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

The Drop and Tilt tool position method for five-axis machining positions a toroidal tool to have two points of contact with a tensor product Bézier surface. The method results in high order simultaneous non-linear transcendental equations that are slow to solve. In this paper, an efficient numerical implementation of the Drop and Tilt Method of multi-point tool positioning on tensor product surfaces is presented. The method was implemented in C++, and is a direct method that does not convert the tensor product surface into an intermediate representation such as triangles or point clouds. The method is successfully demonstrated on a number of tensor product Bézier surfaces.