I can't find much about the Asbury Barker shutter. There are two Asbury Barker patents on pneumatic shutters in Google patents. See patent 477588 and 491794. According to "A century of cameras" by Eaton Lothrop the Barker shutter is a between the lens, two-blade scissors type. The 477588 patent shows such a shutter. If not the same, I think this shutter in the patent is closely related to the one on the Folding Kodak.
The 1892 Kodak catalog mentions the shutter. You can download the catalog as a PDF from Charlie Kamerman's site. Below is the piece about the shutter.