In most cases Post bed machines like this are chainstitchers. Usually for gloves and the like.
This one looks like a 46K1
From ISMACS ""Piqué" stitch (two-thread, double-chain stitch). Combined top-feed and vibrating presser. 5 3/4" clear to right of needle. Speed 700spm. Narrow "post bed" for stitching fingers of gloves."