13. With a as the radius and points 4 as the pivot

points in the pattern, scribe your arcs establishing

points 5.

14. Set your dividers to the length of line b in step

3. Now, using points 5 as the pivot points in the pattern,

scribe your arcs at 6.

15. Set your dividers for the distance between 4

and 6 in the full plan. Using points 4 in the pattern as

your final pivot points, scribe your arcs to establish

points 6.

16. Draw straight lines between the established

points, as shown in figure 12-5 1. Make your necessary

allowances for the seams, and the pattern is completed.

Figure 12-52 illustrates the procedure for the

development of a RECTANGULAR-TO-ROUND

transition piece.

This is also a relatively easy development, and one

that you can make on your own by following the

drawing.

T h e OFFCENTER ROUND-TO-ROUND

transition piece developed in figure 12-53 is a scalene

conic section.

When the difference between the diameters of the

top and bottom is small, as it often is, the vertex--if you

could establish it--would fall in the next stop. When

you have a scalene conic section to develop and that

condition exists, you will have to develop the piece by

the triangulation method. This type of development is

shown in figure 12-53.

Now find the true length of each side of the

To develop the pattern, first draw the orthographic

triangles. The short side of each triangle that points

front view. Then swing in the half-circles at the top and

downward is equal to one-twelfth the circumference of

the bottom. With the front view completed, follow these

the TOP circle. The other two sides of each triangle are

steps:

not shown in true length. Therefore, we must use

1. Divide the top half-circle into six equal parts to

triangulation to determine their true lengths. However,

establish points A, B, C, D, and E.

lines 1-8 and 7-14 are shown in their true length on the

2. Drop vertical lines from these points to intersect

front view.

the top line of the front view at right angles. Number

Work with the solid lines first. (See the top portion

these points of intersection 1 through 7.

of fig. 12-53.) Set up two right angles to use as bases

3. Divide the bottom half-circle into six equal parts

for true-length diagrams and work from point X and

to establish points F, G, H, J, and K.

point Y. Take line 3-10 as an example. Set your dividers

4. Run vertical lines upward to intersect the bottom

to the length of line 3-10 on the front view. Use point X

line of the front view at right angles. Number these

as a center and swing an arc across line XZ. Then set

points of intersection 8 through 14.

the dividers equal to the DIFFERENCE between line

G-IO and line B-3. Use X as a center and swing the arc

5. Construct the front view triangles as shown.

to intersect line XY. A line connecting the two

Note that some of the lines are solid and some are

intersections is the true length of line 3-10.

broken. Make your lines the same way.

12-22