This is basically a myth.
What Hargreaves did was to take the traditional spinning wheel and turn it through 90 degrees to a horizontal position, allowing it to turn multiple spindles at once. The story is that Hargreaves conceived this idea when his daughter (or, in some versions, his wife) accidentally knocked over her spinning wheel, whereupon Hargreaves noticed that it kept working as normal, with the spindle now pointed upright. Hargreaves realised that there was no particular reason the spindles had to be horizontal, as they always had been, and he could place them vertically in a row.
The trouble is that none of Hargreaves's several daughters was called Jenny (or Jennifer); and his wife's name was Elizabeth. The word 'jenny' is in fact an early abbreviation of 'engine', simply referring to a machine or device.
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