Simpson and his wife Hannah had one daughter, also Hannah, who married Jess Root Grant and, in 1822, had a son - Hiram Ulysses Grant - the eldest of six children.
It was while entering West Point Military Academy that the young recruit was erroneously called Ulysses S. Grant.
He tried to get it corrected, but the name stuck. The 'S' stood for Simpson... keeping his Ulster links alive.
During the American Civil War, General Grant accepted the surrender from Confederate General Lee and, in 1869, became America's 18th President.
Grant succeeded fellow Ulster-Scot Andrew Jackson and served two terms.
Grant died in 1885 aged 63 and is buried alongside his wife Julia in the General Grant National Memorial, Manhattan.
His grandfather's home has been restored to that of a typical 19th Century cottage.
Inside, the main room is dominated by a large turf fire, and the original mud wall can be seen in the bedroom.
An outhouse includes a small Civil War exhibition, and outside is a selection of 19th Century farming equipment and the occasional roaming hen.
Surrounding fields are landscaped with play & picnic areas and a Wildlife Garden for budding Attenboroughs.
If the weather's good, it's a nice spot to take time out from the 21st century and lose yourself in the rural heartland. Delightful.
- From Belfast, take M1, then A4 to Ballygawley roundabout. Continue ahead until you see the brown sign. Turn left and follow lane to the Cottage.
Admisson is free as there is no full-time staff on site, though a groundsman lives in adjoining premises and keeps the place looking neat and tidy.