Research On Trajectory Planning For Mesh Surface Based On Conformal Map

Significant research has been carried out to generate tool path for free-form surface recently. However few of them are for triangular meshes except iso-planar tool path. It can't satisfy all demands for machining. So this paper presents a method of generating tool path for triangular meshes based on maps. The method's main process is mapping triangular meshes to parameter region by conformal maps firstly, generating tool path on parameter region secondly and finally mapping tool path back from parameter region to triangular meshes.Firstly, the choice of maps is discussed. The map is the foundation of the whole method. Conformal map is the best choice because it has merits such as little deformation and no grid overlapping, etc. Based on the theory of conformal map, map model is built for planar parametric circle, rectangle and polygon regions. The boundary of parametric region rests with the need of tool path planning. The data structure is presented for the vast data while constructing conformal map. The large-scale sparse matrix is stored as three-number sets.Secondly, tool path is generated in parametric region and a new method for generating spiral tool path guided by spiral in planar is presented. A mathematic model is established to calculate normal vector and curvature of a point on the triangular surface. The calculating model for path interval and step length is developed, too. According to conformal map and relative theory, the relation of path interval between triangular meshes and parametric region is built. Adopting B-spline technology, it is implemented to analytic expression of discrete cutter contact tool path.Finally, tool path is generated on triangular meshes. Cutter contact tool path is mapped from parametric region to triangular meshes by means of conformal map and its reverse map. It can be easily solved by barycenter coordinate, too. The formula is given for calculating cutter location point from cutter contact point. The problem about interference is discussed and solved by adjusting the vector of tool axe. Lastly, cutter location points are calculated according to the calculating model.By using this method, it can generate iso-parametric tool path, Piano tool path, etc. This method's application is deeply discussed and corresponding examples are given. Taking the bicycle seat as an actual example, the spiral tool path, iso-parametric tool path and iso-planar tool path are generated. In addition, every kind of tool path's length and machining time are simulated and the comparison result is analyzed to draw the conclusion.