Contour parallel tool path planning based on conformal parameterisation utilising mapping stretch factors

Parameterisation-based methods for planning tool paths on mesh surfaces have been developing for years. The issue of existing mapping deformation which results in machining error has not been sufficiently addressed. And it still needs particular 3D geometric operations when planning iso-scallop tool path. To handle these, an effective approach to directly generating the iso-scallop paths on the parametric domain utilising anisotropic mapping stretch factors is proposed. The conformal parameterisation algorithm, Angle Based Flattening, is first implemented for the mapping between the spatial mesh and the planar mesh. Then a general method to convert 3D path parameters into 2D, which involves the direction mapping and length mapping based on the mapping deformation analysis, is presented. After that, a non-uniform offsetting method is proposed for retrieving the valid 2D offset paths. Finally, the iso-scallop paths on the parametric domain can be generated using the converted 2D path parameters and the present non-uniform offsetting method, and then the corresponding tool paths are obtained by inverse mapping. Simulation and experimental results are given to validate the feasibility and effectiveness of the proposed methods.