I’m not sure if I understand whether your question is on OA or knee replacements. Since it appears it is regarding knee replacements I am responding to that portion of your questions.
1. Open chain exercises
2. High impact exercises
The focus should be on increase range of motion, particularly if the individuals has OA. Too, development of a ankylosed joint is common with total knee replacement. Once one has reached an acceptable ROM, one can progress to increasing overall functional strength.