Robert Barker (died 1745) was a British physician and inventor. He was a Fellow of the Royal Society from 1732.
Barker invented both a reflecting microscope, exhibited in 1736, and "Barker's mill", a prototype reaction turbine (1743). According to James Dodson, he was a friend of Charles Labelye. He died in London, on 9 September 1745.
Barker's Mill, a rotating device powered by water and Newton's third law, is sometimes described as a 17th-century invention. It is attributed to Dr Robert Barker F.R.S., in 1743. It was published by John Theophilus Desaguliers in his book Experimental Philosophy of 1744. Desaguliers, who himself demonstrated the mill to the Royal Society, attributed the principle involved to Antoine Parent. French terms for the mill are tourniquet hydraulique, moulin de Parent or roue àréaction.
A complex timeline of development ensued.