In a well-known forum for the sale of watches, and what not, I came upon a description by a guy who seems to know his stuff, and has good watches:

"The watch was working, but now it is not. I think the safety pinion came loose and needs to be tightened. Wound tight and the balance is good."

I have any number of watches which are wound tight, and the balance wheel swings, but only part of its arc, slamming to a stop each time and swinging back. I have always suspected a staff problem, but what do you all say?

Steve

Well, I am no expert, but as I recall, a safety pinion comes into play if you release the mainspring click and release all the mainspring's power directly into the watch. The safety pinion will unwind and take most of the force, leaving the rest of the watch relatively unharmed.

Winding a watch would cause the safety pinion to wind itself back into place ready for the next 'accident'. I don't think that it cause the watch to not run.

But like I say, I am not an expert.
One of those will be along shortly to answer your question properly.

Steve,

As Michael says sound like it is not the safety pinion, if you give the watch a gentle turn and the balance swings in one direction then seems to bounce against something, first guess it has overbanked, the pallet has managed to get the wrong side and the roller jewel and cannot pass by there are many reasons for this from staff, jewels, roller problems, escapement and of course one of a thousand things people could have done to it, if you try and force it the first thing to break normally is the roller jewel, if you try and lift the balance out and reset to the other side which may provide a temporary fix be careful not to stretch the hairspring you can quickly run up a huge repair bill in a few simple actions

I agree with Chris.
That condition of overbanking can be caused by a bunch of different failures in the escapement:
Guard pin bent, or too small, or broken.
Too much sideshake in balance pivots.
Too much sideshake in pallet pivots
Too Much amplitude of the balance wheel, caused by many factors including,wrong mainspring, wrong hairspring, or other wrong parts.
You really need to observe the watch to see what the problem is.

Also to address the safety pinion problem. You need to screw it back on, and in some cases, use some light strengh thread locker.