A new iso-parametric machining algorithm for free-form surface

Abstract

In this paper, a new iso-parametric tool path generation technique has been presented for machining truncated free-form surfaces by means of re-parameterisation. Three methods of re-parameterisation have been discussed, namely, the Coons method, partial differential equation method and the newly developed ‘Boundary Interpolation method.’ Tool paths have been generated based on the iso-parametric curves produced by re-parameterisation. The complete mathematical formulations have been given and subsequently their applications have been studied through some typical cases. Case studies show that the Coons and Laplace partial differential equation have some drawbacks in generating tool paths when the surface boundaries are irregular but the new Boundary Interpolation algorithm gives smooth and efficient iso-parametric tool paths by eliminating the problems like overcrossing (in case of Coons method) and uneven distribution of iso-parametrics (in case of Laplace partial differential equation method).