It's called a "spring tool" or "gooseneck tool".
OX Tool made a video on this. His explanation is exactly right. If
you make a holder that looks like his version, and it doesn't
eliminate chatter, make the round hole in the top larger and try
Turns out that spring tools were common in the 1890s, for use on
shapers and planers. The main problem then being solved is
cutting-edge damage due to hard inclusions in the steel or cast iron
of the day - the cutting tool deflected instead of being damaged, and
so simply resumed cutting, not needing to be reground.
Later, spring tools were found to be useful for threading and parting
on the floppy lathes of that day, reducing or eliminating chatter.
The original round gooseneck pattern allowed lateral deflection,
useful for evading hard inclusions, but the sideways motion yielded
drunken threads and parting problems. There were various solutions,
but the simplest solution is simply to make the spring neck
rectangular, so the holder is stiffer laterally than radially
(parallel to the long dimension of the holder).
There are very many patents. Here are some. To get copies, enter
into Google Advanced Patents, proceeding the number by "US" and
dropping the commas and semicolons.
US Pats 1,146,546; 2,242,033
3 months ago