Sheet folding apparatus, image forming apparatus, and image forming system

A sheet folding apparatus, comprising:

• a conveyor to convey a sheet along a main conveying path in a conveying direction;
• a first folding roller and a second folding roller disposed opposite to each other with the main conveying path interposed between the first folding roller and the second folding roller;
• a third folding roller disposed opposite to the second folding roller with a reflux conveying path interposed between the third folding roller and the second folding roller, the reflux conveying path branching off from the main conveying path at a branching position upstream from the first folding roller in the conveying direction and joining the main conveying path at a joining position upstream from the branching position in the conveying direction;
• a guide to switch between a first posture and a second posture, the guide in the first posture preventing the sheet conveyed on the main conveying path in the conveying direction from entering the reflux conveying path through the branching position, the guide in the second posture allowing the sheet to be conveyed from one of the main conveying path and the reflux conveying path to the other of the main conveying path and the reflux conveying path through the branching position;
• a motor to cause the second folding roller to perform either forward rotation in which the second folding roller rotates to convey the sheet on the main conveying path in the conveying direction and to convey the sheet on the reflux conveying path from the joining position toward the branching position or backward rotation in which the second folding roller rotates in a direction opposite to the forward rotation;
• and
• a driving force transmission mechanism to rotate the guide from the second posture toward the first posture in conjunction with the forward rotation of the second folding roller and rotate the guide from the first posture toward the second posture in conjunction with the backward rotation of the second folding roller.