Do you have arthritis? Do not fear!
Your rings can be adjusted to the proper size needed without hurting your knuckles. The options that you have available are the adjustable shank (otherwise known as the arthritic shank), sizing beads, and ring guards. The expenses between the three are notable.
The most inexpensive way is to have a ring guard installed. Ring guards can be installed and removed with ease. (Note: Ring guards can cause scratching on your rings due to the guards being metal, but can be polished out.) Sizing beads are simply balls of metal that are placed in the corners of the shank. Depending on what size you need and what metal you have, the prices vary.
The other option you have is the arthritic shank. The arthritic shank is installed by removing the current shank of your ring and then replacing it with this piece. It works by opening at the bottom of the ring so it can slide on and off with ease. Depending on what style you seek, the price will vary.