Lampshade fitters are located at the centre of a lampshade's spider and allow a lampshade to be fastened to a light fixture. Three common fitter types include the clip, washer and uno.
The term "spider" refers to the arms attached to the top inside rim of the lampshade that hold the lampshade fitter in place.
Clip fitters have a loop of wire extending downward from the lampshade's spider that slides over the top of the light bulb. Torpedo clip fitters are shaped to fit onto elongated bulbs and bulb clip fitters are shaped to fit onto the round-topped light bulbs.
Uno fitters have a hollow round piece situated at the centre of the lampshade's spider that slides over the fixture's socket. Sometimes the uno fitter and socket are threaded which gives the lampshade greater stability.
Washer fitters consist of a washer attached to the arms of the spider. The harp sits underneath the spider and the finial screws onto the harp with the washer fitter sitting between. This entire piece is then attached to the lamp socket.
Consider having your lampshades recovered instead of purchasing new. This way, you can reuse your existing fitter and won't have to worry if the new shade's fitter will work with your fixture's base.