A few things we have learned when laser engraving on coffee cups is the position of the handle and size of the handle matter. If the handle is to large it can cause problems with the rotary attachment. Also, if the handle position is not oriented in a way that the mug can rest comfortably in the rotary, that can also cause issues.
On these particular mugs the customer wanted something on both sides of the mug so we actually ran this mug twice. (I think we could have done it in one pass but to be safe we ran them twice to get good centering)
* Side Note - Ceramic lasers very nicely. Its Clean, and has a super crisp image. We always love engraving on ceramic mugs.