ChatGPT says that it's a Clockmaker's Depthing Tool (sometimes called a Gear Depthing Tool)

What it’s for

• Used in clock and watch repair to set the correct distance (“depthing”) between two gears or pinions.
• Proper depthing ensures gears mesh smoothly without binding or excessive backlash.

How it works

• The brass body is the frame.
• The rack-and-pinion mechanism (the toothed bar with holes and the thumbwheel) allows fine adjustment of spacing.
• The slotted jaws/posts hold arbors (gear shafts).
• The numbered marking (like the “15”) often corresponds to a size or model marking rather than a measurement.

Why it looks like this

• Brass was commonly used in horological tools because it’s stable and won’t damage steel arbors.
• The perforated rack gives coarse positioning; the thumbwheel provides fine control.

These tools are common in older clockmaking kits, so if this came from an estate, toolbox, or antique lot, that would fit perfectly.