A cutting machine for cutting a vegetable product includes a frame, supporting a product flow path, at least three links, pivotally attached to the frame, a cutting plate, pivotally attached to each of the three links at three pivot points and oriented substantially perpendicular to the flow path, a plurality of cutting knives, carried by the cutting plate, each having a generally corrugated configuration defining adjacent peaks and troughs, the cutting knives oriented angularly with respect to each other, and a drive motor, coupled to rotationally drive at least one of the links with respect to the frame, whereby the cutting plate moves in an orbital motion in a plane substantially perpendicular to the flow path, thereby moving the cutting knives sequentially and repeatedly across the product flow path.