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The mathematical models of the basic entities of multi-axis serial orthogonal machine tools using a modified Denavit–Hartenberg notation

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Abstract

The use of virtual techniques as a means of training operators and familiarizing them with the machine tools on which they work has become increasingly widespread throughout the manufacturing industry in recent years. To support the development and implementation of virtual machine tools, this paper constructs the generic mathematical models of the basic building links, joint types, and cutting tools of multi-axis serial orthogonal machine tools. The modeling methodology can support the synthesis of various machine tools with different configurations but similar functions and facilitates the processes of error analysis, numerical control data generation, parameter measurement, and cutting kinematics analysis. The validity of the modeling approach is demonstrated using a six-axis serial orthogonal machine tool for illustration purposes.

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References

  1. Machine Tool Agile Manufacturing Research Institute. Virtual Machine Tool Project description. http://www.mech.northwestern.edu/MFG/AML/VMT/description.html

  2. Schultschik R (1977) The components of the volumetric accuracy. CIRP Ann 25:223–228

    Google Scholar 

  3. Vragov YD (1972) Structural analysis of machine tool layouts. Mach Tool 43:5–8

    Google Scholar 

  4. Kitajima K, Yoshikawa H (1984) HIMADES-1: a hierarchical machine design system based on the structure model for a machine. Comput Aided Des 16:299–307 doi:10.1016/0010-4485(84)90113-1

    Article  Google Scholar 

  5. Chaar JE, Boër CR, Fassi I, Rinaldi R (1998) Automatic composition of the machine tool functional structure in virtual environment. In: Proceedings of the 31st CIRP International Seminar on Manufacturing Systems Networked Manufacturing: integrated design prototyping and rapid fabrication. Berkeley, CA, USA, pp 299–302

  6. Suh SH, Seo Y, Lee SM, Choi TH, Jeong GS, Kim DY (2003) Modeling and implementation of Internet-based virtual machine tools. Int J Adv Manuf Technol 21:516–522 doi:10.1007/s001700300061

    Article  Google Scholar 

  7. Li JG, Zhao H, Yao YX, Liu CQ (2008) Off-line optimization on NC machining based on virtual machining. Int J Adv Manuf Technol 36:908–917 doi:10.1007/s00170-006-0915-6

    Article  Google Scholar 

  8. She CH, Chang CC (2008) Development of Internet-based system for multi-axis surface manufacturing. Int J Adv Manuf Technol (in press). doi:10.1007/s00170-008-1403-y

  9. Denavit J, Hartenberg RS (1955) A kinematic notation for lower-pair mechanisms based on matrices. ASME J Appl Mech 77:215–221

    MathSciNet  Google Scholar 

  10. Kiridena VSB, Ferreira PM (1993) Mapping of the effects of positioning errors on the volumetric accuracy of five-axis cnc machine tools. Int J Mach Tools Manuf 33:417–437 doi:10.1016/0890-6955(93)90049-Z

    Article  Google Scholar 

  11. Mahbubur RM, Heikkala J, Lappalainen K, Karjalainen JA (1997) Positioning accuracy improvement in five-axis milling by post-processing. Int J Mach Tools Manuf 37:223–236 doi:10.1016/0890-6955(95)00091-7

    Article  Google Scholar 

  12. Lin PD, Liu TH (1996) Machining and dimensional inspection of spatial cams on 5-axis machine tools. Int J Adv Manuf Technol 12:356–365 doi:10.1007/BF01179811

    Article  Google Scholar 

  13. Hsieh JF, Lin PD (2005) Drill point geometry of multiple flute drills. Int J Adv Manuf Technol 26:466–476 doi:10.1007/s00170-003-2027-x

    Article  Google Scholar 

  14. Hsieh JF (2008) NC data generation for 6-axis machine tools to produce a helical drill. Int J Adv Manuf Technol 36:535–546 doi:10.1007/s00170-006-0858-y

    Article  Google Scholar 

  15. Paul RP (1982) Robot manipulators mathematics, programming and control. MIT, Cambridge, MA

    Google Scholar 

  16. Lin PD, Tzeng CS (2008) Measurements of active parameters and workpiece home position of a multi-axis machine tool. Int J Mach Tools Manuf 48:338–349 doi:10.1016/j.ijmachtools.2007.10.004

    Article  Google Scholar 

  17. Lin PD, Chen JF (1994) Analysis of errors in precision closed-loop mechanisms. ASME J Mech Des 116:197–203 doi:10.1115/1.2919346

    Article  Google Scholar 

  18. Reshetov DN, Portman VT (1988) Accuracy of machine tools. ASME, New York

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Computer-Aided Engineering, National Formosa University, 64 Wunhua Road, Huwei, Yunlin, 632, Taiwan

    Chuang-Yu Tsai

  2. Department of Mechanical Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    Psang Dain Lin

Authors
  1. Chuang-Yu Tsai
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  2. Psang Dain Lin
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Correspondence to Chuang-Yu Tsai.

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Tsai, CY., Lin, P.D. The mathematical models of the basic entities of multi-axis serial orthogonal machine tools using a modified Denavit–Hartenberg notation. Int J Adv Manuf Technol 42, 1016–1024 (2009). https://doi.org/10.1007/s00170-008-1654-7

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  • DOI: https://doi.org/10.1007/s00170-008-1654-7

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