Re-living the overhead crane training I had at work…
I realise the eye-nut in the first photo is purely a neat version of a wing-nut for the clamp, but I would wary of so modifying an item of lifting tackle lest it find an opportunity to re-live being lifting tackle.
That is one area where you need maximum thread and no risk of an angular pull detaching the fastening.
On which note if the pull is at all angular to the axis of the thread, the eye-bolt or eye-nut should be the collared and screwed down to full contact, with a washer if necessary.
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Tim's comment about dividers (which I think you mean there) sent me my to tool-chest to examine a pair of Moore & Wright calipers (curved legs terminating in chamfered but blunt points, for measuring in particular, solid diameters), with somewhat similar arrangement.
The adjusting-nut is a knurled disc holding a split sleeve that carries the thread. The sleeve is closed onto the thread by its coned end engaging the countersunk outer end of a clearance-drilled bush, which in turn bears against a pillar on one caliper leg- the screw passing through that and secured in a corresponding pillar on the other leg.
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Talking of calipers or dividers…
I've sometimes wondered about that splendidly dotty old "Ancient of Days" painting of a hairy, naked God measuring the Earth with a pair of dividers. I am sure The Creator would have correctly used calipers, but I wonder if the artist did know that too but felt it prudent to depict dividers instead, as prominently as God, and very suspiciously suggesting a certain long-established private-members' club!
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I am also the proud owner of a very distinctive pair of calipers with flat blades (cut from sheet) only about three inches long, with a simple tightly-rivetted joint, reversible for internal and external diameters. I have no idea of their origin as they were among used tools "paid" to me for a workshop task, but definitely not by M&W or other respectable manufacturer.
If not home-made they were most likely a "bunny", or "homer"; and they are shaped and hand-engraved as a pair of rather "large-boned" lady's legs complete with high-heeled knee-boots and fishnet stockings….