581. I'm guessing a pipe or cylinder bore gauge designed to be used with the
cylinder horizontal. The holder and tool would be slid into the cylinder so
that the bottom edges of the holder rested along the bore. This would keep
the tool perpendicular to the bore and exactly on a diameter. The tool can
be adjusted until it's a sliding fit and then removed to read it either
directly off its own scale for rough measurements or more exactly with a
micrometer across the tool.

The way the mass appears to be distributed I doubt if it could be used
easily with a vertical bore. It looks like it would just pivot over centre
and the tool fall out unless you held the tool with one hand while inserting
the whole thing with the other.

It looks a bit clumsy and much less accurate than a dial bore gauge or
telescopic gauge so maybe it's nothing to do with bores at all and is for
measuring a gap in some specific piece of machinery.
--
Dave Baker