What type of armour was common for samurai? I would like to know if the armour had flexible joints versus totally flexible joints. I suppose the flexible joint armour came afterwards. To me some photos look like the user had straight arms all the time which seems like there was not much bend one could make in the elbow.
Samurai is a rather large class ranging from foot solders to the Shogun. All wore different armours. Your question spans around a thousand years of history.
So, generally speaking… A few armours have stiff joints. However, they are specific armours, for example tourney jousting ones. Those are donned for specific tasks and generally require staff to put on and off.
All combat ready armours have flexible joints. If you cannot move on a battle field, you die. That is it. So, samurai armours all had flexible joints.