The arm of my mug was broken. So I made a holder for it. The position is not exactly I wan but anyway it seems ok for use. The inside diameter of the holder is 85mm and 81mm (upper and lower side, respectively.) If it happened to fit your needs, welcome to download it.

By the way, I created this with SketchUp. It is very strange to me that I can't make a real true round circle. Anyone knows how to do it right? Please teach me. Thanks.