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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?

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    $\begingroup$ So you want something like a series of short rods connected by universal joints? $\endgroup$ – mmesser314 Sep 29 '18 at 15:37
  • $\begingroup$ @mmesser314 Now that you highlight it... yes. Yes that seems like exactly what I'm looking for. I'm still curious about the physics question regarding string, but you may have solved my practical problem. $\endgroup$ – SRM Sep 29 '18 at 17:15
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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

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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.

That said, there are clever designs that come close. Ratchet wrench with flexible extension

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.

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Any one-piece string made out of solid material will have the ability to twist. The torque needed to twist the material will depend on its geometry and the shear modulus of the material.

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  • $\begingroup$ Is there any braiding that could eliminate that twistiness? $\endgroup$ – SRM Sep 29 '18 at 17:16
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    $\begingroup$ @SRM - the cables that turn auto speedometers are made with outer wraps of high-turns-per-inch spiral wire, both righthand and lefthand, but aren't suitable for high torque. $\endgroup$ – Whit3rd Sep 29 '18 at 17:21
  • $\begingroup$ That's interesting. So by braiding in both directions, the string resists turn. $\endgroup$ – SRM Sep 29 '18 at 17:32
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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.

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