Giass / c/ <3c3 Gopyiight]^" - COPYRIGHT DEPOSIT: A Practical Course in Mechanical Drawing For Individual Study and Shop Classes, Trade and High Schools BY WILLIAM F.WILLARD FORMERLY INSTRUCTOR IN MECHANICAL DRAWING AT THE ARMOUR INSTITUTE OF TECHNOLOGY With 157 Illustrations, a Reference Vocabulary and Definitions of Symbols CHICAGO POPULAR MECHANICS COMPANY PUBLISHERS 1 ■i>5'^ • .w^^ Copyright, 1912 By H. H. WINDSOR t ( v,^ V €CI.A305934 CONTENTS CHAPTER I Introductory 7 CHAPTER n The Draftsman's Equipment n CHAPTER HI Geometric Exercises with Instruments 17 CHAPTER IV Working Drawings 58 CHAPTER V Conventions Used in Drafting 70 CHAPTER VI Modified Positions of the Object 77 CHAPTER VII The Detailed Working Drawing 81 CHAPTER VIII Pattern-Workshop Drawings 92 CHAPTER IX Penetrations no CHAPTER X The Isometric Working Drawing 121 CHAPTER XI Miscellaneous Exercises , 126 CHAPTER XII A Suggested Course for High Schools 156 REFERENCE VOCABULARY FOR the benefit of those who, for the first time, may meet new terms and expressions in this manual the following vocabulary, with definitions, is appended: Altitude. Vertical height. Angle. Space between two intersecting lines. Apex. Point where converging lines meet. Apices. More than one apex. Arc. Any part of the circumference of a circle. Area. Surface in units of measurement. Bisect. To cut in two equal parts. Bisector. A line which bisects. Chord. The line connecting any two points of an arc of a circle. Circumference. The boundary of a circle. Circumscribe. To draw around. Convention. Customary method or symbol used in pro- ducing a drawing. Decagon. Figure of ten sides and ten angles. Degree. One 360th part of a circle. Diameter. The distance measured across the center of a circle or a line drawn through the center terminating in the circumference. Element. A part which goes to make up the whole. Elevation. A view of an object looking at the front or side. Elliptical. Pertaining to the shape of an ellipse. Equilateral. Equal-sided. Frustum. Remaining portion of a cone or pyramid when the top has been removed parallel to the base. Hemisphere. Half a sphere. Heptagon. Figure of seven sides and seven angles. Hexagon. Figure of six sides and six angles. Horizontal. Parallel to the horizon. Hypotenuse (spelled also Hypothenuse). The diagonal distance between opposite angles of a rectangle or the side opposite the right angle. Isometric. Of equal measurement. Isosceles Triangle. A triangle with two sides of equal length and base angles equal. Lateral. Side. IV REFERENCE VOCABULARY Line. That which has length only. Median. Line drawn from the vertex of an angle to the middle point of the opposite side of a triangle. Nonagon. Figure of nine sides and nine angles. Octagon. Figure of eight sides and eight angles. Orthographic. Derived from two Greek words, orthos. straight and graph, to write. Hence applied to a straight-line drawing determined by projection on H, V and P. Parallel. Lines or planes are said to be parallel when all ooints of one are equally distant from all points of another. Parallelogram. A four-sided figure with opposite sides par- allel and of equal length. Pentagon. Figure of five sides and five angles. Perimeter. The distance measured around. Perpendicular. Any line at right angles to another. Pi (tt). a Greek letter used as a convenient symbol to express the relation between diameter and circumference, tt — 3.1416. The diameter of a circle X "^ = circumference. Plan. A view looking down upon the top. Plane. A surface with length and width and no thickness. Plinth. A prism whose height is less than any one of its other dimensions. Point. That which has position only. Polygon. A plane figure bounded by four or more sides. Prism. A figure bounded by rectangular faces, two of which are parallel. Project. To point toward. Pyramid. A solid with triangular faces converging to a common vertex. Quadrant. The fourth part of a circle. Quadrilateral. A four-sided polygon. Radius. Half the diameter. Radii. The plural form of radius. Rectangle. A plane figure with four right angles of 90° each. Rectify. To make straight or right. Rectilinear. Pertaining to right or straight lines. Rotate. To roll. ^ 'Scalene Triangle. A triangle all sides of which are unequal in length. Section. A view determined by a cutting plane. V REFERENCE VOCABULARY Sector. A radial division of a circle or the space between two radial elements. Segment. The space between the chord and arc of a circle. Semi-circle. Half a circle. Sphere. Ball or globe. A solid with all points of the surface equally distant from a point within, called the center. Tangent. To lie adjacent at a single point. Triangle. A three-sided figure. Trisect. To cut into three equal parts. Truncate. To cut off. Vertex. A common point of several converging lines. Vertical. Always straight "up and down." DEFINITIONS OF SYMBOLS 27rR Circumference of a circle when R — radius. 7rR2 Area of a circle when R = radius. 1 Perpendicular. II Parallel. = Means "equals'" or "is equal to". A. Angles. X Intersecting, or multiplied by, as the case may be. .". Therefore. L Right angle. Two intersecting lines making 90° to each other. Z Acute angle. Two intersecting lines less than 90° to each other. ^^"^ — Obtuse angle. Two intersecting lines more than 90° to each other. H Horizontal. V Vertical. P Profile. GL Ground line. VL Vertical line. VI PRACTICAL MECHANICAL DRAWING CHAPTER I INTRODUCTION IV/TECHANICAL drawing is one of the most popular ^^^ and most profitable subjects of study for the boy or young man of today. It is an essential qualification in most lines of engineering, an almost indispensable accomplishment in many occupations, and often the secret of successful advancement. It is founded upon the science of geometry, which, as applied to drawing, becomes a delightful and interesting subject, and not the difficult study the beginner fears. For illustration, a farmer wishes to know how many gallons of water will fill a tank, the diameter and height being known ; how many bushels of wheat will fill a bin, or how many acres there are in a field a quarter of a mile square. These examples, like many others, illustrate the prac- tical application of geometry, a subject no less impor- tant to the mechanic than the farmer, but a thousand times more interesting to the student than the usual text book. In preparing this manual the author was ever mind- ful of the many circumstances and limitations which have so often combined to deny to aspiring youth the advantages of a complete education. In this day and age competition and industrial conditions demand the best training and skill for every productive effort. What the artisan or mechanic does to improve himself 8 A PRACTICAL COURSE IN intellectually, to this end, increases his efficiency and value to his employer in every respect. In geometry a student is concerned with the theorem of a problem, and the proof, or why it is so. In me- chanical drawing the mechanical operations of con- struction — the actual doing of a problem, graphically, by the use of compass, triangles and other instruments — is considered essential and sufficient. However, this course does not preclude a master's knowledge of the principles of geometry. Any live, wide-awake boy can apply, to a good advantage, these geometric exercises to some project which he desires to work out or invent, without first having studied the subject. The surveyor with his tape and transit, the architect or mechanical engineer with his slide rules and for- mulas, must know these exercises also. If a craftsman desires a brace or bracket for a plate rail, he must know how to 'iay out'' the desired curves and angles. If a boy desires to make a taboret or jardiniere-stand with a hexagonal or octagonal top, he must first solve the geo- metric problem or consequently be unhappy with the results. One reason for not accepting a freehand perspective sketch as a substitute for the geometric drawing lies in the fact that the sketch seldom shows all the informa- tion required for the workman. The sketch deals with outward appearances only and from one viewpoint. The mechanical drawing of an object delineates the actual facts, within or without, and from as many view- points as the object has dimensions. Any hidden or de- tailed information is considered as important as that which is visible, and these details are represented ac- cordingl}^ by suitable conventions, the word convention. MECHANICAL DRAWING 9 in drafting, meaning a customary symbol or m.ethod established by precedent. The freehand sketch is governed by well-known laws of perspective which constitute the language of the artist from the esthetic standpoint. The mechan- ical drawing is represented by customary shop and drafting-room conventions and is the language of the mechanic and artisan. The one develops the power of observation, good judgment and individuality; the other, precision, accuracy and mechanical ability. An advantage that the mechanical drawing has over the sketch is that the workman will not be apt to con- fuse apparent dimensions, as seen from the perspect- ive, with true measurements, as seen from the work- man's drawing. All working drawings are made to scale, and all dimensions are proportional and properly placed. They must be made in such a manner that the ''dumbest" man in the shop will understand them. Otherwise, if an error occurs in construction, the blame attaches to the draftsman. Such a drawing must keep in mind all those who must, of necessity, use it. Me- chanics, designers, engineers and artisans of any trade fully realize the importance of a definite plan of pro- cedure. Bridges, buildings, railroads and canals must be thought out on paper, and their feasibility satis- factorily passed upon, before a mechanic or construc- tion company begins the actual work. Perhaps the most important part, if not the most difficult, is the making of the plans and specifications. The next most important part is working according to the direction of the plans. ^Constructive drawing also finds expression in a mul- titude of shops. A cabinetmaker, machinist, pattern- maker, or contractor, must have intelligent pictures or 10 MECHANICAL DRAWING drawings to guide his hands, and these drawings must be accurate and clear. A draftsman, whether amateur or professional, who fails to make them so, may, through ignorance and carelessness, or both, cause a loss of great consequence to his employer and the world at large. Someone has said : ''Mechanical drawing is the alphabet of the engineer ; without it he is only a hand. With it he indicates the possession of a head.'' It is needless to say that the hand will only do what the head directs. A uniform code of conventions and symbols is re- quired among workmen and shops just as among tele- graph operators. Such a language, if it may be so called, has come to be accepted generally among drafts- men who adhere closely to the modern approved forms, and these will be used throughout this manual CHAPTER II THE draftsman's EQUIPMENT. 'T^HE old saying that a poor workman blames his ^ tools is very nearly if not always true, for if a workman is content to work with an instrument poor in quality or poorly kept, it must be taken that he ex- pects to do poor work. How can a draftsman produce an accurate drawing if the compass legs are not firm and the points blunt, T square nicked, triangles warped, pencil dull, ruling-pen clogged with ink, and many other possible imperfections which would mar the finished drawing? Hence, it goes without saying that to do commendable work one must have good mate- rials, take excellent care of them and keep them in per- fect repair. A complete list is appended below, though not all are required. Those marked with stars are essential ; the others are luxuries : "^Drawing-Board — 16x21 in., inlaid, can be made of A No. I soft white pine by mortising narrow strips across each end of the board. The size is not arbitrary. Local conditions may require smaller boards and thus, of course, smaller plates. Fig. i. "^Drawing-Paper — Whatman's hot or cold-pressed (white) paper. Keufifel & Esser or E. Dietzgen cream paper, size 12x16 in. or 15x20 in.; but size of board and paper to be determined by local conditions, per above. A good bond paper may also be used. Two- ply bristol paper is excellent. For Patent Office draw- mgs three-ply bristol paper is required. "^Thumb-tacks — Comet No. 2 is one of many good tacks. They come in small tin cartons. n 12 A PRACTICAL COURSE IN "^Pencils — 2H and 4H. Sharpen so that the lead is exposed jq or f in. "^Erasers — Faber No. 211, Art Gum, Eberhard typewriter ink eraser, or others as good. "^Scale — Ordinary hardwood rulers will do at first. A triangular boxwood scale, divided into different scales, is best. "^T Square — Should be as long as the board and made of pear wood. Boys can make this in the wood shop. Fig. I. "^Triangles — 30-60-90 celluloid, 8 in. or 10 in. long, 45-90, celluloid, 6 or 8 in. long. Wooden triangles are inaccurate. Fig. i. Emery Pad — Or No. 000 sand-paper, to sharpen pencils. Each pencil should be sharpened chisel- shaped at one end and conical at the other. Use a 2H or 4H-grade. ^French Curve — Celluloid. Lead curves are cum- bersome and expensive. Case or set of Instruments — Containing: *i compass with lead and pen adjustment and lengthening bar. I divider (large). I divider (bowspring) 3 in. long. *i ruHng-pen (large). I ruling-pen (small). I bowspring compass (ink). I bowspring compass (pencil). I box leads. 1 protractor (German make preferable). I penholder and pen. No. 506 and No. 516, ball- pointed. MECHANICAL DRAWING 13 *i bottle Higgins' water-proof ink (black). 1 typewriter erasing-shield (celluloid or nickel- plated). These instruments, including the paper, need not be expensive, f. e., those marked with stars. Cheap brass sets are worse than useless. If it is convenient, the purchaser should consult with a practical draftsman before selecting the materials. Case of Instruments HOW TO USE THE MATERIALS 1. The paper should be tacked in the upper left- hand corner of the drawing-board so that the T square may not slip when drawing the lowest lines on the plate. 2. Thumb-tacks should not be withdrawn by the fingers. Use a knife blade or other flat instrument. 3. To get clean, sharp lines, pencils should be sharpened frequently, but under no circumstances must ridges be made on the drawing by heavy pressure on the pencil. 14 A PRACTICAL COURSE IN 4. Use a soft gum eraser to clean the drawing be- fore inking, that a glossy finish to black lines may be retained. Use ink-erasers for pencil lines only in ex- ceptional cases where the pencil has caused deep ridges in the paper. All division lines should be erased before inking. 5. All dimensions should be stepped off from the scale or ruler, with dividers, and then pricked lightly in the required place on the drawing. Explanation will be given later as to how to scale a drawing properly. 6. Always use the upper edge of the T square, which should be held against the left-hand edge of the drawing-board. Never use the upper edge of the square as a cutting edge. The least nick will cause inaccurate work as long as it is used thereafter. Fig. i. 7. The triangles, which are used to draw oblique and perpendicular lines, should rest upon the upper edge of the T square. Many and various combina- tions of angles may easily be made by combining both the 30-60 and 45-90. The oblique side of the triangle should always be to the right while in use, whether in inking or penciling. Fig. i. 8. The celluloid irregular curve is used in defining curves which are impossible to obtain with the compass. It is composed of many curves, but has seldom the right one, so that it is often necessary to shift it into many positions before required results may be ob- tained. 9. Only tw^o instruments in the case need explana- tion, and this is better acquired by practice. The com- pass legs are jointed so that the nibs of the pen may be square to the surface of the paper while the circle is being drawn. The hand should describe the circle above the paper while in operation, and not remain sta- MECHANICAL DRAWING 15 tionary. The ruling-pen should incline slightly in the direction of the line and should be held so that the nibs of the pen are not in contact with the edge of the T square. To keep the instruments from corroding, polish them with a small chamois skin and five cents' worth of chalk precipitate, or Spanish whiting. Instru- Fier. 1 ment must be kept clean. A thin piece of linen should be drawn between the nibs of the pen after each using, as the air congeals the ink quickly. The pen is filled by dropping the ink from the quill, — which is in the stopper of the bottle, — while being held in a vertical position. It should never be filled over one-quarter inch.' Lines are ruled from left to right and bottom upward. Use the adjusting screw to get the desired width. 16 MECHANICAL DRAWING 10. The German protractor is a semi-circular in- strument graduated into i8o degrees. This is used to obtain angles other than those obtained by the trian- gles. 11. Higgins' inks are waterproof. Should a blot occur, first erase with the ink eraser. (Never use a knife.) Second, glaze the roughened surface by using the back of a bonehandled knife, or soapstone. Third. *'size'' the glazed surface by spreading over it a thin coat of graphite, from a soft pencil. The paper is now ready to re-ink. CHAPTER III GEOMETRIC EXERCISES WITH INSTRUMENTS T^ XERCISE I. — Bisect a line of any length and arc -'-^ of suitable radius. Construction: With radius greater than one-half of AB and points A and B as cen- ters describe intersecting arcs at i and 2. If a line be drawn from i to 2 it will bisect AB. Fig. 2. Fig. 2 Exercise 2, — Erect a perpendicular to a given line (Problem i.) Fig. 2. Second method. Construction: From a given point E outside the given line AB draw a line at any angle to AB. Bisect and inscribe a circle 17 18 A PRACTICAL COURSE IN about CD. Where the circle cuts AB is a point of the ± through point E. Figs. 2 and 3. Exercise 3. — To draw a /^ line through a given point X to a given line AB. Construction : From any point Fig:. 3 B on the given line and a radius equal to BX describe arc. From X and same radius describe a similar arc through B. Lay off BY on second arc = to AX. A line drawn through X and Y is ^ to AB. Fig. 4. Second method. Construction : Draw a line making any angle with AB. With C as center and any radius 20 A PRACTICAL COURSE IN describe an arc making angle 0. Duplicate this angle with given point as center. Fig. 4. Exercise 4. — Divide two lines into proportional parts. Construction : Lay off one line into any number of divisions. Connect the extremities of each line. By means of triangles draw parallels through remaining points. Fig. 5. Exercise 5. — Construct tangents to a given arc of Fig. 8 any radius. Construction : With any radius describe arc of a circle. From the center of the arc to any point of the circumference draw^ a radial line. At the ex- tremity of the radial on the circumference erect a 1. This is the required tangent. Fig. 6. Exercise 6. — Duplicate and bisect a given angle. Construction: Draw any two intersecting lines, making any convenient angle. To duplicate, draw CD with any length. Describe an arc cutting given angle at A and E. With same radius describe arc cutting CD at F. Lay off, with F as center, the distance AE, and draw the other side of angle through C and G. Bisect as in Exercise i. Fig. 7. MECHANICAL DRAWING 21 Fig. 10 22 A PRACTICAL COURSE IN Exercise 7. — To draw angle of 60°. Construction: With any line as a base and any point therein as a cen- ter, describe an arc of any convenient radius, cutting the base line at C. With C as a center and radius AC describe arc at E. A line through AE is 60° to xAB. Bisect to get angle of 30°. Other angles can be easily determined. 22^ 30^ reads 22 degrees and 30 minutes or 22y2 degrees. (Fig. 8.) The table is as follows: 60" (seconds) = i minute (^). 60^ (minutes) = i degree (°). 360^ (degrees) = i circle. [Note the characters (' and ") used to designate minutes and seconds are used also to designate feet and inches. The context will, however, generally avoid confusion as to their meaning.] Can any angle be trisected ? Exercise 8. — By triangles only, divide a semicircle into angles of 15°. Use T square as a base for the tri- angles. Fig. 9. Exercise p. — Rectify a quadrant of a circle. Ap- proximate methods. Construction : Draw a circle of any suitable diameter and divide into quadrants. Draw a tangent of indefinite length at lower end of CD. Through A draw a line making 60° to this tangent. Where it cuts BD determines the length of the arc AD. Any smaller arc can be determined by extending^, through C and the other end of the given arc, a Hne to BD. Fig. 10. Second method. Approximate. Fig. II. AE = BD, Fig. 10. Exercise to. — Construct a right-angle triangle one angle of which is 30*^. The sum of all angles of any triangle is 180°. If a right angle is 90°, what must the remaining angles be ? This exercise is applicable as an MECHANICAL DRAWING 23 aid in determining the pitch or length of a rafter, when the rise and run are given. Pythagoras discovered the principle that the square of the rise + the square of the run equals the pitch squared : X^ -f Y^ =z Z^. Fig. 12. Fig. 11 Exercise 11. — To find approximately the distance across an unknown area by means of similar right angles. Construction: Select a tree or object on the opposite bank or side as indicated at A. Select another Fig. 12 on this side, say D. Lay off a convenient distance from D to C in the line ADC. Select a point B at right an- gles to AD and construct a parallelogram r)ODC. De- termine point X on the ground wdiich is in line with OC 24 A PRACTICAL COURSE IN and BA and measure the distance XO. By proportion, BDX BO AD : BD : : BO : XO .'. AD = XO Lay out the diagram, substituting known values for BD and DC and solve. Fig. 13. Exercise 12, — Equilateral triangle. Construction : Assume any length for a base. With a radius equal to the length of base and each terminal C and D as cen- ters describe intersection at X. Connect this point by lines to C and D. Measure the angles of an equilateral triangle in degrees. What is their sum ? Stained-glass windows are often laid out in Gothic arch forms by this kind of triangle. Fig. 14. Exercise 13. — Isosceles triangles. Construction : On a line of given or assumed lengths and with a radius MECHANICAL DRAWING 25 Fig. 14 greater or smaller than AB proceed as in the problem above. Are all the angles equal? What is their sum? Fig. 15. Exercise 14. — The vertex angle of an isosceles tri- angle is 150°, and its base is 3 inches long. Without protractor make a drawing. The trilium is an early Fig. 15 26 A PRACTICAL COURSE IN spring flower shaped on the order of an isosceles tri- angle. Exercise 13. — Scalene triangle. Base 2;^ inches, and base angles 22y2° and 37/4° respectively. What is the sum of the angles? Of any triangle? Fig. 16. Exercise 16. — Inscribe a square within a 3 inch circle. Without. Fig. 17. Exercise //. — Circumscribe a square about the circle in the problem above. What is the relation of inner to Fig. 16 outer square? The syringa is a four-petaled flower shaped like a square. Exercise 18. — Pentagon within a circle. Construc- tion : Bisect the diameter of the circle. Bisect a ra- dius. With C as center and AC as radius, describe arc at B. With A as a center and AB as a radius, describe arc on the given circle at D. AD is the length of one side of the polygon. Lay off remaining sides and draw a star. Fig. 18. What is the size of an interior angle? Use pro- tractor. MECHANICAL DRAWING 27 Fig. 17 Fig. 18 28 A PRACTICAL COURSE IN Exercise ip. — Pentagon. Construction: Base ij4-i5^- With one radius = to the base length describe arcs from centers i, 2 and 3. Connect i and 2 with 7 and 8 and complete the pentagon. Inscribe a circle within Fig. 19 the figure. Circumscribe a circle about the polygon. Many flower forms — pansy, violet — are pentagonal in shape. Fig. 19. Exercise 20. — Hexagon. Within a circle. Construc- tion : Lay off the radius six times on the circumfer- ence of the circle and connect the points. Without the protractor, what is the interior angle of this polygon ? MECHANICAL DRAWING 29 Use this key : 2n — 4 right angles when n = the num- ber of sides of the polygon. (2X6)— 4X90^ = 120^ n Prove this to be true. Draw a six-pointed star. Fig. 20. Fi£:. 20 Exercise 21* — Hexagon by means of the 30-60 tri- angle. The hexagonal bolt is an illustration of the use of the hexagon. Fig. 20. Exercise 22, — Hexagon without a given circle. Fig. 21 Exercise 2^. — Heptagon within a circle. Construc- tion. Draw a line making any angle with AB. Divide AB into as many equal divisions as the polygon has sides. With A and B as centers and AB as a radius 30 ^^"'^'^^^ 1 / \ \ ^^^^30 k. J Fig. 21 . A- t-r V / / / 1 / 1 / / / L>9 1 t 2\ 3 ^ 5 6 7 7^ Fig. 22 / MFXHANICAL DRAWING 31 describe arcs at C. A line drawn through C and 2, cutting the circle at D, determines the length of one side of the heptagon. This method will apply to any polygon. Use above formula to determine the size of the interior angle. Fig. 22. Fig. 23 Exercise 24. — Octagon within a circle. Construc- tion : Within a circle of an assumed diameter, divided into quadrants, draw bisectors. The circumference is now divided into eight equal divisions. Determine and locate the size of the interior angle by the preceding formula. Fig. 23. Exercise 2^. — Octagon within a square. Fig. 2^). Exercise 26. — Combination of polygons on a given base of i inch. Construction : Proceed as in laying out a hexagon. Bisect the arc A-2. Trisect 2-B. With center 2, draw arcs cutting through C and D at i and 3. 32 A PRACTICAL COURSE IX Points I and 3 are centers of circles circumscribing polygons of the required number of sides. Fig. 24. Exercise 2J. — Inscribe circles about the triangles given in problems 10, 12, 13 and 15. Exercise 28. — Inscribe three circles in the triangle given in Problem 12. Construction: Draw the me- dians of each side or bisect each interior angle. Bisect angle AC. Where the bisector cuts the line OX is the center for one circle. Fig. 25. Exercise 2g. — Five circles tangent to a given circle and each other ; within or without the given circle. Construction : Divide the given circle into live equal parts and bisect each sector. The centers of each circle will be located on the bisector. Draw a tangent at the terminal of a bisector and extend it until it cuts a radial line. Bisect the angle this tangent makes with the ra- dial and extend this bisector until it cuts AB at C, which is the center of one circle. Fig. 26. Exercise 50. — A circle tangent to a given circle and a given line. Construction : With the radius of the required circle added to the radius of the given circle, and C as a center, strike an arc 1-2. Draw a line paral- lel to the given line with the distance = to the radius O of the required circle. WTiere this line and arc 1-2 intersect is the center E for the required circle. Fig. 27. ^ Exercise 31. — A shaft i^ inches in diameter rotates within a ball-bearing consisting of 10 tempered steel balls. ]\Iake a drawing illustrating size of balls re- quired. Fig. 28. Approximate. Construction: Pro- ceed as in problem 29 except that the tangent circles are external to the given circle. Exercise ^2. — Four largest circles that can be drawn within a square. MECHANICAL DRAWING 35 Exercise JJ. — A Maltese cross. Fig. 29. Construc- tion : Draw two equal circles upon the two diameters of a given large circle and proceed as indicated in the drawing. Exercise 34, — Draw a geometric border using the circle as a unit. Nearly all design is geometric in char- acter. Fig. 30. Fig. 28 Exercise 55. — Figure 31 is an original illustration of the Swastika. Exercise ^6. — Geometric monogram within a trefoil. Fig. 7,2, Exercise 57. — Moldings, i. Cyma Recta, Fig. 33. 2. Roman Ogee, Fig. 34. 3. Scotia, Fig. 35. 4. Echinus, Fig. 36. Ogee Arch, Fig. 37. MECHANICAL DRAWING 39 Exercise 38. — The astronomer tells us that the plane of the earth's orbit is called the "ecliptic." This is an ellipse in shape. Draw an ellipse by two methods. The upper half to be constructed as follows: AC=4j^ inches. DE = 354 inches. DM = AB. M and F are centers of all arcs on the ellipse. From C as center lay off on BC any number of points, i, 2, 3, 4, 5, etc. With C-i as a radius and M and F as centers describe arcs. Figr, 37 With A-i as a radius and MF as centers describe arcs intersecting C-i. These are points of the eUipse. Pro- ceed until enough points are determined to locate the curve. The lower half by the circle method is self-evident from the illustration. Fig. 38. Exercise jp. — Trammel method. Fig. 39, Con- struction : Lay oft* on a small strip of cardboard the semi-minor and semi-major axes equal to the dimen- sions of the above problem. Move the point C so that it is always on the line AB and the point E on DF. By 40 A PRACTICAL COURSE IN Figf. 38 Fig. 39 MECHANICAL DRAWING 41 changing the position of the trammel frequently, suf- ficient points can be located at G, on the trammel, to determine a symmetric ellipse. Make GC = DH and GE = AH. Exercise ^o.— Make a full-size drawing of the ellip- tic cam. Fig. 40. Exercise 41. — A point on a connecting rod of a sta- tionary engine describes an elliptic curve in one revo- lution of the crank wheel. With B as the given point lay out the desired curve. The construction for the mechanism m.ay be omitted. Fig. 41. Exercise 42, — Five-point elliptic arch with three radii. Construction: AB, the altitude, and CD, the span, are given. Lay off the major and semi-minor MECHANICAL DRAWING 43 axes. With A as a center and AB as a radius, draw an arc through BE. Bisect CE at F and describe an arc with CF as radius. CG = AB and is 1 to CD. G-3 is 1 to BC, and where G-3 intersects CD at i is a point of the first center of the elHpse. Where it cuts AB at 3 is another. Make AH=BK. With 3 as a center and 3-H as a radius describe an arc through H. With C as a center and AK as a radius strike an arc at Fig. 43 N. With I as a center and i-N as a radius strike arc at 2, which is another point of a center for the elHpse. With the construction duphcated on the right of the illustration the remaining centers are determined. Points I, 2, 3, 4 and 5 are the required centers, and all arcs and facing stones radiate from their respective centers. Fig. 42. Exercise 43. — Cycloid. Fig. 43. A curve generated by the motion of a point on the circumference of a circle which rolls on a straight line is called a cycloid. The figure clearly illustrates the construction. Im- agine the rolling circle to be the end of a cylinder. Exercise 44. — Epicycloid. Fig. 44. An epicycloidai curve is generated by the motion of a point on the cir- cumference of a circle which rolls upon a circle. Exercise 43. — Hypocycloid. Fig. 45. A hypocy- cloidal curve is generated by the motion of a point on 44 A PRACTICAL COURSE IN Fig. 44 the circumference of a circle rolling upon the concave side of a circle. Should the diameter of the generating circle = the radius of the larger circle the hypocy- cloid would become a straight line. These curves are used in constructing the profile of gear teeth. Fig. 46 is a draftsman's method of laying out the forms of teeth theoretically, the method to the right being involute, and that to the left, cycloidal. Fig. 46a is a perspective sketch of the same from a pattern made by a patternmaker in the shop. The size of the rolling circle, 2E, in determining the epi- and hypocy- cloidal curves is not a fixed diameter; however, it is Fig. 45 MECHANICAL DRAWING 45 best to make it one-half the diameter of the pitch circle of the smaller of two engaging gears. In a problem where the diameter of PC, or 2R, and the number of teeth n are given, the circular pitch, which is the dis- 46 A PRACTICAL COURSE IN tance from one tooth to a corresponding point of an- other, CP, must be laid off first on PC. The involute method is as follows : At the radial line 2 draw a tangent 8 where it intersects the base circle at 2. Lay off on this tangent the chord of the arc of the PC between radials i and 2. This is a point of the curve Fiif. 46a of the tooth. Again at radial 3 repeat the above process, but lay off two chords of the arc on tangent 9 instead of one; on 10 three chords, and so on until enough points are secured to define the desired involute tooth curve. Reverse the operations for the CP other side. — = the width of the tooth or space 2 for all purposes in drafting. The lower half of the profile of the tooth is a radial line. The base circle MECHANICAL DRAWING 47 is drawn tangent to the involute line of 15'', through M. Practically the same principle is involved in laying out the cycloidal tooth except that the chords of arcl on PC are laid off on the arcs of the rolling circle Above the line PC the rolling circle generates the epi- cycloidal profile, or addendum, while below, the hypo- cycloidal or dedendum, A = E. The following additional data are given for those who would like to specialize on gear teeth and is ar- ranged from Kent, a well known authority : Addendum = depth of tooth above PC = .35 CP. ) p Dedendum = depth of tooth below PC = .35 CP. J ^ Clearance at root of space = .05 to .1 of CP. (C.) Actual thickness of tooth on PC = .45 of CP. \ Actual width of space on PC = .55 of CP. f * Backlash, or play between engaging teeth = .1 of v_^ J. . Circular pitch = a tooth and space on PC and is more commonly used than diametral pitch. Diametral pitch = a certain number of teeth per inch of diameter of PC. If DP = I CP = 3.1416. == 114 = 2.094. = 2 = 1.571. = 2}i = 1.396. = 2y2 = 1.257. From the above it is seen that a tt (pi) relation exists between circular and diametral pitch, i. e., if w be di- vided by DP the result will be CP; or if tt be divided by CP the result will be DP. Are about equal in machine cut gears. 48 MECHANICAL DRAWING Let n = number of teeth. ttD CP = when D = diameter of PC. n IT. D CP The thickness of rim D := .12 + .4 CP. The width of face, W, Fig. 46a, averages 2 to 2^ CP. The diameter of hub = twice the diameter of shaft. Thickness of web connecting hub and rim varies. Arms are used on larger gears. Holes are often drilled through the web to lighten the weight without destroying the efficiency of the gear wheel. The length of the hub may be flush with the rim, but is usually Yx inch or more longer. The "face" of a tooth is the distance B above PC. The "flank" of a tooth is the distance B be- low PC. ''K," Fig. 46a, shows the position of the core print used in molding the hole for the shaft. Problem i. — Draw the front and side views of a gear wheel having 24 teeth, 2^ diametral pitch, with epicycloidal profile of teeth. Scale, full size. Problem 2. — A pinion for a certain gear has 2y teeth. CP is 1.571 inch. Draw forms of teeth by in- volute method. Scale, half size. Note : A pinion is the smaller of two gears acting together and should not have less than 12 teeth. Problem j. — A recent examination for a city high- school position contained the following question : Make a scale shop drawing of a pair of meshing 50 A PRACTICAL COURSE IN gears of 8 diametral pitch. One gear to be a plain gear, to have ^2 teeth, i-inch face, i-inch bore, one hub ys inch long and to be the driver. The follow- ing gear to be a web gear and to travel at two-thirds as many r. p. m. (revolutions per minute) as the driver. The follower to have a 5/16-inch web, j4-inch rim or backing and 2-inch hubs, one hub being flush and the other J^-inch long. Each gear to be held on the shaft by two kinds of fastenings. All dimensions and de- tails, not here specified, to be assumed at the option of the draftsman to make the mechanism of ordinary and reasonable proportions. Driver and follower to be designated. Driver to be finished all over (f. a. o.) ; follower to be finished (f.) at rim, also on ends and outside of hubs. Note : Profile of teeth not necessary for cut gears. Scale, full or double size. Exercise 46. — Archimedean spiral of one whorl. Construction : With a radius equal to the rise of the spiral AB, and A as a center, describe a circle. Di- vide AB into as many equal divisions as the circle has been divided into sectors. Lay off successive arcs on the radials and draw in the curve. If a spiral of 2 whorls is desired divide AB into twice as many parts as for one whorl. This problem represents a cross section of the Nautilus, a sea shell described by Oliver Wendell Holmes in 'The Chambered Nautilus." Fig. 47. Exercise 47. — Heart plate cam. Fig. 48. The con- struction for this common object may be derived from Exercise 46 and the figure. The sewing-machine bob- bin-winder is one of several applications of its use. Exercise 48, — The involute spiral. This curve is developed by unwinding a string wrapped about a MECHANICAL DRAWING 51 cylinder, the end describing the involute. Construc- tion : Lay ofif tangents at regular intervals to the cylinder. On the first tangent line step ofif the chord of one arc. On the second tangent, two chords; on Fig:. 49 the third, three, etc. Draw the curve through the points. Fig. 49. The involute is used in defining the tooth curve of a gear wheel. Exercise ^9— Helix. Fig. 50. A definition of a helix may be given as the combined vertical and hori- MECHANICAL DRAWING 53 zontal motion of a point about a right line as an axis, no two points of the curve lying in the same plane. The upper part of Fig. 50 shows this part laid out apart from its application to the screw thread. Construction : Lay out the plan and elevation of the thread desired. Fig. 51 54 A PRACTICAL COURSE IN Fig. 52 Fig. 53 MECHANICAL DRAWING 55 Divide the half section of the plan into any number of equal parts and divide the pitch into as many. The curves are obvious from the illustration, which is a single thread. By a single thread is meant the wind- ing of one screw thread about the bolt-cylinder. A double requires two threads parallel to each other; a triple, three, and a quadruple, four. Fig. 55 represents a conventional method of showing the single thread in practice. No attention is paid to the theoretical helical curve in drafting; however, it is essential to have a proper understanding of it. Fig. 54 Exercise 30. — Ionic volute. Figs. 51, 52, 53 and 54. Fig. 51 is an illustration of the volute spiral of an Ionic capital in classic architecture (Fig. 54). In laying 56 A PRACTICAL COURSE IN out such a curve, either method. Fig. 52 or Fig. 53, may be used with the same results. When AB is given (Fig. 51), make the eye of the volute 1/16 of AB and locate its center on the ninth division of AB. Divide Fig. 55 the semi-diagonal of the square into three equal parts and construct squares through these points, as in Fig. 52. Each corner of these squares is a center for quad- rants of the outer spiral starting with radius A. The inner dotted squares are drawn to pair within the first squares, a distance of one-third the space between the first series of squares. Proceed with the construc- tion of the spiral following consecutive radii. The second method is practically the same as the first, just described. The radii of the first quadrants, both inner and outer, are taken on the line CD. Follow the unbroken lines until the spiral is completed. The construction of the diagonal in beginning this method is the same as in Fig. 52. The offset diagonal is equal to one of the smaller spaces on the diagonal. Exercise 5/. — Draw a i-inch bolt of 3 inches length. There are 8 threads per inch. The angle of the V's in the U. S. Standard or Sellers thread is 60°. Note the difference between a single and double V thread in MECHANICAL DRAWING 57 the conventional layout. A square has half as many threads as a V of the same diameter. Show length of bolt from underneath edge of head to the end of the cylinder. Figs. 55 and 88. Ornamental and decorative art implies the use of geometry in laying out designs and patterns in stained or art glass, carpets, wall-paper, oil-cloth, borders, ornamental iron, woodwork and carving, carpentry and cabinetmaking, pottery, china painting, floor-tiling, and in bookbinding. Meyer, in his "Handbook of Orna- ment," says: "In medieval times these geometric con- structions developed into practical artistic forms as we now see them in Moorish paneled ceilings and Gothic tracery." In the exhibit of Indian relics in the Field Museum one may also see traces of geometric design in the tattoo and decoration of the imple- ments of the savage. The history of some of these de- signs is very interesting, particularly the Swastika and the Maltese cross. Geometric motives may be obtained from the flowers. The trilium, daisy, columbine and lilac are illustrations of the triangle, circle and polygon. These may be ar- ranged into rosettes, borders and stencils, using a cir- cle as a unit. The illustration of the trefoil. Fig. 32, is a design of a monogram of an appropriate initial. Problems pertaining to decorative design will not be given in this course, but will be reserved for a later work. CHAPTER IV WORKING DRAWINGS T^ LSEWHERE reference has been made to the ^-^ value and importance of a working drawing in the shops. No rehable workman should attempt a new problem without a working drawing having previously / • / / / / " "^ X / \ / \ <\ 1 \ --^k/ T-^ inch == i foot. Problem 2. — As in Problem i, make a drawing of the stair detail. Risers, 7" ; tread, 10'' wide. Balus- ters 2" square and space equal to the width of baluster. Fig. 92. Problem 3, — Make a working drawing of the forms of joints used in joining represented in the illustration. Scale, half-size. Dimension. Use stock sizes of ma- terials. Fig. 91. Problem 4. — Make a floor plan of your home, a barn or school-room, and show all appointments. Scale Ys" to the foot. Small details are usually drawn larger or to full scale. Problem 5. — An examination in high-school draw- ing included the following: Make to scale >4" to i' arT architect's plan for the upper five-room flat in a modern three-story building. Show by the customary architectural conventions all that is necessary and usual. Outside dimension 22' 6^x36^ CHAPTER VIII PATTERN-WORKSHOP DRAWINGS /^ NE of the most useful applications of the working ^^ drawing is the laying out of patterns, or devel- opments. The theory of such a drawing is found in the study of Descriptive Geometry — a science which all architects and engineers are required to know some- thing about and which is extremely useful to drafts- men, although often avoided. A thorough knowledge of the principles of pattern- making enables the tinsmith or sheet-metal worker to lay out very complicated patterns in a very simple geo- metric manner and thereby save time and material to all concerned. Cutting a pattern so as to be as econ- omical as possible, requires foresight which the usual patternmaker fails to exercise. Tin-plate scraps often may be used to as good or better advantage than new sheets, if conservatively and thoughtfully cut, and in all kinds of work stock should be ordered so that a minimum amount of waste is left. A pattern is a plane surface representing the un- folded sides of an object equal to the perimeter of its right section, the width equal to the altitude of the object, or, rather, the true length of its lateral surface. Develop the surface of a cylinder or prism upon a sheet of bristol paper, allowing ^ inch for lap. Glue the lap and fasten together for a facsimile of the orig- inal. Add bottom and top. In most cases, in beginning a problem, it is only nec- essary to draw the plan and front elevation plus an auxiliary sectional view to show the true size of the cut section. From any of the illustrations, Figs. 93 and 91 MECHANICAL DRAWING 93 95, it will be seen that the object is projected up into the plane of the paper to obtain the auxiliary view. After the pattern is draw^n it is transferred from the manila or bristol paper to the metal by pricking points with a sharp punch along the contour of the pattern, due allowance being made for lap and seam. The double edge shown on the development of the quart measure is for the lock seam shown at A, Fig. lOO. 94 A PRACTICAL COURSE IN PARALLEL METHOD Problem /.—A truncated hexagonal prism is to be developed as shown in Figs. 93 and 94. Use any suit- able dimensions. Construction: Draw the plan and Fig:. 96 elevation, also sectional view, as at A. The width of the section and base is the same as the depth of the prism transferred from the plan view. In the "layout" the various heights of the linear elements of the prism are laid ofif on corresponding parallels in a straight line, equal in length to the perimeter of the base. ^ Problem 2,— A truncated hexagonal pyramid is to be developed, as shown in Figs. 95 and 96, to suitable MECHANICAL DRAWING Fig:. 97 Fiif. 99 Fig:. 98 96 A PRACTICAL COURSE IN dimensions. Construction: Obtain the projections and sectional view as in Problem i. To obtain the development it is necessary to know the slant height of the pyramid. The exterior edges are parallel to the vertical plane ; therefore, their true lengths must be seen at AC. With a compass set with AC as a radius. Fig. 100 describe an arc. Lay off the perimeter of the base on this arc and join all points with radial lines to the center of the arc C. Step off the true length of each cut element, o, i, 2, 3, shown projected on AC; then join as in Fig. 96. To complete the pattern add the section and the base. Problem j. — Develop a frustum of a rectangular pyramid, base 2"xi34" and altitude 3''. Problem 4. — An irregular cone is projected in Fig. 97. Develop by radial lines as in Fig. 96, except that the true length of each element be found separately. MECHANICAL DRAWING 97 Problem 5. — Given the front elevation of a ij/^" cylinder, Fig. 98, draw the plan and develop. Problem 6. — Draw the pattern of a quart measure, Figs. 99 and 100, diameter of upper base 3'', lower 5''. Find the altitude. Note : This problem involves a principle of mensuration. Use either dry or liquid measure. V V = A, or = A, .R2 D2 (.7854) where V =: the volume, or solid contents and A = the altitude. This is approximate. To be exact, the formula should be stated as follows : \ a + ^ + yj a/^ ff = ^^ [3 when a = area of upper base. b =: area of lower base. h = height or altitude. There are 231 cubic inches in a liquid gallon and 2150.42 cubic inches in a bushel. The problem here indicated is one of finding the altitude of the frustum of a cone. vSubstitute the known value of V, the volume, and solve for h as in any equation. Fashion a suitable strip for a handle allowing ^" lap for edges. The illustration, E, Fig. 99, shows the lap over a wire at the top of the cup. A customary rule for lap is 4 X thickness of metal -{- twice the diameter of wire. Problem 7. — An irregular triangular pyramid having an altitude of 4^", the sides of its base 2" or more in length and all lateral edges oblique to all planes of projection, has two lateral edges and base cut by a 98 A PRACTICAL COURSE IN sectional plane perpendicular to V and oblique to H. Draw the three orthographic views and the true size of the section. Develop. Figs. loi and 102. Problem 8. — An irregular oblique quadrilateral prism has a right section resembling Fig. 103. Use suitable dimensions. Its axis is inclined 30° to the right of its base, which is horrzontal. A plane inclined 60° to the left of its base cuts all the lateral edges of the pdsm. Draw the three projections and the auxil- iary or sectional view. Develop, adding the base and sectional view. Problem 9. — Draw three views of a regular vertical pentagonal pyramid, with apex above the base. The rear edge of the base is inclined 15° to the vertical plane of projection, V, the left end of this edge to be nearest V. The diameter of the circumscribing circle of the base is 2" and altitude 4". The pyramid is cut by a plane perpendicular to V and at an angle of 60° to its base. Show the line of intersection in three views, make a sectional view, and develop either trun- cated part. Problem 10. — A circular ventilator projects, through a gambrel roof as shown in Fig. 104. Work out the line of its penetration wnth the roof planes. Develop the ventilator top and also the roof planes, showing the line of penetration. Scale i" = 1^0". Problem 11. — Develop a truncated right cone from the illustration. Fig. 105. Note: Problems 7, 8, 9 and 10 are intended as test problems. Any development of a geometric form is a mathe- matical process, and hence should receive some such consideration. MECHANICAL DRAWING 99 Fig. 101 Fig:- 102 100 A PRACTICAL COURSE IN The following formulas are self-evident and should be committed to memory : 27rR = the circumference of a circle. 7rR2 ziz area of a circle. (7rR2)L = volume of a cylinder when L altitudcc (27rR)L = lateral surface of cylinder. (7rR^)L/3 = volume of cone. (27rR)S/2= lateral surface of a cone when S = slant height. 6(XY/2) = area of a hexagon when X == one side of the polygon and Y = the apothem. Note : The apothem of a polygon is the perpendicu- lar distance from the center of a polygon to one of its sides. 6(XY/2)L = volume of a hexagonal prism. 6(XL) = lateral surface of a hexagonal prism. (2^R)D = lateral surface of a sphere when D — diameter. Problem 12. — Develop a cylinder when R = ^", L = 3"- Problem jj. — Develop a cone when R is given and the volume. Problem 14. — The area of an octagon is 24 square inches. X = ^". Develop full size. Problem 75.— Y = ^'', L = 2>4". Develop. Note : This problem involves a geometric construc- tion of a hexagon without a circle before a develop- ment can be made. Using different data, originate and solve other problems. Problem 16. — Fig. 106 shows the form of a sheet- metal hood for a forge. Scale, half size. MECHANICAL DRAWING 101 Fig. 105 102 Fig. 107 J \ / '. 103 n / t / \ / \ / \ \ 1 / I 1 } 1 / \ 1 \ 1 o o> ® ® L 1 \ \ \ \ \. \ V \ V \ V 1 i_ ^ 7: \ i ^ \ ' j^<\ \ iT ^'^'' 3 \ A ^^: ^ ;I4- \ ^ ^/ \ \'5' \ /, / ~ ' 9- — - ^ V ^^^V,^^ \ / ^'^ N k>^ // '■'H L V M =i \/7 ^.. s-1 /\ XI \ "i A ' ' \ oV. -c - ^V/? //// / / \ . \\ ^v^ /^ '^/ /./ __J \ \: ■■VI — 16-.0'= -* Fig. 120 MECHANICAL DRAWING 117 moves in a plane 1 to the axis XY. Points lO, ii and 12 move perpendicularly to the roof lines drawn through A, B and C. The development of the cone has been described. Fig. 121. Fig. 121 Problem 6. — Develop the pattern for the base of a blower from dimensions given in Figs. 122 and 123. The right and left sides of this base are elliptical cylinders, that is, are not circular in cross section. The true size of the cross section cut by plane Tt' is show^n at X in the plan. This is the line of development, Tt', Fig. 123. The lengths of each element can easily be laid out and the triangular faces added. Draw to suit- able scale. Problem 7. — Develop the slope sheet of a locomotive 118 A PRACTICAL COURSE IN Fig. 122 as given in Fig. 124, one-half to be developed by triangulation. This is one of several practical prob- lems to be derived from a study of the locomotive for purposes of developments. The steam-dome, sand- dome and smoke-stack are other illustrations of right cylinders penetrating the outside cover of the boiler and requiring templets or patterns. Fig. 123 MECHANICAL DRAWING 119 Problem 8. — Draw the front elevation of the tran- sition piece and develop by triangles or the method sug- 125. gested Fig. Fi^. 124 Problem 9. — A regular vertical triangular prism, with a perimeter of 10^2" and 4'' altitude, has its front face inclined backward and to the left at is"". A right 120 MECHANICAL DRAWING square prism of 6^" perimeter and 4" altitude pene- trates the former. Axes of both soHds intersect at their center points. Develop both objects. Fig. 12s CHAPTER X ISOMETRIC WORKING DRAWING A N ISOMETRIC drawing is generally conceded to '^^ be a pictorial or perspective representation, and for practical purposes it has come to be eminently use- ful to the artisan in clarifying hidden constructions. Among draftsmen it has supplemented the freehand perspective sketch on account of the comparative ease with which the picture is made by the instruments. The few principles of isometric drawing may briefly be summed up as follows : a. All vertical edges in the object are vertical in the drawing, as in freehand. b. All horizontal edges, representing right angles 122 A PRACTICAL COURSE IN orthographically, make 30° to the horizontal in the isometric construction. c. Non-isometric lines of edges making other than right angles must be laid ofif orthographically first and then transferred to the isometric drawing. This dis- torts the true length of non-isometric Hnes, but does not mar the pictorial effect. Fig. 127 d. Surfaces, not lying in the same plane, are estab- lished from center-isometric axes. e. Isometric circles are drawn within isometric squares of the same diameter as the given circle. Elliptic or irregular curves are constructed flat, then transferred. Fig. 126. MECHANICAL DRAWING 123 Fig. 128 i24 A PRACTICAL COURSE IN /. Isometric workshop drawings are dimensioned- Dimensions must be placed parallel to the isometric lines. Fig. 127. g. The usual custom of shading an isometric draw- ing is to accent the edges separating light surfaces from dark, assuming the light to come from the left at an angle of 45°. A better method, and one which en- hances the pictorial effect, is to shade all edges which are nearest the observer's eye. This tends to lift the drawing of the object from the paper and relieve the unnatural effect of the isometric construction. Fig. 127 is an illustration of the stub end of a connecting rod and exemplifies the second method described above. There are many draftsmen, however, who do not shade any drawings. The true purpose of shading is to make the drawing more attractive, but aside from this it has no value. h. Invisible lines are seldom shown in isometric drawings except where irregular lines are hidden by regular surfaces and the information desired can in no other way be shown. The illustrations in the text have largely been un- shaded isometric drawings of objects used in the class- room. Problem i. — Make an isometric drawing of a chalk or cigar box with the lid open. Scale, half size. No dimensions. Problem 2. — Select a good-sized spool. Draw in isometric. Scale, double size. No dimensions. Problem 3. — Copy the exercise of the connecting rod. Fig. 127. Scale, full size. Dimension. Problem 4. — Figure 128 represents the base and cap MECHANICAL DRAWING 125 of a pattern for a pillow-block bearing. Scale, full size. Dimension. Problem 5. — The teacher's desk to suitable scale. Do not show invisible lines. Dimension. Substitute a book-case. Problem 6. — A mission chair. Look for non-iso- metric lines. Dimension, and draw to suitable scale. Problem 7. — A shaft-hanger. Scale, half size. Iso- metric. Fig. 129. Fig. 129 CHAPTER XI MISCELLANEOUS EXERCISES Problem /. — To construct the arc of a circle me- chanically when it is inconvenient to determine its radius, Fig. 130, make AB the chord of the arc ACB ; DC and ACB to be kept constant and the position changed so that points A and B remain in contact with lines AC and BC. The resultant points will determine the center and circumference of the required circle. The same problem might be constructed if strips be nailed together as the lines AC and BC suggest with a third strip crossing lines AC and BC parallel to AB, anywhere, to hold the angle firmly thus made. Problem 2. — A graphical method for finding the distance AB across a pond when the land in triangle FED is inaccessible. Set a stake at C in line with AB prolonged. Set another, D, so that C and B can be seen from it. Also a third stake, E, in line with BD prolonged so that DE equals BD. Set a fourth stake, F, at the intersection of EA and CD. Measure AC, AF and FE. Show that AB is a fourth proportional to AF, AC and (FE— AF). Draw a line through D parallel to AB. D bisects BE. DX is always AB. Fig. 131. 2- Problem 5. — Draw an involute cam which involves the construction of the involute curve on page 51. A cam is a very useful mechanical device which gives various motions to machine parts at regular in- tervals of time. It is generally in the form of a flat 126 MECHANICAL DRAWING C 127 Fig:. 130 disk, although sometimes cyHndrical in shape. Har- vesters, printing presses, sewing machines, looms and steam-valve mechanisms employ a considerable use A PRACTICAL COURSE IN ^ANGLE OF ACT/ON Fiff. 132 of cam constructions, Fig. 132, To draw an involute cam with a given rise in a given angle of action, use the following: Let A = rise of the follower or throw, And X = the radius of the base circle C. As in the figure, the angle of action is 120 degrees, A = % X, % being the ratio of the arc through MECHANICAL DRAWING 129 LU X LU X H li. tn O 1-4 h- .a" z h UJ n CL O > UJ o - (Vi (n which the cam works, to a semicircle or straight angle. 2 = 44/21 X, assuming tt to be 3 1/7. X, or the radius, = 2/44/21 = 2x21/44 =1 42/44 in., or nearly i". 180 A PRACTICAL COURSE IN We assume ^f as being most convenient. With this radius draw the base circle C, and construct tangents upon which to lay out the involute curve. The ma- chine itself will determine the diameter of the disk. Lay off the rise of the follower on tangent i, and di- vide this into as many parts as tangents have been constructed. With center O, draw concentric circles to corresponding tangents from the points on the axis of the follower (F). THE HELIX Problem 4. — Fig. 133 shows the development of a helical curve as unwrapped from a cylinder. If the surface of the cylinder be laid out on paper and a diagonal line be draw^n and the paper wrapped about the cylinder, the line will then illustrate the helix. Problem 5. — The application of the helix may also be seen in coil springs, two illustrations of which are given. Fig. 134. The constructions may be laid out as in Fig. 50, page 52. As in a screw thread the pitch of the helix is the distance between two opposite points lying on the 'curve and the same cylindrical ele- ment. In drawing the spring, use the helical curve as a centerline. Draw a number of slnall circles equal to the diameter of the round coil desired. The con- tour may easily be defined by drawing tangent helices to these circles. If square or rectangular material is used, draw the helices from each of the four corners, A, B, C, D, of the cross section. Problem 6, — Make a coil spring from 5" round steel, 3!/^" inside diameter, i^'' pitch and 6" long. Problem 7. — Make also a square spring out of half- inch material, i^'' pitch, 4" outside diameter and 6" length. MECHANICAL DRAWING 131 Problem 8. — Determine the length of material re- quired in each preceding problem. c D ff IB Fig. 134 SHEET-METAL PROBLEMS On page 91 references were made to the value of knowing how to lay out a pattern or template for sheet- metal problems. To the sheet-metal draftsman more particularly than any other the use of geometric methods in drafting is most practical. A great many problems of a sheet-metal character are, at least, in part warped surfaces. Such surfaces are non-developable by any regular method. In the development of Fig. 97, the cone is first divided into elements of regular intervals, say 12 in all, and their true length determined by revolving each fore- shortened element parallel to the vertical view. Any two true elements laid out with the chord of their basal arc will form a triangle. Adjacent triangles are 132 A PRACTICAL COURSE IN constructed in a similar manner and the pattern com- pleted. Problem p. — Fig. 135 is an illustration of a tran- sition piece for a smokestack or blower. Draw to scale of i'^ equals I'-o'^ Fig. 136 shows the pattern when laid out. By observation it will be seen that planes A, B, C, D, are triangles whose true shapes can easily be deter- mined from the projections. The four corners are sections of oblique cones which have been previously described. But a shorter method of finding the true length of these elements is to find the hypotenuse of a right angle the base of which is the distance from X or Y in the plan, to points 3, 4, 5 and 6 in the plan. The altitude of each triangle is the projected vertical altitude as seen in the front view. Lay off the sides anywhere as at OP and draw each hypotenuse. These are the true lengths desired in the pattern between planes A, B, and C. 1"he true lengths of other ele- ments are found in a similar way. As the section of the top is a circle taken at an angle of 30 deg. from a horizontal, an auxiliary view will show a true circle as in the front, or top view. A semicircle will suffice. Divide into an equal number of points for convenience and project back to the corresponding: plan and eleva- tion. Connect these points with R, X, Y and Z, and proceed with the development. Lay off plane A first. Fig. 136. With 6 as a cen- ter, strike an arc equal to 6 — 5 (on the section) and the pattern with Y as a center and a radius equal to 5 — 5 at OP. Continue this process until each of the longer diagonals are used, half on each side of plane MECHANICAL DRAWING 133 \2l3^^ Fig. 135 134 A PRACTICAL COURSE IN A. When all of the longer diagonals are used add planes B and C, and then add the diagonals laid out on the left of OP. The plane D is bisected to show a symmetrical development. Fig. 136 Problem lO, — Fig. 137 is the layout and working drawing of the base of a smokestack. The top of the base is circular in shape while the ends are semi- oblique cones.- Make a development of ^ the lateral surface similar in shape to Fig. 136, scale i'' equals i^-o". In this problem it will be necessary to find the true length of all elements by revolving the true length (of all) parallel to the vertical plane upon which the front view is projected. To do this use X' as a center and MECHANICAL DRAWING 135 X^ — 6 as a radius. Strike an arc upon — X'. Project up to the plane AB. Connect the newly found point with X and the line will now be seen in its true length as it is parallel to V. Fig. 137 When the plane CD cuts the new position, X' — 6 will be the true length of that portion w^hich consti- tutes the surface and can be laid off on X^' — 6 of the development. Fig. 138. 136 A PRACTICAL COURSE IN Fig. 138 Problem ii, — Fig. 139 is an illustration of a gro- cer's scale scoop. The development of A is a pattern of the portion of a cylinder which a tinsmith would be required to lay out for a template. Substitute suitable dimensions and draw. Draw a center line X-X to begin. Divide the end view of section A into a convenient number of similar (equal) parts. Project back to X-X. The circumference of section A is next laid out in de- MECHANICAL DRAWING 137 Fig. 139 velopment anywhere convenient and the points pro- jected to corresponding places. SECTIONS OF WORKING DRAWING The value of being able to make sections in a draw- ing where possible constructive difficulties may arise later, is a part of the draftsman's business. Sections are very helpful in showing interior constructions and in a complicated drawing are absolutely necessary. In the illustrations, the sections are shown by cross hatching lines, the relation of adjacent parts being 138 A PRACTICAL COURSE IN Fig. 140 shown by drawing the hatch Hnes at different angles. To determine the location of sections, pass planes through the geometric centers of the object, both ver- tical and horizontal. On pages 92 and 93 and else- where of chapter VIII, sections were made of geomet- ric solids and their developments required. Figs. 140 and 141 are sections of small machine parts and illus- — rrr ^ 1 r . t ' — -^ ___^_^^ ' 7'" I ^8 4 \ 1 ^ [ - - - / ___— Fig. 141 MECHANICAL DRAWING 139 I" 2 n ^^ '?^////////////.zA ^ u Fig. 142 trate the practical value of such a construction. Fig. 142 is a sole plate for a. pillow block. Make freehand sketches of each of the sectioned illustrations in order to get a pictorial view of the object. Problem 12, — On page 67 is an illustration of a core box for a pipe tee. Fig. 143 is an isometric illustration of a pipe-tee Fig. 143 140 A PRACTICAL COURSE IN pattern but not for the box just referred to. Make three views from the illustration, full size. Problem is. — Fig. 144 is an illustration of a pat- tern for a pedestal bearing. Make three views, g' I'-O". y Fig. 144 Problem 14. — Fig. 145 is an assembly drawing of a simple machine vise. Make a detail drawing filling all blank dimensions as indicated in Figs. 146 and 147. Those dimensions which are apparently omitted should MECHANICAL DRAWING Ul Fig, 145 142 A PRACTICAL COURSE IN I <> TAP roR Jmach i 3C/?^IV ^O THD3. M^ o TAP/ 20THD5 G ( ji OIL h -- P , J ^ T \ 1^ t ^i__^ f — -M '_j J 1 1 ^ 1 1 r 1 1 1 1 1 Q E ^-^^ DRILLED WHCN IN PO'S/T/ON TAP TO FIT SCREW -^-^''riLISTER HD. MACH. SCREW 2 WANTED i"LONG ^ 4 WANTED / LONG 4" ^y^AT HD. MACH. ^C/^EW 4 WANTED 4 LONG 60: ^\ T^ DRILL FOR 4 fLAT HD. MACH SCREW '■i^ & Fig. 147 144 A PRACTICAL COURSE IN be supplied by the student; but reference should be made to the assembly drawing before so doing. Make a full-size drawing of the assembled vise before the detail drawing. Alake a stock list as suggested on page 86. Notes on the detail drawing have reference to the work of the machinist in ''finishing" the cast- ing after it has been molded from the pattern. Such information is essential to a workman and eliminates hazardous guesses and mistakes as well as loss of time and material. The arrangement of pieces and parts should be very carefully planned on the drawing paper. In so doing much more can be placed on one sheet. Problem 15, — Figs. 148 and 149 represent a small jack screw in section and detail. Make three views and dimension. Problem 16. — Fig. 150 is an illustration of Hooke's coupling. Three views and section. Problem //. — Fig. 151 is a side crank arm. Make three views and section at X-x. Problem 18. — Fig. 141, page 138, is a turnbuckle. Make three views and section. Make a drawing of each problem above to scale as suggested. Use suitable diameters in each case and section. Problem 19. — Make an isometric drawing of the mission footstool as shown in Fig. 152. INTERSECTIONS AND PENETRATIONS Problem 20. — The three views of a stub end of a connecting rod are shown in Fig. 153. To find the curve of intersection, of the cone and prism, pass vertical planes A, B, C, D, cutting both the cone and rectangular prism. Each plane cuts a circle from the cone and a rectangle from the prism. Where these MECHANICAL DRAWING 3'' 145 Fig. 148 146 A PRACTICAL COURSE IN /^ ^ R 8/' OlOOi ' 'I" 3 THREADS PER INCH Fie. 149 figures intersect is a point of the curve desired. The same method is used in finding a curve of intersection MECHANICAL DRAWING 14' Fig. 150 Fier. 151 148 A PRACTICAL COURSE IN __- — _(_.__•__ 18^ I ^le^ *2: /o ::d "*i^~.r' .1 ^ .1. I ,1 -/- [f I I I i._i_. L_J Fig:. 152 of a cone and hexagonal prism, or the chamfered por- tion of a hexagonal nut. MECHANICAL DRAWING 149 Fig. 153 150 A PRACTICAL COURSE IN LETTERING EXERCISES A great deal of the difficulty which comes to the beginner in lettering is due to a vague idea of the shape of the individual letter. No draftsman, however experienced, can produce well formed letters without a clear picture of the shape of each letter and for this reason the beginning student should read and follow these suggestions closely. Use practice paper, before commencing one of the exercises below. INSTRUCTIONS 1. Make the vertical stroke of A, first, then the slanting stroke. 2. Make the bottom part of B wider than the upper. 3. Letters C, G and Q are modifications of the letter O. 4. Keep the bottom part of the letter D full. 5. The lowest bar of the letter E is a little longer than the upper bar. The middle bar is shortest and slightly above the center as in F. 6. Draw the two outside bars of the letter H first. Horizontal bar is slightly above center. 7. The letter J is a portion of the letter U. 8. Make the short bar of the letter K slope from the upper end of the first bar. 9. Letter M is broad. Draw the two outside bars parallel, first, before the intermediate, likewise in the letter N. 10. Letters P and R are similar. Keep the top full. 11. The letter S may best be made inside the letter O, with the bottom part a little wider and fuller. ALL LETTERS SLOPE HALF THE H/GHT ^y\\m >o-fn /£^/r^ /^m 'L y /^ — ^^ L J L / ^6 ^ ^2" ■4-5 « an/JKL R NOFQnB / / ^ I ^ / / ~U VWK ' ;t- ^^ 'i CARL SCHURZ HIGH SCHOOL ABCDEFGHIUKLMNOPQR STUVWXYZ THE QUICK BROWN FOX JUMPS OVER THE* LAZY DOG Fie. 154 152 PENCfL EACH LETTER/NG SHEET ON CROSS SECT/ ON RARER RRO\//DED FOR THAT RURROSE AND SUBM/T EACH RENC/l^LED 1./NE TO THE INSTRUCTOR ^OR H/S OR/T/C/SM. /N OO/NG TH/S THE STUDENT W/l^L. ^A\/E T/ME ANa /MRROVE H/S STANDARD OR V^ORKMANSH/R MORE RAR/DLY. USE A 2H RENC/L. CON/CAL RO/NT, AL.L. DRAW/NGS SHOUi-D BE KERT NEAT AND CLEAN. S RACES BET\A/EEM V^ORDS SHALL NOT VARY RROM LESS THAN ^ TO MORE THAN S D/V/S/ONS ON THE CROSS SECT/ON ^ARER, SRACES BET\A/EEN RARAGRARHS SHOULD BE DOUBLE THE SRACE BET\A/EEN 1./NES. A S/NGLE SRACE /S SURR/C/ENT TO SERARATE L/NES /N THE RARAGRARH. INDENT EACH NEW RARAGRARH. USE A LARGE RE/\^ BOLDER \A//TH A >3/G ER REN RO/NT, HEER THE RENRO/NT CLEAN TO ALLOW A STEADY RLO\A/ OR /A/ZT. THE /NK CLOGS THE REn's ACT/ON VERY QU/C/fwi.mH-a i / m i ' t ? iw i - t^^ iiz attMa a^ 33 ^^ .? >5 ae 77 « a sio. /e / /6 / /e 3 /6 /" /^' 3'^ /^^ 5^^ 3^^ 7' a ^ e 2 a ^ a / s / 3 e / 2 a 3 -4 7 a / e / 4 3 a / 2 s5 S 3 7 a /6 7 /e // /a /3 /© /© 29 3a /< >5 7 /e 9 /© // /6 /3 /6 /6 29 3a 3 /6 5" /6 7 /6 16 If 16 13 16 15 16 29 32 32 3^ 32 3 32 32 32 Fig. 156 /3 32 23 32 2Q 32 MECHANICAL DRAWING 155 12. Make the first bar of the W slope slightly to the right. Keep the letter broad. 13. Letter V is the letter A upside down. 14. Widths of all letters are in proportion to their heights and should be always so considered. 15. Common practice among draftsmen employs the use of the sloping Gothic letter. Vertical letters are commonly used, however, but are more tedious to make look well. Problem 21. — Make an exercise on >^-in. coordi- nate paper of Fig. 154. Each small figure pertains to the number of spaces upon the section paper. This exercise is a study in form and proportion and should be executed with much precision and care. Use 2-H pencil, conical point. Problem 22. — Fig. 155 is an exercise in lettering one space high. Herein is the application of the exer- cise in Fig. 154. Problem 23. — Read the material over carefully and apply the directions included therein. Hard practice is a good master. Fig. 156 is an exercise of figures and fractions on cross-section paper. The draftsman's figures are quite different from the commercial figure and hence should be scrutinized closely. Fill in all vacant spaces and strive for uniformity as in previous exercises. Problem 24. — Fig. 157 is an exercise in block let- tering quite often used in designs for covers, titles, headings, etc. Note the divisions of the height are 5 instead of 8. CHAPTER XII A SUGGESTED COURSE FOR HIGH SCHOOLS Group I. Geometric Exercises Problem i. — Bisect a given right line and arc. Problem 2, — Erect Is to a given line (any method). Problem j. — Draw parallel hnes (two methods). Problem 4. — Divide a given line into proportional parts. Problem 5. — Construct tangents to a given arc of any radius. (Fillet.) Problem 6. — Duplicate and bisect a given angle. Problem 7. — Without triangles construct A. of 30°, 6o^ 75^ 45^ 22«-30^ 37°-3o'- Problem 8. — By triangles only divide a semicircle into angles of 15"^. Problem p. — Rectify a quadrant of a circle (two methods) . Approxmiate. Problem 10. — Triangles (trilium — trefoil). a. Right angle (rise, run and pitch of a gable roof rafter) x^-{-y^ = s^. To find the distance across an unknown area — a stream, lake or park; also to find altitude of a tree. b. Equilateral. (Isometric square — Gothic arch). c. Isosceles. d. Scalene. Query : How find the area of any triangle ? What is the sum of all angles of a triangle ? Problem 11. Square (bolthead plan — swastika — syringa). 156 MECHANICAL DRAWING 157 Problem 12. — Polygons (pansy, violet — crystals). a. Pentagon — star (three methods). b. Hexagon — bolthead plan (two methods) — star. c. Heptagon. d. Octagon — taboret top. e. Combination of a, b, c, d on a given side of i". 2n — 4X90 Prove all polygons by the formula when n n = the number of sides of polygon. Use the pro- tractor to verify. Problem /j. — Circles : a. Three circles within an equilateral triangle. b. Draw circles tangent to each other and the given circle, within or without. c. Gothic arch. d. A circle tangent to a given circle and line. e. A circle tangent to two given circles which are not tangent to each other. Note : The smallest circle is not acceptable. */. A shaft i^" in diameter rotates within a ball- bearing consisting of twelve tempered steel balls. Make a drawing showing size of balls required. g. Four circles within a square. //. Maltese cross. i. Geometric circular borders. j. Moldings — cavetto, cyma, reversa, cyma recta, ogee, scotia. Problem 14. — Ellipses and elliptic curves (conic sec- tions — ecliptic). a. Focal method ; circle method. b. Trammel method. c. Five-point elliptic arch. 158 A PRACTICAL COURSE IN d. Greek, Persian and Gothic arches. e. ElHptic cam. "^f. The path of a point on a connecting rod in one revolution. *^. Cycloid. ^ *//. Epicycloid. ^ (Gear teeth.) i. Hypocycloid. J 4; Hyperbola. [ (Conic sections.) Problem ij, — Spirals : a. Archimedean spiral of one or more whorls. b. Ionic volute (Ionic capital). "^'r. Heart plate cam (sewing-machine bobbin- winder). "^J. Involute (gear teeth). '^c Helix-screw thread, clutch coupling. Biographical. — From the encyclopedia read the biog- raphies of Archimedes, Pythagoras, Euclid, Vignola. It is intended that the number of problems should be arranged on the plate according to the local conditions of the class-room. Large plates, say 1 5^x20", are more comprehensive but require less time for execu- tion in proportion to smaller plates. Such problems in this outline which have not been given in the text are not essential, but, if desired, may be obtained from the instructor. Those who expect to study design are not required to complete the entire course of mechanical drawing. The problems marked by {^) may be omitted in this group. Group 2. Projections, L Working drawings, 1. Three views of a cylinder. 2. Three views of a prism. MECHANICAL DRAWING 159 3. Two views of a plinth — one view given 4. Three views of a pyramid. 5. Hexagonal nut. 6. Crank arm. 7. Small pedestal bearing. 8. Taboret or stand. g: Coat-hanger. 10. Knife-box. 11. Tailstock. 12. Tool-rest. Note : The first eight problems are not to be di- mensioned. Substitutes may be selected for these objects where and when these are not available or advisable. Problems 8 to 15 are to be dimensioned carefully. Models are to be preferred to a drawing at the beginning of this course, so that the absolute rela- tion of object to drawing will be established as early as possible. 13. Detailed working drawings from machine parts. 14. Working drawings from isometric blueprints. 15. Working drawings from sketches (freehand). //. Revolution — Axes of symmetry. 1. Draw three views of a prism, plinth or pyramid. 2. Draw three views of No. i when revolved about a vertical axis 30°, contra-clockwise. 3. From No. 2 revolve object about side axis through 30° to the left. 4. From No. i revolve the object forward about a front axis 20^. 5. From No. 2 revolve the object backward about a front axis 25°. 6. From No. 5, 30^ about a side axis, to the right. 7. From No. 4, 15° about a vertical axis. 8. From No. 5, 15° to the right about a side axis. 160 MECHANICAL DRAWING Several plates involving the modified positions of geometric figures should be drawn that the theory of projections may be perfectly clear. Learn the three laws of revolution given. ///. The point J line and plane. (For advanced stu- dentSc) Draw in both first and third angles. 1. Find H and V projections of a point i^^" in front of V and 2^" above H. Two inches below" H and i^" behind V. Always open the first angle. 2. Draw the projections of a line which is ^ to the H and V planes, 134/' above H and 2" in front of V. 3. Draw two views of a line oblique to H and /^ to V ; oblique to V and ^ to H ; oblique to H and V. 4. Find the true length of lines in No. 3. What is the difference between the projected length and the true length of a line ? 5. Pass a plane (a) / to H; (&) / to V; {c) // to P; (d) 1 to H, and any /_ with V; (^) 1 to (V) and any /_ with H and P. 6. Find the intersection of a and £>, also d and c in 5. IV, Development of surfaces for patterns of sheet- metal and tinsmithing. L Parallel lines. Cylinders, prisms, etc. 2. Radial lines. Cones, pyramids, etc. 3. Method of triangles. Warped surfaces. 4. Method of revolution. Frustums and trunca- tions. ' 5. Method of parallel planes ; oblique planes. Pen- etrations. V\ Penetrations zvith developments included. VI. Shades and shadows. VII. Mechanical perspective. MAR 13 1912 LIBRARY OF CONGRESS 01 9 719 929 5