MECHANICAL DRAWING PROJECTION. ] APPLIED MECHANICS. 



785 



Fig. 4. 



Fig. 5. 



where only three sides are visible, none of them squares, 

 and no two alike : not a single angle or dimension equal 

 to those in he die itself. And yet the picture may be a 

 perfectly true delineation of the die as it 

 appears to the eye of an observer. Now, if 

 a workman were furnished with such a pic- 

 ture, and required to make a die according 

 to it, he could have no conception of its 

 form and dimensions. For instance, he 

 might cut a piece of plate to the shape of 

 an irregular six-sided figure, with three lines engraved 

 on it, meeting at a point near its middle, and certain 

 dots marked at the distances indicated on the picture. 

 He would then have made a solid body, which, viewed 

 in one direction, would certainly present the appearance 

 of the picture. Even if the picture were shaded, and 

 marked by dotted lines, indicating the invisible edges of 

 the die, as in Fig. 5, he could not, without further in- 

 formation as to its meaning, construct a 

 solid body such as would answer to it. He 

 would have to be told that it was a solid, 

 <iaving six equal flat sides, which, viewed in 

 * certain direction, and at a certain distance 

 from the eye, under light falling upon it at 

 a certain angle, presented the appearance of 

 the picture. He would then either model all conceivable 

 kinds of six equal-sided bodies, and try each in the given 

 or he would work out, geometrically, some other 

 i ies of the body, such as might enable him to con- 

 it. If, on the other hand, instead of having such 

 a perspective picture presented to him, he had a drawing 

 like Fig. 3 placed before him, and were told to make a 

 piece of ivory of such a shape that each of its six sides 

 should be exactly of the form drawn, and either of its 

 dimensions, or of some given multiple or fraction of these 

 dimensions as for instance, for every inch on the 

 drawing, three inches in the die itself he would at 

 once comprehend and execute the work required of him. 

 DRAWING CYLINDERS. In like manner, if a 

 Fig. 6. cylinder, or roller, were pictured as it 

 appears to the eye, with its light and 

 shadow, as in Fig. 6, the workman 

 might guess at its form, but could 

 ascertain nothing as to its dimensions. 

 But if he were told to make a thing 

 of which Fig. 7 is the drawing, one- 

 quarter of the full size, he could at 

 once form his material to its proper 

 diameter and length, by measuring the drawing, and 

 allowing an inch in his work for every quarter of an 

 inch on tho drawing. Fi _ 7 



PROJECTION. The / --. p- ^ _-'- _-.- 

 object of mechanical f >. 



drawing is, therefore, / i I 



not to present a deline- 

 ation of any object as 

 it appears to the eye, 

 but to furnish the exact figures and dimensions of its 



Fig. 8. 



. G 



parts, in such an intelligible manner, that solid materials 

 VOL. i. 



Fig. 9. 



may be fashioned into shapes, whose parts shall have 

 similar forms and proportions. The principle on which 

 mechanical drawing is founded, is that of projection 

 on plane surfaces, which we shall now endeavour to 

 explain. 



Suppose a sheet of paper were cut to the form A B D 

 E C H (Fig. 8), and folded across where marked by the 

 dotted lines H G and H F, the two parts A B G H 

 and C H F E being turned up so as to stand at right 

 angles or square to H G D F, and to one another as in 

 Fig. 9, forming, as it were, three sides of a square box ; 

 then each of these three portions of the paper becomes 



what is called a " plane 

 of projection," for re- 

 IB ceiviug the representa- 

 tion of one of the sides 

 of a solid body placed 

 somewhere within the 

 imaginary box, of which 

 they form the sides. 

 Let us suppose, for in- 

 stance, that a die were 

 suspended within the 

 box (Fig. 10), and that 

 from every point in each 

 of the surfaces of the die exposed to the three sides of 

 the box, lines were supposed to be drawn perpendicular 

 or square to those sides as indicated by the dotted lines ; 

 then the lines joining the intersections of the dotted 

 lines, with the upright and horizontal surfaces, would 

 enclose figures accurately 

 representing, in form and 

 dimensions, the respective 

 sides of the die presented 

 to them. The paper be- 

 ing then unfolded, would 

 contain a mechanical 

 drawing of the die (Fig. 

 11), exhibiting accurately 

 the forms and dimensions 

 of three of its sides. In 

 order to get a drawing of 

 the other three sides, the 

 other sides of the imaginary box might have similar 

 figures projected or thrown upon them. It is evident 

 that whatever be the situation of the die, as to distance 

 from either of three planes of projection, there will be 

 no difference in the drawing ; the form delineated will 

 be the same, though it may appear on a different part of 

 the paper. 



The names usually given to the three drawings of an 



Fig. 11. 



Fig. 10. 



object are these : The projection on the horizontal plane 

 or bottom of the box, is called the plan : and the pro- 

 jections on the vertical planes or upright sides, are called 

 elevations. One of the elevations may be called the side 

 elevation, or side view ; and the other the end elevation, 

 or end view ; while the plan, when projected upwards, 

 or on the top of the box, is sometimes called the bird s- 



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