Abstract
In this paper, a novel approach of linear octree is employed to represent discrete tools and build their swept volumes along machining trajectories. Firstly, a data structure of linear octree is defined as the base of geometrical transformations. The linear octree can be extended into leaf nodes in the deepest level for simplifying homogeneous transformations, and all leaf nodes in the deepest level can also be concentrated into a linear octree for saving storage capacity inversely. Secondly, tool trajectories are interpolated as short lines, and swept volumes between neighbor interpolation points are defined as the Minkowski sum of their cell sets at both locations. Thirdly, equations of the rotation matrix for local coordinate system, roll, pitch and yaw angles of tool orientations are established to define the global rotation motions. Finally, a case of discrete sphere tool and its swept volume modeling are studied to validate the proposed approach.
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