I agree first impression is a rug making sliding hook tool, but I think this is much larger, and there is no needle. Also the slide is tapered, and has locking bolts.
It appears to be some sort of stretcher - I have seen hat stretchers with a tapered core, but this is for something without an end (top). It does look like it could be used in leatherworking, but I cannot see what would need stretching,or would fit this... It's much too small for something like horse collars....
Something like hoserie, or garment sleeves/collars comes to mind.... 17 to 19 1/2 is a large shirt collar size - is that the circumference of the narrowest point of the tool at that setting???
How about a pre-made bow tie makers fitting guage??????