Problem 50
THE FRUSTUM OF A SCALENE CONE
89. The Frustum of a Scalene Cone.—Triangulation is the universal tool of the Sheet Metal Draftsman. Any surface capable of being developed can be developed by this method. However, in the case of the cone and the cylinder less laborious methods are available which are just as accurate. In many problems that cannot be classed as parallel line or tapering form developments, there is a shorter method known as Development by Sections. This method is generally employed in problems where solids can be cut into two equal parts by the cutting planes. Figure 290 shows a frustum of a scalene cone cut by a vertical plane in such a manner as to divide it into two equal parts. Figure 291 shows one of these halves placed so that the cutting plane assumes a horizontal position. If the semicircular ends (profiles) were divided into four equal parts, and perpendiculars dropped from each of these points to the base lines, a model cut along these hues would show the sections as pictured in Fig. 291. It is evident that hues 1-A and 5-E are true length hues, while C-4, 4-D, etc., are upper bases of trapezoids and must be developed. After the pattern has been developed, a cardboard model of Fig. 291 made from Fig. 292 and the diagram of sections, Fig. 293, should be constructed to aid in the visualisation of future problems. Figure 292 is a plan or top view of the object with half-profiles attached to each end. These half-profiles are divided into equal parts and extension lines carried to lines 1-5 and AE as shown. The divisions are then numbered and lettered. Before the base lines of the sections can be drawn in, the order of sections must be determined. The standard adopted for triangulation can still be adhered to and the order would read A-2, 2-B, B-3, 3-C, C-4, 4-D, and D-5. Since lines l-A and 5-E are true lengths they need not be mentioned in the order. Having determined the proper order, the base lines on the plan are now drawn in as shown in Fig. 292.
The diagram of sections. Fig. 293, is now constructed by drawing short horizontal lines equal in length to the several base lines of Fig. 292 and with numbers and letters that correspond to the order adopted. Perpendicular lines are erected at each end of
