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Analytical Forward Kinematics for Two Kinds of Typical Tripods Part II: Analyzing for Their Workspaces, and Performances of the Forward Kinematics

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Intelligent Robotics and Applications (ICIRA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7506))

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Abstract

The 3-P VPHS and 3-P VSP parallel mechanisms (where P, R, and S standing for prismatic, revolute, and spherical joints, respectively, and the subscripts V and H indicating that the direction of the P joint is vertical or horizontal, and the joint with underline symbol means the joint is active) are two typical mechanisms that can be applied to articulated A/B-axis tool heads with parallel structure. This paper focuses on the applications of the forward kinematic for these two kinds of typical tripods. Based on their analytic forward kinematics methods, their workspaces with geometrical constraints are analyzed, their performances are compared with the J-matrix iteration methods in terms of precision, stability and efficiency. The results show that the proposed methods are of high precision, stability and efficiency, and are easy to use, when dealing with the location and error analysis in on line real-time control and the prediction or analysis of their mechanical characteristics.

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References

  1. Liu, X.J., Bonev, L.A.: Orientation Capability, Error Analysis, and Dimensional Optimization of Two Articulated Tool Heads With Parallel Kinematics. ASME, Journal of Manufacturing Science and Engineering 130, 011015-1–011015-19 (2008)

    Google Scholar 

  2. Wahl, J.: Articulated Tool Head, WIPO Patent No. WO 00/25976 (2000)

    Google Scholar 

  3. Bonev, I.A.: Geometric Analysis of Parallel Mechanisms, Ph.D. thesis, Laval University, Quebec (2002)

    Google Scholar 

  4. Xi, F., Han, W., Marcel, V., Ross, A.: Development of a Sliding-leg Tripod as an Add-on Device for Manufacturing. Robotica 18, 285–294 (2000)

    Google Scholar 

  5. Xu, Y.N., Xi, F.: A Realtime Method for Solving the Forward Kinematics of a Tripod with Fixed-length Legs. Journal of Manufacturing Science and Engineering Transaction of ASME 128(2), 204–212 (2006)

    Article  Google Scholar 

  6. Xu, Y.N., Liu, X.J., Wang, J.S.: Analytical Forward Kinematics for Two Kinds of Typical Tripods. Part I: Closed-Form Solutions for Forward Kinematics Methods. In: Su, C.-Y., Rakheja, S., Liu, H. (eds.) ICIRA 2012, Part I. LNCS (LNAI), vol. 7506, pp. 282–293. Springer, Heidelberg (2012)

    Google Scholar 

  7. Luh, C., Adkins, F.A., Haug, E.J.: Working Capability Analysis of Stewart Platforms. Journal of Mechanical Design, Transactions of the ASME 118(2), 220–227 (1996)

    Article  Google Scholar 

  8. Merlet, J.P.: Design a Parallel Manipulator for a Special Worksapce. International Journal of Robotics Research 16(4), 545–556 (1997)

    Article  Google Scholar 

  9. Stamper, R.E., Tsai, L.W., Walshg, G.C.: Optimization of a Three DOF Translational Platform for Well-Conditional Workspace. In: Procedings of the 1997 IEEE International Conference on Robotics and Automation, Albuquerque, New Mexico, pp. 3250–3255 (1997)

    Google Scholar 

  10. Carretero, J.A., Nahon, M.A., Podhorodeski, R.: Workspace Analysis and Optimization of a Novel 3-DOF Parallel Manipulator. IEEE Trans. Rob. Autom. 15(4), 178–188 (2000)

    Google Scholar 

  11. Kumar, V.: Characterization of Workspaces of Parallel Manipulators. Journal of Mechanical Design 14(3), 368–375 (1992)

    Article  Google Scholar 

  12. Gosselin, C.M.: Determination of the Workspace of 6-DOF Parallel Manipulators. Journal of Mechanical Design 112(3), 331–336 (1990)

    Article  Google Scholar 

  13. Kim, D.I., Chung, W.K., Youm, Y.: Geometrical Approach for the Workspace of 6-DOF Parallel Manipulators. In: Proceedings of the 1997 IEEEE International Conference on Robotics and Automation, Albuquerque, New Mexco, pp. 2986–2991 (1997)

    Google Scholar 

  14. Pond, G.T., Carretero, J.A.: Kinematic Analysis and Workspace Determination of the Inclined PRS Parallel Manipulator. In: Proc. of 15th CISMIFToMM Symposium on Robot Design, Dynamics, and Control, Paper No. Rom04-18, Montreal (2004)

    Google Scholar 

  15. Haug, E.J., Luh, C., Adkins, F.A.: Numerical Alogrithms for Mapping Boundaries of Manipulators Worksapces. Journal of Mechanical Design, Transactions of the ASME 118(2), 228–234 (1996)

    Article  Google Scholar 

  16. Adkins, F.A., Haug, E.J.: Operational Envelope of a Spatial Stewart Platform. Journal of Mechanical Design, Transactional of the ASME 119(2), 330–332 (1997)

    Article  Google Scholar 

  17. Marco, C., Massimo, S.: The Effects of Design Parameters on the Workspace of a Turin Parallel Robot. The International Journal of Robotics Research 17(8), 886–902 (1998)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, P.R. China, 100084

    You-Nan Xu, Xin-Jun Liu & Jin-Song Wang

  2. Mechanical & Electronical Engineering, East China Jiaotong University, Nanchang, Jiangxi, P.R. China, 330013

    You-Nan Xu

Authors
  1. You-Nan Xu
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  2. Xin-Jun Liu
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  3. Jin-Song Wang
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Concordia University, H3G 1M8, Montreal, Canada

    Chun-Yi Su

  2. Mechanical and Industrial Engineering, Concordia University, 1515 St. Catherine St. West, Montreal, Quebec, Canada

    Subhash Rakheja

  3. School of Creative Technologies, The University of Portsmouth, PO1 2DJ, Portsmouth, UK

    Honghai Liu

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© 2012 Springer-Verlag Berlin Heidelberg

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Xu, YN., Liu, XJ., Wang, JS. (2012). Analytical Forward Kinematics for Two Kinds of Typical Tripods Part II: Analyzing for Their Workspaces, and Performances of the Forward Kinematics. In: Su, CY., Rakheja, S., Liu, H. (eds) Intelligent Robotics and Applications. ICIRA 2012. Lecture Notes in Computer Science(), vol 7506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33509-9_27

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  • DOI: https://doi.org/10.1007/978-3-642-33509-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33508-2

  • Online ISBN: 978-3-642-33509-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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