Talk the hind leg off a dog

OK, I know what you're thinking, this sounds like me. And it is - he he! Still, I'd like to know how it came about. The connection between talking endlessly and the leg coming off an iron pot escapes me. Any ideas?

We (Ky., W.Va.) say: Talk the hind leg off a dog.

OK, well that's equally strange really. What's the connection between the removal of limbs or legs and talking too much?

In the UK it's not a 'dog', but a 'donkey'. This still doesn't explain the origin!