An apparatus for guiding a plank along a transfer path and towards a cutting assembly. The apparatus includes an auto-centering lateral displacement mechanism maintaining support plates and corresponding guide and drive elements equidistant relative to the transfer path and includes: at least one pair of fixed length vertically extending driving shafts connected to each one of the support plates, the driving shafts each having a lower end connected to the corresponding support plate and being angularly movable relative to a vertical axis according to the lateral position of the corresponding support plate; at least one bushing assembly mounted to the upper section of the frame and receiving therein the upper end of a corresponding one of the driving shafts; and a fixed length connecting shaft extending between the driving shafts of the at least one pair of driving shafts, at the upper end thereof.