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Combine
Cutting the grain in the field is known as harvesting or reaping. Separating the grain from the plant is known as threshing. Harvesting and threshing once was two separate jobs, but machines called "combines" save farmers time by both cutting and threshing in one step.

In a full day a man with a sickle could harvest half an acre. He could thresh five or six bushels of wheat with a flail and in another day then he would have to winnowing or seperate the grain from the chaff. So machines that could do all some or all of these steps at the same time were much welcomed.

In 1793 Thomas Jefferson had a threshing machine made from a model he imported from England that had non patented threshers since the mid 1700's.
Boyce Reaper 1799
In 1828 Samuel Lane patented a machine that could reap and thresh; first combine design patented in the United States.

In 1834 the first actually used and practical threshing machine in US was make by John and Hiram Pitts.
Cyrus Hall McCormick patented his successfull reaper, also in 1834.

Steam Combine 1879
“1885 … Tulare County farmer George S. Berry began building a self-propelled steam Combine. Stripping down and redesigning a twenty-five-horsepower straw-burning Mitchell & Fisher steam boiler, Berry mounted it on a frame, Placed five-foot-wide drive wheels in front, and added smaller steering wheels to the rear. The device was large and cumbersome, measuring thirty-eight feet wide and nearly just as long. Seeing it run backwards, with the rear wheels doing the steering, local field hands regarded it as a joke, But a year later, as the wheat crop in Tulare County neared harvest, Berry decided to test his contraption. Everyone for miles around took the day off from work and joined people from all parts of the state to watch the demonstration. At sunrise, Berry started his engine and began cutting a twenty-foot-wide swath. Moving at about three miles per hour-about twice as fast as a horse drawn combine- he kept at it all day, and by nightfall had harvested, threshed, and sacked 160 acres of grain. Spectators had witnessed the first steam-propelled farm machine. [Quoted from Beasts of the Field by Richard Steven Street]
Horse drawn Combine
By the 1890's combines started to become popular in the Western US. Early combines were driven by as many as 16 or more horses. Massey Ferguson 410 Combine

Sources: Beasts of the Field, From Man to Machine