The pivoting action sickle drive has a low profile allowing incorporation in or below a floor of a header of a plant cutting machine to allow passage of cut plant material thereabout. The drive includes a substantially flat rotatable input element, and a drive arm connected eccentric thereto for eccentric rotation along an epicyclical path. The arm extends to a connection with a pivot arm of a pivot element that connects to a knife arm that drives a sickle knife assembly, such that the pivot element, knife arm and knife assembly will be reciprocatingly driven by the eccentric rotation of the drive arm. A second drive can oppositely drive a second sickle knife assembly, such that opposite forces generated by the drives will cancel. The drives can be packaged in a forwardly tapered or curved enclosure, and the pivot elements can be correspondingly shaped to streamline the drives.