As someone who has bursitis in both hips and underwent PT for it, and was ordered to do only NON-impact cardio (hard to find, let me tell ya) and strength training that wouldn't effect my hips AT ALL, I totally get where you're coming from...
I do agree completely with SIMONEKP...100%. Always ask your doctor, we are not medical professionals.
That said, there are definitely arm and ab exercises that you can do seated and not have it effect your knee... If you engage your abs and crunch down, you will still work the muscles...you could also try lying on your bed with your torso partly off (and legs lying across the bed to keep any straing off that knee!!) and doing crunches that way. You can also stand (if allowed to stand), link your fingers behind your head, engage your abs, and twist down (right elbow toward left hip, left elbow toward right hip)...
For arms, you should be able to do some seated shoulder presses and dumbbell curls (make sure not to brace with your legs, though!!), and for triceps you could do the pullovers (hold the weight behind your head with both hands and pull over your head, using the triceps to lift it)...
Definitely (DEFINITELY) check with your doctor, but as long as you're not using your leg AT ALL (not for bracing, lifting, bending, etc), you should be okay, in my personal experience.
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