A frame apparatus for holding a flexible lance positioning mechanism adjacent to and spaced from a heat exchanger tube sheet includes an upper guide rail, a lower guide rail, a positioner rail supported from one of the upper and lower guide rails and guided by the other of the upper and lower guide rails, and a rail clamp assembly fastened to a portion of a tube sheet. This rail clamp assembly has a flat plate member fastened to the tube sheet, a base plate spaced from the flat plate by one or more threaded shafts, and one or more clamp fingers rotatably fastened to the base plate. Each clamp fingers is operable to rotate toward the base plate when the base plate is drawn against the flat plate or beam member by rotating the threaded shaft, thus drawing the rail securely to the flat plate of the clamp assembly.