Word for "difficult to twist or turn"

"Torsional resistance" or a "high torque" setting would probably fit. (http://www.dictionary.com/browse/torsional)

I think you could call it stiff:

1c : impeded in movement —used of a mechanism
_{from m-w.com}

Examples from the web refer to a vehicle's "stiff suspension", a piano's "stiff action", and so forth, indicating that it takes greater force or effort than normal to make the tires bounce or the keys to play a note.

The (very rare) noun torsibility actually means just about what you want. From Merriam-Webster:

resistance to torsion; also : tendency (as of a twisted rope) to untwist

Since "torsion" is twisting, this is essentially a word for "difficulty of twisting". It was originally used for describing materials rather than mechanisms (it's a measure for wire, like tensile strength), but I think it could be easily extended to other things that are twisted. So you could say

Due to the (high) torsibility of the mechanism, it was difficult to twist.

Except...it might possibly mean exactly the opposite of what you want. From Collins Dictionary (emphasis added):

the ability to be twisted

the degree of resistance to or the capacity of recovering from being twisted

And their "American" definition (on the same page):

ability to undergo, or resistance to[!], torsion

These definitions appear to me to be in direct conflict with themselves, and half in conflict with the M-W definition. If you're using the "ability to twist" meaning you would need to say

Due to the low torsibility of the mechanism, it was difficult to twist.

which is essentially the exact opposite of the first suggested sentence. Now, with that particular sentence, I think either formulation would be understood purely from context. But a harder case would be if you said something like

A detent is added to a mechanism to increase/decrease torsibility.

If your audience already knows what a detent does, either formulation would be understood. But if you want to define detent for an audience that isn't already familiar with it, this would probably be confusing.

Bottom line, the word is probably rare enough that your audience would just roll with the word however you use it, so long as you're consistent (but there's a very slim possibility that you will run into someone who has heard it before, in a way that's not consistent with however you choose to use it).

I'm not sure this helps you at all, but torsibility is so very close to suiting your needs (and also the most self-contradictory definition I've ever seen) that I had to post it.

High torsional stiffness combines the best of BenL and Hellion's answers. It is both technical and specific. Or, torsionally stiff (per AlanT's comment).

e.g.