There is disclosed a coupling device for operations on live elements to attain equipotential conditions. The device comprises two conductive jaws connected to a preferably nonconductive handle. The jaws are adapted to be switched between a closed configuration, in which they are in mutual contact and surround an area adapted to receive a live element, and an open configuration in which the contact portions of the two jaws are spaced apart from each other. The two jaws have respective entry tapering portions adjacent to the contact portions and mutually converging to cause the contact portions to move apart from each other when the live element is pressed against the entry tapering portions, thereby causing the jaws to switch from the closed configuration to the open configuration against the action of an elastic member. The two jaws have respective exit tapering portions adjacent to the contact portions and mutually converging to cause the contact portions to move apart from each other when the live element is pressed against the exit tapering portions, thereby causing the jaws to switch from the closed configuration to the open configuration against the action of an elastic member.