res 



AIM'LIED MECHANICS. [MBCHANICAL DRAWING SCRKWS. 



on the elevation B, connecting the points a and 6, anil 6 

 and o, respectively. Now recollecting that a regular 

 Flf. 11. 



screw implies that while the roller makes any part of a 

 turn, tho pencil must make an advance through the same 



of its pitch, we will divide the circumference of A 

 into four equal parts by the points d, e, f, g, and also tho 

 two pitches a 6 and 6 c into four equal parts, marked by 

 tli.' points h, k, I, m, n, p. Then we know that while the 

 roller has turned one quarter round, so as to bring the 



of its surface e to the pencil, the pencil itself has 

 moved one quarter of its pitch along, so as to be at the 

 point h. If then we trace a line of projection from e 

 along the elevation, and a line square to it from h, the 

 point e., where these lines cross, must be a point in the 

 projection of the thread. In the same manner, tracing 

 lines from /and </ and from k and I crossing them, we 

 get other points, /, and </, , in the thread ; and repeating 

 the process for the next thread, we get the points e.,, /.,, 

 and Sl similarly situated in it. But though we might) 

 between the points d,, e,, /,, Arc., draw any sort of lines 

 straight or crooked, we should not be warranted in 

 assuming them to be the proper representations of the 

 screw. We can, however, again subdivide the circum- 

 ference of A and the pitch on B, and thus get a number 

 of other points, as indicated in part on Fig. 22, which 

 Fig. 22. 



tical mode of making such a drawing would be to sot out 

 the points of one portion of the curve, such as a o 4 , by 

 tin- method indicated on Fig. 22, to shape a piece of 

 card-board or thin wood to fit it, and then murk- 

 ing out the proper distances a 6, a, &,, ., li.,, b c, 

 6, c,, 6, c., c d, e l d,, c 3 d 3 , <tc., and applying the 

 shaped card to these points successively, trace by a 

 pen or pencil as many repetitions of the curve aa 

 might bo required. By a similar process, inverting 

 the card, the elevation of tho curves as they would 

 appear through tho roller were it transparent, as 

 indicated by the dotted lino in Fig. 23, could be 

 repeated. 



Recurring to Fig. 24, let us now suppose that all that 

 part of the surfaceof the roller contained between the 

 Fig. U. 



double threads were cut down to a certain depth, so as to 

 leave a real solid screw-thread prominent, such as would 

 be produced by winding a square wire obliquely round a 

 cylinder. Our method of drawing this would be as fol- 

 lows (Fig. 25) : The transverse section shows two circles, 

 one the boundary of tho outside of the prominent thread, 

 and the other the roller on which it is wound, or the 

 bottom of the cutting made in the solid roller. Let half 

 of both these circles be divided into any number of equal 

 parts, and let the length o 6, which tho thread tra\v 

 during half a turn, be divided into the same number of 

 equal parts ; then, by drawing tho vertical lines from 

 the points where o 6 is divided, representing the dis- 



Fig. 25. 



must be in the projection of half the screw. A curved 

 line traced through these points, will then be a correct 

 representation of half the thread ; and as the thread is 

 perfectly regular, tho same form of curve will be repeated 

 at the equal intervals of pitch, from d 1 to/,, and d., to 

 / 2 . The intermediate parts of the thread from/, to c/ 2 , 

 and from / 2 to d A , being traced on the side of the roller 

 where y is, cannot be visible at the same time as the 

 other portions : but if they could be seen, as in the case 

 of a transparent roller, they would be symmetrical with 

 the visible parts, but inverted, as indicated by the dotted 

 lines in Fig. 23. 



Next let us suppose that two pencils were held against 

 Fig. 23. 



the roller a little distance apart, so as to trace twoscrew- 

 .'1s parallel with each other ; the side elevation of 

 this, a* in Fig. 24, presents merely a repetition of tho 

 proper curved line* at the proper distance apart that is 

 to say, if any number of straight lines were drawn 

 parallel to tho axis or sides of tho roller, tho portions of 

 thaw straight lines intercepted by the screw-curves, viz. , 

 a b, a, 6,, a x 6,, A-c., also c d, c, d,, c., d. t , A-c., A-c., 

 would be all equal to one another. The ordinary prac- 



tances traversed by the describing point along the roller 

 in equal portions of a half revolution ; and by drawing 

 horizontal lines from tho points into which the half cir- 

 cumferences of the inner and outer circles arc divided, 

 representing the equal portions of the half revolution ; 

 the points, at which these vertical and horizontal lines 

 cross each other, are points in the two screw curves re- 

 spectively. A card shaped to each of these can bo used 

 to repeat them at equal intervals along the roller, so as 

 to represent the continuation of the thread. A little 

 consideration will show what portions of these lines would 

 be visible in a side-view, and what parts would bo con- 

 cealed. It is usual to show, by full lines only, the visible 

 portions, the invisible parts being marked, when neces- 

 sary, by dotted lines. 



( Hher curves can be treated in the same way 

 as screw-curves, the general principle being tho 

 same to all namely, finding tho projection of 

 a number of points through which tho curve 

 must pass, and tracing through those points, a 

 continuous curved lino as nearly as the e\ > 

 judge or the hand execute. The greater the 

 numljcr of points projected, the more nearly accu- 

 rate will bo the drawing of tho curve. But a little practice 

 in drawing, and careful olw.rvation, soon enable a 

 draughtsman to trace projections of curves with suffi- 

 cient accuracy without requiring very many points for 

 their determination. The drawing of a screw-curve, 

 such as we have described, is as dillicult as any of the 

 projections that ordinarily occur in mechanical drawing. 

 Wo have, therefore, dwelt upon it at some length, !> 

 convinced that the student who sees his way cl< 



