This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data., {"references":["Y. Takeuchi, T. Watanabe, \"Generation of 5-Axis control collision-free\ntool path and post-processing for NC data,\" Annals of the ClRP. 41/1\n(1992) 539-542.","A. Rüegg, P. Gygax, \"A generalized kinematics model for three to five\naxis milling machines and their implementation in a NC,\" Annals of the\nClRP. 41/1 (1992) 547-550.","S. Sakamoto, I. Inasaki, \"Analysis of generating motion for five-axis\nmachining centers,\" The Japan Society of Mechanical Engineers. 59/561\n(1993) 1553-1559.","R. S. Lee and C. H. She, \"Developing a postprocessor for three types of\nfive-axis machine tools,\" International Journal of Advanced\nManufacturing Technology. 13 (1997) 658-665.","R. Md. Mahbubur, J. Heikkala, K. Lappalainen, J. A. Karjalainen,\n\"Positioning accuracy improvement in five axis milling by post\nprocessing,\" International Journal of Machine Tools and Manufacture.\n37/2 (1997) 223-236.","Y.H. Jung, D.W. Lee, J.S. Kim, H.S. Mok, \"NC post-processor for 5-axis\nmilling machine of table-rotating / tilting type,\" Journal of Materials\nProcessing Technology. 130-131 (2002) 641-646.","C. H. She, C. C. Chang, \"Development of a five-axis postprocessor\nsystem with a nutating head,\" Journal of Materials Processing\nTechnology. 187-188 (2007) 60-64.","C. H. She, Z. T. Huang, \"Postprocessor development of a five-axis\nmachine tool with nutating head and table configuration,\" International\nJournal of Advanced Manufacturing Technology. 38 (2008) 728-740.","M. Rahman, J. Heikkala, K. Lappalainen, \"Modeling, measurement and\nerror compensation of multi-axis machine tools. Part I: theory,\"\nInternational Journal of Machine Tools and Manufacture. 40 (2000)\n1535-1546.\n[10] L. M. Zheng, H. Lin, R. L. Gai, Postprocessor based on generalized\nkinematics model of five-axis machine tools,\" International Journal of\nComputer Integrated Manufacturing Systems. 16/5(2010) 1006-1011.\n[11] J. Andres, L. Gracia, J. Tornero, \"Inverse kinematics of a redundant\nmanipulator for cam integration. an industrial perspective of\nimplementation,\" Proceedings of the 2009 IEEE International\nConference on Mechatronics, Malaga, Spain, April 14-17, 2009.\n[12] F. Nagata, Y. Kusumoto and K. Watanabe, \"Intelligent machining system\nfor the artistic design of wooden paint rollers,\" Robotics and\nComputer-Integrated Manufacturing. 25 (2009) 680-688.\n[13] C. H. She, R. S. Lee, \"A postprocessor based on the kinematics model for\ngeneral five-axis machine tools,\" Journal of Manufacturing Processes.\n2/2 (2000) 131-141.\n[14] S. Ashmall, \"Post-processors for general purpose N.C. processor,\nProceedings of the Institution of Mechanical Engineers, 186/25 (1969)\n551-556.\n[15] C. H. She, C. C. Chang, \"Design of a generic five-axis postprocessor\nbased on generalized kinematics model of machine tool,\" International\nJournal of Machine Tools and Manufacture. 47 (2007) 537-545."]}