A machine and method for applying braid by means of a braiding machine to a mandrel, where the mandrel has a shape that approximates a wheel but has an irregularly varying radius of curvature. The machine includes drive/positioning wheel assemblies that are used to continuously reposition a cross-section of the mandrel relative to the braiding machine such that a center point of cross-section of the mandrel is maintained to be coaxial with a braiding point of the braiding machine as the mandrel (18) is rotationally advanced by the drive/positioning wheel assemblies. Repositioning of the drive/positioning wheel assemblies is controlled by a computer numerical control (CNC) controller, based on information describing one or more radiuses of curvature for sections of the mandrel and a current position of the mandrel relative to the drive/positioning wheel assemblies.