MECHANICAL DRAWING PERSPECTIVE. ] APPLIED MECHANICS. 



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of these ends, and that we looked directly down upon it, 

 we should see its plan, which is a hexagon (A, Fig. 17). 



Fig. 17. 



Again, looking directly on the angle formed by the two 

 ides a and 6, we should see the elevation C, showing 

 the two retreating sides a and 6 ; and looking direct on 

 the Hide c, we should see the elevation B, showing the 

 full front view of c, and views also of the two retreating 

 sides 6 and d. The dotted lines represent portions of the 

 suppoaed parallel rays of light proceeding from the angles 

 of the object, and prolonged to form lines, projections, or 

 drawings of the two views, the position of the top and 

 bottom lines f these projections being determined by 

 the height of the prism, which we suppose to be given. 



Let us now suppose that the same prism is to be made 

 with a circular hole passing through its centre from end 

 to end, we may show the same views as before, and in 

 addition to them two sections, as in Fig. 18. 



Fig. 18. 



The lines A A and B B, through which the sections or 

 cuttings are supposed to be made, are marked on the plan, 

 and the sections are formed exactly like the elevations, 

 by tracing the different points of the object where the 

 section lines cut it. We have hatched or drawn diagonal 

 lines across the solid parts which are supposed to have 

 been cut asunder, in order to distinguish them, by a sort 

 of shading, from the open circular part where no solid 

 material is supposed to have been cut through. 



We will now take a somewhat more complicated draw- 

 ing as an illustration for instance, a toothed wheel (Fig. 

 I' 1 /, in front elevation, sectional plan on the line A A, 

 and elevation as seen edgeways, which wo shall call side 

 elevation. 



In this case, as in the former, the dotted lines are 



drawn parallel to each other from the different visible 

 points or edges, and furnish us with the positions of 

 these in the side elevation and plan ; the width of the 

 teeth and thickness of the material being supposed to be 

 known independently. 



Fig. 19. 



Fig. 20. 



PROJECTION OF CURVES. By the same method, 

 drawings of curved surfaces may be made, some consi- 

 deration being given in each case to the mode most suit- 

 able. Let us take for an example a, drawing of a screw . 

 In the first place, we must understand what a screw is. 

 Suppose a cylinder or roller were revolving round its 

 axis, and that while it was so revolving a pencil or sharp 

 point were held against it If the point were at rest 

 while the roller revolved, a simple circle would be de- 

 scribed on the surface of the latter. But suppose that 

 while the roller revolved, the point were made to traverse 

 lengthways along it, then a screw-line would be drawn oil 

 the surface (Fig. 20). 



The pencil having begun to mark the roller at a, and 

 having advanced to 6, while the roller has made one 

 complete turn, the screw line a cb would be marked on 

 its surface. As we could not see both sides of the roller 

 at once, we can only draw the part a c of the screw as 

 visible, the other part c 6 being marked by a dotted line 

 to show that it exists, and would be seen were the roller 

 transparent. The whole line o c 6 would be called a 



thread or com- 

 plete turn of the 

 screw ; and the 

 distance a 6 would 

 be called the 

 pitch, or distance 

 between two ad- 

 jacent threads. It 

 is clear that were 

 the roller to con- 

 tinue to turn, and 

 the pencil to ad- 

 vance, the thread 

 would continue to 

 be marked as far as the surface of the roller might ex- 

 tend. The screw marked in the figure would be techni- 

 cally called a "drunken thread," or be said to be of 

 irregular piich, as the relation between the velocities 

 with which the roller revolved, and the pencil advanced 

 respectively, is not of a fixed or constant character. 



But if, while the roller revolved uniformly or with 

 regular and equal velocity, the pencil also advanced uni- 

 formly, a thread would be traced perfectly regular and 

 equal in all its parts, or a true screw, such as is used in 

 mechanics, would be formed. We will now draw such a 

 screw. Let A (Fig. 21) be the end-view or section of the 

 roller, which is merely a circle, and let B be a side eleva- 

 tion ; a being the position of the pencil when it began to 

 mark the thread, 6 its position after one complete turn, 

 and c its position after two turns ; it is our object to find 

 the shape of the line, or at least its drawing or projection 



\o, 



