Simple Designs for Sheet Metal Working 



XIII. — Other interesting problems 

 developed by means of radial lines 



By Arthur F. Payne 



Director of Vocational Education, Johnstown, Pa. 



THOSE of you who have worked out 

 the radial line problems as demon- 

 strated in the last two issues will 

 have acquired an understanding of the 

 fundamental principles of the methods of 

 pattern development by means of radial 

 lines, that will make these more complex 

 problems easy to understand and develop. 

 The new points introduced in these 



One method of developing a pattern to 

 make a hopper for entering a round pipe 



problems are the use of old principles in 

 new ways, and the use of short cuts. If 

 any difficulties are experienced in working 

 these problems it will be of advantage to 

 review the problems of the last two issues. 



The illustration (Fig. 1) shows the 

 method of developing the pattern for a 

 hopper entering a round pipe. A more 

 technical statement of the problem would 

 be "the development of a cone intersect- 

 ing a cylinder;" sometimes these technical 

 statements are confusing if the terms 

 used are not understood. In the previous 

 problems, the base of the cone has always 

 been placed at the bottom; in this one the 

 base is at the top and the apex at the 

 bottom; this makes it appear different, 

 but the method of developing this problem 

 is exactly the same. Another new point 

 is that to save time and labor we have de- 

 veloped only one quarter of the pattern, 

 using only one-quarter of the bottom 

 view. The steps taken for the develop- 

 ment of the pattern are as follows: 



First, draw the front view, A, the exact 



size wanted. Betore we have gone very 

 far we shall find that we cannot complete 

 the front view without the aid of the end 

 view, B. The joint hne of the cone and 

 cylinder is not absolutely necessary to 

 develop the pattern, and the method of 

 finding the joint line has been explained 

 earlier in the series, but as this problem 

 offers a splendid chance to review, it is 

 deemed advisable to take advantage of 

 the opportunity. Second, to complete the 

 front view by drawing the joint line, we 

 must draw the end view, B. Third, draw 

 the top view, C, of the base of the cone on 

 both front and end view, divide these half 

 circles as usual and project the points to 

 the base lines and then to the apex. 

 Fourth, be very careful about numbering 

 these points as a mistake will cause a lot 

 of trouble. In the front view point 

 number 1 is in the center of the base line 

 and at the top of the half circle as indi- 

 cated by the arrow line, but on the end 

 view the same point number 1 is on the 

 left hand side because we are looking at 

 the problem from a different view point. 

 Fifth, to get the joint line on the front 

 view, A, project lines across from end 

 view, B, where the radial lines from the 

 base to the apex cross the joint line be- 

 tween cone and cylinder. On the front 

 view, A, where these projected lines cross 

 the same numbered lines going from the 

 base to the apex, place a cross, then con- 

 nect these crosses with a freehand curve 

 and the front view will be complete. 



To develop the pattern will be easy 

 enough for the students of this series who 

 have completed the preceding problems. 

 Briefly the steps are: First, draw the 

 pattern arc, 1-5, getting correct length by 

 stepping off the spaces from the top 

 view, C. Second, project the radial lines 

 from the point of intersection with the 

 joint line to the line apex-1, to get the 

 true lengths as was done in all the pre- 

 ceding problems. Third, swing these 

 lines over to the pattern until they cross 



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