Go Row

For warming up, the rowing machine gives the most bang for your time. In addition to getting your heart rate up and getting the blood going, it works most muscle groups in your body. (And if you are a swimmer, rowing is good training for your sport.)

If your arms get tired too soon, change your technique. 

• Push with your legs (you should feel the top part of your thighs working), and keep your arms extended as you glide back. 
• When you reach the end of the movement, lean your torso back (without rounding your back) and pull the handle all the way towards your tummy. (For variation, you can pull the handle towards your chest instead of your tummy. This works a different part of your back.) 
• When you complete the motion, return to the starting position. Slide as far forward as your flexibility will allow; don't return just midway. But don't go too far forward either, lest you strain your back.
  

Try to complete the rowing stroke in one fluid motion, not in stilted steps. Start slow until you get the hang of things. Maintain your posture and never round your back.

Oh piddlewinks, blahblahblah, just watch the video. It sounds complicated, but rowing is worth the rewards.

p.s. Avoid the machine if it aggravates your shoulder and knee issues.
p.p.s. Rowing is not weight-bearing, so be sure to supplement it with other activities that are.