Abstract: The present invention relates generally to bending a workpiece to form a desired configuration and, in particular, to a method and apparatus for forming bends “out of sequence,” i.e., in a time sequence different from the spatial sequence of the bends on the workpiece. The apparatus of the present invention include a bending system for bending a workpiece and a positioning system for positioning the workpiece relative to a bending region so that bends can be formed in various locations across the bending region. By virtue of the disclosed structures, a series of bends can be formed on a workpiece at various locations within the bending region. Bends can be formed out sequence and without advancing the workpiece relative to the bending region.

Abstract: A method for generating curves and an associated method for operating a curve forming device are disclosed. According to a preferred implementation, the curve is formed as a piecewise series of arc segments (14' and 16'). The shapes of the segments (14' and 16') are derived by defining a control polygon (P.sub.0, P.sub.12, P.sub.3), defining an outbound polygon (P.sub.0, P.sub.1 ', P.sub.2 ', P.sub.3) relative to the control polygon, and determining centers of curvature (18' and 20') and radii for the segments (14' and 16') relative to the outbound polygon. The resulting curve can be two or three dimensional and can be expressed in conventional numerical control languages for implementation by curve forming devices.

Abstract: The present invention relates generally to bending a workpiece to form a desired configuration and, in particular, to a method and apparatus for forming bends "out of sequence," i.e., in a time sequence different from the spatial sequence of the bends on the workpiece. The apparatus of the present invention include a bending system for bending a workpiece and a positioning system for positioning the workpiece relative to a bending region so that bends can be formed in various locations across the bending region. By virtue of the disclosed structures, a series of bends can be formed on a workpiece at various locations within the bending region. Bends can be formed out sequence and without advancing the workpiece relative to the bending region.

Abstract: A method for generating curves and an associated method for operating a curve forming device are disclosed. According to a preferred implementation, the curve is formed as a piecewise series of arc segments (14' and 16'). The shapes of the segments (14' and 16') are derived by defining a control polygon (P.sub.0, P.sub.12, P.sub.3), defining an outbound polygon (P.sub.0, P.sub.1, P.sub.2 ', P.sub.3) relative to the control polygon, and determining centers of curvature (18' and 20') and radii for the segments (14' and 16') relative to the outbound polygon. The resulting curve can be expressed in conventional numerical control languages for implementation by curve forming devices.