Overview

LuteCAD is a desktop parametric modelling program available for Windows, Mac and Linux. It is supplemented by the online Lofting Assistant , which converts  session files to  downloadable 2d plots of the section-  and rib stave profiles.


Bowl cross-section
LuteCAD  implements a generalized elliptical bowl cross-section. This provides both for the oblate forms which evolved from the Renaissance and the earlier semicircular form probably extant in Europe up until the Middle Ages.

Rib variation
Semicircular cross-section bowls can be made from ribs cut identically to a single stave-like master stencil (Fig.1).  LuteCAD allows you to also create ‘hybrid’ bowls by individually varying the sweep angle each rib sweeps out about the bowl axis  (Fig.2) .
While in the semicircular case the rib stencils always have mirror symmetry about their long axis, in the more general elliptical case this is no longer so , as can be seen in the Lofting Assistant default example.
The ribs should not be too thin (the maple ribs of Fig.2 are borderline unfeasible in practice!) Note that the inlaid spacers which commonly feature in lutes and ouds are not ribs in the sense described here.

Fig.1 Bowls derived from a single rib stencil
Fig.1 Bowls derived from a single rib stencil
Fig.2 Hybrid sweep angles ϕ
Fig.2 Hybrid sweep angles ϕ.

Open string length (OSL)
This is adopted as a central fiducial lengthscale by LuteCAD. That is, a change made to OSL will automatically scale related parameters such as neck- and soundboard length, bowl girth etc.

Rib and neck mitre joint
The ribs of the bowl are anchored at the base end of the soundboard by a thin block shaped like a half-disk, called the stem, and at the neck end by the foot (Fig.3).
In lutes, the foot is usually mitred at a slanting angle to receive the neck. In ouds, by contrast, the neck mitre cut is typically perpendicular.
LuteCAD constrains the foot geometry such that in the limit of a high rib count it becomes a half-cone. The lute-style slanting mitre angle θ is then given by the conic section construction of Fig.4

θ = atan (w/2h -1)

where w and h are width and thickness of the neck at the joint. When w>2h the joint surface describes a perfect half-ellipse, becoming semicircular in the special case w=2h.

Fig.3. Rib anchoring at stem and foot, respectively the base and neck ends of the soundboard
Fig.3. Rib anchoring at stem and foot, respectively the base and neck ends of the soundboard
Fig.4 Relationship of the mitre angle θ to neck width w and thickness h at the foot joint, for fixed cone aperture α=45°
Fig.4 Relationship of the mitre angle θ to neck width w and thickness h at the foot joint, for fixed cone aperture α=45°

Bowl assembly  on a jig
Fig.3 is strictly figurative, insofar as the soundboard would normally be attached only after the bowl assembly is finished, the assembly relying traditionally on a mould or jig, upon which the ribs can be faired up in situ for cutting and filing. Fig.5 shows a typical jig structure, comprising transverse stations mounted on a backbone.

Rib cutting patterns of the type generated by the Lofting Assistant  can considerably simplify  the fairing-up process.

Fig.5  Plywood jig, with stem and foot secured in place
Fig.5 Plywood jig, with stem and foot secured in place

Peg box and neck rabbet joint
The iconic tension-breaking crook at the head of a lute is achieved with a rabbet joint as shown in Fig.6. LuteCAD constrains the crook angle to lie within 30° of the perpendicular. A little bit of play on this angle is needed to prevent the strings from impeding each other inside the peg box, but if it is increased too far it will tend to strain the joint.

Fig.6 Rabbeting neck and peg box to form the crook
Fig.6 Rabbeting neck and peg box to form the crook