Mechanism is provided for enabling an overedging or other edgetreating machines automatically to operate progressively about the periphery of successive flexible work pieces, especially those of fabric having margin configuration including portions of constant convex curvature. Several improvements and refinements relating, for instance and without limitation, to automatic corner turning, to marginal label securement in the course of each operating cycle, so called sewing-off near the end of the cycle, ''''kickout'''' of the work piece from the operating zone, and associated thread cutoff, all contribute towards increasing productivity and relieving burden on an operator to the extent that the operator may simultaneously attend more than one machine.