STACK - ANNBX «" GRAMMAR GRADE PROBLEMS ■f- IN MECHANICAL DRAWING |gl ■ BENNETT ^■X^^9 ^^^^^^^K. J 1 1 III - M' ^^m 1 ■ 1 1 GRAMMAR GRADE PROBLEMS IN MECHANICAL DRAWING CHARLES A. BENNETT ILLINOIS, AND THE MANUAL ARTS PRESS PEORIA. ILLINOIS Copyright by Charles A. Benneli 1916 FOREWORD This collection of simple problems in mechanical drawinj^ has been prepared to meet an evident need in teaching the fundamentals of this subject in grammar grades. It ought to be true that the habits formed in the first use of drawing instruments in the grammar grade classroom or workshop would never have to be unlearned, even tho the pupil became an architect, an engineer, a designer, or a draftsman, and that in so far as he learns mechanical drawing at all in these grades, he would learn what is fundamentally correct; he should learn the elements of correct expression in this universal language of the industrial world. It ought to be true, also, that his work in mechanical drawing, while not at first following 'exactly the same course of models or problems as he follows in woodworking, would be parallel or closely related to the shopwork, and, in its later stages, occupy the same relation to the shopwork that the draftsman's work bears to that of the mechanic. How to accomplish this result is the problem which this little book attempts to help solve. Alone, the book can do no more than half solve the problem, but when used under the direction of a trained and efficient teacher, it can help in forming right habits and in acquiring practical skill in simple drafting. In the preparation of this little book the author is especially indebted to the students who have been in his classes at Bradley Polytechnic Institute during the past few years. They have suggested many of the problems, and their later experiences in teaching mechanical drawing to grammar grade classes have furnished valuable data which has been freely used in these pages. Peoria, Illinois, July, 1916 2065970 CONTENTS Foreword To THE Teacher To THE PCPIL Tools and Supplies Group I Horizontal and Vertical Lines — Lay-out of Sheet. (12 Problems.) Lettering .Sheet A. Group II Horizontal and Vertical Lines — Dash Lines ■ Selection of Views. (12 Problems.) Lettering Sheet B. Group III Page S4 Inclined Lines — Foreshortening — Use of Triangles. (12 Problems.) 40 Sheet C. Group IV 4'> The OctuKon and the Hexagon. (S Proljlems.) Lettering Sheet D. 4G Group V 48 The Circle -C( ines — Sections. (12 Problems). Group \T 04 Tangents. (12 Problems.) Group VH 00 Working Drawings. Selection of V'iews — Detcr- minati(m of Scale — .\rrangcment of View.s — Lines — Lining in — Selection of Dimen.sions — Placing of Dimensions — Figures — Dimensioning Circles and Arcs. (5 Problems.) TO THE TEACHER It is assumed by the author that in every class in mechanical drawing there will be marked individual (lilTerences in ability of pupils. This fact, however, does not demand that instruction be entirely individ- ual. On the contrary, it is believed that far better results can be obtained, especially in the early stages of the course, if some class instruction be given. Indeed, class instruction becomes almost a practical necessity under the conditions in most schools where grammar grade boys are taught. In order to provide for class instruction when most needed and to recognize individual capacities, the jirohlems in this book have been arranged in groups according to fundamental stages in the process of learning to draw, and in each group there have been placed a rather wide range of problems; some are very simple, others much more difficult. // is not expected that any pupil will work out all the problems in any one group, but it is intended that each shall work enough to enable him to master the essential processes of the group and be prepared to proceed successfully with the problems of the following group. The notes in each group are not intended to take the ])lace of instruction, either class or individual, which should be given by the teacher, but they are intended to be a valuable supplement to such instruc- tion. From a study of these notes the teacher will readily see what principles and processes should be emphasized in each group. For example, it is easily seen that in the first group the emphasis is placed on the proper use of the tools, (a) in making measure- ments, and (b) ia drawing the several lines constitut- ing the lay-out of the sheet. Time and effort, on the part of both teacher and pupil, will be saved by giving plenty of drill in making lay-outs. The teacher should be sure that every pupil is forming just the right habits in this fundamental process in the first grouj). Teachers Often fail to get satisfactory results in me- chanical drawing chiefly because they are la.x in this first step in the use of rule, tee-square, and triangles. Wrong habits formed here are difficult to eradicate. After insuring the formation of correct habits of pro- cedure in the use of instruments, the next most import- ant concern of the teacher is to lead the pupil to gain power in visualization. The constructive imagination of the pupil must be developed. He must be led to see views of the object not shown on the paper before him, in order that he may represent them. To assist in accomplishing this purpose: (1) some of the problems are given with both the perspective view and the three GRAM>[.\R C.RADE TROBLEMS IX iMECIIAXICAL DRAWIXG views of orthographic projection; (2) some are given with the perspective view only; (3) others present two views to find a third, which is sometimes a sectional view; and (4) still others require the student to w-ork entirely or in part from specifications. No one of these methods of presenting a problem should be employed all the time; in order to get surest results in visuaHza- tion all should be employed during the course. The question of requiring freehand solutions of the problems before making the mechanical drawings of the problems is left entirely open to the teacher. Experi- ence would seem to indicate that such sketching should not be a prominent part of the work of the first six groups, but may well be given emphasis in the seventh. There is a third phase of elementary mechanical drawing which this book emphasizes; namely, lettering and the use of conventions in dimensioning. Ability to do good lettering cannot be learned in a few hours; it comes only with thoughtful and extended practice. Comparatively short exercises at frequent intervals are more interesting and more economical of time and effort than large sheets of lettering. The lettering problems are, therefore, placed between groups of other problems instead of together. But the teacher should feel at liberty to use the lettering sheets out of the order given in the book. The teacher who wishes to be most successful in the use of the problems in this book will consciously and continuously keep in mind the three points of emphasis mentioned above; namely: (1) The correct method of procedure in the use of instruments, especially in making lay-outs. (2) The progressive development of the power to visualize. (3) Frequent, thoughtful work in lettering, and later, in dimensioning. No dimensioning is to be done on finished drawings before Group VII. All the problems in this book are intended to be worked out in pencil only. No inking should be done until the high school is reached, or until a larger portion of time is given to mechanical drawing than is usual in the grammar grades, and not then until good work in pencil has been done. TO THE PUI'IL A working drawing is a i)usiness letter to a niccluuiie. We learn mechanical drawing in order to be aulj to make good working drawings. Mechanical drawing is then a kind of language, a means of transmitting ideas from one person to another. It is a form of expression that is universally understood by workmen of all nationalities. A workman in Russia or Italy or Japan can read your drawing if it is properly made, and \ou can read the drawings made in these foreign coun- tries even tho you do not know a word of their spoken language. At the present time when nearly every man hopes lo build a home or a machine or a boat or a factory or some other structure, and when mechanical ideas are commonly carried from factory lo customer, some- times across the ocean, by means of mechanical draw- ings, it is desirable that every boy study this universal language of industry. He should at least be able to read the simpler forms of it, which he can readily do in the grammar grades, and learn lo use il lo some extent as a means of expressing his ideas. This Ixjok is, there- fore, intended lo help you in learning a new language. TOOLS AND SUPPLIES Each member of the class should be supplied with the following :- Drawing Hoard Tec-Scjuare 45° Triangle 3o''-6o° Triangle It is desirable tliat these be selected with reference to accuracy and durubilit}'. To ^et the best results standard tee-S(|uares and triangles are essential. If, however, a lower-priced tool must be purchased the "Springfield Kit," board 19x13 in., is suggested. This is manufactured by The .Milton Bradley Co., Springfield, Mass. Scale .■\ny flat foot rule accurately graduated to sixteenths of an inch will do, but it is desirable to have one that does not have graduations extending to the end. For an inexpensive rule of this type the " Xala Rule" manufactured by M. B. Bourland, Peoria, lU., is suggested. Compass It is very difJiciUt to find an inexpensive pencil compass with a sufficiently firm and durable joint. In the long run it is best to pay the price of a medium grade instrument of standard design, such as is sold by all drawing instrument dealers. In case this is impossible the course can be carried on, though not with the best of results, by using a very inexpensive compass of the type of Eagle No. 376 made by the Eagle Pencil Co., New York. Thumb-Tacks The inexpensive stamped steel tack is satisfactory. Pencil Eraser Drawing Paper in sheets 9x12 in. Two are needed: a hard pencil, 2H, 3H, or 4H for the lay-outs and an H or F or No. 3 for lining and lettering. To get the best results, leads or pencils of the same grade of hardness should be provided for the compass. I Soft. < This need not be a high-grade paper. Trarinc Paner Cfor I et 1 ^'^'^ '"'^y ^^ '■^" ''°"'' paper used in typewriting or the inexpensive tracing paper used by architects. 1 idc o ipci viui c - .p(^^ ^. disadvantage of the latter is in the fact that it comes in rolls and must, therefore, be cut into tenng) m sheets 6x9 m. smaU sheets. PROBLEMS GROUP I Horizontal and Vertical Lines — Lay-out of Sheet Problem I A. The first problem in this group is to draw three views of a block of wood that is 1 " thick, 4" wide and 7 " long. Fig. 1 is a perspective drawing, or picture of this block. Fig. 2 shows the three views to Fig. 1 be drawn. By looking at Fig. 2 again, and at Fig. 1 , you will see that the top view in Fig. 2 represents what you would see if you were to look down at the block in the direction indicated by the arrow a, Fig. 1 ; you would see a rectangle 4" by 7". In a similar way if you were to look at the front of the block in the direction in- dicated by the arrow b. Fig. 1, you would see the rectangle 1 " by 7", shown in the front view in Fig. 2. You will now see what the end view in Fig. 2 represents. Be sure to notice how these views are arranged: The front view is below the top view, and the end FROHT VIEW view is at the end of the top view representing the end of the block where the view was taken. This is the most natural and convenient way of arranging \dews of blocks and many other simple objects. Now that you understand what you are going to draw, you are ready to take a sheet of drawing paper. This should be 9" by 12". Fasten it to the drawing GRA-M.MAR GRADE PROHLEMS IN ^MECHANICAL DRAWING xjuikI logclhcr with luiard by placing a thumb-tack in each of the four corners. In doing this be sure that the lower edge of your paper is square with the lefl-iiand end of your drawing board accomplish this. t 'Wnir teacher will show vou how to t rig. 3 To have the sheet of drawing look well when it is completed, a border line should be drawn on the sheet. It is customary to draw this border line first, and then arrange the views in the enclosed space. Fig. 3 indi- cates the position of this border line. The wider space at the left end of the sheet is allowed for binding the sheets together in book form at the end of the course. Three holes can be laid out and punched in the wide space on each sheet, and all bound together with a cord or with brass fasteners. In laying out the border line it is important lliat you use the instruments in just the right way. If you are ever going to do accurate and rapid work in mechan- Fig. 4 ical drawing you must form correct habits in the use of the tools, and the first lesson is none too early to begin. Be very particular then to proceed as follows: (1) With the scale placed vertically on your sheet, make a short line or mark (not a round point or dot) Yi" from the bottom of the sheet, and another 8" above this one. (Habits of accurate work can be formed better by measuring from one edge of the sheet GROUP I — HORIZONTAL AND VKRTUAL 1J\ES 13 than from both edges. Discuss this with your teacher. What will you do if your sheet does not measure exactly 9" in width?) (2) With the head of the tee-square held firmly against the left end of your drawing board, draw a light horizontal line thru each of the marks just made. This line should extend almost the entire length of the sheet, Fig. 4. (3) With the scale in a horizontal position on the sheet make a mark 1 " from the left end of the sheet and another 1014" to the right of this one. (4) With the head of the tee-square held firml\- against the left end of your drawing board and one of the triangles held firmly against the upper edge of the tee-square, draw a light vertical line thru each of the marks just made. Draw the lines long enough to cross the two horizontal fines, Fig. 4. Probably your triangle will not be large enough to draw all of the line at once. If this is the case you will have to extend the fine after moving your tee-square and triangle to a new position. Be sure that the second part of the fine joins accurately to the first part. Allow the horizontal and vertical lines to extend past each other at the corners as shown in Fig. 4. Remember thai these lines are all to be very light. To test the accuracy of your work, place the scale on the drawing in a horizontal position and see whether the vertical lines arc just IOI2" apart. Then put the scale in a vertical position and see whether tlic iiori- zontal lines are just 8" apart. \'ou are now ready to draw the three views of the block inside of the border just drawn. But before you can do this j'ou must consider the placing of the views with reference to each other and to the border. Fig. 5 shows a satisfactory arrangement. The following facts may be noticed and may serve as a guide in later problems: — (1) The space between views is less than between a vieia and the border. The space between the top view and the front view, for example, which is 3^", is less than the space between the front view and the lower border which is 1 ". (2 ) The space at the left between the border and a view is the same as that between the border and a view at the right. CRAM MAR (IRADl-: PROBLEMS IX iMECHAXICAL DRAWIXG (3) Space above the mews at the lop of the sheet is greater than the space below the views at the bottom in order to provide a place for the title; otherwise to look well, it would be a little less instead of greater than the space at the bottom. Fig. 6 of the main divisions of the rule, the one-inch mark, for example, on the lower border line. Then measure upward from this border line, first 1 ", then 1 ", then V2". then 4", according to the dimensions in Fig. 5, making a short mark at the end of each distance. Fig. 7 (4) The title is Ys" high, and is nearer to the top virej than to the border. In this case it is Yi" from the top view and 5^" from the border. Fig. 5. With this arrangement of views and these dimen- sions in mind you are now ready to complete the lay-out of the sheet. // is important that you proceed strictly according to the follounng directions: — (1) Place the scale vertically on the sheet, with one (2) Thru these four marks, with tee-square, draw- horizontal lines about as long as those shown in Fig. 6. In drawing these lines make the top one first, and then work downward. (3) Place the scale horizontally on the sheet with one of the main divisions on the left border hne, and measure distances for the four vertical lines as shown in Fig. 5. GROUP I -HORIZONTAL AND VKRTRAL I.IXKS lo (4) Thru the marks thus made, draw vertical lines as shown in Fig. 7. Draw the left line firsl, working toward the right. (5) Add the guide lines lor the title as shown in Fig. 5 and Fig. 8, and the lay-out is complete. the vertical lines, beginning with the left one and working toward the right. In this way you work on the sheet as a whole all the time, and not on one view at a time. Do not erase any of the light lines left at the corners. , 1 ' ' Fig. 8 Fig. 9 The ne.xt step is to go over the border lines and the outlines of the three views with a softer pencil, making a heavier line. The effect will then be as shown in Fig. 9. In order to form habits that will lead to speed and accuracy in this work it is important that you go over all the horizontal lines first, beginning with the top one and working down, and then that you go over These are a sign of good technique. They indicate that you worked to cross lines instead of trying to work to points. It is far better at the beginning of the course to work without using an eraser at all. The last step in the process of making this sheet is putting in the letters of the title as in Fig. 9. These may be put in now, or if your teacher prefers, all titles to sheets in this group may be put in after the practice 16 GRAMMAR GRADE PROBLEIMS IN MECHANICAL DRAWING thai Ihi in lettering at the end of Group III. No dimensions are to be placed on drawings in this book until you come to Group VII. After the drawing is completed, write your name, or letter it on a line yg" below the bottom border line, and at the right-hand corner, Fig. 9. Problem Ib. This problem is just like the iirst one e.xcept that one corner is rabbeted out, Fig. 10. (1 ) You will therefore make the lay-out of the sheet just as The only difference is that there are two rabbets instead of one. Problem Id. This problem is a little more complex than I B and I c because the rabbet runs all the wav Fig, 10 you did for the first problem; see page 12 and Figs. 3 to 8. (2) Then draw the lines to represent the rabbet. If you have made the lay-out as indicated above you will have no serious difficulty in completing the front view to correspond with the other two. (3) The drawing should be finished in the same way as Problem I A, Fig. 9. No dimensions are to be placed on the finished drawing. Problem Ic. If you have worked Problem I b your teacher may not ask you to work this one. In working this one follow the directions given for Problem I b. as Problem I A, Fig. 9. Fig. 11 around the block. In working this problem, (1) Make the lay-out exactly as required for Problem I A, Fig. 8. (2) Then add the lines to represent the rabbet, and you will have the complete lay-out as shown in Fig. 11. (3) The drawing should be finished in the same way GRULl' I — llDRIZOM'AL AND VERTICAL LINES BLOCK rl r- U-[^ RABBETED BLOCK 1- } '' *" 1 DRAW FRONT VltW TONGUED BLOCK 1 ■* f - OKAW FRONT VIEW BLOCK WITH LUG 18 GRAMMAR CIRADK FROBLKMS IN MECHANICAL DRAWING Problem Ie. Draw lop, fmut antl cud views. In working this problem, (1) .Mal