Can a (finite) collection of disjoint circle arcs in $\mathbb{R}^3$ be interlocked in the sense in that they cannot be separated, i.e. each moved arbitrarily far from one another while remaining disjoint (or at least never crossing) throughout?
(Imagine the arcs are made of rigid steel; but infinitely thin.)
The arcs may have different radii; each spans strictly less than $2 \pi$ in angle, so each has a positive "gap" through which arcs may pass:

Of course, if one could prove that in any such collection, one arc can be removed to infinity, the result would follow by induction.
But an impediment to that approach is that sometimes there is no arc than can be removed while all the others remain fixed.

Another approach would be to reduce the *piercing number* of the configuration:
the number of intersections of an arc with the disks on whose boundary the arcs lie. If the piercing number could always be reduced in any configuration, then it would "only" remain to prove that if there are no disk-arc piercings at all, the configuration can be separated.

Intuitively it seems that no such collection can interlock, but I am not seeing a proof. I'd appreciate any proof ideas—or interlocked configurations!