It's used to locate holes precisely when rebushing plates (such as in clockmaking).
The center post is put into the existing hole, and each leg is set to a different distance and angle. The legs are then lightly tapped with a hammer to make a reference indentation in the plate.
The tool is then set aside. The existing hole is drilled out and a solid piece of bushing material pressed into place. Once done, the tool is retrieved, the legs located in the dimples they made, leaving the center precisely located where the center of the original hole was. it is then tapped to make a mark where the new pivot hole is to be drilled.
There are usage variations that can include using one or more existing pivot holes to locate, but the principle is the same.
Commonly used for clock repair, although I don't think I've ever seen one that wasn't made of brass. They're also made in 3-point versions.