ECHAMCAL DRAWING AND PRACTICAL DRAFTING UC-NRLF C 2 CHARLES H. SAMPSON MECHANICAL DRAWING AND PRACTICAL DRAFTING By Charles H. ampson, B. S. Head of Technical Department, Huntington School, Boston, Mass. In charge of the courses in Shop Drawing, Architectural Drawing, Plan Reading, Shop Sketching, and Machine Design as conducted by the University Extension Department of the Massachusetts Board of Education. Author of "Algebra Review," "Woodturning Exercises," "Assignment Man- ual of Algebra," "Pattern Making," and various courses for the University Extension Department. MILTON BRADLEY COMPANY SPRINGFIELD - MASSACHUSETTS 1920 B/4/a,. Copyright MILTON BRADLEY CO. 1915 PREFACE. Although there are many excellent works on the market covering in a more or less complete way the subject of Mechanical Drawing and Practical Drafting, it has been my experience that most of these are not sufficiently extensive and practical to admit their use in schools where it is necessary to devote a large amount of time to the subject, or in classes composed of men wishing instruction of a practical nature. The course as herein presented has proven its worth, and large numbers graduated from it have experienced no difficulty in securing and retaining drafting positions. Sufficient ground is covered in the elements of Mechanical Drawing to insure a solid foundation for the work of a more practical nature following. I hope that this book will prove to be all that I think it to be. I am exceedingly anxious to make any desirable improvements, and would therefore welcome suggestions from either the teacher or the man in the office. Several important changes have been made in this edition. Material has been added which should improve the course presented, and every effort has been made to make the work as it should be. It is hoped that these changes and additions will prove valuable to both the teacher and student and add greatly to the efficiency of the book as a means of properly imparting a knowledge of the subject which it represents. This text is especially intended for use in the class room. Every effort has been made to produce an ideal text for this purpose. Respectfully, Charles H. Sampson. 4360S8 THINGS A GOOD DRAFTSMAN SHOULD REMEMBER. (READ CAREFULLY.) Be neat and accurate, and keep busy. Study the problem before attempting its solution. Don't be afraid to ask intelligent questions. Keep the pencil sharp and the instruments clean. Always clean a pen before using. Use the T square by placing the head on the left hand side of the board. Use the triangles against the T square. Become familiar with the use of the scale as soon as possible. Practice lettering continually. It is well to learn to make both the slant and vertical types, but it is better to be good at one than just fair at either. The general appear- ance of a drawing depends largely upon the lettering. Always make a pencil drawing complete, even though it is to be inked or traced. When inking or tracing a drawing, draw the lines in the following order: Center lines (very light, dot and dash); all arcs and curves; full straight lines; dotted straight lines; cross section lines (45 degrees when possible); arrowheads; dimensions; lettering; border line and title. Make dotted and center lines lighter than the others. The drawing should always be checked before being inked or traced. The title should include the name of the object drawn, the scale used, by whom drawn, the date finished, and the number of the drawing. Learn to make sketches from actual machine parts, and remember that a sketch isn't worth much unless it is properly dimen- sioned. Before starting to trace a drawing it is well to rub the cloth well with "ponce" or powdered chalk. When erasing use a pencil eraser, especially if the surface is to be inked over again. Erase light'y. Make shade lines by drawing several lighter ones. Dimensions under two feet are usually expressed in inches; those over two feet in feet and inches. Make the sheet balance. Draw to as large a scale as possible. INSTRUCTIONS (REAP CAREFULLY) ALL SHEETS TO BE 14i' * 2O*" OUT3IPE PIME NSIONS UNLESS OTHER- WISE SPECIFIED. ALL MARGINS TO BE J'WIPE. UNLESS CALLED FOR DIFFERENTLY. ALL TITLE5 ARE TO 5E PLACED IN THE LOWER RK3HT HAND CORNE:^ ANP ARRANQEP AS BELOW. Po NOT INK OR TRACE A PRAW1N<5 UNLE55 IN^TRUCT1ON5 CALL TOR SUCH WORK. Do NOT PLACE THE PATE UPON THE PRAWINS UNTIL IT 15 FINISHED. Do NOT INK INSTRUCTIONS ON ANY SHEETS. FOLLOW DIMENSIONS . NEVER 5CAL.E A PRAWIN<5 WHEN IMKIN^ LETTERS HAKE ALL STROKES POWN (O) OR TO THE reHTg. MAKE ARROW HEAPS LIKE THIS^- NOT LIKE THIS). foRM.ALL LETTERS ANP FIGURES 50 TWAT EACH WOULD FILL A PARALLELOGRAM IF Pi?OPE(?IY CONSTROCTEP 6S B 33 . HAKE FRACTION TH05 | x/ ; MiXEP NUMBER'S Ss" fe ^REPRESENTED BY CINCHES BY ''. %'-&. JITLC Of PRAWINQ .XALE ' /,///>, Fig. 3 Fig. 4 Erasing is more or less of an art. When it becomes necessary to erase, use a pencil eraser. The resulting surface will then be smooth. Cultivate a light touch. That is, do not "bear on" too heavily when erasing. Every student should have a cleaning eraser for use in cleaning dirt and surplus lines from the drawing. "Art Gum" is recommended. Great care should be observed in the matter of keeping the pencil sharp. If a fine round point is always kept on the lead it maybe used for both lines and lettering. Some prefer a chisel point for use when lines are to be drawn. It is suggested that the pencil be sharpened at both ends. A point is then available for all purposes because one may be made a chisel point. Q! s 8* ADC D E rGHUKLMNQPQF^TUVWXYZ' I 2 3 4 5 6 7 8 9 OZZ^ZZZZZZZ3 ABCPFFGHl JKI MNOPO^^TUVWXVZ -] a be defqhij x4 8 C&FF G/-//JKL MMOPQK5TUVWX YZ~ r offor/m &// //her of /efrerj my/- > <&rfnr/fy /oca fed. LETTERING SCALE. FULL. . BY PATC. T'LATE No } tt 1 u o CD 1U Q L or * 1 / \ \ / S \ / \ i fe D / ^ V / A \ / ^ / / \ \ V / \ \ / \ t_ s ) ^/ l_ 1 \ / \ / / \ / \ / 7 2 \ / N / S S / S V / \ \ / \ s * ' ' / \ \f / S \ / ^ N^_ / \ \ \ / \ \ / < s \. \ \ \S S \ ' \ \ \ f \ x / _^ \ \ \ S / \ / s / ; \*" K I cr i r ~\r ] 7 ^ <** "r? 1 -^ r ty N D }} in Z JgAt/C^Htf Off '*&" >, sAotVff M /0/ff?, /* w/ft ## >/ The jmall leHe / \ / / s / S f -v / / / j *? / / P c ^ 4 ""1 _H / / < e^ / / /- 7 \- S / \ / ?/-/mfcf ///>& at LETTERING '/y /Ae ftr& . Tfc wafff yxrtej a/v fo tefl/fa/ SCALE fuuu ^IZE vy atrs*?f>ofee/. /VmsA #r/s p&fe as 9 sfiodvy mfajv/vd e x 3. GEOMETRICAL PROBLEMS All geometrical problem plates are of the standard size (141" x 201"). The space inside of the f" margin on plates 3, 4, 5, 6, 7, 8, and 9 is to be divided into six equal parts. Five of these parts are to be used for problems. The sixth space, in the lower right hand corner, is reserved for the title, name, date, etc. Great care should be observed in the solution of these construction problems. Fine lines are necessary for clean, accurate work. The instructor may well add to those given, especially if the students are taking a course in Plane Geometry. These problems are to be done in pencil. GEOMETRICAL DEFINITIONS. A straight line is a line such that if any part be placed upon any other part the parts will exactly coincide. A perpendicular bisector of a line is a line perpendicular to it and dividing it into two equal parts. A curve is a line no portion of which is straight. An angle of ninety degrees is formed by one line perpendicular to another. An angle is the amount of opening between two lines intersecting in a common point. Angles are measured in degrees. A protractor is used for this purpose. A circle is a plane bounded by a line, called a circumference, all points of which are equally distant from the center of the circle. Two lines are said to be parallel to each other when they will not meet, no matter how far they may be produced. The mean proportional between two quantities is equal to the square root of their product. A square is a plane surface bounded by four equal, straight lines, all the angles being right angles. A triangle is a plane surface bounded by three straight lines. A hexagon is a plane surface bounded by six straight lines. In a regular hexagon all of these lines are equal. A regular hexagon can be divided into six equilateral (all sides equal) triangles. A pentagon is a plane surface bounded by five straight lines. An octagon is a plane surface bounded by eight straight lines. A circle is inscribed in a triangle when the sides of the triangle are tangent to the circle. A circle is circumscribed about a triangle when the sides of the triangle are chords of the circle. A line is tangent to a circle when it has only one point in common with the circumference. A right triangle is a triangle containing a right angle. The two perpendicular sides are called legs; the other side, the hypotenuse. A rectangle is a four-sided, plane figure, all of whose angles are right angles. The adjacent sides are of unequal lengths except in the square. The diagonal of a square, or other four-sided figure, is a line joining two opposite corners. A rhombus is a four-sided, plane figure, all of whose sides are equal and whose angles are not right angles. A trapezoid is a four-sided, plane figure, two of whose sides are parallel. The other two sides are not parallel. (The above constitute a very small part of the total number of geometrical definitions. They are given because of their relation to the following geometrical problems.) 10 F..a F'1-1- There are many other drawing instruments to be used by the student after the completion of Plate 2. These are described below. Fig. 1 is a representation of a pair of bow dividers. It is used for spacing off equal divisions on a line. It can be set to a certain dimension and as many multiples of that dimension, as desired, taken. Fig. 2, called the bow ink compass, is used for the purpose of drawing small circles in ink. Fig. 3 shows the bow pencil compass. This is used for drawing small circles in pencil. When a straight line or a curve, not a circle, is to be drawn in ink, the instrument illustrated by Fig. 4 is used. This is called a drawing or ruling pen. Ink is dropped between the nibs from the quill which comes in the drawing ink bottle. To use it, set the thumb screw in such a position as will give the desired width of line and draw to the right for horizontal lines; upward for vertical lines, if line is at left, and down if at right side of paper. (See illustration on page 6.) Always keep the thumb screw outward and slope the pen toward the body. When it is necessary to draw large circles in either ink or pencil, the instruments shown by Fig. 5, Fig. 6, Fig. 7, and Fig. 8 are used. The section (Fig. 6) is inserted at A when pencil arcs are to be drawn; the section (Fig. 7) when ink arcs are desired. The extension bar (Fig. 5) is inserted between either of the sections (Fig. 6 and Fig. 7) and the main part of the instrument if one wishes to draw unusually large arcs or circles. The legs of the compass should always be bent so that the axis of the lead or pen is perpendicular to the paper. Fig. 9 shows a longer pair of dividers than illustrated by Fig. 1. This instrument is used for the same purpose as the bow divider and also for transferring dimensions from one drawing to another. It is quite necessary, if good work is to be accomplished, that the pencil point be always sharp. The sandpaper pad (Fig. 10) is used for this purpose. The irregular or French curve is used for drawing a continuous curve, not the arc of a circle. There are many different types of these. A common one is illustrated by Fig. 11. The important thing to remember in the use of this article is that no attempt should be made to draw too much of the curve at one time. Set the curve to correspond with as many points as possible and then draw only a short distance. Shift the curve ahead and draw another short distance. Fig. 12 shows one form of erasing shield. This is used to protect nearby lines when a place is to be erased upon. Just a word regarding paper, ink, and thumb tacks. Use no cheap paper or ink. "Strathmore" detail paper is excellent for pencil work; "Whatman's" hot- pressed for ink work. No ink is better than "Higgins." Thumb tacks are of many sizes and shapes. The ones with a beveled edge are preferable because the T square will slide over them easily. r,,s 11 INSTRUCTIONS. Problem 1 Draw any line A B. Using A and B as centers and taking a radius greater than one half of A B, swing arcs intersecting at 1 and 2. Draw the bisector through 1 and 2. Problem 2 Draw any arc A B. Connect ends of the arc by the chord A B. Bisect the chord, using method of Problem 1. The bisector of the chord bisects the arc. Problem 3 Draw any angle ABC. Taking B as a center, draw any arc 1-2. Taking 1 and 2 as centers and a radius greater than one half of the distance 1-2, swing arcs intersecting at 3. Draw the bisector through B and 3. Problem 4 Construct a right angle by drawing AB and BC perpendicular to each other. Using B as a center, swing any arc 1-2, Using the same radius and taking 1 and 2 as centers, describe arcs B-3 and B-4 respec- tively. Draw the trisectors B-4 and B-3. Problem 5 Draw any line AB and another line AC, making any angle with it. Assume that AB is to be divided into six equal parts, and lay off on AC six equal divisions of any convenient size. Draw 6-B and through the points 5, 4, 3, 2, and 1 on A C draw lines parallel to 6-B. These lines will divide A B into six equal parts. (Draw the lines parallel to each other by using the triangles one against the other.) 12 ' t t "2 PROBLEM < To BISECT A STRAIGHT LINE PROBLEM 2. Tb BI5EX1T AN ARC OF A CIRCLE PROBLEM 3 Tb BISECT AN ANGLE. x x \ v x \ \ V Tb TRI5ECT A RIGHT AN<5LE ABC Sr % \ \ \ % S\ \ \ \ v s \ \ \ \ \ \ A 3 b c d e & PROBLEM 5 TO DIVIPE A LINE INTO ANY NUMBER OF GEOMETRICAL PROBLEM 5 PRAWN 3Y DATE PLATE NO. 3 INSTRUCTIONS. Problem 6 Draw any line C D and divide it into any number of unequal parts. Draw any other line, as A B, of a different length than C D. Draw A-4, making any angle with A B, and on it lay off the same distances as given on C D. Connect 4 with B, and through points 3, 2, and 1 draw lines parallel to B-4. These lines will divide A B into the same proportional parts as C D. Problem 7 Draw any circle. Draw any diameter, as 1-5. Using 1 and 5 as centers, describe arcs passing through the center of the circle. The distances 1-3, 3-6, 6-5, 5-7, 7-4, and 4-1 are equal. Problem 8 Draw any line B C, and take any point A above it. Using A as a center, describe an arc cutting BC in two points, as 1 and 2. Taking 1 and 2 as centers and using a radius greater than half of 1-2, swing arcs inter- secting at 3 and 4. Draw the perpendicular through 3 and 4. Problem 9 Draw any line A B. Using A as a center, swing any arc. With same radius swing arcs from 1 and 2 as centers. Using 2 and 3 as centers, swing arcs intersecting at 4. Draw the perpendicular A-4. Problem 10 Draw A B, and at any points 1 and 2 erect perpendiculars, using the method of Problem 9. Set the compasses to a radius E F and swing arcs cutting the perpendiculars at 3 and 4, using 1 and 2 respectively as centers. Draw C D through 3 and 4. 14 4- A A \\ / s \\ / \ \ \ \ / ^ \ , - ^ p AT-, / \ B J \ ^ 2 V- ^ PROBLEM 7 To PIVIPE A CIRCLE INTO six EQUAL PARTS X --...--' / X^ PROBLEM 8 TROM A POINT A ABOVE THE LINE PC TO DRAW A PERPENDICULAR. TO BC. * <* i i i n C I i 3 p PROBLEM 6 To WIPE A LINE AD INTO W1E PROPORTIONAL FfcRTS AS CC>. x- /\ 4' "~"^ N \ ' ! r GEOMETRICAL P!?OeLEM5 PRAWN BY PATTE PLATE NO ^ T T >|C ^ ^-!-x. x ,x-TH ! \ n \ ,' 12 e A < PROBLEM 9 ON A GIVEN LINE AB TO ERECT A. PTRPENPICULAR AT A A PROBLEM lo To PRAW CP P/\RAU(_eU TO AB AT Av PI5TANCE EF ABOVE IT. INSTRUCTIONS. Problem 11 --Draw any line AB and take any point C above it. From any point 1 on A B swing an arc through C. Using C as a center, and the same radius, describe arc 1-3. On 1-3 take a distance equal to 2-C. Draw D E through C and 3. Problem 12 Draw any angle BAG. Using A as a center, describe an arc as 1-2. Draw a line D F, and taking D as a center draw an arc having same radius as 1-2. On arc 3-4 take a distance equal to 1-2. Draw D E. Problem 13 Draw any two lines AB and CD, and take any point F between them. Using F as a vertex draw any triangle F-2-1. Take point 4 anywhere on CD, and draw 4-E and 4-3 parallel to 2-F and 2-1 respective!,. Draw 3-E parallel to 1-F. Draw the line through E and F. Problem 14 Draw any two lines AB and CD. Draw another line EF whose length is greater than AB plus C D, and on it take 1-2 equal to A B and 2-3 equal to C D. Bisect 1-3, using the method of Problem 1. Taking 4 as a center, describe the semi-circumference. At 2 erect a perpendicular to E F. 2-5 will be the mean proportional between 1-2 and 2-3. (The mean proportional between two quantities is equal to the square root of their product.) Problem 15 Take any line A B. At B erect a perpendicular, using method of Problem 9. Using B as a center, draw arc A-1. Using A and 1 as centers, draw arcs B-2 and B-3-2 respectively, thus determining the remain- ing corner of the square. 16 c^ ^^\ *^C \ I N \ / \ r?^^ " \ p ^--^^^N \ N \ 3 ^, \ 3*^ C'^**' I V \E__ - f""""" \ / \ ^^\ \/ '''' A ' <"- 2 & A 1' C A f PROBLEM H PROBLEM 12 PfJOBLEM )"5 THROUGH A POINT C TO PRAW A LINE 16 CONSTRUCT AN ANGLE EQ.UAL TO A THROUGH A GIVEN POINT F"TO PRAWAUNE PARALLEL. TO AD. GIVEN ANOL.E ABC VHICH WOUL.P MEET INTERSECTION OF AP AMP CD. PROPOCEP. / X * 1 c \/ \ > A n \ M * a U / ^ S\ "-i N <5EOMtrTI?lCAL PROBLEMS A C 17 ^^ / PRAWN BY \' J PROBLEM 15 ON A GIVEN LINE AS TO CONSTRUCT A SQUARE PATE PLATE NO. 5 PROBLEM 14-. Tb FINP THE MEAN PROPORTIONAL. BETWEEN AB ANP CP. 17 INSTRUCTIONS. Problem 16 Take any line A B. With A and B as centers, and a radius equal to A B, swing arcs intersecting at 1. Draw A-1 and B-1. Problem 17 Draw any three lines A B, CD, and E F. Taking A as a center, and a radius equal to E F, swing arc G H. Taking B as a center, and a radius equal to C D, describe arc L M. Complete the triangle. Problem 18 Draw any line A B. Using A and B as centers, and a radius equal to A B, swing arcs intersecting at O. Using O as a center, and the same radius, draw the circle. A-5, 5-4, 4-3, 3-2, and 2-B are each equal to the radius of the circle. Problem 19 Draw a square, as A B C D, and draw the diagonals AC and B D. Using A, B, C, and Das centers, describe arcs passing through 1. Connect points where the arcs cut the sides of the square to obtain the octagon. Problem 20 Draw a line A B. Using A and B as centers, and A B as a radius, swing arcs intersecting at 2 and 9. Draw M N. Using 9 as a center, describe an arc through A and B, cutting the first arcs drawn at 3 and 5. Draw 3-4-6 and 5-4-7. Draw A-7 and B-6. Taking 7 and 6 as centers, and a radius equal to A B, swing arcs inter- secting at 8. Complete the pentagon. 18 PROBLEM 16 ON A GIVEN LINE TO CONSTRUCT AN EQUILATERAL. TRIANGLE. A C- PROBLEM 17 THREE SIPR OF A TRIANGLE. TO CONSTRUCT THE FIGURE.. PROBLEM 18 ON A LINE A& TO CONSTRUCT A REGULAR 5^-Ov\ I''',-'- x ^-?! ^:~~- B PROBLEM 19 WITHIN A SQUARE. TO CONSTRUCT AN OCTAGON PROBLEM 2O ON A GIVEN LINE A& TO CONSTRUCT A PENTAGON PROBLEM? PRAWN PY PLATE NO 19 INSTRUCTIONS. Problem 21 --Draw any line A B, and at A and B erect perpendiculars, using method of Problem 9. Bisect the right angles formed by the perpendiculars and A B produced. A-1 and B-2 will be sides of the octagon. Draw 1-2 and take 3-5 and 4-6 equal to A B. Take 5-9 and 6-10 equal to A-3 or B-4. Draw a line through 5 and 6 and take 5-7 and 6-8 equal to 1-3 or 2-4. Problem 22 Draw any triangle. Bisect any two angles, using method of Problem 3. The intersection of the bisectors is the center of the inscribed circle. Problem 23 Draw any triangle, and bisect any two sides, using method of Problem 1. The intersection of the bisectors is the center of the circumscribed circle. Problem 24 Draw a circle, and take any point A on the circumference. Draw a radius produced through A, as O P, and on it from A lay off equal distances A-2 and A-3. Using 2 and 3 as centers, erect a perpendicular at A. This will be the required tangent. Problem 25 Draw any arc of a circle. Take any point A on the arc and draw any chord A-1. Bisect A-1 and draw the bisector. Taking A as a center, swing an arc through 3 and lay off 3-4 equal to 3-5. Draw the tan- gent through 4 from A. 10 .. _ T 5 6 SI;- '""^' I ^JX ,*r-37 -\-pr-A, PROBLEM 21 ON A GIVEN LINE AB TO CONSTRUCT AN OCTA 7'fay. Tfte e////>se of r/y. f u draw) >y of ffa/77/fl&!}. ~%?te a strip of popfr and ' an/ts fdye /ay o/f ff=* nwor aw or 5" and A/- snmor ax/i or 3~ A&ep Are fv/af off #?e m//?or ax/s 0/?a f #K /w/7/ Z? a/ways os? f he major. S/x>f'ft?ffo//7fc3 ofr/n/netf y fFvo/v/ha tfie Sre. the fnn??/0? e .f^e asid '// at centers afraw ." TA Place no dimensions on finished sheet Difference major and minor U ELLIPSES 5CALC FULL SIZE BY RLATE NO fO 25 recfang/es of d/mffns/bns as q/ven f/s/na fbe . af o/ Me second -/-haf a/ #x? 6y per tote , /I 5 /f caffed Me afocitJa or>J PE foe doub/e a ca//eAf orcft'/taff. Place no dimensions on the finished Sheet PARABOLA ANP HYPERBOLA SIZE. ^"^ N0 H 26 DIMENSION UNE.- ARROW HEAP FVLU LIN( 5HAC7E UNE. POTTEC? LlNE. CENTER LINE o czv7Wf/7Ar//~ sco/f 7* f&f *****#. cro,s-f*ct, on //nes ore dro^n MALI. IRON WR006HT STEEL- LEATHER. WROUGHT IROM OL-ASS WOOC> 5TANI7ARI7 LINES ANP CR05S SECTIONS PRAWN Bf PATE. PLATE NO 12. 27 \ toy ay/ fyvongskt so ftaf genera/ of jfntJhed jfieef M'// &$ Me /rtv sheet: USE OF TRIANGLES BY PATE NO. !>- 28 or? very ///XT /itfes . /2tPSr. roef/us antf a/>riv center fcj on S* />'/7f. SHADING SCALE FULL SIZE PRAWN BY PATE. PLATE NO 29 ORTHOGRAPHIC PROJECTION. Orthographic projection is a process in drawing by the use of which we find the projection of lines, surfaces, or solids upon three planes, namely, the horizontal, the vertical, and the profile. To illustrate how these planes are related to one another, may we suppose that an object such as a rectangular pyramid has been placed upon the bottom of a rectangular box. The top of the box represents the horizontal plane, the rear or front face the vertical plane, and the right hand face the profile plane. Projections of the object may be obtained upon all of these planes by drawing HORIZONTAL PLANE HANE. A perpendiculars from the several points of the object to the different planes. The points at which the perpendiculars pierce the planes are the projections of the points of the object upon the planes. If the points are connected, the projection of the faces will be obtained. If the three planes of projection are made into one, the three views of the object will appear as we must represent them. Take particular notice of the fact that lines not parallel to the planes appear shorter in the projection. In orthographic drawing objects appear as they are projected, not necessarily as they actually are. Dimension all plates from now on unless otherwise specified. 30 START WITH THIS Y1CW IN CENTER. OF 5HEET. I -tt 77i/j ihtrr ftpftttms tfie ft/a and Snypf of a cub? sAo^ft in var/ous posrf-ions. TT>e f/noi afipeor&n(f of //* f/wbecf sherf sfiou/a be Mf above CUBE FULL SIZ N BV PATE. PLATE NO 15 31 7fe> fop, f/z>/?f am/jje/e v/ewj of a pns/r? arp j frown aAavf. /IB and CPare draws? //? crvy canve/?/e/?f- p/ace. O / used ' o//?fc obfowea ttx? front and j/cte v/ews. Make the " EECTANQULAR PYRAMIP/ PENTAGONAL PRI5M 5CALE FOUU SIZE. BY CVKTE. P4-ATE NO . ID 34 f s [ Tf i i J ,* i -IN 1 V > 1 i i i INSTRUCTIONS PRAW ON WHITE. PWER W1P INK . T(?Y TO GET A NOTICEABLE DISTINCTION BCTWECN THE pirrecENT KINPS OF UNts FOLU LINES ABC TO BE. Hf/NyiER THAN OOTTFD AW p(MEN5lON LiNfS MACHINE DETAIL 5CA.LC FULL- SIZE PRAWN BY PATE NO. 35 MAKE A PRAWINC IN ORTHOGRAPHIC PROJECTION OF A HEKA<5ONAL PRISM HAVING AN ALTITVPE OF 3", THE DIAMETER OF THE INSCRIBED CIRCLE OF THE BASE BEIN<3 }|". ONE OF THE NARROW FACES IS TO REST ON THE HORIZONTAL PLANE , THE HEXAGONAL. BASES SEIN-.- tX G/rm*7/?p shows /fie ftp ffnyram/aas s/iawn . fenfth of edge sir/fta one Cfftitif O'as a cf/ffer and 'O'C. ff a raJ/f/s. P/viecr //urn C> fi> /I. Od vf/7/ A /A? focf/us ib me otrfa/'n/ng fCVf LOPMENT Or A PYRAMU7 o PRAWN BY PATE PLATE NO. 42 BI5CCT THC ANGLES TO OBTAIN THf VTRTCX Jff}/rucr/am p^ ^ fa^ jyf ajfa.frxffyy fo a/ yfo attain ft* font v of fne pyramid ' /a /he uwa/ manner 6/s/fy O'a) a cm/er d?sc/rh?orcs cuff//y / of xy.ond z Prq/ect abw fo get d. Band C P/zrv QA.OB and OC /Jake attain ft* font vw /IN . . . ffv fr/ony/e Q eyao/ /c /6e a;e of ftf py&m/c/ Tfc /a/era/ faces cansfntcted //? fne/r frue size ufvn Me edges a/ Q Thu // fc/fas an eterase /or /fie sfadenf DELVCLORTACNT Or-TRlAN of the cyAMftr. '"" ' "- "' ' *"" ffte c/rcu/ar Pases. r^ i R PKAWN BY 44 f ?/*? frzwf /j on. /oy o/S Z?-f- (//v/iw/75 foe/? eq.ua/-fo one of /A? 2-^ aivh/ons of- the c/rctffr?fereace of //w base. Pra\*/ -ftx? c/rcufar base fanaent -to the an or any &aHMt*r pofah DEVELOPMENT OF A CONE. SCALE rOLI Pf^AWN BY PIA7E NO. 45 II IN. I 234- I I I I ! I | I I i | I I | I i I ' I I i I M i ! i i | i I t I ' i la I I LJ ^ Tfif space 6-8 ffioy 6f erf 8 any convenient- ' t -.. .-vA^ j*. DEVELOPMENT OF AN E1DOW run. SIZE. BY PATE 0/2 PLATE No. AD 46 I F71? DC YELOPMENT Or & RCCIWWUUK PRI5M CUT BY A PLANE. SCALE FULL 5RE- BY NO. 47 r PfVELOmENT CF RECT. PYKAMIP CUT BY PLANE, -ei roui- srzE- PK.A.Vv'M BV TE: MO. 48 PEYELOPMPNT OF HEXA50NM. PYRAMIP CUT BY PLANE. PLATE NO 14- 3 4- sr V* 7 cy//nder as c/ ne . of /A" /afera/ surface as of //?e /cw thf top view equals twice the distance Mttin the front view. He should a/so remember Hiat a/lofthf distances in the development from O to the curve I9-I3-/9 ore obtained from rhe line O-20 in the front vie* and should not be measured on any other e/empnt. Plate 35 -drawn on an entirely separate sheet- tal/s fora development of the object /eft af/er the cone has been cut by the fl/anp A \-8. Thf dratviny of this exercise shout-rE NO. 55 INSTRUCTIONS TRANSFER THIS DRAWING TO THE REGULAR SIZE SMBET UMNG THE PIVIDEEJ ANP MAKING THE DRAWING ON THE OTHER. SHEET TWICE. TME, SIZE SHOWN HERE.- DEVELOP THE OBJECT, COT OUT THE. PEVELOPMBNTi AND PASTE. THEM TOGETHER TO FOR.M THE OBJECT ILLUSTRATED IN THE VPPER, RiCHT HAND COK.NER.. W>E. THIN PA.PE.R. ALLOV- I_AP TOR. PEVCLOPMENT PROBLEM BV PATE- NO 56 PLATE 40. Select any one of the objects sketched on the following page, draw its development full size, cut it out, and paste it together. Do not forget to allow for the lap. 57 PEVELOPMENT SCALE njL-U. SIZE. PRAWN BY PATE. PLATE NO . 40 58 DETAIL AND ASSEMBLY DRAWING. The more practical work of the course begins with Plate 41. All work must be laid out in pencil first, and the pencil drawing must be just as complete as the finished drawing is to be. Neat work is exceedingly important. The appearance of the plate will depend much upon the way the lettering is done. Many sketches are given, but this does not imply that students are to make a sketch. Follow dimensions and make a finished drawing. Ink or trace accord- ing to directions. Students should study the several plates very carefully before proceeding with the work. Pages 60 and 61 contain sketches of the objects drawn on the plates designated. These sketches should be carefully studied before and while drawing the object in orthographic projection. Several plates require that a sketch be made of an object, the object measured, and the dimensions obtained to be put upon the sketch. This should be very carefully done, a particular effort being made to get all of the neces- sary dimensions on the sketch. All assembly drawings must represent the very best skill of the student; Great care should be taken with the drawing of the different kinds of lines. No assembly drawing is to contain free-hand lettering. All letters must be drawn with the instruments. When a drawing is to be traced stretch the tracing cloth over the drawing and ink in the same way as when a pencil drawing is inked. The dull side of the cloth is generally used. 61 /fate apenc// drowny and ink // SECTION ON A B-C CRANK PIN WASHER 5CAUE ITJL1- SIZE DRAWN BY PATE PLATE NO. ^ 62 /fade a penal 'drawing and ink it BOLSTER CHAFING PLATE 40 PLATE N042 63 /m/ntef/ons . a fxnc// o/nzw/np anS-rd: fr CENTER 5CALC1 6'- 1 FOOT PRAWN BY PATE PLATE: NO. 64 opend/dmwf/y skefcf) and ink if-. 3PRINS LINK 5EAT y o/Sfo i'K 4 > * COOMTCR.SONV ( i" 4-4 i y M ^rfe TLL C^^ 1 X Htfi "-A.". 7'-4- 17ETML Or CYLINDER EQUALIZER" ^" -I FOOT PRAV/N BY NO. 66 //: c// e/nwuy of M,s 5fo/f? art /'c/?a of a/- We soix? ///?? penc// ontf / HOOK.. FULL. SI'Z BT 86 PLATE 60. THE CYCLOID. If a mark was made upon the circumference of a circle at the exact point of contact with a plane, the mark, as the circle revolved along the plane, would follow a curve called the cycloid. To generate this curve, draw any circle, as D E F, and divide its circumference into any number of equal parts (in this case use twelve). Draw a straight line tangent to the circle at F, and on it lay off six divisions, each equal to a division of the circle. From a, b, c, d, e, and f draw perpendiculars cutting the center line of the circle. Taking these points as centers, swing arcs. On these arcs lay a-6 equals one division of the circle; b-7 equals two divisions; and so on until point 11 is obtained. Connect the points to obtain the curve. Draw the circle DEF two inches in diameter. THE ARCHIMEDEAN SPIRAL The spiral is a curve which makes one or more revolutions round a fixed point, but does not return to itself. To construct the Archimedean Spiral, draw any circle and divide it into any number of equal parts. Divide the radius into the same number of equal parts, and draw concentric circles through these points of division. The intersections of these circles with the diameters will give the points of the spiral. Connect 1, a, b, c, d, e, f, g, h, k, m, and n to obtain the curve. Take 1-7 in this case as five inches. THE INVOLUTE. If a perfectly flexible line was wound round any curve and kept stretched as it was gradually unwound, any point in the line would trace another curve called the involute of the curve. Draw any circle (in this instance two inches in diameter) and divide it into any number of equal parts. Draw tangents to the circle at each point of division, a-2 equals one division of the circle; b-3 equals two divisions, and so on. Connect the points obtained for the desired curve. 87 THE ARCHlplEPEAN SPIRAL THE cvcLotc? THE. INVOLUTE.. 5CALE PULL. CONSTRUCTION /^ r^ . 6O PLATE 61. THE EPICYCLOID. When a circle rolls round the edge of another circle instead of along a straight line the curve called the epicy- cloid is generated. Draw the pitch circle, taking any convenient radius. (Take 4?" here.) Draw the generating circles of any diameter less than the radius of the pitch circle. Divide one of the generating circles into any number of equal parts, and starting at A lay off these divisions on the pitch circle. In this case take six on each side of A. Draw radial lines through these points of division and obtain a, b, c, d, e, and f. Taking a, b, c, d, e, and f, and also g, h, i, j, k, and I as centers, swing arcs using the radius of the generating circle. Take 6-n and 6-t equal to one division of the generating circle; 7-u and 7-o equal two divisions; and so on until the curve is complete. At the left construct another curve similar to the one given. If the generating circle rolls inside of instead of outside of the pitch circle, the curve obtained is called the Hypocycloid. 89 GENERATING CIRCLET- THE EPICYCLOIP GEOMETRICAL CONSTRUCTION SCALE. FVL.U SJ-Z PRAWN BY TMO. . Ol 90 PLATE 62. Figure 1 is a representation of a "heart" cam. This type of cam is used when a movement both up and down is desired gradual and constant. Draw the friction roller C in any convenient position. Draw the 5h" circle and assume that B is the maximum position of the center of the roller. Divide the distance from B to C into eight equal parts, and divide the 5\" circle into twice this number. Draw the radial lines through the points of division on the circumference. Set the com- passes to the radius of the roller, and taking the intersections of the radial lines and the circles as centers, draw the dotted circles. Starting at A, draw the outline of the cam tangent to the circles. The right half of the cam is here drawn. The student is expected to complete the whole cam. This is to be inked. Figure 2 shows a cam designed to produce a compound motion. Draw a circle of 5i" diameter, assume the lower position of the center of the roller to be at A, and divide the distance from A to B into six equal parts. The entire circumference is to be divided into twelve equal parts. Set the compasses to the radius of the roller, and draw the dotted circles as shown. Starting at C, draw the outline of the cam tangent to the dotted circles until the 270 line is reached. Divide the circumference from 270 to 330 into twelve equal parts, and draw radial lines through these points of division. Also divide EF into 12 equal parts and draw arcs through the points. The intersections of the arcs and the radial lines will give the points necessary for a gradual return from G to the starting point. In this particular cam the motion rises two spaces in 60, rests for 30, rises two more spaces in 60, rests for 30, rises two more spaces in 60, rests for 30, gradually returns towards original position in 60, and rests for 30 before actually reaching there. This drawing is to be inked. 91 io CAM PE5KSM FVL.U SI/TE. BY PATE. PL-ATI NO 62. 92 SYMBOLS GEARING FORMULXE. TO FIND FORMUUE Diametral Pitch . . . . - P Diametral Pitch .... p 3.1416 P' Circular Pitch .... . - P' Circular Pitch P' 3.1416 P Pitch Diameter . . . . - D Pitch Diameter D N P Center Distance . . . . - C Center Distance c N+N, 2P Addendum . . . . ; . - S Addendum Q P' 3.1416 Dedendum . - d Dedendum d Clearance . - F Clearance F 0.157 P Thickness of Tooth . . . - T Thickness of Tooth . . . . . . . T .48P' Space between Teeth . - W Space between Teeth . . . . . W = .52P' Outside Diameter . . . . - O Outside Diameter o N+2 P Number of Teeth . . . . - N Number of Teeth .... . . . . N = PxD Length of Rack . . . - L Lenath of Rack L NP' 93 TEMPLET FOR GEAR TEETH. When it is necessary to show the teeth in a complete gear wheel, it would require much time and labor to draw each tooth separately. This labor is saved by constructing an accurate pattern or templet of the proper tooth outline and tracing the outlines of the whole number of teeth in the gear from the pattern. In constructing the templet, proceed as though drawing one tooth of the gear. The pitch, addendum, deden- dum, and clearance circles are drawn, and the complete curve of one half the tooth laid out. Only one side of the tooth outline need be drawn, as in tracing around the templet in the finished drawing half the teeth are drawn first and the other half formed by turning the templet over with the reverse side uppermost. This makes the two sides of the teeth similar. The templet is cut out in the form shown in the cuts illustrating the involute and cycloidal templets on the following pages. The divisions marking the tooth widths and spaces are laid off on the pitch circle of the finished drawing, and the templet pinned on with the center point at its lower end directly over the center of the pitch circle of the drawing. Then by revolving the templet the right sides of all the teeth are traced at the points already deter- mined on the pitch circle. By reversing the templet the teeth are completed as described above. The templet should, if possible, be cut from medium weight cardboard, as the clean-cut edge of the tooth outline will retain its proper shape longer when a large number of teeth are to be drawn. Sometimes the draftsman is called upon to draw gears of a certain definite size which have become standard in certain lines of work. The temp- lets may then be constructed of some durable substance, such as hard rubber or celluloid, and filed away for future use. 94 TEMPLET FOR INVOLUTE TEETH. FIGURE 1. (1) Draw the pitch, addendum, dedendum, and clearance circles. (2) Draw the perpendicular radius oa prolonged, intersecting the pitch circle at b. (3) Draw the line of obliquity x y through point b at an angle of 15 with the horizontal line b z. (4) With o as a center draw the base circle tangent to the line x y at the point c. ' (5) From c lay off to the left on the base circle the divisions c-1, c-2, c-3, etc., and to the right the divisions c-6, c-7, etc. These divisions should each be less than one tenth the diameter of the base circle. (6) At the points 1, 2, 3, 4, etc., draw the tangents to the base circle T,-1, T 2 -2, T 3 -3, etc. (7) Using the radius c b with point c as cen- ter, draw the tooth curve as far as the first tangent T, from b, thus giving point d on tangent Ti. (8) Taking the next radius cd, the curve is continued to the next tangent T 2 , giving point e. (9) By successively using the remain- ing radii, ce, cf, etc., the curve is carried a little beyond the outside or addendum circle. (10) The lower part of the tooth curve between the pitch and base circles is obtained by using the radii c b, c k, and en. (11) The tooth edge below the base circle is radial to center o, and the fillet joining the side of the tooth to the whole depth or clear- ance circle is drawn with a radius equal to one seventh the distance between two adjacent teeth taken on the adden- dum circle. INVOLUTE RACK WITH STRAIGHT FLANKED TEETH. FIGURE 2. (1) Draw the addendum, pitch, dedendum, and clearance lines. (2) From a lay off the linear pitch a b which corresponds to the circular pitch in circular gears. (3) Then after locating point c, which gives the tooth width, draw all left-hand sides of the teeth, such as d e, through the pitch points at an angle of 75 with the pitch line. (4) The right-hand edges of the teeth are also drawn at 75 from the pitch line, but in the opposite direction of obliquity. (5) The fillets at the bottom of the space are drawn with a radius equal to one seventh of the distance between two adja- cent teeth measured on the addendum line. TEMPLET FOR CYCLOIDAL TEETH. FIGURE 3. (1) Draw all gear circles as in the drawing of the involute templet. (2) Draw radius o a intersecting pitch circle at point b. (3) From b lay off on the pitch circle the divisions b-1, b-2, b-3, etc., to the right, and b-7, b-8, b-9, etc., to the left. (4) From points 1, 2, 3, 4, etc., draw the internally radial lines to the pitch circle, and from points 7, 8, 9, etc., draw the externally radial lines to the pitch circle. (5) With a radius less than one half the radius of the pitch circle, and with r, as a center, draw the first internal generating circle pc tangent to the pitch circle at point 1. (6) With the same radius, and with the points r 2 , r 3 , r 4 , etc., as centers, draw the other internal generating circles. (7) The external generating circles are drawn with the same radius from points r 7 , r 8 , etc. (8) Set the dividers at the distance b-1 on the pitch circle, and from point 1 lay off this distance b-1 on the first generat- ing circle p c. (9) On the next generating circle lay off two divisions, each equal to b-1, from point 2. (10) On the next generating circle lay off three divisions, each equal to b-1, from point 3. (11) Continue to lay off these divisions on the generating circles until they pass below the clearance circle. (12) The points d, e, f, g, give the direction of the tooth curve between the pitch and clearance circles. (13) Using the same length, b-1, step off one division from point 7 on the first external generating circle. (14) By laying off two divisions from point 8 and three divisions from point 9 we get the points h, k, m, and n, which give the direction of the upper part of the tooth curve. (15) Connecting points n, m, k, h, b, d, e, f, and g, the whole curve of the tooth is obtained. (16) The fillet at the bottom of the curve is drawn with a radius equal to one seventh the distance between two adjacent teeth measured on the addendum circle. APPENPUM ^} OUUIPE ClRUE H CIRCLE: CLEARANCE. TLfMPLET 97 PLATE 63. Draw a spur gear of 22 teeth, 3" circular pitch. Use the involute method. PLATE 64. Draw a spur gear of 24 teeth, 1 diametral pitch. Use the cycloidal method. PLATE 65. Draw a rack and pinion of 18 teeth, 2" circular pitch. Use either method. (The complete gear in the above problems cannot be constructed to full scale. If full scale is used, draw as much of the gear as possible. These drawings should be inked.) 98 BEVEL GEARS. The method of laying out bevel gear blanks is shown in Figure 4. (1) Draw the center lines of gear shafts A B and C D 90 apart and intersecting at point 0. (2) From O measure down on line C D a distance of one half the pitch diameter of gear Y and draw the pitch line E F of gear X parallel to the line A B. (3) From O measure to the left on line A B a distance of one half the pitch diameter of gear X and draw pitch line G H of gear Y parallel to line C D. The two pitch lines will intersect at point J. (4) From K on line A B measure off the distance J K on line G H locating point M. This gives the pitch diameter J M of gear Y. (5) From L on line EF measure off the distance J L locating point N. This gives the pitch diameter J N of gear X. (6) Draw the front cone pitch lines M, O J, and O N. (7) Through M and perpendicular to M draw the back cone line M P, and from point P perpendicular to J draw the back cone lines JP and J Q. By drawing a line from through point N the last back cone line Q N is obtained. (8) From M lay off the addendum distance M-1, the dedendum distance M-2, and the clearance 2-3. (9) These distances are also laid off from points J and N, giving points 4, 5, 6, 7, 8, 9, and 10. (10) Draw the lines 0-1, O-2, O-3, O-4, 0-5, 0-6, O-7, O-8, O-9, and O-10. (11) The length of the tooth face 1-12 is made about one third the length of the front cone line 0-1. (12) The proportions of such details as the thickness of metal in the gears, the length of the hubs, and the diameters of the shaft bores, are left to the student to design. The cross-sectioned portions show where the metal would be cut if a plane were passed through the two gears. 2-4- aitf 26 fee?/? - /- as H \ I o /yo/f- oj cve/ aeerj of \ -!' ~-<- ?sho/te of \ 5EVEL GEAR. SCALE To em. PETCRMINEP' PATE PLATE MO. 100 ISOMETRIC PROJECTION. Isometric projection is a method of drawing by means of which a pictorial effect can be obtained without destroying the relative proportions of the several parts of the object. Measurements taken on the vertical or thirty degree lines of an isometric drawing are in their true length. No dimensions should be taken on any other lines than these. When drawing the plates numbered 67, 68, 69, and 70, draw the top and front views as given and dimension them. Place no dimensions or letters on the isometric. These are given here merely to show the connection between the two types of projection (Orthographic and Isometric). All isometric drawings are to be inked. 101 ra* a 3" cv&e as.jfawn //? fi# /. /Safe fovs /6 ' /wes / Me /v/j/afe /?a;s?fi a/ /fie s/tfes Jfv/n Mf efio ce/?ferj . fj ///j fn?r /?ef&sory /o obfan c/rc/e /J o6/-o//?f^/y f/?e sah/ /TO ISOMETRIC PROJECTION SCALE: FULL SIZE- PRAWN BY PATE. f -7 l NO- QD / 102 cv o VI (0 I5OMETRIC PROJECTION SCALE V1 FOOT PATE. NO / Q . DO 103 IJL- 12- 7 ISOMETRIC PROJECTION SCALE FULL SI^E PRAWN BY PATE. , PLATE. NO. 104 I50METRIC PROJECTION SCALE FULL SIZE. NO. CVsTE. 105 PLATE 71. For this, the final isometric drawing, lay out a sheet whose outside dimensions are 2(H"x29" with a border of H". On this sheet make an isometric drawing of some fairly complicated machine. The one made on Plate 58 is suggested. The measurements may be taken directly from this with the dividers and transferred to the isometric. Make all letters with the instruments. Make the drawing on white paper ("Whatman's" is suggested) and ink it. 106 PERSPECTIVE DRAWING. If one were to look out of the window at a building, and if a line could be drawn from every point of the build- ing to the eye of the observer, the points on the window where the lines pierced it would be the ones to be con- nected if a picture of the building was to be drawn upon the window. The window corresponds to the picture plane in perspective drawing the plane upon which the observer and object rest is the horizontal plane called the ground -the plane parallel to the ground and passing through the eye of the observer is the plane of horizon. Study Plate 72 very carefully and note the following: A B is a top view of the picture plane C D is a front view of the plane of horizon E F is a front view of the ground plane. The station point (the point at which the observer stands) is usually taken at about one and one half the height of the object in front of the picture plane. This point must be selected to show the object to the best advantage. The line of horizon is generally taken from five to six feet above the ground. Note that the vanishing points are obtained by drawing lines from the station point parallel to the faces in the top view until they intersect the picture plane, and then dropping perpendiculars to the line of horizon. Note how lines are drawn from each point of the object in the top view to the station point and perpendiculars, then dropped from the intersections of these lines with the picture plane. Obviously, in reality, the object would never be against the picture plane. Plates 72 and 73 show it in this position, but this is done so that the student will master the principles of perspective easier. The remaining plates are to be drawn with the object away from the picture plane. All of the perspective drawings are to be inked and shaded. If all dotted and construction lines are drawn in red ink the general appearance of the drawing will be greatly improved. 107 TOP VIEW OF Pit i UKE PLANE \ r V f STATION POINT V-N|SHIN<3 POINT LINE OF HORI'ZON'T? p SCAUE- -a"=lF-OOT PATTE. MO. 70 . (A- 108 manner t of for ffa p/vceay'np as??. a /o ffa pic. fare jcxtyn? /h f* w/ PERSPECTIVE t7f?AWING 5CALE 4^' = < FOOT BY PATE. PLATE. NO. 109 PERSPECTIVE: SCAUE. 3;" = I FOOT PRAWN BY PACTE: 110 Show? o//r/3 /n ant/ curve are /s co//ec/ Xb /V/t facf //? . )o'-o" v 4. AJ-(\ * \ / IR'-O' \ JW5PKTIVE DRAWING PRAWN BY PLATTE NO. 111 Mvdom fr e asjtrft ^ at-* - #' forotrr /fate aknv//itp or? /a/ye g/ver? fore ~7/3/tt/er (/vfartce} e/vfff /fe ofr/Kfe/y /fie peapec//w fehvce/? Me '//&?? and xcfe vtews Draw PERSPECTIVE PRAWN BY PATE PLA.TC NO. "7<5 112 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. NOV 9 1936K LD 21-100m-8,'34 04210 UNIVERSITY OF CALIFORNIA LIBRARY