Always found flexible drill shafts fascinating but can't really find a good place that either explains how they transfer torque or show a simulation of their torque dynamics. This is pretty much the only thing I could find about how it works:
https://www.youtube.com/watch?v=pL4z7pnJ418
However even here it is explained that the torque is transferred as if the shaft was rigid. But this seems to be an issue with newtons third law. If you can manage to bend the torque 90 degrees then you have changed the plane where the action and reaction torque acts on and thus break newtons third law. Unless the shaft also carriers a bending force along its length to cancel out the primary torque.
Doesn't a string of Cardan U-joints in a pipe explain it ?
I think it should be viewed as a chain of infinitely increasing bevel gears, each gear representing a local deformation of the shaft, allowing for a transition from discrete to continuous view.
For the system to work, the assembly must be rigidly held when the shaft is rotated, as seen in the video (two attachment points at 90°, with the end free to rotate). Without this arrangement, attempting to rotate the shaft would cause the assembly to rotate. If we include these holding forces, we can conclude that the change in orientation of the shaft does not change the angular momentum of the entire assembly.
What is misleading is viewing only the flexible shaft as an isolated system, when it is not; the support must be included in the analysis.