A machine for automatically assembling equipment composed of parts at least some of which are arranged on a carrier includes a movable table which supports the carrier and which moves in two orthogonal directions in a horizontal plane. A tray is supported on the table and has additional parts or tools arranged thereon for use during assembly. A mounting surface extends above the plane of the movable table and has first and second portions parallel to the two orthogonal directions. At least one working unit is attached to at least one of the portions of the mounting surface for selective engagement with the parts and the tools on the tray upon movements of the movable table in assembling the equipment.