Simple Designs for Sheet Metal Working 



X — Radial line development of patterns for cones and parts of cones 

 By Arthur F. Payne 



Forroer Director of Vocational Education, Columbia University 



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MOST of the patterns developed in 

 this series up to the present time 

 have been for objects cylindrical 

 in shape. The majority have been elbows 

 and tees. These cylindrical patterns all 



Cylindrical patterns all belong to the 

 parallel line group. All lines parallel 



belong to the parallel line group, that is 

 all the lines in the drawing are parallel 

 lines as in Fig. 1, which was demonstrated 

 in the June, 1917, issue. 



In Fig. 2, we see the first problem of the 

 group of patterns developed by means of 

 radial lines. The patterns developed 

 by this method are all of objects that are 

 conical in form. In the illustration we 

 have a perspective drawing of a cone, 

 marked A, also a front view marked B, 

 a bottom view marked C, and the pattern 

 for the cone. The three parts of a cone, 

 base, apex, altitude, are also indicated. 



The method of developing the pattern 

 for this simple cone is easily understood. 

 First, draw the front view B the size 

 desired. Second, draw the bottom view 

 C, which is, of course a circle, the diameter 

 of which is equal to the base of the cone. 

 Third, divide the bottom view into six- 

 teen equal parts. Fourth, set your pencil 

 dividers with one point at the apex of the 

 cone and the pencil point at the right 

 corner of the base, then draw the arc D-K. 

 Get the correct length by measuring one 

 of the spaces on the bottom view and 



stepping it off sixteen times on the arc 

 D-E. Draw the lines from both points 

 numbered one and the pattern for the 

 cone is complete. This pattern is merely 

 the size and shape obtained by tracing the 

 outline of a cone rolled once around on a 

 sheet of paper. 



Fig. 3 shows the development of the 

 patterns for a megaphone. It will readily 

 be seen that this megaphone is simply two 

 cones with their tops cut off and joined 

 together. When the top of a cone is cut 

 off, it is called a "truncated cone." To 

 develop the patterns for these two "trun- 

 cated cones," which make the megaphone, 

 first, draw the front view as shown at B. 

 Second, draw bottom view as shown at C. 

 Third, to get the pattern of the large 

 "truncated cone" B, we must first locate 

 the "apex" of the cone, in other words, we 

 must complete the cone. This is now 

 done by the dotted lines meeting at F. 

 Next we proceed in the same manner as 

 we did in Fig. 2, that is, we divide the 



13 12 



Patterns developed by radial lines are 

 all of objects that are conical in form 



bottom view into sixteen parts, place the 

 pencil dividers at F-G^ draw the arc D-E^ 



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