'unevenly-driven' is a modern compound formed from the adverb 'unevenly' and the past participle 'driven'. 'Unevenly' derives from 'uneven' + the adverbial suffix '-ly'. 'Uneven' itself comes from Old English elements 'un-' (not) and 'efen/efen' (level, even). 'Driven' traces to Old English 'drīfan' (to drive), via past participle forms that produced modern 'driven'.

'uneven' appeared in Middle English as 'un(e)ven' (from Old English 'un-' + 'efen'), later taking the adverbial suffix '-ly' to form 'unevenly' in Modern English. The verb 'drīfan' in Old English produced past forms (Middle English 'driven'), which stabilized as the past participle 'driven' in modern usage. The compound 'unevenly-driven' is therefore a recent descriptive formation in Modern English combining those parts.

Initially the components meant 'not level' ('uneven') and 'to drive' (past participle 'driven'); together they originally described something that had been driven. Over time the compound came to be used specifically to describe mechanisms or motions characterized by non-uniform driving — i.e., driven in an uneven manner.