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Some of the absolute basic exercises that should be performed if you are bed-bound include ankle pumps, heel slides and rolling from side to side to change position. Doing these exercises regularly several times a day will help from developing blood clots, pressure ulcers or bedsores, and contractures (shortened, tight muscles).
Squats are a very useful exercise to make it easier to get up from a chair, off the toilet and out of bed. If this is difficult, try the sit-to-stand variation first or if too easy, do the supported squat variation instead. It can also be helpful if you have one-sided weakness, like after a stroke.