Device for fastening a holding part on an eyeglass lens placed on a plate, comprising an arm adapted to receive removably said holding part, a carriage on which said arm is able to pivot between a raised loading end position and a lowered fitting end position and a frame on which said carriage is mobile in a straight line between a retracted rest end position and an advanced end of travel end position, drive means and, operative between said drive means and either said arm or said carriage, a transmission system such that, at least when said carriage is in the vicinity of its advanced end of travel position, said arm is in its lowered fitting end position, said device further comprising locking means operative between said arm and said carriage to lock said arm releasably to said carriage when the arm is in its lowered fitting end position.