Abstract
A continuous-curvature smoothing algorithm is developed to approximate the linear tool path for high speed machining. The new tool path composed of cubic Bézier curves and lines, which is everywhere G 2 continuous, is obtained to replace the conventional linear tool path. Both the tangency and curvature discontinuities at the segment junctions of the linear tool path are avoided. The feed motion will be more stable since the discontinuities are the most important source of feed fluctuation. The algorithm is based upon the transition cubic Bézier curve that has closed-form expression. The approximation error at the segment junction can be accurately guaranteed. The maximal curvature in the transition curve, which is critical for velocity planning, is analytically computed and optimized. The curvature radii of all transition Bézier curves are also globally optimized to pursue the high feed speed by a linear programm model. Therefore, the algorithm is easy to implement and can be integrated into a post-process system.
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References
Boyd, S., Vandenberghe, L.: Convex optimization. Cambridge University Press (2004)
Cheng, M., Tsai, M., Kuo, J.: Real-time NURBS command generators for CNC servo controllers. International Journal of Machine Tools and Manufacture 42(7), 801–813 (2002)
DeRose, T.D., Barsky, B.A.: Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines. ACM Transactions on Graphics (TOG) 7(1), 41 (1988)
Erkorkmaz, K., Altintas, Y.: High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. International Journal of Machine Tools and Manufacture 41(9), 1323–1345 (2001)
Farin, G.: Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code. Academic Press, Inc., Orlando (1996)
Feng, J., Li, Y., Wang, Y., Chen, M.: Design of a real-time adaptive NURBS interpolator with axis acceleration limit. The International Journal of Advanced Manufacturing Technology 48(1), 227–241 (2010)
Lasemi, A., Xue, D., Gu, P.: Recent development in CNC machining of freeform surfaces: A state-of-the-art review. Computer-Aided Design 42(7), 641–654 (2010)
Magid, E., Keren, D., Rivlin, E., Yavneh, I.: Spline-based robot navigation. In: 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2296–2301 (2006)
Pateloup, V., Duc, E., Ray, P.: Bspline approximation of circle arc and straight line for pocket machining. Computer-Aided Design 42(1), 817–827 (2010)
Walton, D., Meek, D.: Curvature extrema of planar parametric polynomial cubic curves. Journal of Computational and Applied Mathematics 134(1-2), 69–83 (2001)
Waltona, D., Meekb, D.: G2 blends of linear segments with cubics and Pythagorean-hodograph quintics. International Journal of Computer Mathematics 86(9), 1498–1511 (2009)
Yang, K., Sukkarieh, S.: An analytical continuous-curvature path-smoothing algorithm. IEEE Transactions on Robotics 26(3), 561–568 (2010)
Yau, H.T., Wang, J.B.: Fast Bezier interpolator with real-time lookahead function for high-accuracy machining. International Journal of Machine Tools and Manufacture 47(10), 1518–1529 (2007)
Zhang, L.B., You, Y.P., He, J., Yang, X.F.: The transition algorithm based on parametric spline curve for high-speed machining of continuous short line segments. The International Journal of Advanced Manufacturing Technology 52(1), 245–254 (2011)
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Bi, Q., Wang, Y., Zhu, L., Ding, H. (2011). A Practical Continuous-Curvature Bézier Transition Algorithm for High-Speed Machining of Linear Tool Path. In: Jeschke, S., Liu, H., Schilberg, D. (eds) Intelligent Robotics and Applications. ICIRA 2011. Lecture Notes in Computer Science(), vol 7102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25489-5_45
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DOI: https://doi.org/10.1007/978-3-642-25489-5_45
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