Trajectory Model of J-Type Groove and its Curve Fitting of B-Spline
This paper describes the complexity and particularity of the trajectory of tube-sphere intersection and derives mathematical model of the track; according to characteristics of B-Spline curve, the track intersecting curve is partitioned ,and determine the mathematical relationship between the control points (deBoor point) and the data points of J-type groove; using cubic non-uniform irrational B-Spline theory, generate segments of approximation curves, then first and last point of each segment are constrained, so that combination curves can be seen as a whole curve with C1 continuity; programming the trajectory of the preprocess module with C# language, it has advantages of approximate accuracy and high efficiency, thereby it can increase accuracy and precision of welding terminal position, so that the overall system has a metronomic characteristic.
C. L. Chen et al., "Trajectory Model of J-Type Groove and its Curve Fitting of B-Spline", Applied Mechanics and Materials, Vols. 58-60, pp. 1396-1401, 2011