Chapter IV: Part 4

In working drawings light lines only are permitted; shade lines are wider than the working lines, and in reading scale measurements the extra thickness of line would make a difference.

Instead of representing the shadow as it is really cast by the object, the edges which cast the shadow are determined, and all the views are treated as if the light came from behind and from the left, downwards, at an angle of 45° to the horizontal line, as shown by the arrows in figs. 245 to 248.

The lower and right-hand outlines of projecting parts will cast shadows, and the student should make them of extra width.

Fig. 249: In shading curves, divide the center line as before (see page 146) and describe circles from center, _D_; these lines are not to be shaded in penciling, but when inking. The figures represent two rings, _A_ and _C_, and spaces, _B_ and _D_. The outside of a surface is shaded according to circle 1, and the inside surface according to circle 2. This will give the desired shading, but it makes a drawing incorrect, and therefore shading is not used in working drawings.

This shading is accomplished by inking the circle first with regular width of line; then with the same radius remove the point of compasses from the _true center_, placing it outside, according to the desired position of the shaded line, and describe an arc of a circle.

In fig. 250 divide center line as before; with the 45° triangle or set square, draw through the center the diagonals shown by dotted lines; and through the points _A_, _B_, _C_, etc., draw the perpendiculars, cutting the diagonals; from the points of intersection draw the horizontal lines, completing the squares.

Now, take a radius of half an inch, and in the corner of each square draw with the bow-pencil a circular arc meeting the pencil lines exactly; with the bow-pen _ink in the arcs_ first, then ink carefully the lines joining with the arcs; all lines must be of the same width; put in the shade on arcs and lines as in fig. 249; and, finally, erase the pencil lines at corners, etc.

Section-Lining.

Cross-hatching has been defined in the “preliminary definitions” to drawing; this term represents the practice of drawing diagonal lines representing the interior of an object, shown as a piece cut in half or when a piece is broken away. This is done to make more of the parts show, or to exhibit more clearly the nature of the materials; hence section lining and cross-hatching tell the same thing, _i. e._, the drawing of diagonal lines, usually at an angle of 45°, to show that the object is broken away and the interior designed to be represented.

Fig. 251.]

Fig. 252.]

Fig. 253.]

Fig. 254.]

Fig. 255.]

Fig. 256.]

Fig. 257.]

Fig. 258.]

Figs. 251 to 258, inclusive, show the section lining and cross-hatching by which it is customary to represent the various materials entering into a construction.

In fig. 259 is outlined a representation of a section of a cog-wheel; section 1 being the wood cogs; 2, the iron wheel, and 3 the wedges at the root of the gear. It would be impossible to convey the same ideas by ordinary plan or elevation drawing; all the objects on the same page are more clearly represented by the use of section lines or cross-hatching.

Sectioning is executed by drawing a series of parallel lines about ³⁄₃₂ inches apart. Lay the 45° triangle on the upper edge of the T-square and draw the top-most line of the sectioning. Then slide the triangle along the T-square for each successive line. The sectioning should be inked in without previous penciling and the lines should be finer than the lines of the general drawing.

Various devices are in use for mechanically equalizing the distances in section lining, but the trained eye is the most practical method. When two abutting pieces are sectioned, the section lining on one piece slants in an opposite direction to that on the other.

To draw an object to be sectioned on both sides of its center line, only one side is sectioned, while the other side is drawn in full.

Sections are necessary in nearly all machine drawings; they are usually taken horizontally or vertically, but they may be taken in any direction; the position of a section should be shown by a line upon the object; this line is called the cutting plane.

In fig. 261 is shown the hub of a wheel, it is also a sample of work for practice.

Fig. 260 shows the mode of representing two different materials in one plane, or a section may be represented by the darker portion, and the lighter shaded portion being a surface resting on the section.

Fig. 261 shows the section of a shaft surrounded by the surface of a wheel.

TINTS AND COLORS.

For special purposes of illustration drawings are made which must be tinted. In such cases the paper must be expanded and stretched evenly all over its surface; otherwise when the moist tint is applied the paper will wrinkle and get out of shape; to do this cut the paper at least half an inch less in size than the drawing board; lay the paper face down, turn up a margin or edge of about three-fourths of an inch all round, then dampen the paper with a sponge and clean water; allow it to soak for a few minutes until it is evenly dampened or moistened all over, turn the paper upside down (face up).

Apply strong paste to the under side of the margin all round; rub down, on the drawing-board, working from the center of the board outwards so as to exclude the air and prevent creases or furrows. The board is then inclined and left to dry slowly; make sure that the paper is all well pasted and every part of the edges attached to the board.

If tracings are required to be tinted or shaded, the color may be applied before the tracing is cut off, or what is more usual, the color may be applied on the back of the tracing; then there is no liability to wash out the lines.

Mechanical drawings are seldom tinted, but are mainly produced in India ink. Where, however, a fine effect is desired, working drawings are colored, so as to show at a glance the material of which the different parts are to be made.

The colors required are few but should be of the best quality. Besides India ink the following water-colors are generally used:

1, Neutral-tint. 2, Prussian Blue. 3, Chrome Yellow. 4, Gamboge. 5, Raw Sienna. 6, Carmine. 7, Vermillion. 8, Venetian Red. 9, Sepia. 10, Indigo. These come in hard cakes.

Certain colors and tints represent different metals and materials as follows:

Wrought Iron--Prussian Blue.

Steel--Carmine and Prussian Blue, mixed to give a purple shade.

Steel Casting--Same as the above darkened by Venetian Red.

Cast-Iron--Neutral Tint made of India Ink, indigo, mixed with a little carmine.

Brass--Gamboge or Chrome Yellow.

Babbitt--Emerald Green; sometimes light mixture of India Ink.

Copper--Purple Lake.

It is sometimes found necessary to prepare a highly finished and shaded drawing of the work in hand. Such elaborations, in fact, are much admired by the uninitiated, although the complete shading of the drawing is no criterion as to the scientific value of the machine. An illustration of this is told in the note.

NOTE.--A consulting engineer had to lay before a board of directors
plans of horizontal engines for their consideration. One of these
drawings was of a very superior machine, but being only depicted
lineally was at once rejected by them, for a highly finished
representation of a very inferior apparatus. The engineer, wishing to
induce the board to decide for the best, suggested that the matter
should be postponed to a future day, and in the meantime had the
drawing of the superior machine highly colored and finished. At the
next meeting the directors unanimously decided that this was the very
one which they preferred and had chosen.

Reproducing Drawings.

When once finished, one or more copies of drawings are frequently required; these are produced, 1, by blue printing, as described before; 2, by tracing. A tracing is a mechanical copy of a design or drawing, made by reproducing its lines as seen through a transparent medium--as tracing-cloth or tracing-paper.

Tracing-cloth is a thin linen fabric, coated with size; this is called _tracing-lines_; _tracing-paper_ is so prepared as to be transparent, so that it will receive marks either in pencil or with pen and ink.

Tracing-cloth must be fastened to the board, over the drawing, by pins or other tacks; moisture or dampness should be carefully avoided and the drawing done on the smooth side of the cloth.

When tracing cloth will not take ink readily a small quantity of pounce may be applied to the surface of the cloth and distributed evenly with a piece of cotton waste, chamois, or similar material, but the pounce should be thoroughly removed--by washing--before applying the ink.

In making tracings the same order is followed as described under the section “Inking”--to repeat: 1, ink in the small circles and curves; 2, ink in the larger circles and curves; 3, then all the horizontal lines, beginning at the top of the drawing and working downward; 4, next ink in all the vertical lines, commencing at the left and moving back to the right; 5, draw in the oblique lines; 6, all the center lines red (carmine), and dimension and reference lines in blue (Prussian blue) or _vice versa_. The figuring and lettering should always be done with India ink, thoroughly black.

BLUE PRINTING.

Copies of drawings or parts representing details and measurements are frequently needed for the office, pattern shop, machine and blacksmith shop, etc. These copies are best made by printing on sensitized or specially prepared paper, from tracings drawn on transparent cloth or paper, as hereabove described. The original design may be guarded with the utmost care for long preservation, but the blue prints, so called, are for ready reference and use without much regard to the length of time they are to be in existence.

The usual practice is to carefully trace from the drawing on transparent cloth or paper an exact reproduction of it, filling in all detail lettering and sizes or figured dimensions.

This tracing is fixed in a frame similar to a picture frame, with the side on which the drawing is made next to the glass: 1, place the sensitized side of the paper (which has been prepared previously) against the back of the tracing; 2, fix soft padding against the back of the paper and fasten it up so that both paper and tracing are compressed firmly against the glass, permitting no creases or air spaces between them.

This should be done in a darkened room; 3, expose for three to six minutes, according to the intensity of the sun; 4, take the sensitized paper out of the frame and quickly wash well in clean running cool water, and the drawing will appear in white lines on blue ground; 5, hang the print up by one edge so that the water will run off and the print will soon dry and be ready for use.

TEST-PIECES.

To make good blueprints, being guided only by the appearance of the exposed edge of sensitized paper, requires considerable experience. Very often, especially on a cloudy day, the edge looks just about right, but when taken out of the frame and given a rinsing, it is only to find that the print looks pale because it should have been allowed to remain exposed for a longer period.

Now simply take a small test-piece of the same paper (say about 4 inches square) and a piece of tracing cloth with several lines on its surface and lay these small pieces out at the same time the real print is being exposed, and cover these samples with a piece of glass about 4 inches square. As a general rule, we can find a place on top of the frame for the testing-piece, and by having a small dish of water at hand for testing the print by tearing off a small bit and washing same to note its appearance, the novice can get just as good results as the experienced hand without danger of failure.

BLACK PROCESS COPYING.

This is accomplished by specially sensitized paper by which a fac-simile of the original drawing can be made; that is, black lines upon white ground. It also avoids the objection to the blue print paper of shaded drawings which show light and shade reversed.

The prints made by the process are said to be absolutely permanent and can be altered, added to or colored the same as original drawings.

The sensitized paper is sold ready for use, but it can be prepared by dissolving two ounces of citrate of iron and ammonium in eight ounces of soft water; keep in a dark bottle, also, one and one-third ounces of red prussiate of potash in eight ounces of water; keep in another dark bottle; when about to use mix an equal quantity of each in a cup and apply in a dark room with a soft brush or sponge to one side of white rag paper, similar to envelope paper, let it dry and put away in a dark place until required for use.

Drawing Office Rules.[1]

[1] NOTE.--A. W. Robinson, M.E., Montreal, must have all credit for
these admirable rules and regulations. They bring into a single focus
the whole science and art of mechanical drawing.

There are drawing offices where from ten to nearly one hundred people
are busily employed in making new plans and sketches by the hundreds,
and where thousands of completed drawings are filed for reference or
for changes, as these are needed in the shop management.

To be introduced for the first time into such a company is a trial for
the “new man” both of nerve and manners, and a test as well of skill;
nothing helps more at such a time than an acquaintance with the rules
and routine of the office, for the old saying holds good in a drawing
office, of “doing in Rome as the Romans do.” The author of this book
has felt this strangeness in a new position and so adds the following
model-rules for the guidance of the student when first entering a
regular position in an office where many are employed and where
success depends upon a systematic ordering of the work in hand.

SIZE OF DRAWINGS.

1. The standard size shall be 23 inches by 36 inches, subdivided into half, quarter and eighth sheets.

2. Full-size drawings shall be reserved, as far as possible, for general views and parts not capable of being shown on smaller sheets.

3. All shop detail shall, as far as possible, be shown on quarter and eighth sheets.

CHARACTER OF DRAWINGS.

4. Detail drawings shall, as far as possible, classify the different kinds of works, such as castings, forgings, shafts, levers, piping, etc. Different kinds of work shall not be shown on the same detail drawing.

5. All shop drawings liable to repetition shall be traced and blue-printed. All temporary details, requiring only one copy, may be made on sketch sheets and press copied.

6. A shop drawing is to be considered as an order or instruction to the shop, and not merely as a statement or illustration. For this purpose it must convey clearly and distinctly all the information necessary to make the article.

7. Every dimension necessary to the execution of the work is to be clearly stated by figures on the drawing, so that no measurements need to be taken in the shop by scale. All measurements to be given with reference to the base or starting point from which the work should be laid out, and also with reference to center lines.

8. All figured dimensions on drawings to be plain, round vertical figures, not less than one-eighth inch high, and formed by a line of uniform width and sufficiently heavy to insure printing well. No thin, sloping, or doubtful figures, or diagonal-barred fractions will be tolerated. All figured dimensions below two feet to be expressed in inches.

9. All center lines to be alternate dot and dash in fine black line. All dimension lines to be double dot and dash, with a central space for the figure, and of such strength as to show on blue-print more faintly than lines of drawing. Lines of drawing to be bold and clearly defined in proportion to the scale, and may be shade-lined by making the right-hand and bottom lines heavier. No ornamental shading or other “frills” allowed on shop drawings.

10. Every drawing, whether whole or half-sheet, shall have the title, date, scale and number of the sheet stamped in lower right-hand corner, and the quarter and eighth sheets printed on top.

11. The name of the drawing, as given in the title, is invariably to consist of two divisions in one line separated by a hyphen. The first division is to state the general name of the thing or machine, and the second name is to clearly designate the part or parts represented (or if a general view should so state). The wording of titles should be submitted to the chief engineer or head draughtsman for approval.

12. Each drawing shall bear the name of the draughtsman and examiner, the surname being used without initials.

13. Drawings of piping details shall be made in diagram form, using standard symbols.

14. All detail parts for standard or repetition work shall be shown unassembled as far as possible.

DRAWING SYMBOLS.

15. Detail shop drawings should state:

(a) The pattern number of every casting in plain figures of larger size than the dimension figures.

(b) The material of which the parts are made, using symbols as follows: C.I.--Cast iron. W.I.--Wrought iron. M.S.--Machinery steel. H.S.--Hammered steel. Bs.--Brass. Bbt.--Babbitt. Bz.--Bronze. C.R.S.--Cold rolled steel.

Other materials write full name.

(c) Finished surfaces will be indicated by “f” written on the line or surface to be finished. When not so marked it is understood that the part is to be left black or rough. In cases where finish might be presumed but not required, follow the figured dimensions by the word “cast,” if a casting, and “rough,” if a forging.

STANDARDS.

16. The following standards shall be strictly adhered to as given in the tables noted:

(1.) Table of standard diameters of shafting and key seats.

(2.) Table of standard stock sizes of rounds.

(3.) Table of standard stock sizes of flat steel.

(4.) Table of standard clearance fits.

(5.) Table of standard symbols for notation of riveting.

(6.) Table of standard symbols for pipe fittings.

Also such other standards as may be adopted from time to time.

NUMBERING OF DRAWINGS.

17. Drawers and filing cases shall be numbered consecutively. Drawers shall contain 100 sheets each, and filing cases 200 sheets each, and to be fully indexed. Drawings shall be numbered by a number indicating both drawer number and serial number in the drawer--thus, 7,604 is the fourth sheet in drawer 76, etc.

18. Drawing numbers shall be checked off the index as required, and the index posted up in uniform handwriting by the clerk.

19. Standard size drawings shall be kept in drawers and quarter and eighth sheets in filing cases. All drawings shall be indexed by an index sheet kept in each drawer or case.

CHECKING.

20. All drawings must be approved before being traced. When tracing is completed it will be given immediately to the chief draughtsman, who will have a preliminary print made and carefully checked, before being used.

PATTERNS.

21. All patterns shall bear the number of the drawing on which they are first detailed, followed by a serial letter, according to the number of patterns on the drawing.

22. Standard patterns used repeatedly and liable to be ordered from in repairs must not be changed. Other patterns may only be changed when absolutely necessary and by order. When so changed they will bear the original number and letter, followed by A for the first change, B for the second change, and so on thus: 4860 AB is the second change in pattern 4860 A.

SKETCH BOOKS.

23. Each draughtsman will be supplied with a sketch book by the company, in which he shall make all his notes, calculations and data referring to his work, and under no circumstances shall notes of value be made on loose sheets. Each entry should invariably be commenced with the subject and date, and full notes made of data on which the calculations were based, and the results obtained clearly stated. These books are to remain the property of the company.

IN GENERAL.

24. Changes in drawings, sketches or order lists issued to the shop shall only be made when authorized by the chief engineer, or, in his absence, by the chief draughtsman, and when so authorized shall be made by the order clerk.

25. The names of all similar parts in order lists and drawings are to be uniform.

26. Tracings must be kept in safe, for blue-printing purposes only. Office copies of blue-prints must be used for references.

27. No drawing, print or photograph shall be taken from office without permission.

NUMBERING WORKING DRAWINGS.

There are a great many different systems used in indexing drawings, most of which have some good points, but very few are sufficiently elastic to cover a wide field. A plan based upon the decimal system of notation is very simple, and, as there is no practical limit to the number of subdivisions, it can be expanded indefinitely. Following are the main outline features of the system as adapted to the needs of drawing offices belonging to large works.

The main division numbers, 000, 100, 200, 300, etc., are used respectively for all plans and general sheets referring to the division concerned. 100 includes general plans covering more than one department, and all small-scale plans with cross references to departments covered.

The class or tens divisions contain general drawings of the subdivisions, the subclasses or units divisions being limited to details only. Further subdivisions would probably be necessary in some cases. A card index with cross references and written by someone who knew what to do is an essential part of the system.

Gearing.

Under this heading the author has grouped some information relating to
a subject of wide interest and one sure to interest a student of
mechanical drawing.

The diagrams are intended for exercises in drawing, _i. e._, to be
redrawn as parts of practice; the text is to be studied not only for
the good to be gained from the study of gearing, but as an example of
the way in which written or printed descriptions are necessary to
explain a subject illustrated by drawings.

_A gear_ is primarily a toothed wheel; gearing is a train of toothed wheels for transmitting motions; there are two chief sorts of toothed gearing, viz., spur gearing and bevel gearing.

_A spur wheel_ has teeth around the edge pointing to the center; commencing at the center, a spur wheel may be said to consist of a hole, square, octagonal or round, for its axle or shaft; a hub; the web, body or arms; a rim, and the teeth; see fig. 263.

_A spur wheel_ has teeth on its circumference which run parallel to its shaft; wheels as shown in fig. 271 are termed _helical wheels_; these are similar to spur wheels except their teeth are arranged upon different angles to the shaft.

_A bevel_ is a slant or inclination of a surface from a right line, hence a bevel wheel is one whose teeth stand beveling or at an oblique angle to the shaft, or towards the center; see fig. 267.

_Miter wheels_ are bevel wheels of the same size, working at right angles with one another; see fig. 268.

_The diameter of both spur and bevel wheels_ is measured and calculated neither from the outside nor from the bottom of the teeth, but on the pitch circle. When we speak of the diameter of a spur or bevel wheel, we mean the diameter of the pitch circle, without any reference to the form of tooth.

_The addendum circle_ of a toothed wheel is as shown in illustration, fig. 264; _addendum_ means “something added,” and, as shown in the figure, it is the part added beyond the pitch “line” or circle.

_The pitch line_ is the most important one in gearing; the “pitch line” or “pitch circle” is supposed to be the working circle. This is shown in P--P in fig. 274.

_The periphery_ of a wheel is the extreme circumference, as N in fig. 274.

All parts of gear-wheels consist of portions, to which have been given generally accepted names. Fig. 264 shows the “addendum circle” and the “pitch line” as marked. The teeth and rim are shown in white, and the other portions are indicated by the names.

_The circular pitch line_, as opposed to the diametral pitch, is the same as the pitch circle. It is a line which bisects all the teeth of a toothed wheel.

_The rolling circle_ is the same as the circular pitch line.

_Diametral_ means pertaining to a diameter or the length of a diameter; hence a diametral pitch is a system of measures or enumeration based upon the diameter instead of the circular pitch line; it is used very generally in spacing for fine tooth gear. Wheels of this description usually have their teeth cut in a gear-cutting machine, _i. e._, medium and fine tooth gears.

_A cog wheel_ is the general name for any wheel which has a number of cogs placed around its circumference.

When the teeth of a wheel are made of the same material and formed of the same piece as the body of the wheel, they are called _teeth_; when they are made of wood or some other material and fixed to the circumference of the wheel, they are called _cogs_; see fig. 265.

_A pinion_ is a small wheel. When two toothed wheels act upon one another, the smaller is generally called the pinion. The terms _trundle_ and _lantern_ are applied to small wheels having cylindrical bars instead of teeth. The teeth in pinions are sometimes termed _leaves_; in a trundle, _staves_. See fig. 273.

The wheel which acts is called a _leader_ or _driver_; and the wheel which is acted upon by the former is called a _follower_ or the _driven_. When a screw or _worm_ revolves in the teeth of a wheel, the latter is termed a _worm wheel_ or _worm gear_; see fig. 270. When a pinion acts with a rack having teeth, we speak of _rack_ and pinion. When the teeth are on the inside of the rim, and not on the periphery, the wheel is termed an _internal gear_; see fig. 272.

Two wheels acting upon one another in the same plane are called _spur gear_; the teeth are parallel with the axis. When wheels act at an angle, they are called _bevel gear_.

_Friction gear-wheels_ are those which communicate motion one to the other by the simple contact of their surfaces.

In frictional gearing the wheels are toothless and one wheel drives the other by means of the friction between the two surfaces which are pressed together.

Grooved friction wheels are used to give greater cohesion than can be obtained by the plain surface.

Fig. 263 shows a pair of spur-wheels in gear. The dotted circles which meet are the rolling circles, called the “pitch line” or “pitch circle.”

A spur mortise wheel is similarly shown in fig. 266; it is very like in appearance to a spur wheel; it differs essentially in that the teeth are separate cogs, fixed in singly to the rim; see also fig. 265, page 201.

NOTE.--The teeth of spur wheels cast from a pattern must of necessity
be larger at one side than at the other, because the teeth must have
taper to permit the extraction of the pattern from the mould;
therefore, in fixing wheels to gear, the large side of one should meet
the smaller side of the other; should the two large sides come
together the teeth will meet only at the large side, and the teeth
will probably break away from the excessive strain on that point.

_Skew gearing_ are bevel wheels working out of center; the teeth do not form radial lines from the wheel center.

Fig. 267 shows a pair of bevel wheels in gear as described on page 199. A bevel mortise wheel, _i. e._, one having cogs inserted in its rim instead of teeth.

A bevel wheel and pinion must be made to suit one another by both having teeth forming together an angle of 90°, therefore they are pairs, or proportioned in the number of teeth one to the other. Any other proportion used would not exactly gear and would be termed a “bastard” gear.

Fig. 268 represents a pair of miter wheels in gear; it will be noted that the shafts, when connected, will be at right angles to each other, the wheels being in all particulars of the same dimensions; the figure answers the purpose of a much longer description, if given in words.

A miter-wheel can easily be known by putting a square upon the face of the teeth, which are always at an angle of 45° with one another, irrespective of size.

_A miter-wheel_ is a particular kind of bevel-wheel, the bevel being limited to an angle of 45° in each wheel.

The curve of the teeth in bevel-gears, when correctly formed, changes constantly from one end of the tooth to the other, therefore bevel-gears whose teeth are produced with a forced cutter are not theoretically correct.

Fig. 269 represents a rack and pinion: the teeth in this form of gear are shaped similarly to those in the spur wheel, shown on page 198, with the difference that the teeth of one are on a circle and on the rack are made on a straight line.

A flange or addition to the end of a tooth and the rim connecting them together is used to strengthen the teeth. This extends from the root to pitch line when the wheel and pinion are both flanged: if only one is flanged it extends from the root to the addendum.

Fig. 270 illustrates a worm and a worm wheel, sometimes called screw gears. This is a slow but powerful method of transmitting power, one revolution of the worm only moving the wheel the distance of one tooth and space.

_A worm gear_ is a spur wheel with teeth at an angle to the axis, so as to work with a worm which is a _screw_, or has teeth shaped in the form of a spiral wound round its circumference; the screw or worm is called an endless screw, because it never comes to a stopping place in the circumference of the wheel.

Fig. 271 represents a gear with helical teeth. It is similar to a spur wheel, and is used in place of same in heavy and slow moving machinery, the formation of teeth preventing--in large measure--the jar or concussion noticeable in common spur gears.

In recent years the speed at which gearing is run has been greatly increased. A striking instance is that of a pair of _cast-iron_ helical wheels, 6 ft. 3 in. diameter, 12 in. wide, making 220 revolutions per minute, the speed of the pitch line being 4,319 feet per minute; these wheels are running continuously and with little noise. There is also a _cut_ gear in a mill in Massachusetts, 30 feet in diameter, and the speed of pitch line is 4,670 feet per minute.

_An internal or annular gear wheel_ is one in which the faces of the teeth are within and the flank without the pitch circle, hence the pinion operates within the wheel. See fig. 272.

In internal geared wheels there is almost an entire absence of friction and consequent wear of the teeth, as compared to ordinary spur gearing.

Fig. 273 shows a _crown-wheel_ which has pin teeth which are fixed by one end only, on its side face and gear into a trundle wheel.

_A trundle wheel_ has no teeth, properly speaking. Instead of teeth, it has pins as shown on illustration, fig. 273, arranged like the rungs of a ladder between two walls. See page 201.

_Trains of Gears._--When two wheels mesh--that is, engage with each other--as in fig. 263, one axle revolves in the opposite direction to the other; but when internal gears mesh as shown in fig. 272, the shafts revolve in the same direction; three or more gears running together are often called _a train of gears_.

Maximum speed of gears under favorable conditions for safety is comparatively--

Ordinary cast-iron wheels, 1,800 feet per minute.
Helical cast-iron wheels, 2,400 feet per minute.
Mortise wood cog wheels, 2,400 feet per minute.
Ordinary cast-steel wheels, 2,600 feet per minute.
Helical cast-steel wheels, 3,000 feet per minute.
Cast-iron machine cut wheels, 3,000 feet per minute.

It is not, however, advisable to run gears at their maximum speeds, as great noise and vibration are caused.

Designing Gears.

This section is introduced into the work for a double purpose; 1, as
an exercise in drawing; 2, as a study in accurate measurements. It is
a sample of the work that the advanced student in mechanical drawing
will be confronted with as he puts in practice the theory of the art
of drawing.

Some sample rules are given in the following pages to aid in
calculations relating to gears, and still others are given under the
section “Useful Rules and Tables” at the end of the volume; these are
to be carefully studied.

To accurately divide the pitch circle of a gear wheel by hand requires both patience and skill. On the accuracy of spacing lies the essential requisite of a good gear wheel.

The drawing in plate, fig. 274, illustrates a pair of spur wheels, shown in gear, the office instructions for which being:

“Required, _a detail plan_ of a pair of spur wheels; dimensions: wheel, 76 teeth, 3¹⁄₂ inches pitch, 7-inch eye, 6 arms; pinion, 19 teeth; scale, 1¹⁄₂ inches = 1 foot.”

The drawing, as illustrated, is the result of the above instructions, all pencil lines being removed, and this result is worked out as follows:

76 teeth × 3¹⁄₂ inches, pitch = 266 inches in circum. = 7 ft. 0¹¹⁄₁₆ in. diam. = 3 ft. 6¹¹⁄₃₂ in. radius; with this measurement as represented on scale, draw line _P P_ on drawing. This is called the pitch line.

Draw next diameter line, produce or extend this diameter line for pinion, and with radius of 10¹⁹⁄₃₂ (19 teeth × 3¹⁄₂) from pitch line of wheel, draw pitch line of pinion.

Take any point in this pitch line of wheel, mark off 3¹⁄₂ inches as represented on scale, mark this around the pitch line, it will be the center of each of the 76 teeth; then the breadth of thickness of each tooth (= pitch × 0.475) must be marked from these centers, then mark from _P L_, length of tooth to point (= pitch × 0.35) and _P L_ to root (= pitch × 0.4), draw circles for outside of teeth _N_ and root of tooth _O_; now with compass set to the pitch (3¹⁄₂) of the wheel, draw the outer portion from pitch line of tooth.

The radius will center in the pitch line of next tooth where thickness of tooth has been marked; after finishing outer portion of both sides of teeth, set the compass from _center_ of tooth with radius to the thickness marked on pitch line and draw the portion of tooth from pitch line to root.

Now mark off with dividers and draw thickness of rim (= pitch × 0.5), divide this line into six parts, draw radii for centers of arms; draw the bore hole 7″ and the thickness of metal for hub same as pitch.

On radii lines of arms, draw the breadth of arm at rim (= pitch and thickness of tooth), increase in breadth approaching the center (1″ per foot), draw the thickness of feather of arm (= pitch × 0.35); draw web on inside of rim (= pitch × 0.375); fill in arcs for the joining of arms in rim and hub (radii = pitch × 0.8) and feather to rim and hub (radii = pitch × 0.37).

Proceed in similar manner, completing the teeth of pinion, and when pencil lines are all in, ink the drawing, erasing all needless lines.

_P P_ shows the pitch line; _B_, thickness of tooth; _c_, breadth of space; _A_, the pitch; _E_, clearance at root; _N_, the addendum of tooth; _O_, the root of tooth; _H_, length of tooth from pitch line to point; _I_, length of tooth pitch line to root; _G_, whole length of tooth; _F_, thickness of rim; _J_, web or feather on rim; _K_, breadth of arm; _L_, thickness of feather; _M_, hub, or thickness round the eye.

NOTE.--It must be remembered that no fixed standard has ever been
agreed upon for these proportions, and workshops differ considerably
in practice.

The number of teeth, their proportions, pitch and diameter of pitch circle are frequently determined on the “Manchester” principle. This system originated in Manchester (Eng.), and is now generally used in the United States for determining diameters and number of teeth, which, of course, regulate speeds. The principle is not applicable to large wheels, but is limited in its application to small wheels, or wheels having “fine pitch,” as will be seen in the following explanation, which is introduced as very useful and indispensable knowledge for the acquisition of the student in mechanical drawing.

The “pitch” of teeth has already been stated to be the distance from center of one tooth to the center of another on the “pitch line,” measured on the chord of the arc. In determining the number of teeth or pitch of wheels on this principle, the pitch is reckoned on the _diameter_ of the wheel, _in place of the circumference_, and distinguished as wheels of “4 pitch,” “6 pitch,” “8 pitch,” etc. In other words, this means that there are four, six, or eight teeth in the circumference of the wheel for every inch of diameter.

In designing gears to transmit power the stress on a tooth is calculated; it determines the breadth or width and also the thickness of the tooth on pitch line; the space between the teeth is in proportion to the thickness of tooth, and the thickness of both combined (one tooth and one space), measured on the pitch line or circle, is the pitch of the wheel.

From the pitch all the proportions and measurements for the sizes and strength of the parts of the wheel are taken _by rule_, and a symmetrical form is produced.

In machine drawing the practice is to represent wheels by circles only; the teeth are never shown except on enlarged details and then only in very rare instances; the circles drawn are always the _pitch lines_ or the rolling points of contact of the wheels.

The addendum circle is seldom if ever used in practical drawing. Should it be necessary to show it in an exceptional case, the circle would be represented by “dotted” line.

The shape of tooth and mode of constructing it, as practiced in drawing offices, differs from the true theoretical curve of the tooth, although very minutely.

In all calculations for the speed of toothed gears the estimates are based upon the pitch line, the latter standing in the same place as the circumference of a pulley.

To find the _diameter of a gear-wheel_ multiply the number of teeth by the pitch, divide by 3.1416.

To find the _pitch of a gear-wheel_ multiply the diameter by 3.1416 and divide by the number of teeth.

To find the _number of teeth in a gear-wheel_ multiply the diameter by 3.1416 and divide by the pitch.

The _breadth of wheels_, where practicable, should be at least three times the pitch.

Fig. 276 shows a scale for proportions of teeth; it is divided into tenths and used thus:

Say wheel is 2″ pitch, then from pitch circle to addendum will be 3¹⁄₂ tenths, and from pitch circle to root of tooth will be 4 tenths measured at the 2″ line on scale, and so on.

The decimal proportions already given in example, page 210, are adopted in many workshops. Many others use the proportions approved of by Sir William Fairbairn, which are:

Table of proportion of gears:

Depth of tooth above pitch line .35 of the pitch.
Depth of tooth below pitch line .40 of the pitch.
Working depth of tooth .70 of the pitch.
Total depth of tooth .75 of the pitch.
Clearance at root .05 of the pitch.
Thickness of tooth .45 of the pitch.
Width of space .55 of the pitch.

The diameter of a wheel or pinion is invariably the diameter measured on pitch circle, except it is specially described otherwise, thus the diameter “over all,” etc.

The shape of the curved face of the teeth of gears extending from the root to the addendum is the curve conforming to the passage of the teeth described on its fellow entering and leaving, as they rotate or roll together on their pitch circles.

The curve of teeth outside the pitch circle is called “the face,” and the curve from pitch circle to root is called “the flank.”

The difference between the width of a space and the thickness of a tooth is called clearance or side clearance.

The play or movement permitted by clearance is called the backlash; clearance is necessary to prevent the teeth of one wheel becoming locked in the spaces of the other.

Wheels are in gear or geared together when their pitch lines engage, _i. e._, when the pitch circles meet.

Wheels to be geared together must have their teeth spaced the same distance apart, or in other words, of the same pitch.

The teeth of spur wheels are arranged on its periphery parallel to the wheel axis, or shaft on which it is hung.

The teeth of a bevel wheel or bevel gears are always arranged at an angle to the shaft.

When the _teeth_ of bevel gears form an angle of 45° they are called miter wheels.

Miter wheels to gear must be of equal sizes.

A crown wheel is a disc that has teeth which are on its side face; that is, teeth on a flat circular surface all parallel to the axis of the wheel.

A rack has teeth on a flat surface or plane all parallel to one another.

A gear cut by machine is called a _cut gear_. It has teeth with less clearance than cast wheels, which are not so true or perfect, and therefore require more clearance.

A worm with even a light load is liable to heat and cut if run at over 300 feet of rubbing surface travel. The wheel teeth will keep cool, as they form part of a large radiating surface; the worm itself is so small that its heat is dissipated slowly.

A worm throws a severe end thrust or strain on its shaft.

_Steel Gears._--There is great economy in the use of cast-steel over cast-iron in gears; the average life of the former is nearly twice as great as of cast-iron gears. And, apart from their longer life and efficiency, there is less danger of breaking.

The most accurate teeth, strongest and most uniform in wearing, are to be found in steel gears cut from solid stock, or made by cutters of proper shape.

Fig. 275 shows an elevation and a vertical section of a spur wheel. From these views the various parts in spur gears can be better understood, as they are represented here in combination, and the wheel in its entirety.

_AA_ is the horizontal center line, _BB_, _BB_ the vertical center lines, _II_ and _II_ the pitch lines, _N_ thickness of tooth, _O_ space of tooth, _D_ total depth of tooth, _C_ breadth of face, _F_ diameter on pitch line, _P_ diameter over all, _G_ diameter of hub, _E_ diameter of hole, _H_ depth of hole, _L_ thickness of rim, _M_ thickness of web.

Much has been and still is being written on gearing. No general rule is followed by the writers; the elementary principles given will enable the student to master spur gearing, and bevel and combinations of many kinds of wheels will afterwards be found easier to delineate than the numerous lines seem to indicate.

Working Drawings.

From the “plans” made in the office are produced “working
drawings”--which represent in detail the work to be done to exact
measurement and of material, as indicated, by the pattern-maker, the
foundry, the forge, the shop, and finally, by the erector of the
completed mechanism.

How to satisfactorily fulfill the directions contained in these
drawings, representing only a part of the work, so that it will fit,
with needed accuracy, to all other parts of the design, is the task
before each separate worker.

It is by means of this division of the process of manufacture through these drawings, that scores and hundreds of men can be employed at the same time upon a single engine or machine; thus, while handwork has been superseded by machines in many quarters, the art of drawing has not been narrowed nor diminished, for no drawings or designs have yet been made by machinery, nor are they likely to be.

It is thus that a good designer and draughtsman “projects” or extends himself, to the advantage of many fellow workers.

The drawing, fig. 277, shows a simple form of pillar crane: it consists of an upright cast-iron pillar, which is bolted on a cap stone, under which is the foundation plate not shown in the drawing; the boom is of rolled steel, supported by steel tie rods, and provided with rollers at the base; the hoisting gear is shown in broken lines and circles; all as seen in the drawing.

Figs. 278, 279 and 280 show a drawing of a “hydraulic beam bending machine” in three views; fig. 280 is a plan, fig. 278 is an end elevation, and fig. 279 a side elevation, and a portion of the latter in section shows the interior construction.

NOTE.--These three views are a practical illustration of drawings for
a machine of the following dimensions: this machine has a bed 3 × 5
feet in area, with 27 holes in each side for the bending pins. The
frame and cylinders are made of cast iron, the rams of machinery
steel, and the slides for holding the bending blocks, of steel
casting. The distance between the bending blocks is 17 inches. The
cylinders are copper lined, 8 inches diameter, and the rams have a
6-inch stroke. The rams, which are independent and single acting, are
returned by counterweights placed as shown under the table. The
cylinders can be operated independently from either side of the
machine by an arrangement of valves and levers. The machine complete
weighs about 7,500 lbs.

The drawing, page 222, shows three views of a power punching press.

Fig. 282 is a side elevation.

Fig. 283 a front elevation.

Fig. 281 a vertical sectional view; from these views the proportion, general arrangement and disposition of the automatic devices can be easily understood; it may be well to call particular attention to the automatic clutch on the top shaft and the tripping device.

This drawing, fig. 284, shows a side elevation in section of a self-adjusting piston-rod packing.

_A_ is the gland, _B_ is the piston rod, _C_ is a brass sleeve which contains the packing _D_, _E_ is the cylinder cover, _F_ is a coil spring. It will be seen that the spring _F_ abuts on a bushing in the bottom of the stuffing box and is prevented from scoring the piston rod by stepping over the ends of the bushing and follower. All as shown in the drawing.

The drawing, fig. 285, shows a sectional view of a large pulley fixed on a “quill,” or hollow shaft: the driving shaft passes through the hollow shaft and is attached to the friction clutch shown at the right-hand end; this friction clutch drives the hollow shaft and pulley.

Fig. 286 shows the mechanism, called the link-motion, employed to
reverse an engine, or to enable it to be run in either direction. Many
forms of link-motion have been devised, but the Stephenson form, as
shown in the figure, is, however, the one in almost universal use.

This drawing shows shading and the mode of figuring the parts for identification.]

Figs. 287 to 289 represent a bumping-post for the end of railway tracks, reproduced on an enlarged scale from the columns of the _Engineering News_.

In addition to the lettering and dimensions, admirably shown in the drawings, the following description is appended to show how printed text and mechanical drawings mutually aid in practical--or commercial--usage.

The unique feature of the arrangement shown, is that the center line of the post does not coincide with the track, thus adapting itself to the nature of the blows of a car-bumper, as received in the single-post style of the mechanism.

BUMPING POST FOR RAILWAY TRACKS.

The post is a 15-in. steel I-beam, resting on a base plate ³⁄₄-in. thick, and supported by anchor rods 1³⁄₄ ins. diameter, with upset ends held by nuts on a heavy forging bolted to the top of the post. These rods extend forward and outward to clear the rails, and then pass vertically through a 4 × 6-in. angle iron crosstie, and an ordinary wooden tie, extending down to an anchor block or deadman buried in the ground 6¹⁄₂ ft. below the top of the rail.

Vertical braces or spreaders are fitted between the anchor timber and a longitudinal timber under the ties, so as to prevent the loosening of the anchor rods when the post is struck. The rods are held in position against the rails by steel forgings bolted to the rail with 1-in. turned bolts. An oak striking block, 12 × 12 ins., 3 ft. long, is bolted between angle iron brackets on the face of the post.

Front View.

Fig. 291.

Side View.

Scale, 3 in. = 1 ft.]

To Read Working Drawings.

One of the advantages resulting from a knowledge of practical
draughting is, that it enables a mechanic to _read_ a drawing when
given him as a guide for his work. It is getting every day more
general among draughtsmen to figure exactly and minutely every part of
their drawings which are made to a scale.

Drawings are almost always made “finished size,” that is, the dimensions are for the work when it is completed. Consequently all the figures written on the different parts indicate the exact size of the work when finished, without any regard to the size of the drawing itself, which may be made to any reduced and convenient scale.

Even in full size drawings this system of figuring is not objectionable. It is a system which should be followed whenever a drawing is made “to work to,” for it allows the workman to comprehend at a glance the size of his work and the pieces he has to get made. Figuring makes a drawing comprehensible even to those who cannot make drawings.

A working drawing should be made, primarily, as plain as possible by the draughtsman; second, the workman should patiently and carefully study it, so that it is thoroughly understood.

In studying a drawing, the object it is intended to represent should be made as familiar as possible to the mind of the student, so that he may fill out in imagination the parts designedly left incomplete--as in a gear wheel where only two or three teeth are drawn in, that he may see, mentally, the whole.

The following is a description of reading drawings when dimensions are not figured. Here we have a piece of machinery represented by fig. 290, and the information we have is that it is to scale, three inches = one foot. Now, with scale and dividers, we can arrive at its actual dimensions.

Measurements should be first taken _with the dividers from the drawing_, and then the dividers applied to the scale to which the drawing is made; this scale is always marked on the working drawing; if the dividers are set to the length of the base of the example, fig. 290, they will measure, on an ordinary two-foot rule, three and three-fourths inches, _but if applied to the three-inch scale they will read_ one foot three inches, the actual length of the part; the “reading” is from the scale; thus, in both figures the drawings are “three-inch scale.”

Now, 3 inches is one-fourth of a foot, hence 3³⁄₄ × 4 = 1 ft. 3 in., the full size, and so on for all parts of the drawing.

Fig. 291 shows _a side view_ of the “steady rest,” illustrated in front elevation, fig. 290; from the scale as before we get the sizes; the two views combined give length, breadth and thickness of the parts.

In some figures it is necessary to show end views, also section views, to enable all measurements to be read from the drawing.

Patent Office Drawing Rules.

U. S. PATENT OFFICE RULES.

AS APPLIED TO PREPARATION OF DRAWINGS.