Manual of Purpose-Made Woodworking Joinery

Three- centred method 143

left and right, as indicated at HIJ, to describe a true

semi- ellipse.

APPROXIMATE SEMI- ELLIPTICAL

ARCHED SHAPES

These approximate semi- elliptical shapes, as previously

mentioned, are preferred for brick or stone arches, as

they simplify the setting out and give the bricklayer

or stonemason definite centre points from which to

check the radiating geometric- normal lines of the

voussoir joints.

THREE- CENTRED METHOD

Figure 8.5(g): Set out (as a rod on a white- emulsioned

sheet or half- sheet of hardboard) the major axis,

equal to the span and bisect this to create the semi-

minor axis, equal to the rise required, as described

initially. Draw a diagonal line from A to C (the

chosen or given rise). With E as centre, describe

semi- circle AB to create F. With C as centre, strike

an arc from F to give G. Bisect AG to give centres H

and I. With E as centre, transfer H to create J. Draw

a line through IJ to give L. HIJ are the three centres

required to describe the semi- ellipse. Draw sector-

shapes AK from H, KL from I, and LB from J, to

cut through the rise at C and complete the required

shape.

curve (or parts of it) as and when the hardboard aid is
in position.

LONG- TRAMMEL METHOD

Figure 8.5(e): This is similar to the previous method,
except that the semi- major and semi- minor axes form
a continuous measurement on the trammel rod; the
outer marks thereon are moved along the axes, while
the inner mark, 0 (zero), plots the path of the semi-
ellipse. This method is better than the previous one
when the difference in length between the two axes is
only slight. Note that the springing line on each side
of the span – and the rise of the semi- minor axis –
has to be extended to accommodate and relate to the
trammel rod.

PIN- AND- STRING METHOD

Figure 8.5(f ): This method uses focal points on the
major axis (the springing line). These are shown here
as F and G – and either point equals AE or EB on a
compass, struck from C to give F and G. To describe
the arch shape, drive small, round- headed wire nails
into points F, C and G, with their heads protruding.
Pass a piece of string around the three nail- shanks and
tie tightly. Make a simple pencil- jig, if possible and
cut a notch in a pencil – as shown at C^1. Remove the
nail at C, replace with pencil- and- jig and rotate to

AF E G

C H

J

IC^1

B

Plan

Pencil jig

Figure 8.5 (f) True semi- ellipse by pin- and- string method.

AE

H

I

KG

C

F

J

L

B

Figure 8.5 (g) Approximate semi- ellipse by three- centred

method.

AE

C

B

=EC

=AE

Trammel

O

Figure 8.5 (e) True semi- ellipse by long trammel method.