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

A.

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

lines.

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.

vertex A.

6. Sketch in the contours through the established

9. Using vertex A as a center, transfer distances

points.

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.

cone.

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

be found.

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

12-20