auxiliary and Section Lines Fig. 27 Undercut Tracing Ruler Fig. 28 1. Center lines. 2. Large circles and arcs. 3. Small circles and arcs with the bow pen. 4. Irregular curves with special curve. 5. Horizontal lines with the T-square. 6. Vertical lines with T-square and triangles. 7. Inclined lines in groups, e. g., 30, 45, and 60. 8. Other oblique lines. 9. Dimension and auxiliary lines. 10. Section lining, dimensions and notes. BEVELLED AND RAISED TRACING RULES (46) For tracing, the two rulers shown in Figs. 28 and 29 are indispensable. With the bevelled ruler, Fig. 28, it is possible to rule across inked lines without any danger of blotting. The raised ruler of Fig. 29 saves an 86 MECHANICAL DRAFTING. 6 inch section from 18 inch beveled celluloid ruler sold by Frederick Post Company. Screw the point thru one-eight inch. Cut off on top and file smooth. Fig. 29 immense amount of time, as it makes it possible to con- tinue tracing no matter how many ink lines are still wet. CONVENTIONAL LINES (47) The conventional lines shown in Fig. 27 are standard and should be followed strictly. Concerning the hidden lines, it may be said that no one thing except dimensions will add to or detract from the appearance of a drawing more than care or lack of it in the correct draw- ing of hidden lines, both as to the uniform length of the dashes and uniform space between dashes. In tracing, follow strictly the weights given in the figure for these various conventional lines. SCALES (48) Architect's scale. The spaces representing feet on the architect's scale are divided into twelve equal parts, making it possible to draw, without any interpo- WORKING DRAWINGS. 87 lation, plans, etc., of objects whose dimensions are given in feet and inches. Engineer's scale. On the engineer's scale the inches are divided into various numbers of subdivisions, these numbers being multiples of ten; i. e., the inches are divided into 10, 20, 30, 40, 50, or 60 divisions. By use of this scale without any interpolation maps may be made and drawings plotted directly from field notes in which the distances are all given in feet and tenths of feet. Mechanical engineer's scale. Recently a scale has been placed on the market on which the spaces repre- senting inches have been divided into halves, quarters, eighths, sixteenths, etc. Likewise a scale that combines all of the three scales just described. Mechanical engi- neers will find it to their advantage to own one or both of these. Scale versus size. A drawing made to such a size that one-half inch on the drawing equals one foot on the object drawn, is said to be made to one-half scale. How- ever, if the drawing be made so that one-half inch on the drawing represents one inch on the object the drawing is said to be made one-half size or to a scale of " to V. MECHANICAL DRAFTING. CHAPTER 5 FASTENERS (49) In every field of construction the builder finds it necessary to hold the component parts of the whole together by means of fasteners. Among the numerous kinds and varied shapes of fasteners, several are of such universal importance that the draftsman as well as the mechanic must be entirely familiar with the method of manufacture and manner of representing them on draw- ings. Among others, rivets, keys, bolts and screws are to be specially noted. The several kinds of rivets with their customary conventional representations will be found in the appendix. Brief mention is made of the common standard keys in Art. 59. The greater portion of this chapter will be devoted in main to the most widely used fasteners, Bolts and Screws. THREADS (50) The Helix. The helix is a mathematical curve often wrongly termed the Spiral. It is generated by mov- ing a point on any surface of revolution, around and along the axis of revolution. The motion of the point in both directions is generally uniform but may be variable in either or both of its motions. Thus we may have cylindrical, conical, spherical and many other forms of helices. On Bolts and Screws the thread is almost always a cylindrical helix. For special purposes the FASTENERS. thread may be a conical helix. The threads on water pipes and their connections are of this class. Fig. 1 shows the geometric method of constructing a cylindrical helix, which form will always be understood when the term Helix is used. The distance (x) is called the pitch of the helix and may be assumed at will. In con- structing the helix the pitch dis- tance is divided into the same number of axial divisions as is the projected circle. From a mathematical stand- point, a thread is simply a helix cut around and into a solid cone or cylinder. THREADS CLASSIFIED (51) V and Square threads. Threads may be divided into two general types or groups, called V threads or Square threads accord- ing to the shape of the tool used in cutting them. Each of these groups may be further classified as Single, Double, Triple threads, etc. This latter classification depends upon the number of separate threads that are turned on one bar of metal. All threads are in general Single threads except in cases where rapidity of motion is required without a corre- sponding increase in coarseness of thread. Some ex- Fig. 3 90 MECHANICAL DRAFTING. amples of the foregoing mentioned threads are shown in Fig. 2. Single V Threads. The V thread is the usual thread found on bolts and screws. It derives its name from the re- semblance of its profile to the letter V. There have been devised numerous modifications of this thread intended to make it stronger and more durable and in some in- stances to fit special classes of work. Fig. 3 shows the profiles of some of these modified V threads. Of these FASTENERS. 91 several types the U. S. Standard (Seller's) thread is the most used in this country. Sizes and dimensions for this class of threads will be found in the Appendix. Sharp V U. S. Standard Fig. 3 Square threads. In cases where a thread is con- stantly being drawn or loosed or where heavy loads are Square B & S Worm Thread Fig. 4 to be lifted, the square thread finds an important place due to the reduced friction over the V thread. This 92 MECHANICAL DRAFTING. thread finds a further field of usefulness in transmitting motion. As with the V thread, many modified forms have been devised. Fig. 4 illustrates a few of these forms. DEFINITION OF THREAD TERMS (52) Crest, Root. The sharp edge of the thread is known as the crest; the depression line as the root, Fig. 5. The term crest or outside diameter is used to denote the diameter of the crest of the thread and is assumed equal to the diameter of the bar. The diameter of the bottom of the grooves is known as the root diameter and is approximately equal to the crest di- ameter of the nut or the diameter of tap drill. Pitch. For bolts and screws of various diameters the size of the threads must vary, hence the number of threads per linear inch must vary. For each size bolt or screw there is a standard number of threads per linear inch which is often improperly termed the pitch of the thread. The distance B, shown in Fig. 5, denotes the pitch of the thread on the bolt. It should always be understood that when the term pitch is used the distance between two adjacent threads is meant, whether the thread is single, double, or triple. In the case of the latter two threads the term lead is used to denote the distance between crests on the same helix. FASTENERS. 93 CONVENTIONAL REPRESENTATION OF THREADS (53) As noted above, the projections of threads on planes parallel to the axis of the threads are curved lines. As each thread requires two helices for its complete projec- tion root and crest, Fig. 2 standard conventions have been evolved to represent the differ- ent threads. On large threads the curved lines are replaced by straight lines; the projec- tion of the thread remaining otherwise the same. Examples Single Single Single Fig. 6 Pig. 7 of these conventions are shown in Fig. 6. On threads one inch or less in diameter the profiles are omitted altogether and the forms shown in Fig. 7, A, B and C are used. In drawing these conventions care must be used not to make the slope of the lines too great, one- half the pitch being right. The spacing may be done by eye but should conform in a relative way to the number of threads on the several bolts or screws on a drawing. MECHANICAL DRAFTING. Light pencil guide lines should be ruled limiting the length of the short heavy lines which should be equal to the root diameter of the thread. When threads are to be shown as invisible lines, the convention as shown in Tapped Hole in Section Pig. 8 A Fig. 8 is recommended. Altho possessing no appear- ance of a thread it is easy to construct and is universally understood by mechanics. Fig. 8 represents the conven- tional way of showing threads in tapped holes, the largest diameter being known as the diameter of the thread. In some instances threads may be made left handed. FASTENERS. 95 Care should be taken to show such threads by the proper slope of the lines. Also attention is directed to the change in direction of slope for threads in sectioned parts. These variations may be understood more fully by ref- erence to Fig. 9. Conventional Representation of Screw Threads Right Hand Fig. 9 Right Hand BOLTS AND NUTS (54) Bolts. There are three distinct classes of bolts in use at the present time called carriage, machine, and stud bolts. Each is made from a rod of iron, threaded on one end to receive a nut, and, with the exception of the stud bolt, having the other end shaped into some form of head. Carriage-Bolt Fig. 10 Carriage bolts. A carriage bolt may be denned as a bolt with an oval head; its shank is squared from %" to 94" under the head, the side of this square being a 96 MECHANICAL DRAFTING. little larger than the diameter of the bolt. This bolt is used in woodwork and when drawn into a hole the square under the head takes a grip in the wood and prevents turning while the nut is drawn. The nut being thinner than the ordinary nut the whole effect is to give a more finished appearance to this class of work, especially after painting. Fig. 10 is given to further explain this class of bolts. Fig. 11 Machine bolts. Machine bolts are divided into a number of classes, each class being named either from its peculiar shape or its distinctive use. The dimensions FASTENERS. 97 of the several parts of all such bolts have been standard- ized, tables arranged, and the construction and size of every part of any particular size bolt is perfectly definite. Hexagonal and square-headed bolts. Inasmuch as these two classes of bolts are usually dealt with in the same table of dimensions, it will perhaps be as well to include both in this discussion. In Fig. 11 is shown the conventional manner of representing hexagonal and square-head bolts in a mechanical drawing. It will be noticed that the hexagonal bolt is so placed that three faces of both the bolt head and the nut are visible and the square head bolt is so placed that two of its faces are visible. This placing should be strictly adhered to, espe- cially in machine sketching where it may be necessary to show the kind of bolt by only one view. Likewise it will be seen that on both bolts the outer corners of the heads and nuts have been ground or turned off until the face of the head and nut is a circle tangent to the hexagonal or square limits of the head or nut. This bevel on the head or nut is called the chamfer of the head, etc. In constructing the end view of any bolt the chamfer circle is first drawn (the diameter of this chamfer circle will be found in table under head of (t Distances Across Flats" or "Short Diameter") and the hexagon or square circumscribed by means of the 30x60 or 45 triangles. No other method should be used for obtaining the hex- agon or square. The geometric construction of- these bolts should be entirely familiar to the draftsman, and Fig. 11 should be thoroly studied and mastered in every detail. Fig. 12 should also be consulted in this connection. MECHANICAL DRAFTING. Oval Fillister Hd. Mach. Screw '''TMp'l'm 't'.^[/j/f~^py^ Flat Fillister lid. Mach. Screw Round Hd. Mach. Sc Flat Conical Oval Dog Pig. 12 FASTENERS. 99 Stud bolt. On account of the particular use and form of the stud bolt it deserves special mention. It has no head and is threaded on both ends nearly up to its center. In places where a headed bolt is impracticable the stud bolt is screwed into the tapped hole in the piece of metal; the part to be clamped in place is then slipped on the projecting end and an ordinary nut used to draw the piece tight. The bolt thus serves the second purpose of being a guide in assembling which makes it almost indispensable in places where machine parts are removed and re- placed very often. Fig. 13 illustrates this impor- tant bolt. Fig. 13 Nuts. A carriage or machine bolt nut may be denned as a square or hexagon of steel or wrought iron of any desired thickness with a threaded hole thru the center. They need no classification, since they differ only in shape, thickness and finish. They may be square or hexagonal, very thick or quite thin, and if rough they quite likely have been punched from sheets of wrought iron or steel, while the finished nuts have been cut from square or hexagonal bars of steel, Fig. 11. DIMENSIONING BOLTS (55) Length, diameter. The length of a bolt is always understood to be the distance from the end to 100 MECHANICAL DRAFTING. the under surface of the head. In placing a note on a drawing designating the size of bolt used, the diameter, length, and pitch of thread should be given in the order named, followed by the kind of bolt wanted; e.g., l"x 4"x 8 thrds. per in. Fin. Hex. Bolt. If the bolt is to be a U. S. Std. bolt, only the length and diameter are needed. On large or long bolts the threaded length should be given. SCREWS (56) Definition. A screw may be defined as a rod of iron or steel threaded on one end and containing a square, hexagonal, or slotted head on the other by which the screw is turned. Screws are divided into four gen- nj \M\i\v\\\jg> Lag Screw Wood Screw ShouJder. Scrcv Fig. 14 eral classes wood, set, cap, and machine screws. Figs. 12 and 14 illustrate some of the types most commonly used. Tables of dimensions may be found in the Appen- dix. In listing screws on a drawing the method outlined in Art. 55 for bolts should be followed. FASTENERS. PIPE THREADS 101 (57) Many times the engineer is required to deal with plans in which water, steam or gas pipes are used. In order to make all connections wa- ter or steam-tight the threads are turned with a standard taper of V to 16". Care should be taken to specify this kind of thread when used on a drawing and to designate its size by giving the inside diameter of the pipe and not the outside diam- eter as is done on bolts and screws. Fig. 15 further illus- Complete Threads Imperfect Threads Fig. 15 Starter or Taper Tap Medium or Plug- Finishing or Bottoming Fig. 16 trates this type of thread. Tables of pipe sizes and threads will be found in the Appendix. 102 MECHANICAL DRAFTING. SHOP OPERATIONS (58) Taps and Dies. The usual method of cutting V threads is by means of tools known as taps and dies. Figs. 16 and 17 furnish general information concerning these shop tools. The tap is used for cutting the threads Dies. Fig. 17 in nuts and also for threading holes drilled in parts of machines. Dies are used for threading bolts and screws and other rods of iron not greater than V in diameter. FASTENERS. 108 Fig. 20 "Woodruff Key 104 MECHANICAL DRAFTING. Square threads, threads not having a standard pitch, and all large threads are turned on the lathe. KEYS AND KEYWAYS (59) In fastening wheels, pulleys, etc., to shafts two classes of fasteners may be used, set-screws or keys. Set-screws may be used to advantage in all cases in which the twisting force on the shaft is very small. It is not wise to use such a fastener on large pulleys or in cases in which the load is likely to be very great. In this latter case one of three varieties of key may be used according to the nature of the machine. These keys and keyways are (a) Keys on flats, Fig. 18; (b) Straight Fig. 21 seated keys, Fig. 19; (c) Wood- ruff keys, Fig. 20; (d) Round keys, Fig. 21. It is clearly seen that the first type of key has a very limited use, and owing to the fact that the Woodruff key is patented, the straight keys and seats have the most general use. In this type of key, it is seen, Fig. 19, that one-half of the recess is milled or cut into the shaft (this groove being known as a keyseat) while the other half of the recess is cut into the hub of the pulley and is known as the keyway. When fitted over each other they should form nearly a square, the height being slightly less than the width. The keys used in this connection are cut from square bars of cold rolled steel and filed to a slight taper on one side only, so that when driven in far enough they wedge FASTENERS. 105 between the hub and shaft, thereby preventing the pulley both from sliding along the shaft in either direction and from turning about the shaft. 106 MECHANICAL DRAFTING. CHAPTER 6 SHOP TEEMS, TOOLS, MACHINES Draftsman's Use of Shop Terms. (60) Certain terms that are in common use in the workshop are used by the designer and draftsman in the form of a direction to the workman. Such words as "drill," "tap," "ream," "finish," etc., are shop terms directing the workman to perform the operation indi- cated. When these words are used on a drawing, the lettering should be so placed that there will be no con- fusion in determining to exactly what part of the ob- ject the term applies. Leaders should point to the part referred to if the meaning is not clear without them. If additional wording other than the simple term is needed, the English language should be used in such a way that the meaning of the note cannot be misunderstood. Ordinarily, working drawings sent to the shop are made so complete that the same drawing will answer for the pattern-maker, blacksmith, and machinist. In this case, each workman uses only that part of the information on the drawing that applies to his work. Some large shops follow the method of making a separate drawing for each of these workmen, so that he will be supplied only with the dimensions and notes that apply to his par- ticular work. FINISH (61) A casting or forging is in a rough state when it comes from the foundry or forge shop and if certain parts are to be machined, they are marked "finish" or simply SHOP TERMS, TOOLS, MACHINES. J07 "f" on the drawing. The most convenient way of indi- cating that a surface is to be finished is to place the letter "f" across the straight line projection of the surface. In Fig. 1, the upper and lower faces of the block are to -4 Drill -i I I toe. i be machined. Since the dimensions given on the draw- ing indicate the size of the finished object, surfaces marked with an "f" will indicate to the pattern-maker or blacksmith that allowance for the tool cut must be made on the casting or forging. The note "f all over" placed under a detail drawing means that the entire surface of this part is to be ma- chined. The operations coming under the head of "finish" will in general be performed on lathes, planers, or shapers such as are shown in accompanying cuts. 108 MECHANICAL DRAFTING. MILL (62) In the shop operation required in cutting slots, grooves known as key seats, also other similar opera- tions, Fig. 2, a machine known as a milling machine Cut on Milling Machine Pig. 2 is used. The cutting tools resemble the common type of circular saw and operate on the same principle. As seen on pages 109 and 110, which are horizontal milling- machines, the cutter is fastened rigidly to the revolving shaft or arbor while the piece of material to be machined is clamped to the table and the table moved, either by hand or automatically, slowly under the cutter, as a log is fed into the saw of a sawmill. For special work mill- ing cutters of many odd designs are made, as seen on pages 111 and 112. The machine shown on page 113 is known as a vertical milling machine, the shaft or arbor in this case being vertical. To prevent vibration in the arbor of the horizontal machine (this vibration being SHOP TERMS, TOOLS, MACI11NKS. 109 HOBIZONTAL MILLING MACHINE 110 MECHANICAL DRAFTING. HOKTZONTAL MILLING MACHINE SHOP TERMS, TOOLS, MACHINES. Ill MILLING CUTTEES 112 MECHANICAL DRAFTING. MILLING CUTTERS SHOP TERMS, TOOLS, MACHINES. 113 VERTICAL MILLING MACHINE 114 MECHANICAL DRAFTING. known as chatter) and consequent rough work of the cut- ter, chatter braces, shown below, are being put on most machines of late design. The note used to indicate any desired milling operation may be as follows: "2" mill"; the two inches indicating the diameter of the milling cutter; or "Mill %" key seat, 4" long," "Mill i/ 8 " slot, W deep," etc. HOEIZONTAL MILLING MACHINE WITH CHATTER BRACES Since economy of time is a large item in shop work the designer will do well to study carefully the many pos- sibilities of the milling machine. Next to the lathe and drill it is perhaps the most efficient machine in use. SHOP TERMS, TOOLS, MACHINES. 115 TWIST DBILLS 116 MECHANICAL DRAFTING. DRILL PRESS SHOP TERMS, TOOLS, MACHINES. 117 DRILL (63) The term "drill" may be applied to all holes of small diameter up to two inches, which do not need a high finish. Holes which are to be tapped for screws or which are to receive a bolt or which are later to be finished to a larger diameter with a reamer may be cut on a drill press with a twist drill. On pages 115 and 116 are shown twist drills and drill presses of various designs used in performing the shop operation termed "drill." BORE (64) In all cases where a round hole is to be machined and the hole is either so large that a twist drill cannot be used or it is desired to give such a finish to the hole as is impossible in the inevitably somewhat rough work of the twist drill, the work will be done on a lathe by means of the short boring tools or by cutting tools in connection with the boring bar and the operation will be termed boring instead of drilling. The note referring to such an operation is 1" bore, etc., the dimension referring to the diameter of the hole. Such boring operations are performed on a lathe or boring machine, pages 118 and 119, and are ordinarily necessary on holes whose diameters are greater than two inches. Twist drills larger than two inches in diameter are not in very com- mon use as it requires an extremely heavy drill press to operate them satisfactorily. If a cylindrical part is to fit into a bored hole, the terms "driving fit," "forced fit," "turning fit," etc., will tell the kind of fit that is required. The 'dimension given will indicate the size of the part MECHANICAL DRAFTING. SHOP TERMS, TOOLS, MACHINES 119 120 MECHANICAL DRAFTING. REAMERS REAMERS SHOP TERMS, TOOLS, MACHINES. 121 to be fitted into the hole and the necessary allowance for the desired fit will be made in the boring operation. REAM (65) Wherever a small hole is to be given a certain taper or is to be given a finish not possible with a twist drill or is to be cut to a very exact dimension, a tool known as a reamer, page 120 should be used and the term applying to such an operation is ream. This operation of course presupposes that a hole slightly less in diam- eter has already been cut with a twist drill, or bored on a lathe. CORE (66) The term core is used in connection with cast- ings only and indicates that the hole referred to is to be produced by a core (a hardened cast of sand of the desired shape and size), which is placed in the mold when the casting is made. The pattern-maker must make provision for the core in the construction of the wood pattern of the casting. . "Core V/a"" means that a core 1%" in diameter will be used in the mold. The cored hole will of course be as rough as the surface of a rough casting. TAP (67) The term tap applies to the shop operation required in cutting V threads in holes of comparatively small diameter ; that is, less than one and one-half inches. The note used to indicate that a certain hole is to be threaded to a certain pitch is as follows : %" tap x 13 pi. 122 MECHANICAL DRAFTING. On pages 101 and 102 are shown a series of standard taps and likewise both bolt and pipe dies used in cutting V threads on bolts, pipes, etc. TAP DRILL (68) A tap drill is a twist drill of the common type, named a tap drill in this case because it has been used in drilling a hole which is to be threaded to receive a screw. HARDEN, TEMPER, ANNEAL (69) These are terms which have to do with the heat treatment of the machine parts in question and there- fore will be interpreted by the workmen in the forge shop. FILLET (70) It is a well recognized principle of mechanics that a break is much more likely to occur in sharp Fig. 3 Fig. 4 corners of a machine than elsewhere, the corner seem- ing to furnish a starting point for the break. For this reason, and others which need not be mentioned, all corners found on castings are seen to be slightly rounded, SHOP TERMS, TOOLS, MACHINES. 123 Fig. 3. This rounded corner is known as a fillet; like- wise the material which is used to make this fillet in pat- terns takes the same name. In Fig. 4 is shown the method of making such filleted corners in patterns. The triangular piece shown is made of wood, shaped by driv- Shape of the Fillet Fig. 5 Fig. 6 ing thru a Die, Fig. 5, as dowel pins, or of hard wax rounded by a heated rod, Fig. 6, or it may be of leather which can be purchased in coils of any length. The leather fillets, of course, are most convenient for very irregularly shaped pieces. The radius of the arc of such fillets is quite generally 14"; however, it is necessarily a matter of machine design and for very large pieces the radius must be greater than 14". BEARINGS (71) Brasses. In certain types of machines it is desirable to use brass for bearings rather than the com- bination of lead and zinc and copper. Such bearings are ordinarily made in halves, constructed so as to permit of a slight adjustment, Fig. 7. These half bearings are commonly known as brasses. Babbit. The alloy of lead, zinc and copper mentioned above is commonly known as babbit. The greater the amount of zinc and copper, the harder this compound is. Two of the material advantages of babbit for bearings 124 MECHANICAL DRAFTING. are, that the metal is cheap, and such bearings can be easily replaced by a workman of but ordinary experience. Babbit lining is poured while molten into the cast iron casings with the shaft in place. Fig. 7 LIBRARV SCHOOL ISOMETRIC AND OBLI MANUAL ARTS *ND HOME ECONOI SANTA BARBARA, CALIFORNIA CHAPTER -7 ISOMETRIC AND OBLIQUE PROJECTION EXPLANATION OF PRINCIPLES (72) If through a given point called the origin three lines be drawn at right angles to each other, as the three adjacent edges of a cube, we have the usual mathemat- ical coordinate axes X, Y, and Z. These axes taken in pairs determine three planes, such as the three coordi- nate planes used in Chapter 3. If now an object with rectangular or square faces, for example a cube, be placed in the first angle, and be viewed in turn in the direction of the axes X, Y, and Z, the figure in each case will appear to be simply a square. These squares projected on their respective coordinate planes give, of course, the ortho- graphic projections of the cube, and it should be remem- bered that the square seen, if the cube is viewed in the direction of the X axis, represents the entire object and not merely the face of it. Thus we see that one face only is visible, in general, in each view. If now we imagine a line drawn in such a direction as to make equal angles with X, Y, and Z, for example, the diagonal of the cube, and view the object in the direc- tion of this line, it is apparent that three faces will be visible, although now none shows as a rectangle, nor do we see any of the edges in their true lengths. However, all the edges of the cube parallel to axes X, Y, and Z are equally or proportionally fore- shortened if seen in the direction of this new axis, known as the isometric axis. The plane perpendicular to the isometric axis is 126 MECHANICAL DRAFTING. known as the isometric plane, and the projection on this plane of any* object viewed in the direction of the iso- metric axis is known as an isometric projection. The sheet of paper or blackboard may, of course, be conceived as the isometric plane, on which the projections of the three axes X, Y, and Z will be right lines making 120 degrees with each other and the projection of the iso- metric axis will be their point of intersection, Fig. 1. This point of intersection may also be termed the origin. Fig. 2 Fig. 3 DIRECTRICES (73) The orthographic projections on the isometric plane of the three coordinate axes X, Y, and Z are known in the drawing as the directrices, and occasionally as the isometric axes. Since the coordinate axes make with each other equal angles, their projections (the directrices) also make equal angles (120 degrees) with each other. This being true, when it is desired to make any isometric projection, the directrices may be drawn immediately through any chosen point and at 120 degrees to each other. One of the directrices is usually taken vertical, Fig. 1 ; however, the arrangements shown in Figs. 2 and 3 are frequently used. ISOMETRIC AND OBLIQUE PROJECTION. ISOMETRIC SCALE 127 (74) Since the coordinate axes are oblique to the isometric plane, their projections are shorter than the axes themselves. However, since each axis makes the same angle with the isometric plane, one inch measured on each of the three axes will project in equal lengths on tho isometric plane. For all ordinary purposes, in Origin Fig. 4 making an isometric projection, it is more convenient to lay off the projections of lines which are parallel to X, Y, and Z equal in length to the actual lines. It is seen, of course, that the projection made with such measurements represents the object as being about fifty per cent larger than it actually is. Since the direct use of the scale in measuring these lines full length makes so much for convenience and only enlarges the view, this procedure is usually followed. If, on the other hand, it is desired that the projection be mathematically cor- rect, the projection of all lines parallel to X, Y, and Z must be measured according to the isometric scale. Since each coordinate axis makes with the isometric plane an 128 MECHANICAL DRAFTING. angle of 35 16', if we assume the hypotenuse AB of the right triangle, Fig. 4, to be one of the coordinate axes, BC the isometric axis, and CA the isometric plane, viewed edgewise, the isometric projection of any given length BE on the axis BA would project on the plane with a Fig. 5 length equal to Ce. Figs. 5 and 6 illustrate simple methods for obtaining the isometric scale. (75) Problem 1. To construct the isometric projec- tion of any parallelepiped. Construction. Cube 2" on edge, Fig. 7. Thru point are drawn the axes OB, OA, and OC, making with each other angles of 120 degrees. From 0, along OA, measure with the isometric scale 2"; the same along OC and OB to points D, E, and F. OD and OE then represent the two adjacent sides of the base, and lines from D and E parallel to OE and OD complete the base. In similar manner the vertical faces DOF and Fig - 7 ISOMETRIC AND OBLIQUE PROJECTION. 129 FOE are completed; then draw the top base FS and finally the faces SD and SE. IRREGULAR OBJECTS (76) Inasmuch as all but a very small percentage of machine parts are either of rectangular shape or can easily be enclosed in such a box or parallelepiped, the isometric projections of irregular objects are easily constructed with the aid of such an enclosing parallelepiped, Fig. 8. In most cases it will be found necessary to section the object in order to show the interior portion or cross-section, Figs. 9 and Pig. 8 CIRCLES (77) Problem 2. To construct the isometric projec- tion of a circle, Fig. 11. 8 point method. ABCD is the isometric projection of a square in which a circle is inscribed. On edge AB con- struct a square and inscribe in it a circle. Draw the hori- zontal diameter of this circle and diagonals of the square. The points of tangency of the circle with the square and the 4 points of intersection with the diagonals constitute the desired 8 points. If the diagonals of the parallel- ogram be drawn the isometric projections of these 8 130 MECHANICAL DRAFTING. Pi. 10 ISOMETRIC AND OBLIQUE PROJECTION. 131 points may be obtained as shown and the ellipse drawn thru them by means of the irregular curve. Fig. 11 Approximate mechanical method. The isometric projection of a circle which lies in a plane parallel to the plane of any two isometric axes will always be an ellipse inscribed in a rhombus ABCD, whose acute angles A and are 60 degrees, and which itself is the isometric projection of the square circumscribing the circle repre- sented. The ellipse may be approximated with satisfac- tory exactness if made of arcs of circles as illustrated in Fig. 12. From the obtuse angles B and D perpendiculars are dropped to the opposite sides. Then with radius R equal to DE and centers B and D vthe arcs HF and GE are described; with cen- ters K and L, and radius r equal to LE, the small circles are de- scribed completing the approxi- mate ellipse. Fi e- 12 132 MECHANICAL DRAFTING. DIMENSIONING (78) In placing dimensions on an isometric drawing, the same rule must be followed as in orthographic work- ing drawings ; the dimensions must read from left to right or from the bottom up. In following this rule it will be found always that the dimension lines are parallel to the coordinate axes, never otherwise. In giving the diam- Fig. 13 eters of circles the method shown in Fig. 13 is preferable to plac- ing the diameter directly on the isometric of the circle. On in- spection of Fig. 14 it is seen that there are actually three faces of the object to be dimensioned and in giving the dimensions for face No. 1, which is parallel to the isometric plane No. 1, it must first be decided what directions consti- tute from left to right and from bottom up. The same thing must be decided for faces 2 and 3. In Fig. 15 is given a key which will be useful in dimensioning. In con- ISOMETRIC AND OBLIQUE PROJECTION. 133 nection with this key it will be necessary for the student, in placing dimensions, to decide merely to which face of this key his dimensions are parallel, Figs. 9 and 10. OBLIQUE PROJECTION (79) Inasmuch as circles are so rarely found in such positions that their projections are true circles in iso- metric projection, a variety of projection has been de- vised in which it is possible so to place circles that their projections are circles and are easily drawn. This is known as oblique projection. In oblique projection as in the isometric projection just discussed, we have one plane of projection. The line of sight is always assumed oblique to the plane of projec- tion. We may call this line the oblique axis. If two of the coordinate axes are placed parallel to the plane of projec- tion and projected thereon by lines parallel to the line of sight, the projections will be unchanged in relation to each other. In projection the third axis will, however, be foreshortened and inclined to the other two at an angle other than 90. This angle may be varied at will accord- ing to the angle of inclination of the oblique axis with the plane of projection, but is usually assumed at 30, 45, or 60 with the horizontal. These projections of the coordinate axes are called the directrices. DIRECTRICES AND CO-ORDINATE PLANES (80) Thru the origin, 0, Fig. 16, (a) and (b), are drawn three directrices as shown; one horizontal, a second vertical, and the third to the right or left at 45, 30, or 134 MECHANICAL DRAFTING. 60 with the horizontal, preferably 45. These three lines represent lines at right angles to each other, and may be compared to the three adjacent edges of a cube. Taken two and two, these directrices include coordi- nate planes as follows : OA and OB, plane 1, or the plane of true circles; OB and OC, plane 2, a second vertical plane, and OA and OC, plane 3, a horizontal plane. DIMENSIONING (81) In oblique as well as in isometric projection, the problems of dimensioning are threefold ; i. e., any object drawn may have faces parallel to each of the three coordinate planes in Fig. 17. In placing dimensions for constructions on these faces it is necessary, of course, to decide what di- Fig. 18 rections constitute from left to right and from bottom up. The key in Fig. 18 may be used in a manner similar to that of the key given for isometric projection. Inspec- tion of Figs. 19-23 may serve to clear up any doubtful points, both in dimensioning and in construction. OBLIQUE SCALE (82) If equal distances be measured from along the axes OA, OB and OC, Fig. 24, the distance along ISOMETRIC AND OBLIQUE PROJECTION. 135 Oblique Projection of Stuffing Box. Fig. 19 136 MECHANICAL DRAFTING. Oblique Projection of Shaft Coupler. Fig. 20 ISOMETRIC AND OBLIQUE PROJECTION. 137 Fig. 21 MECHANICAL DRAFTING. ISOMETRIC AND OBLIQUE PROJECTION. 139 Oblique Projection of Flanged Pipe Tee. Fig 23 140 MECHANICAL DRAFTING. OC will appear to be longer than those along OA and OB ; hence, for symmetry, it is necessary to make use of Fig. 24 Oblique Scale for 45' Oblique Scale for 30' Fig. 25 the oblique scale in measuring any distance along OC. The oblique scale is obtained by measuring off inches, etc., on the hypotenuse of a 45, 30, or 60 triangle and projecting these inches upon either of the legs for 45, long leg for 30 and short leg for 60, Fig. 25. (83) Problem 3. To draw the oblique projection of a parallelepiped. Construction. Cube V on edge. Thru a chosen point, 0, Fig. 26, draw the three axes OA, OB, and OC. Along axes OA and OB measure V to D and S, and with the oblique scale meas- ure 1" along OC to B. Com- plete the parallelograms ODMB, OSLB, and DNSO; then the re- maining faces may easily be added. CIRCLES (84) Point E, in face TLBM, Fig. 27, is the center of a circle 34" diameter. Since this is the face of true ISOMETRIC AND OBLIQUE PROJECTION. 141 circles, the circle may be constructed with the compass. If it is desired to draw the projections of circles lying in faces TNSL or NTMD the 8-point method explained in isometric projection may be used. In cases where rapidity of construction is more important than sym- metry, it is common practice among draftsmen to omit the use of the oblique scale altogether. Then if the oblique axis be drawn at an angle of 30 degrees to the horizontal, it will be noted, in Fig. 28, that face NM is now of such shape as to convert the oblique projection of any circle placed in that face into an isometric projection, and the mechanical method of constructing that isometric pro- jection, shown in Fig. 12, can and should be used. If, on the other hand, the oblique axis be drawn at an angle of 60 degrees to the horizontal, Fig. 29, the face NL is now of such shape as to convert the oblique projection of any circle placed in it into an isometric projection which can be constructed mechanically by the method of Fig. 12. 142 MECHANICAL DRAFTING. With some care it will usually be possible, in making the oblique projection of any object containing circles, so to place the object that the oblique projections of some of the circles are true circles, while the projec- tions of the remainder become isometric when the ob- lique axis is drawn either at 30 or 60 degrees to the horizontal. Fig. 29 IRREGULAR OBJECTS (85) All that has been said on this subject under isometric projection applies as well in oblique projection. It is perhaps unnecessary to suggest that when making any oblique projection care should be taken so to place the object that most of the circles will appear as true circles. SHADES AND SHADOWS IN ISOMETRIC AND OBLIQUE PROJECTION (86) Shades and shadows, in isometric projection as in orthographic projection, are used merely for the ISOMETRIC AND OBLIQUE PROJECTION. 143 natural appearance which they give to a drawing. Hence, as in orthographic projection, the draftsman has con- siderable freedom in determining both the direction and the length of the shadows. Before proceeding with a problem in shades and shadows it will perhaps be well to define a few of the terms and state the fundamental principles which govern construction. Direct light. All light which comes to any body di- rectly from the source (the sun, arc lights, etc.) is known as direct light. Indirect light. All light which reaches objects in an indirect way, e. g., by reflection from other objects which are in direct light, is known as indirect light. Shade. Any portion of the surface of an object from which the direct light is excluded by some part of the same object is said to be in shade. This shaded surface may also be known as a shade. Shadow. Any portion of the surface of an object from which the direct light is excluded by some part of another object is said to be in shadow, and for convenience may be called a shadow. PRINCIPLES 1. All rays of light in these problems are regarded as parallel; hence, when the direction of the first ray has been assumed, all others must be considered parallel to it. 2. The shade or shadow of a given point on a given surface is the point in which a ray thru the given point pierces the given surface. 3. Any ray used to determine the shade or shadoiv of a given point may in reality be a ray of light ; however, 144 MECHANICAL DRAFTING. in this discussion it will be known as a shadow ray; see Miller's Descriptive Geometry, Art. 124. 4. If a line AB is parallel to a plane, e. g., H, the shadow of AB on H is parallel and equal in length to AB. Fig. 30 5. If lines AB and CD are parallel the shadows of AB and CD on any plane must be parallel, i. e., the shadows of parallel lines are parallel. 6. If a line AB is oblique to H, AB and its shadow on H will meet at the point in which AB pierces H. 7. The shadows of parallel lines on parallel planes are parallel. (87) Problem 4. To find the isometric or oblique projection of the shade and shadow on H of a given object. Given. Isometric and oblique projections of Cross, Figs. 30 and 31. ISOMETRIC AND OBLIQUE PROJECTION. 145 Req'd. Isometric and oblique projections of shade and shadow on H. Beginning with point as an origin, a line may be drawn in any desired direction, e. g., Oa, to represent the shadow of OA, and point a assumed in any desired posi- Fig. 31 tion as the shadow of point A. Aa is the isometric pro- jection of the shadow ray thru A, and all other shadow rays must be parallel to Aa. Since AB is parallel to H, its shadow db is parallel and equal in length to AB. BC is parallel to OA, hence its shadow be is parallel to Oa, and c is determined by shadow ray Cc. CD is parallel to H, hence its shadow cd is parallel and equal in length to CD; d may likewise be located by the shadow ray Dd. Since the plane GCDK is parallel to H, the shade of GE on this plane is parallel to Oa, see Principle 7, and e is located by the shadow ray from E. EF is parallel to 146 MECHANICAL DRAFTING. GCDK, hence the shade line from e is parallel to EF; to find the shadow of F draw the shadow of MF parallel to Oa; the intersection of this shadow line with the ray thru F locates f. The shadow of EF is paralled to cd; fn is parallel and equal in length to FN. It is readily seen from the direction of Oa that the face AOM must be in shade, likewise BCD and GEFK and space KGteh. The isometric projections of the shadows of the re- maining points are located successively as those already found. MACHINE SKETCHING. 147 CHAPTER 8 MACHINE SKETCHING (88) Definition. A machine sketch may be roughly defined as a freehand working drawing. To the engineer no one accomplishment is of more value than the ability to make rapidly accurate, legible machine sketches. A draftsman or shop foreman may be called upon at any time to make a hasty sketch of some broken machine part which perhaps cannot be removed without shutting down the machine for a day or two. A construction engineer putting in some new machin- ery may find that some plates, fixtures, etc., designed especially for the job, are all wrong, and he must imme- diately send in sketches of what is wanted. A bridge engineer may find his work held up by the breaking or absence of some peculiarly shaped piece, or may need some special fixtures to handle difficulties pecu- liar to the job. Likewise, it is understood that all machine forms are devised in the mechanic's brain and must be placed on paper in some approximate form before it is possible to make a mechanical working drawing. In all of these and hundreds of other cases which are inevitable, the ability to sketch rapidly and well is indis- pensable, and the man who finds himself called upon to make a sketch and is not well grounded in its principles, will find himself seriously handicapped. PAPER (89) It will be seen that the nature of the situations 148 MECHANICAL DRAFTING. which require sketching will demand the use of scratch paper or a notebook. Cross-section paper is invaluable for this purpose, as it aids materially in the rapid and accurate sketching of the several views. NATURE OF DRAWING (90) As in a mechanical ivorking drawing, a machine sketch consists of a number of views (top and front; top, front, and left end, etc.) of a machine or machine part. These views are true orthographic projections, hence projections of each other, as in working drawings. Never show more views than are necessary to explain clearly the construction; of course, two are a minimum; varia- tions in this respect will be mentioned later. PENCIL SKETCH STROKE (91) For sketching it will be better to use a com- paratively soft pencil, H or 2H, as it is desirable to show marked distinction between the outlines of the object and dimension and section lines. In drawing lines, whether short or long, the sketch stroke should be used. The sketch stroke is merely a succession of short strokes in the desired direction, and, as a result, the line will, of course, be somewhat ragged, consisting of a number of short overlapping lines. How- ever, by this method it will be found possible to approxi- mate a straight line much more closely than by a con- tinuous stroke. SIZE OF DRAWING (92) The work being freehand and done usually under adverse conditions, sketches are not made to scale; numerical dimensions are depended upon en- MACHINE SKETCHING. 149 tirely for sizes. As an aid in approximating propor- tions of the different parts of a machine, the follow- ing scheme will be found useful: Suppose after care- ful inspection it is decided that only two views are necessary, and these front and right end. You have perhaps a 5 x 7 notebook at hand and must place these two views, with dimensions, on this size sheet. Estimate the ratio of the length of the object to its width and height and block out roughly on the sheet the proper pro- portional spaces, for the two views, making them as largo as possible. Then measure off on a lead pencil with the thumb-nail a distance equal to the length you have given the space for the front view, and, holding the pencil hori- zontally and about 1' from the eye, move off from the machine until the space from the end of the pencil to the thumb-nail just covers the length of the machine. Stand- ing in this position and using the pencil in this manner, the several parts of the machine may be rapidly sketched in their proper sizes. PROCEDURE (93) In making a machine sketch, the greatest speed and accuracy will be attained by following some system. The following will be found valuable : 1. Decide on the number of views necessary, and decide which these should be. 2. Estimate ratio of length to width of machine and block out on sheet proportional spaces for above views. 3. Sketch in all outlines (working on all views at the same time). Do not attempt to finish one view en- tirely before working on the other ; when a line is placed on one view, place its projection on the other view so that all views are finished at approximately the same time. 150 MECHANICAL DRAFTING. 4. Sketch in dimensions, auxiliary, and section lines. The reason for placing on dimension lines while making up the views is, that each detail of the piece as it is drawn may suggest a necessary dimension that perhaps would be overlooked if left until later. A break should be left in each dimension line. No attempt need be made here to distinguish between outlines and other lines. 5. Go over the sketch carefully and increase the weight of outlines so that the construction shows easily. 6. Obtain from the machine with calipers and rule all dimensions already indicated on sketch. Always place on overall dimensions as a check. 7. Be liberal with notes. SHORT CUTS (94) To save time, the following short cuts are permissible : 1. In drawing objects of familiar shape, wheels, etc., the hub, two spokes, and a short portion of the rim is sufficient. 2. Where objects are symmetrical with respect to a center line, e. g., gate valves, etc., it is sufficient to show only one-half of object, limiting the portion drawn by the center line. The other half may be drawn in when time permits, if desired. 3. Where objects are symmetrical about two center lines at right angles to each other, it will be sufficient to show only one-fourth of the object. 4. Where any part cannot be shown well in detail, e. g., bolts, holes, fasteners, etc., explanatory notes may be substituted e. g., %" drill; %" x 10 pi. tap; % He*. Hd. Mach. Sc.; etc. PERSPECTIVE. 151 CHAPTER 9 PERSPECTIVE (95) Tho it is impossible to give here any complete explanation of the principles of perspective, it has been deemed advisable to attempt sufficient explanation to enable one to understand a few of the basic principles. It is readily seen that no one view of a working draw- ing of any object can present to the eye the natural appearance possessed by a crayon or charcoal drawing. The reason is, that in making a working drawing the eye was imagined at an infinite distance from the object, an assumption so unnatural as to give rise immediately to results of an unnatural appearance. PERSPECTIVE DRAWING (96) Definition. A perspective drawing of an object is such a representation of that object on a given plane or sheet of paper as will present the same appearance as the object itself when the eye is in a certain position with respect to the object. The plane on which the perspective drawing is made is called the picture plane, and, for reasons which need not be given here, is usually taken vertically. PRINCIPLES OF CONSTRUCTION (97) The principle on which perspective construc- tion is based is as follows: The vertical picture plane is placed between the eye and the object (that the draw- ing may be smaller than the object), and lines of sight or visual rays drawn from the eye to the various points 152 MECHANICAL DRAFTING. of the object. The points in which these lines pierce the picture plane are respectively the perspectives of the corresponding points of the object. If lines be drawn connecting these piercing points in their proper order, a perspective drawing of the whole object is obtained. Fig. 1. PICTURE PLANE AND POSITION OF OBJECT (98) Since perspective drawings are made mostly from working drawings, the vertical plane of OrtJlO- graphic projection is used as the picture plane and the object placed in the third angle. POSITION OF POINT OF SIGHT (99) The point of sight is, of course, in front of the vertical plane, and may be in either the first or fourth angles, according to the nature of the view desired; i. e., if it is desired to make a drawing showing the appear- ance of the object when directly in front of it, the point of sight would be in the fourth angle. PRINCIPAL POINT IN PERSPECTIVE (100) The projection of the point of sight on the vertical plane is called the principal point in perspective, and is of prime importance in construction. Inasmuch PERSPECTIVE. 153 as the vertical projections of points are designated thus, a', b', (f, etc., the vertical projection of the point of sight, S, will be indicated by s'. PRINCIPAL POINT THE VANISHING POINT OF LINES PERPENDICULAR TO THE PICTURE PLANE (101) It is a familiar fact that as one stands near a long straight section of railroad track the two lines of rails appear to meet off in the distance. So it is with any set of parallel lines; if the eye follows them for a distance and, when speaking geometric- Fig. 2 ally, we give this distance a value of infinity they all appear to meet in one point. This point we call their vanishing point. When our line of sight follows out these parallel lines to infinity, where they appear to meet, for all practical purposes the line of sight is parallel to the given set of lines. Reference to Fig. 2 may serve to make this explanation clearer. Point S represents the position of the eye. A cube BD rests on a horizontal 154 MECHANICAL DRAFTING. plane on the other side of the picture plane. The four parallel edges, AB, CE, etc., of the cube are produced as indicated by dotted lines to the right; if they are pro- duced an infinite distance they will appear to meet, and the line of sight from S to the apparent meeting or vanishing point is the line thru S and V. Then, as ex- plained above, if SV meets AB, CE, etc., at infinity, it is parallel to them. But AB, CE, etc., are perpendicular to the picture plane; therefore the line thru S and V out to this vanishing point is also perpendicular to the pic- ture plane and must pass thru s', the projection of S on the picture plane. As viewed from point S, the four edges, AB, CE, etc., which we have produced to infinity, do not in reality appear to be parallel lines forming the edges of a long prism, but seem to represent the four edges of a long pyramid. To return to the perspective, suppose we wish to represent this long pyramid on the picture plane as seen from S. According to Art. 97, lines are drawn from S to the several points of the pyramid; the line from S to the imaginary apex at in- finity pierces the picture plane at s'; and the lines from S to A, C, D, and F pierce the picture plane at i Ci d^ f l ; then &! Ci di /i -s' is the perspective of the pyramid. From this explanation it is seen that the perspective of all lines perpendicular to the picture plane meet at s', the vertical projection of the point of sight. For this reason s' is called the vanishing point of perpendiculars. The fact that perpendiculars do converge at s' affords an easy method of constructing the perspective of any object when placed in a certain position. Lines from S to the other points of the cube are seen to pierce the picture plane in points on the perspectives of these perpendicu- lars, giving the figure b t Oi Ci d^ /i g lt This figure repre- PERSPECTIVE. 155 sents the cube as seen from S. Face ABEC is not visible from S. THE HORIZON IN PERSPECTIVE (102) Any line which is perpendicular to a vertical plane is horizontal. In Fig. 2 the lines AB, CE, etc., are horizontal lines and, when produced an infinite distance, appear to meet in a point on what we commonly call the horizon. Then the line of sight from S to this meeting point becomes a horizontal line, and the perspective of the horizon will be the horizontal line drawn thru the point s'. The horizontal line lying in the picture plane 156 MECHANICAL DRAFTING. and passing thru the vertical projections of the point of sight, s', is also called the horizon. SPECIAL POSITION OF THE OBJECT (103) If the cube in Fig. 2 be moved until face ACDF coincides with the picture plane, then this face becomes its own perspective and each line on this face is shown in its true value ; i. e., a circle shows as a true circle, etc. From this it follows that the perspective of any circle whose plane is parallel to the picture plane will be a true circle; its diameter will be less or greater than the true diameter, however. MECHANICAL CONSTRUCTION OF A PERSPECTIVE (104) Inasmuch as all lines in perspective are shorter than the lines which they represent, except in the case of lines which lie in the picture plane, it will be best to put one face of the object or one face of a circumscribed parallelepiped into coincidence with the picture plane, in order that we may have a foundation of actual measure- ments on which to base our construction. COORDINATES (105) The position of the point of sight with respect to some chosen point, A, of the object will hereafter be given as follows: x = distance of point of sight to right or left of A as x is + or . y = distance of point of sight above or below A as y is + or . z = distance of point of sight before the point A; e. g., x = 3", y= - 4", z = 6" locates S 3" to the right and 4" below A and 6" before the picture plane. PERSPECTIVE. 157 (106) Problems. To draw the perspective of a cube 114" on edge, one face of the cube coinciding with the picture plane ; x = 2", y = 1", z = 4". A is taken at corner A. Fig. 3 Construction. See Fig. 3. Draw well toward the top of the sheet a horizontal line G. L., the intersection of the horizontal and vertical planes. Since the picture plane coincides with the verti- cal plane this line, G. L., represents the picture plane as 158 MECHANICAL DRAFTING. seen from the top. Construct in a convenient position the top view b-fc-da-gj of the cube, the line da-fc, which repre- sents the front face of the cube, coinciding with G. L. At any desired distance directly below the top view, draw the square ajid di which is the front view of the cube. The point of sight S is to be located by the three co- ordinates given with reference to the point A on the cube. First, locate S as viewed from above. The top view of S (lettered s) is 2" to the left of a (x = 2) and 4" in front of a (z=4"). The square b-fc-da-gj, G. L., and s now represent respectively the cube, the picture plane, and the point of sight as they appear looking down from above. Second, locate S as viewed from the front. The front view of S (lettered s') is V to the left of a, (x = -2) and V above a^ (y=l"). The square ttif^ddi and s' now rep- resent respectively the cube and the point of sight as viewed from the front. The square ajiddi is the perspective of the front face of the cube since this face lies in the picture plane. Draw lines from a^ f lt d, and di to s'. This figure s' aif^ddi then is the perspective of the long pyramid spoken of in Art. 101. The perspectives of the edges of the cube that are perpendicular to the picture plane will lie along these lines just drawn to s'. For example, the perspective of the edge AG is a^i, lying along a^ s' and it is only neces- sary to locate 0i on this line. To locate g lt draw sg and where it crosses G. L. at v drop a perpendicular to G. L. until it intersects a a s'. Since sj coincides with sg, j^ will lie directly below g : on drf' and the perspective of the left side of the cube is completed as a^gijidi. A horizontal line from #1 produced until it interesects /is', completes the perspective of the cube. It is easily seen that sg is the PERSPECTIVE. 159 top view of a line of sight from S to G and was drawn to ascertain the distance v d to the left of the edge FD of the cube at which the line of sight pierces the picture plane. It is desired to place a small pyramid on top of the cube, the edges of its base parallel to the edges of the cube and its apex P directly above the center of the top face. Construct the top and front views of the pyramid in place and proceed with the construction of the perspective of the base as shown. The perspective pi of the apex is the point in which the line of sight sp pierces the picture plane and is found by dropping a perpendicular from the point where sp crosses G. L. until it meets s' p'. The per- spective of the pyramid is then readily completed. In certain instances, a left side view will be an addi- tional aid in constructing the perspective. In Fig. 3, the square V'g" fa" tt'cf' j", G^ L^ and s" represent respectively the cube, the picture plane and the point of sight as viewed from the left. The line s"p" represents the line of sight from s to the apex p of the small pyramid as viewed from the left and a horizontal line drawn from v" meets s'p' at p lm It will be readily seen that the per- spective could have been determined from the left side and front views without the use of the top view at all. The use of both top and left side views is usually unneces- sary. CIRCLES IN PERSPECTIVE (107) The 8 point method may be used in construct- ing circles in perspective. This is illustrated on the cube in Fig. 3. The diagonals can easily be drawn and the points of tangency of the perspective with the upper and lower lines /j g^ and dj_ j l determined by drawing a ver- tical line thru the intersection of the diagonals. 160 MECHANICAL DRAFTING. IRREGULARLY SHAPED OBJECTS (108) Any irregularly shaped object may be easily drawn in perspective by first enclosing the object in a parallelepiped and referring the several constructions of the object to lines of the parallelepiped. POSITION OF POINT OF SIGHT (109) Considerable care and judgment must be used in placing the point of sight, for it is easily understood that a house viewed from a point only two feet in front of it would look absurd; however, its perspective can be constructed as easily under such circumstances as any other. It is well to estimate approximately from what particular position we would likely view that object to obtain the best view, taking into account the size of the object in this estimate. The point of sight may then be placed accordingly. For large objects a safe rule is to place the point of sight in front of the object a distance equal to twice the greatest dimension. For smaller objects we may increase this to 4 or 5 times the greatest dimension. APPENDIX 162 MECHANICAL DRAFTING. PHOTOGRAPHIC REPRODUCTIONS Blueprinting. Blueprinting is in short a process of simple photographic reproduction on sensitized paper, of drawings which have been made on some translucent material; this material may be tracing cloth, tracing paper, or ordinary paper oiled after the drawing has been finished. In common practice the process is some- what rough as one would infer from a glance at the average print; however, with care it can be carried nearly to the same limits of refinement as other photo- graphic printing. BLUEPRINT PAPERS Occasions may arise when it is necessary to sensitize paper for blueprinting; however, unless absolutely nec- essary no draftsman should ever bother to coat his own paper, for it is a tedious and most unsatisfactory proc- ess. The machine-coated papers sold by any of the in- strument companies in 10 or 50-yard rolls of any width and of any desired thickness or quality of paper is cheap, keeps well for months in a tin tube, and always gives better results than paper coated by the amateur. For prints which must stand extra hard use, either mounted paper (cloth-backed paper) or blueprint cloth (a smooth, hard-surfaced, sensitized cloth) should be used; the latter, however, seldom gives the sharp detail obtainable on paper. Below is tabulated information that will be of value in ordering papers or cloth. APPENDIX. 163 Blue Print Paper and Cloth PAPER CLOTH WEIGHT USE WEIGHT USE Extra thin For sending thru mail. Not satisfactory for shop use, too thin. Extra thin L