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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