A three-claw opening-shrinking machine synchronized through connecting rods comprises a supporting seat, a telescopic arm, a first rotating arm, a second rotating arm, a first jaw, a second jaw, a third jaw, a first connecting rod mechanism and a second connecting rod mechanism, wherein the telescopic arm is connected to the supporting seat and can move up and down; the first rotating arm and the second rotating arm are symmetrically positioned on both sides of the telescopic arm respectively; the first rotating arm and the second rotating arm are rotationally connected to the supporting seat through a first pin shaft and a second pin shaft respectively; the first jaw, the second jaw and the third jaw are connected to the first rotating arm, the second rotating arm and the telescopic arm respectively; the first connecting rod mechanism and the second connecting rod mechanism are symmetrically positioned on both sides of the telescopic arm respectively; the top ends of the first connecting rod mechanism and the second connecting rod mechanism are fixed on the first rotating arm and the second rotating arm through the first pin shaft and the second pin shaft respectively, and the lower ends are hinged together; and the lower end of the telescopic arm is connected to the hinged part of the lower ends of the first connecting rod mechanism and the second connecting rod mechanism. Under the action of an acting cylinder and through the first connecting rod mechanism and the second connecting rod mechanism, the first rotating arm and the second rotating arm rotate around the axial lines of the first pin shaft and the second pin shaft, the telescopic arm moves telescopically on the supporting seat, the first jaw, the second jaw and the third jaw are driven by the first rotating arm, the second rotating arm and the telescopic arm to act simultaneously, and the jaws shrink or open.