knee strengthening

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I'm looking for some knee strengthening exercises. I've already had three knee surgeries for instability and cartilage damage, and something has tweaked in my one knee that is causing quite a lot of pain doing simple things like lunges (I can get down into a 90 degree bend but can not get up to save my life currently) and going down stairs (going up is uncomfortable, but going down them is torture.) I have an orthopedic doctor appointment at the end of the month, but I don't want to stop going to the gym while waiting!

I've been going to pilates in the meantime, but am wondering if anyone has any good knee strengthening exercises or cardio ideas (no pool available though sadly) that don't involve squats or lunges (ideally those that go beyond just basic initial physical therapy as well.)

Thanks so much for any help or suggestions!