If the rails (or what ever they are called) on the bottom of the chair are segments of a circle, then is should not be too hard. You just need to find the center of the circle, and position the origin (pivot point) at the center of the circle.

If the rails are not segments of a circle, you probably could still get it to work by using ERC, but it could be tricky,  and the exact details of the ERC would depend on the chair. It would probably be easier to do it, than to explain how to do it. If you wanted to send me the files, I could try to set it up for you, but can't guarantee success.