I have no experience with psychiatric patients, but assuming I want to restrain someone by myself without anyone getting hurt, my position of choice would be the wrestling hammerlock position with the other person face down. In this position, you have control of the near side arm with it behind the back and your weight on top. You have one hand free.
From behind with your weight on top controlling the near arm and body, you can hold the person down without them being able to attack you effectively with hands, arms, legs, or teeth. You can see what the other person is doing with their hands in case they have a weapon. You can put your knees on the ground to lessen the pressure if desired.
Hammerlock is a wrestling term, not a judo or BJJ one. The wrestling hammerlock is not about putting the joint in a position where leverage will damage the joint. It is simply about putting the person's arm behind them where you can control it and they cannot use it effectively. If you want to lock the joint in the sense that additional motion can cause damage, you take the wrist and walk it up the back, pulling the elbow along with it. For control alone without a shoulder lock, you can pin the hand behind the waist, well within normal range of motion.
Contrast this with what can happen in a judo kesa gatame position. The person on the bottom has an arm free with you in front of them; they can grab your ears or hair, poke you in the eyes, and grab things that you cannot see behind you. Since there are no points for controlling the person on their back versus their front, put them on their front and remain behind them.