Manual of Purpose-Made Woodworking Joinery

142 Geometry for curved joinery

semi- elliptical arched shape is so called because only

half of the ellipse is used.

TRUE SEMI- ELLIPTICAL ARCHED

SHAPES

True semi- elliptical shapes, such as produced by 1)

the intersecting- lines method, 2) the intersecting- arcs

method, or 3) the concentric- circles method, are not

shown here because they are not normally used by

carpenters when producing wooden arch- centres for

bricklayers. This is because these true methods of

setting out do not give the bricklayer the necessary

centre points as a means of radiating the geometric-

normal of the voussoir- joints. And the arch- shaped

frames, doors or windows, that invariably have to

relate to brick- built arches, must follow the same

setting out. However, before moving on to the more

common approximate semi- elliptical shapes (which

give the bricklayers their centre points), three practi-

cal methods of setting out true semi- elliptical shapes

are shown below.

SHORT- TRAMMEL METHOD

Figure 8.5(d): Draw the major and semi- minor axes as

illustrated and to the span and rise required. Obtain

a thin lath or narrow strip of hardboard, etc as a

trammel rod. Mark it as shown, with the semi- major

axis A^1 E^1 and the semi- minor axis C^1 E^2. Rotate

the trammel in a variety of positions similar to that

shown, ensuring that marks E^1 and E^2 always touch

the two axes; then mark off sufficient points at A^1 /C^1

to plot the path of the semi- ellipse. In technical

drawing (on a small scale) a flexi- curve aid or French

curves can be used to link up the points and describe

the semi- ellipse – but in a workshop (full- size scale)

situation, I have used a long, narrow strip of hardboard

as a flexible aid, with another person marking the

only in one direction; and this forms an elliptical
shape that now requires (for reference purposes) two
axes – like vertical planes – at right- angles to each
other, passing through the centre. The long and the
short lines (planes) that intersect through the centre
of ellipses are referred to as the major axis and the
minor axis.
As illustrated in Figure 8.5(c), the axes on each
side of the central intersection, by virtue of being
halved, are called semi- major and semi- minor axes. The

Figure 8.5 (a) Cone- produced ellipse and (b) cylinder-
produced ellipse.

(a) (b)

(a) (b)

A
E

B

D

C

Major axis

Minor

axis

Figure 8.5 (c) Axes of the ellipse: ABCD = ellipse axes;
ABC or ABD = semi- ellipse axes; AE or EB = semi- major
axis; CE or ED = semi- minor axis.

A

=AE

=CE

C

Trammel

E A^1 B E^1

C^1 E^2

Figure 8.5 (d) True semi- ellipse by short- trammel method.