This is a tool from Theatro del Mvndo y de el Tiempo, a book of star maps by Giovanni Paolo Gallucci, Miguel Perez, and Sebastian Muñoz. I found it in the David Rumsey Map Collection, the “Celestial” gallery.
The Theater of the World and of Time is a translation of a Latin work into Castillian Spanish. Apparently, Gallucci was the author, Perez the translator, and Muñoz the publisher — at least, that’s what I can garner from the Cervantes Virtual Library entry on the book. The Linda Hall Library reveals that it was originally published in Venice in 1588 as Theatrum Mundi, and is pretty packed with illustrations of constellations and their mythological namesakes.
There’s a full copy of the book here, in the Internet Archive.
No clue about how to use this instrument, though. It seems a little like a compass. I imagine it helped determine angles and distances. There are some figures in the book that seem like paper cutouts which might have been usable to calculate the relative speeds at which planets and stars seem to move across the sky, using interlocking circles and spinnable pointers… so in some ways, this was like a pop-up book, but for Early Modern scientists rather than toddlers.
Interesting, the way information-sharing changes.