Numerical implementation of drop spin and tilt method for five-axis tool positioning for tensor product surfaces

This paper presents an extension of multipoint machining technique, called the Drop Spin and Tilt (DST) method, that spins the tool on two axes, allowing for the generation of multiple contact points at varying distances around the first point of contact. The multiple DST second points of contact were used to manually generate a toolpath with uniform spacing between the two points of contact. The original DST method used a symbolic algebra package to position the tool on a bi-quadratic surface; our extension is a numerical solution that allows positioning a toroidal tool on a tensor product Bézier surface, which we tested on bi-degrees 2, 3, 4, and 5. On the three bicubic surfaces we tested, the average number of initial seeds for our numerical method was less than 5 across all three surfaces, and the average number of Newton iterations was less than 20 except when the curvature of the tool closely matches the local surface curvature (in which case more iterations were required). Furthermore, we investigate the spread of possible second points of contact as the tool is spun around these two axes, demonstrating the feasibility of using the method to control the machining strip width.