Research on algorithm of tool-path planning for 5-axis NC machining based on double quaternion

In order to handle positions and orientations of tool with a unified manner in 5-axis NC machining, a tool path planning method based on double quaternion was proposed. With the identity of cutter points and the points in double quaternion space, the mapping from position and orientation points in 3D space to elements of double quaternion space is constructed. The interpolation problem of position and orientation is transformed to interpolation curve design in double quaternion space. Based on spherical linear interpolation theory and Bezier recursive algorithm, a Bezier curve of double quaternion was designed, which is also the tool path including positions and orientations. Simulations show that the generated Bezier curve of double quaternion can effectively complete a smooth adjustment for position and orientation of tool path. This paper provides a new method of tool-path planning for 5-axis NC machining based on double quaternion, and the validity of the algorithm is proved.