Abstract: A system is provided for welding a workpiece (10, FIG. 1) along a predetermined weld line (12) that may be of irregular shape, which includes the step of forming a lip (32) on the workpiece to extend parallel to the weld line, and moving the workpiece by engaging the lip between a pair of rotatable members (34, 36). Rotation of one of the members at a constant speed, causes the workpiece to move so that all points on the weld line sequentially pass a fixed point in space (17) at a constant speed, so that a laser welding beam can be directed at that fixed point to form a weld along the weld line. The workpiece can include a reuseable jig (24) forming the lip, and with the jig constructed to detachably hold parts (22, 20) to be welded at a position wherein the weld line of the parts extends parallel to the lip on the jig.