Limited range of motion can greatly decrease the effectiveness of any workout. An article in the Toronto Star suggests trying a choreographed dance, similar to Zumba, to gradually eliminate the restriction in movements.
Start with a gentle warmup that will loosen the joints and muscles that will be used. The length of the warmup should be 3 songs. Begin adding 4 dance moves that you will repeat over the length of the songs. There are endless options with things like semi-squats, various bending and arm movements. Continue adding new moves that challenge but do not cause discomfort. Try memorizing a set of moves and repeating them to work out both your memory and your body.
Find a playlist that suits you for a fun exercise that will get easier with repetition.