Agricultural header with linearly displaceable flex arms

An agricultural harvester, comprising:

• a chassis;
• a controller;
• and
• a header carried by the chassis, the header comprising:
• a header frame;
• a flexible cutterbar carried by the header frame;
• a plurality of flex arms coupled to the cutterbar;
• a flex arm drive assembly coupled to at least one of the flex arms and configured to selectively, linearly displace the at least one coupled flex arm in a vertical direction relative to the header frame, the flex arm drive assembly comprising:
• at least one gear configured to rotate;
• a gear rail engaged with the at least one gear and coupled to the at least one coupled flex arm;
• and
• a motor coupled to the at least one gear and the controller and configured to selectively rotate the at least one gear, the controller being configured to output a gear motor drive signal to the motor to cause selective rotation of the at least one gear, wherein rotation of the at least one gear causes vertical displacement of the at least one coupled flex arm;
• and
• a float sensor operably coupled to the controller and configured to output float signals corresponding to a clearance of at least a portion of the cutterbar relative to a ground plane, the controller being configured to determine a float adjustment by the at least one coupled flex arm to float at least the portion of the cutterbar at a defined level and output the gear motor drive signal to the motor to cause vertical displacement of at least the portion of the cutterbar by the float adjustment.