Systems and methods for reciprocating a cutter of an agricultural harvesting head

Systems and method for linearly displacing an object, such as a cutter or other component, in response to a rotation of a pivotable arm are disclosed. The systems and method encompass one or more actuators, such as hydraulic cylinders, to pivot a pivotable arm pivotable about an axis. A flexible component coupled to an end of the pivotable arm is displaced in response to the rotational motion of the pivotable arm. Movement of the flexible component in response to rotation of the pivotable arm is converted into linear motion via curved surface on which the flexible component rides. The pivotable arm is rotated in response to actuation of one or more actuators, such as one or more hydraulic cylinders, coupled to the pivotable arm.