Stephen Mann

In this paper, we give a method for positioning a toroidal tool on a tensor product surface with two points of contact. By firing vertical rays and circular rays from the tensor product surface to the toroidal cutting surface, we can find these two points of contact by solving only quadratic equations, whereas previous methods typically solve transcendental equations using iterative methods. The new method is faster than the methods presented in literature and is independent of the method used to define the part surface. In addition to general applicability, test results on three sample surfaces are presented.

We implement and test a multi-point machining tool positioning technique that positions the tool using only a variation on gouge checking. The result is a method that is roughly twice as fast as an earlier method that performed a numerical search to find a tool position with multiple points of contact with the design surface. A GPU implementation provides an additional factor of ten speedup. Verification of the method was done via simulation and machining and measuring physical parts.