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Closed-form inverse kinematics of 6R milling robot with singularity avoidance

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Abstract

For a 6R milling robot, it is necessary to convert the postprocessing cutter locations (CL) into the robot’s revolute joint variables. This paper introduces an algorithm for calculating the forward and inverse kinematics of a 6R robot according to the CL data generated by conventional CAD/CAM systems. A redundant mechanism is analyzed to avoid the singular configurations and joint limits. The Denavit–Hartenberg (D–H) convention is referred to for developing the forward kinematics, and a closed-form solution of the inverse kinematics is presented by means of kinematic decoupling. A fundamental approach with modifying factor for avoiding singularity are developed with regard to three-axis and five-axis CL data. A gap bridging strategy is applied to reduce the jerk motion caused by tool retraction and cut paths connection. Finally, the result is conducted to simulation and machining test to verify the algorithms.

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References

  1. Abele E (2007) Spanende Bearbeitung mit Industrierobotern, Forschungsprojekt ADVOCUT: Entwicklungen und Industrie-transfer. Institut für Produktionsmanagement, Technische Universität Darmstadt

  2. Sorby K (2007) Inverse kinematics of five-axis machines near singular configurations. Int J Mach Tool Manufact 47:299–306

    Article  Google Scholar 

  3. Affouard A, Duc E, Lartigue C, Langeron JM, Bourdet P (2004) Avoiding 5-axis singularities using tool path deformation. Int J Mach Tool Manufact 44:415–425

    Article  Google Scholar 

  4. Munlin M, Makhanov SS, Bohez ELJ (2004) Optimization of rotations of a five-axis milling machine near stationary points. Comput Aided Des 36:1117–1128

    Article  Google Scholar 

  5. Chang PH (1987) A closed-form solution for inverse kinematics of robot manipulators with redundancy. IEEE J Robot Autom 5:393–403

    Article  Google Scholar 

  6. Siciliano B (1990) Kinematic control of redundant robot manipulators: a Tutorial. J Intell Robotic Syst 3:201–212

    Article  Google Scholar 

  7. Yoshihiko N (1991) Advanced robotics redundancy and optimization. Addison-Wesley Publishing Company, Boston

    Google Scholar 

  8. Phillip JM (1990) Introduction to robotics. Addison-Wesley Publishing Company, Boston

    Google Scholar 

  9. Mittal RK, Nagrath IJ (2003) Robotics and control. Tata McGraw-Hill, New Delhi

    Google Scholar 

  10. Paul RP (1981) Robot manipulators. MIT Press, Cambridge

    Google Scholar 

  11. Spong MW, Vidyasagar M (1989) Robot dynamics and control. Wiley, New York

    Google Scholar 

  12. Siciliano B, Khatib O (2008) Springer Handbook of Robotics. Springer, Berlin

    Book  MATH  Google Scholar 

  13. Tchon K, Muszynski R (1997) Singularities of nonredundant robot kinematics. Int J Robot Res 16: 60–76

    Article  Google Scholar 

  14. Nof SY (1985) Handbook of industrial robotics. Wiley, New York

    Google Scholar 

  15. Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming theory and algorithms. A John Wiley and Sons, Inc. Publication, New Jersey

    MATH  Google Scholar 

  16. Maaß J, Kolbus M, Bier C, Wobbe F, Schumacher W, Raatz A, Hesselbach J (2008) In: 3rd International Colloquium of the Collaborative Research Center SFB 562:285–296

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Beihang University, 100191, Beijing, China

    Wenlei Xiao

  2. Institute of Machine Tools and Production Technology, TU Braunschweig, Langer Kamp 19b, 38106, Braunschweig, Germany

    Henning Strauß, Torsten Loohß, Hans-Werner Hoffmeister & Jürgen Hesselbach

Authors
  1. Wenlei Xiao
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  2. Henning Strauß
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  3. Torsten Loohß
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  4. Hans-Werner Hoffmeister
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  5. Jürgen Hesselbach
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Correspondence to Wenlei Xiao.

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Xiao, W., Strauß, H., Loohß, T. et al. Closed-form inverse kinematics of 6R milling robot with singularity avoidance. Prod. Eng. Res. Devel. 5, 103–110 (2011). https://doi.org/10.1007/s11740-010-0283-9

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  • DOI: https://doi.org/10.1007/s11740-010-0283-9

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