The vertically printed rods are sometimes a problem. If there are badly printed layers, they will break if the torsion due to friction of the threaded gears is too high. And sometimes the overhang of the threads is also making troubles.
This design is a variation of the sliding jaw of my "OTHER Machine Vise". The threaded rods are split in half, and they have a larger pitch. So they can be printed horizontally without any support material. The two halves are screwed firmly into the sliding jaw block. Maybe the parts need to be glued (in my case it wasn't necessary).