A nodary, also called a hyperbolic catenary, is the Delaunay curve traced by a focus of a hyperbola as the hyperbola rolls without slipping along a line. Its smooth periodic continuation has loops and self-intersections. Revolving the nodary about the rolling line gives a nodoid (Delaunay 1841, Bendito et al. 2014).
For a hyperbola with semiaxes 
,
put 
and 
.
For real 
, the two focal pieces can be written
 |  |  |
(1)
|
 |  |  |
(2)
|
After suitable translations parallel to the rolling line, joining the pieces at their limiting endpoints and continuing periodically gives
the nodary. A single sign over finite 
describes only a portion of the full generating curve
(Bendito et al. 2014). The distance from the
rolling line varies between 
and 
. The resulting nodoid
has mean curvature of magnitude 
.
