Author
Abstract
This paper presents an analytical study on the path command eneration for linear interpolation of blanking dies cavities defined by free form closed curves. These curves are highly used in mechanical applications like dies, cams, molds, etc. An integrated algorithm is presented in this paper to machine these cavities. When the coordinates of the free form curve's nodes are given(based on the shape of the die cavity), the proposed algorithm automatically generates the required tool path in three phases: phase (1) Generation the mathematical representation of the curve that passes through all the given points using the Four Point Interpolation technique. Phase (2) Optimum approximation of the generated curve into a sequence of linear segments passed on the intended accuracy tolerance. Phase (3) Tool path generation of the approximated segments using linear interpolation. This research also focuses on the algorithm can control the approximating error efficiently resulting in the fewest number of linear segments.
The closed curve of the die cavity is constructed from more than one curve segments; therefore the conditions of C¹ continuity are adopted in this paper for joining the curve segments. The proposed system software is most characterized by its elimination of any manual intervention involved in closing the boundary curve of the die cavity and in cutter offset determination.
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