I am looking for a string that can bend and flex easily but not twist. I want it to be able to snake through pipes, around bends, but not allow rotation of the thing at the end of the string. The closest I have been able to come is a chain -- the links tend to retard the rotation. But retarding the rotation isn't enough for the project I'm wanting to build, and honestly, the chain is heavy. So that got me thinking... is it even possible to have a string that can bend but not twist? Is there some geometry of forces that would allow such a substance? Does it exist?
A variant on bicycle chain (which bends only in one plane) can be made that has some links with the pivot axes perpendicular; such a chain will drape into any curve, but will be stiff against torsion applied to the ends. This is the equivalent of a chain linked with universal joints or constant-velocity joints. Universal Joint wikipedia
It seems to me that any linkage that is long and thin enough to bend will be too long and too thin to be able to resist twisting.
There seem to be several different designs in circulation. One way, I suppose, would be to have two spiral wires, tightly wound, one inside the other, winding in opposite directions, and the inside wire tightly around a flexible but highly non-compressible core.
The fact that the flexible extension can be used to tighten bolts and nuts shows that it can transfer a high torque from the wrench to the part.
I would consider a different approach. Why should you care about the twist along the entire string if the only thing you need is to eliminate rotation at the end of the string? Maybe you should just measure the orientation of the thing at the end of the string (using accelerometers (measuring the direction of the gravity force) or some kind of gyroscope) and correct the orientation using some actuators.