A little Googling revealed
In the early 19th century Joseph Machin and Company were one of the principal manufacturers of china and earthenware rivalling makers such as Wedgwood, Spode and Minton. However, due to the bankruptcy of the Stoke-based factory in the late 1830s the
name disappeared from public knowledge.
This must be an ancestor of Arnold Machin, but a little further investigation didn't turn up a family history that would have proved it. Can anyone provide more information?
Here are a few links that might help:
Joseph Machin history
Joseph Machin cups