the view. Because of this, you will have to find the
2. With center 0 and radius OB, draw a half-plan
TRUE LENGTH of some of the lines.
beneath the base line BC. Divide the half-plan into an
equal number of parts and number them as shown.
The true length of lines on transition pieces is found
3. From these points on the half-plan, draw lines
by triangulation. Using triangulation, the surface of the
perpendicular to the base line BC. From the points at
orthographic front view or elevation is divided into a
which these lines intersect line BC, draw lines to vertex
number of triangles. Then the true length of each side
of all triangles can be determined. This true length is
then transferred to the development.
4. Number the points of intersection on line DE,
as shown in figure 12-50.
The general procedure for triangulation pattern
development is as follows:
5. From the points of intersection of line DE,
draw lines parallel to the base line BC and number the
1. Construct the front view elevation and plan view
points of intersection on line AC.
in full scale.
6. With vertex A as a center and with dividers set
2. Step off the plan view into four equal spaces.
to a distance equal to AC, draw an arc for the stretchout
3. Project the points stepped off on the plan view
of the bottom of the cone.
to the elevation (front view). Then draw the divisional
7. Set the dividers equal to the distance of the
step-offs on the half-plan and step off twice as many
4. Determine the true length of all the sides, edges,
spaces on the arc as on the half-plan. Number the
and divisional lines.
step-offs 1 to 7 and back to 1, as shown in figure 12-50.
5. Develop the pattern from a center line, using the
8. Draw connecting lines from these points to
true length of all of the lines.
6. Sketch in the contours through the established
9. Using vertex A as a center, transfer distances
Al through A7 on line AC to each of the corresponding
lines in the stretchout.
7. Add the necessary allowances for the seams.
10. Join these points of intersection on the
The TWISTED SQUARE transition piece shown in
stretchout and a curved line to enclose the pattern of the
figure 12-51 is quite simple to develop by triangulation.
Both of the openings, top and bottom, are parallel
11. Add allowances for seaming and edging, and
to each other. The centers of the openings are both on
the pattern is complete.
an axis perpendicular to the base. Because the openings
are centered and have the same shape, the pattern could
Thus far we have studied three principal methods
be obtained from a quarter-plan. However, a full-plan
of sheet metal development: angular, parallel line, and
will be used here to illustrate the procedure. Here are
radial line development. Through the use of these three
the steps to be followed in making the layout:
methods you can solve a large number of sheet metal
layout problems. However, patterns for some objects
1. Construct the elevation and plan views as
are not readily developed by these methods. For
shown in figure 12-5 1. The numbered lines indicate the
example, a transition piece that changes the
elements that are shown in their true lengths. The
cross-sectional area of a duct from one geometric shape
lettered lines are those for which the true length must
to that of another must be developed by triangulation
rather than by the previous methods.
2. Extend the elevation's base line to the right of
the elevation. Construct a perpendicular to the
extension that is equal in length to the height of the
elevation object. Mark these points A and H.
It is often necessary to change the shape or area of
a duct or pipe. This change is accomplished by
3. With your dividers, measure the distance from
transition pieces and other special fittings.
point 5 to point 6 in the full-plan view. From point A,
on the extended base line, mark this distance to get point
Most of the lines of the orthographic views on a
b. A line drawn from point b to point H is the true length
transition piece are not shown in their true length
of line b in the plan.
because the lines slant away from the surface shown in