In the case of sankyo (or tenkai kote hineri), the most common way to escape the technique is to drop one's elbow.
Of course, a well executed tenkai kote hineri prevents that from happening.
Any kote hineri (rotational wrist lock) or kote gaeshi (supinating wrist lock) can be escaped with a judicious punch aimed at Tori's nose or to be fair, any body parts.
In addition, if one's wrist is heavily muscled then it is possible to just force the write to untwist.
All wrist locks are aids to a technique (either throw or pin) and not the technique.
Better results are achieved with balance breaking and wrist locks than with just wrist locks.
Unless the intent is to cause grievous bodily harm by snapping the wrist 1 .
In this case, the lock can cause dislocation, tendon tears, and bone breaking.
Depending on the level of balance breaking, indirect harm can as well be inflected.
1 :
I am not a lawyer nor do I play one on TV .
That said, causing grievous bodily harm will get you into trouble with the law whatever the situation and reasons for doing it.
martialarts.stackexchange.com/users/82/Sardathrion - against SE abuse
Holds like sankyo rely on crossed extensor reflex action - the sensation of pain causes reflexive activity in other parts of the body.
This is most effective when the opposing side of the body has nothing to leverage against, i.e. no wall or floor to push against.
This means you can continuously adjust or tweak the hold to prevent the opponent punching or grabbing you.
One very simply way to nullify the pain from sankyo so that you can then counter it is to put your forehead to the back of the wrist that is being manipulated.
I'm sorry to say I don't know why it works - from my experimentation
I don't believe it's due purely to bio-mechanical reasons because the attacker can still be cranking on the wrist
(it may have something to do with interrupting the pathway of the nerve impulse).
Of course placing your head in that position can lead to further danger - so don't leave it there for too long!
martialarts.stackexchange.com/users/70/slugster
A non-Aikido solution, is to simply hammerfist or punch the back of the grabber's hand or their fingers, smashing it to get free.
We see twice in the video the guy gets a countergrip before the grabber shifts position and increases pressure, so the reach is there, and few people consider their hands as striking targets.
There's also the possibility of stomping the grabber's feet, however
, it's harder to get off given that the grabber has a good read on any weight shifts through the pressure of the lock itself, and it's not as immediately easy to target like the hand on your arm which you can target by feel, instantly.
martialarts.stackexchange.com/users/1598/Bankuei
We have a similar throw in the the style I practice
but It's only taught to higher grade students for the reason that it's very hard to get that grip in the first place.
Once you have the grip on the fingers the throw isn't too difficult but to get it requires: The receiver of the technique must have their hand open (ie not in a fist)
The receiver must not move the hand when you try to grab it.
You can learn a lot about balance when you do this technique
but I don't think this is going to come up much outside a dojo.
Open hand strikes are one thing but if your opponent is good enough to catch one of your strikes you are probably in trouble anyway either in self defence or anywhere else.
However the first thing you should do if caught this way is relax the arm muscles.
This makes it harder to manipulate the body using the arm and also reduces the pain caused by the stretch.
Then anchor the elbow to the body.
If your elbow ends up high you are in big trouble as you can see in the video.
martialarts.stackexchange.com/users/6503/Huw Evans
There is always a counter technik; also inside the Aikido (other than punching and kicking)
For every technique there is a twin technique which could be used as counter, like ying yang principle.
The concept is called Kaeshi waza .Of
course I would not suggest to resist the sankyo grip if your opponent/partner tori has solid control over you, it might harm your joints.
But there are 2 maybe 3 points of time which you can use for your kaeshi , if tori makes a small failure: Shortly before the sankyo grip seated, tori needs to slow down alittle.
As already suggested, you can try to drop your elbow,control opponent's wrist and with the other elbow of yours you cango for a quick kote gaeshi .
After sankyo grip seated, tori screws the controlled hand with a direction to the top and immediately sinks it for the throw/leading to the ground.
He can lose the control for a second exactly at this moment.
You can once again drop your elbow and go for a kote gaeshi .
Does not happen often, but tori can slightly lose the control during the leading to the ground.
You can try to make a forwards roll ( mae-ukemi ) and loosen the grip.
martialarts.stackexchange.com/users/6654/Endery
As can be seen here in  this video , it seems impossible to escape from the  sankyo  grip.   Is there a way to escape from it (including self defense options)?
How to escape from a sankyo grip?
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<self-defense><technique><aikido><grips>
martialarts.stackexchange.com/questions/6126
martialarts.stackexchange.com/users/6750/Avi
In the case of sankyo (or tenkai kote hineri), the most common way to escape the technique is to drop one's elbow. Better results are achieved with balance breaking and wrist locks than with just wrist locks. However, a non-Aikido solution, is to simply hammerfist or punch the back of the grabber's hand or their fingers, smashing it to get free.     The most common way to escape from a Sankyo grip is to drop the elbow, and a  non-Aikido solution is to  punch the back of the grabber's hand or their fingers, smashing it to get free. 
Themost common way to escape from a Sankyo grip is to drop the elbow. A non-Aikido solution is to  hammerfist or punch the back of the grabber's hand or their fingers, smashing it to get free.    