Probably made in the 1920s by G.M.Grace (and of a type often referred to as a rose engine slide rest, this wonderful "false rocking spindle" unit is of a type as exhibited by the maker at the Model Engineering Exhibition of 1931 and is now fitted to the Goyen lathe.
Because of the large mechanical disadvantage in using a cam to produce the wavy component of a rose-engine pattern, the handle that  turned the cam spindle also caused the drive to reverse through the lathe's changewheels to rotate the headstock spindle. Otherwise of a similar type, there is the Pudsey Dawson slide rest, a slightly less complicated affair, and also types of a  rocking slide rest' where the whole assembly is caused to rock under the control of a rosette mounted on the spindle nose. 
As an example of how the system worked, take the case of creating a daisy-like engraving on a workpiece held in the headstock spindle nose. The cam required would probably be egg-shaped and fitted to a shaft laying across one end of the slide. If the main slide feed screw is then geared to the headstock spindle at a ratio of, say 12 to 1, turning the slide handle twelve times would cause the headstock spindle (and hence the workpiece) to rotate once.
Parallel to the shaft holding the cam is a rocking bar; at one end this is caused to rub against the cam (and so follow its profile) while near the other end it pivots about an adjustable pin and pulls on a steel ribbon fixed to a spring-loaded anchor point. The ribbon is firmly attached to a sliding block at the front of the slide rest, through which runs the pivoted cutter-bar holder.  When the cam is rotated twelve times the cutter will also move from side to side twelve times and, with luck and a correct setting of the engraver, produce a daisy outline on the work.
Fully adjustable, results can be varied by, for example, altering the position of the pivot pin to vary the size of the daisy shape, by change the gear ratio to give a different number of petals or the engraving made to look more like a rose by using a cam with a different profile. In addition, the cam can be rotated between each cut so that second and subsequent cuts overlap the earlier. In order to find a pleasing result, much experimentation is required, and doubtless many false starts made. So, as dawn breaks for the second day, the bleary-eye ornamental turner might still no nearer to the ideal pattern…
The first three photographs below show the Grace slide rest more or less as found while the last two show it rebuilt and functional..