Knee strengthening exercise suggestions?

[havocthecat]

Before I go all out and hire a personal trainer (which, uh, I cannot afford given the dance costs in my life), does anyone have any links to suggested knee and leg strength training exercises for someone who a) does not have much in the way of equipment and b) has knees which are moderately fucked? (Ligament and/or tendon strain, plus arthritis.) Also I have balance issues due to various reasons that are too complicated to get into here.

Please keep in mind that I am not looking for medical or insurance advice and can gauge and manage my own needs in respect to that.

Thank you!