half-plan into an equal number of parts and number
them as shown.
3. With vertex A as a center and with dividers, set
a distance equal to AC and draw an arc for the
stretch-out of the bottom of the cone.
4. Set the dividers equal to the distance of the
step-offs on the half-plan and step off twice as many
spaces on the arcs as on the half-plan; number the
step-offs 1 to 7 to 1, as shown in the illustration (fig.
5. Draw lines connecting A with point 1 at each
end of the stretch-out. This arc, from 1 to 7 to 1, is equal
in length to the circumference of the bottom of the cone.
6. Now, using A for a center, set your dividers
along line AC to the length of AD. Scribe an arc through
both of the lines drawn from A to 1.
The area enclosed between the large and small arcs
and the number 1 line is the pattern for the frustum of
a cone. Add allowance for seaming and edging and
your stretch-out is complete.
Triangulation is slower and more difficult than
parallel line or radial line development, but it is more
practical for many types of figures. Additionally, it is
the only method by which the developments of warped
surfaces may be estimated. In development by
triangulation, the piece is divided into a series of
Figure 2-52.Radial line development of a frustum of a cone.
triangles as in radial Line development. However, there
is no one single apex for the triangles. The problem
becomes one of finding the true lengths of the varying
oblique lines. This is usually done by drawing a true,
An example of layout using triangulation is the
development of a transition piece.
The steps in the triangulation of a warped
transition piece joining a large, square duct and a
small, round duct are shown in figure 2-53. The steps
are as follows:
1. Draw the top and front orthographic views
(view A, fig. 2-53).
2. Divide the circle in the top view into a number
of equal spaces and connect the division points with AD
(taken from the top part of view D, fig. 2-53) from point
A. This completes one fourth of the development. Since
the piece is symmetrical, the remainder of the
development may be constructed using the lengths from
the first part.
It is difficult to keep the entire development
perfectly symmetrical when it is built up from small
triangles. Therefore, you may check the overall
symmetry by constructing perpendicular bisectors
of AB, BC, CD, and DA (view E, fig. 2-53) and
converging at point O. From point O, swing arcs a
and b. Arc a should pass through the numbered
points, and arc b should pass through the lettered
FABRICATION OF EDGES, JOINTS,
SEAMS, AND NOTCHES
There are numerous types of edges, joints, seams,
and notches used to join sheet-metal work. We will
discuss those that are most often used.
Edges are formed to enhance the appearance of the
work, to strengthen the piece, and to eliminate the
cutting hazard of the raw edge. The kind of edge that
you use on any job will be determined by the purpose,
by the sire, and by the strength of the edge needed.
The SINGLE-HEM EDGE is shown in figure
2-54. This edge can be made in any width. In general,
the heavier the metal, the wider the hem is made. The
allowance for the hem is equal to its width (W in fig.