Sangeet Prabhaker is a prosthetic and creature effects artist and he's showing off some of the work done from Game of Thrones. Here's how he made Jaime Lannister's handless arm:
He keeps his real arm wrapped underneath!
But since he's not always in the same clothes, he's got to have different arms:
He's also done some amazing work on Catelyn Stark too:
And Stannis' daughter: