# zbMATH — the first resource for mathematics

A manifold approach to generating iso-scallop trajectories in three-axis machining. (English) Zbl 1300.70004
Summary: A novel approach of iso-scallop trajectory generation for smooth manifold surfaces has been developed. Firstly, by defining homeomorphism mapping relations and differentiable structures, the smooth manifold surface is mapped into several Euclidean planes, thus its trajectory generation can be decomposed into planar curve-filling tasks. Secondly, in the generation of direction- parallel trajectories, the calculation of the cutting interval and the curvature is given, depending on the generation of the first curve in the projection view. Thirdly, after automatic adherences of inverse projection curves, the filled curves are mapped into the original surface inversely to form trajectories. Although the required trajectories are iso-scallop, the trajectory intervals are variable according to the curvature changes at the projection point, which is advantageous to improving the trajectory quality. The proposed approach has appealing merits of dimensionality reduction, which decreases the algorithm complexity. Finally, numerical and machining examples are given to illustrate its feasibility and validity.
##### MSC:
 70B15 Kinematics of mechanisms and robots
Full Text:
##### References:
 [1] Chiou C, Lee Y. A machining potential field approach to tool path generation for multi-axis sculptured surface machining. Comput-Aided Des, 2002, 34(5): 357–371 · Zbl 1383.70003 · doi:10.1016/S0010-4485(01)00102-6 [2] Shan C W, Zhang D H, Liu W W. Spiral machining tool path generation for blade with compound surfaces. Comput Integr Manuf Syst, 2008, 14(11): 165–169 [3] Stephen P R. A closed-form solution to the problem of optimal tool-path generation for sculptured surface machining on multi-axis NC machine. Math Comput Model, 2006, 43(3–4): 222–243 · Zbl 1187.74262 · doi:10.1016/j.mcm.2004.08.014 [4] Sang C P. Tool-path generation for Z-constant contour machining. Comput-Aided Des, 2003, 35(1): 27–36 · Zbl 05860957 · doi:10.1016/S0010-4485(01)00173-7 [5] Lee D, Kim S, Kim H, et al. Incomplete two-manifold mesh-based tool path generation. Int J Adv Manuf Tech, 2006, 27(7–8): 797–803 · doi:10.1007/s00170-004-2239-8 [6] Ding H, Zhu L M. Global optimization of tool path for five-axis flank milling with a cylindrical cutter. Sci China Ser E-Tech Sci, 2009, 52(8): 2449–2459 · Zbl 1354.70019 · doi:10.1007/s11431-009-0168-3 [7] Tournier C, Duc E. A surface based approach for constant scallop height tool-path generation. Int J Adv Manuf Tech, 2002, 19(5): 318–324 · doi:10.1007/s001700200019 [8] Tournier C, Duc E. Iso-scallop tool path generation in 5-axis milling. Int J Adv Manuf Tech, 2005, 25(9–10): 867–875 · doi:10.1007/s00170-003-2054-7 [9] Ahmet C, Ali U. A novel iso-scallop tool-path generation for efficient five-axis machining of free-form surfaces. Int J Adv Manuf Tech, Published online, doi: 10.1007/s00170-010-2698-z [10] Feng H Y, Li H W. Constant scallop-height tool path generation for three-axis sculptured surface machining. Comput-Aided Des, 2002, 34(9): 647–654 · Zbl 05860918 · doi:10.1016/S0010-4485(01)00136-1 [11] Li H W, Feng H Y. Efficient five-axis machining of free-form surfaces with constant scallop height tool paths. Int J Prod Res, 2004, 42(12): 2403–2417 · Zbl 1059.68146 · doi:10.1080/00207540310001652905 [12] Lee E. Contour offset approach to spiral toolpath generation with constant scallop height. Comput-Aided Des, 2003, 35(6): 511–518 · Zbl 05860997 · doi:10.1016/S0010-4485(01)00185-3 [13] Kim T. Constant cusp height tool paths as geodesic parallels on an abstract Riemannian manifold. Comput-Aided Des, 2007, 39(6): 477–489 · Zbl 1206.65096 · doi:10.1016/j.cad.2007.01.003 [14] Chen X S, Chen W H. Lectures on Differential Geometry. 2nd ed. Beijing: Peking University Press, 2001. 1 [15] Chen Z, Fu Q. A practical approach to generating steepest ascent tool-paths for three-axis finish milling of compound NURBS surfaces. Comput-Aided Des, 2007, 39(11): 964–974 · Zbl 05861457 · doi:10.1016/j.cad.2007.06.010 [16] Park S, Choi B. Tool-path planning for direction-parallel area milling. Comput-Aided Des, 2000, 32(1): 17–25 · Zbl 05860722 · doi:10.1016/S0010-4485(99)00080-9 [17] Ren B Y, Tang Y Y. Geometry Modeling Theories and Their Applications in NC Machining. Harbin: Harbin Institute of Technology Press, 2000. 120–124 [18] Sun J. Computer Graphics. Version 3. Beijing: Tsinghua University Press, 1998. 349–350 [19] Chen X B, Xiong C H, Xiong Y L. Efficiency evaluation of machining trajectories by using S curve-acceleration mode (in Chinese). J Huazhong Univ Science and Technology (Natural Science Edition), 2008, 36(2): 1–4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.