I remember using one or two similar years ago when I served my apprenticeship ( fitter/turner.. Lonnnnnnggg time ago

) we called them 'swan necks' . the idea was , working in a fitting shop with overhead crane trundling along, blacksmith's shop at the end of the shop with the air hammer thumping away plus other machinery etc. there was a lot of vibration coming through the concrete floor, so when we had a particular job that required a fine finish, crankshaft / bearing journals or such like, the spring in the bow or 'swan neck' would absorb & dissipate the majority of that vibration from the tool tip. No doubt Bills comment stand valid as well & I don't dispute any other reason either, just that's my main understanding as I recall..

Cheers
George