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Exact Inverse Solution for a 7R Manipulator Based on a Novel Screw-Based Sub-problem

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Advances in Mechanism, Machine Science and Engineering in China (CCMMS 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

Inverse kinematics (IK) is a significant theoretical foundation for the real application of redundant manipulators. In existing methods, the Denavit-Hartenberg (DH) conversion and screw-based IK sub-problems have been utilized to calculate the inverse solution, but would be limited by some special manipulators’ configurations or cannot obtain exact solutions. In this paper, an exact inverse solution for a 7R manipulator is modeled based on screw theory. In the modeling, firstly assuming that the first joint is known, the total motion of all joints are divided into three steps of operational motions: Rotation about the second, third and fourth joints; Rotation about the five and six joints; And rotation about the last joint. Problems for the first two rotations can be both modeled based on a novel screw-based sub-problem. Finally, the angular displacements of six joints are formulated explicitly in terms of the redundant joint angle. Using the proposed method, all exact solutions can be obtained by traversing values of the redundant angle. The effectiveness and efficiency of the proposed technique is validated using a simulation in MATLAB.

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References

  1. Farzan S, DeSouza GN (2013) From dh to inverse kinematics: a fast numerical solution for general robotic manipulators using parallel processing. In: IEEE/RSJ international conference on intelligent robots and systems. IEEE, 2507–2513

    Google Scholar 

  2. Tan YS, Cheng PL, Xiao AP (2010) Solution for a new sub-problem in screw theory and its’ application in the inverse kinematics of a manipulator. Appl Mech Mater 34(35):271–275

    Article  Google Scholar 

  3. Cheng H, Gupta KC (2010) A study of robot inverse kinematics based upon the solution of differential equations. J Robot Syst 8(2):159–175

    Article  MATH  Google Scholar 

  4. Yin F, Wang YN, Wei SN (2011) Inverse kinematic solution for robot manipulator based on electromagnetism-like and modified DFP algorithms. Acta Automatica Sinica 37(1):74–82

    MathSciNet  Google Scholar 

  5. Zhao YJ, Dong XJ (2010) A new solution to the inverse position analysis of the redundant serial robot. J Shanghai Jiaotong Univ (English Edition) 15(5):610–614

    Article  MATH  Google Scholar 

  6. Huang LS, Jiang RK (2013) A new method of inverse kinematics solution for industrial 7DOF robot. In: Proceedings of the 32nd chinese control conference. IEEE, 6063–6065

    Google Scholar 

  7. Crenganiş M, Breaz R, Racz G, Bologa O (2012) The inverse kinematics solutions of a 7 DOF robotic arm using Fuzzy Logic. In: IEEE conference on industrial electronics and applications (ICIEA) IEEE, 518–523

    Google Scholar 

  8. Pfurner M (2016) Closed form inverse kinematics solution for a redundant anthropomorphic robot arm. Comput Aided Geom Des 47(1):163–171

    Article  MathSciNet  MATH  Google Scholar 

  9. Lee HY, Liang CG (1988) Displacement analysis of the general spatial 7-link 7R mechanism. Mech Mach Theory 23(3):219–226

    Article  Google Scholar 

  10. Duffy J, Crane C (1980) A displacement analysis of the general spatial 7-link, 7R mechanism. Mech Mach Theory 15(3):153–169

    Article  Google Scholar 

  11. Huang QL, Wu J, Xiong R (2012) A solution of inverse kinematics for 7-DOF manipulators and its application. In: Proceedings of the 10th world congress on intelligent control and automation. IEEE, 3711–3717

    Google Scholar 

  12. Chen WH, Yang MM, Yu SQ, Wang TM (2014) A hybrid algorithm for the kinematic control of redundant robots 5, 4438–4443.

    Google Scholar 

  13. An HH, Clement WI, Reed B (2014) Analytical inverse kinematic solution with self-motion constraint for the 7-DOF restore robot arm. IEEE/ASME Int Conf Adv Intell Mechatron 2014:1325–1330

    Google Scholar 

  14. Xu J, Liu Z, Cheng Q, Zhao Y, Pei Y, Yang C (2019) Models for three new screw-based IK sub-problems using geometric descriptions and their applications. Appl Math Model 67:399–412

    Article  MathSciNet  MATH  Google Scholar 

  15. Chen QC, Zhu SQ, Zhang XQ (2015) Improved inverse kinematics algorithm using screw theory for a six-DOF robot manipulator. Int J Adv Rob Syst 12(10):140

    Article  Google Scholar 

  16. Sun JD, Cao GZ, Li WB, Liang YX, Huang SD (2017) Analytical inverse kinematic solution using the D-H method for a 6-DOF robot. In: 2017 14th international conference on ubiquitous robots and ambient intelligence, 714–716

    Google Scholar 

Download references

Acknowledgements

Supported by China Postdoctoral Science Foundation (No. 2021M700301), Scientific Research Project of Beijing Educational Committee (No. KM202210005031), and Beijing Post doctoral Research Foundation (No. Q6001211202101, Q6001211202102)

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Authors and Affiliations

  1. Institute of Advanted Manufacturing and Intelligent Technology, Beijing University of Technology, 100124, Beijing, China

    Tiantian Liu, Tianyue Gan & Jingjing Xu

  2. Key Laborary of CNC Equipment Reliability, Ministry of Education, School of Mechanical and Aerospace Engineering, Jilin, China

    Zhifeng Liu

  3. Machinery Industry Key Laboratory of Heavy Machine Tool Digital Design and Testing Technology, 100124, Beijing, China

    Tiantian Liu, Zhifeng Liu, Tianyue Gan & Jingjing Xu

Authors
  1. Tiantian Liu
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  2. Zhifeng Liu
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  3. Tianyue Gan
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  4. Jingjing Xu
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Corresponding author

Correspondence to Jingjing Xu .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Tsinghua University, Beijing, China

    Xinjun Liu

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Liu, T., Liu, Z., Gan, T., Xu, J. (2023). Exact Inverse Solution for a 7R Manipulator Based on a Novel Screw-Based Sub-problem. In: Liu, X. (eds) Advances in Mechanism, Machine Science and Engineering in China. CCMMS 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-9398-5_109

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  • DOI: https://doi.org/10.1007/978-981-19-9398-5_109

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-9397-8

  • Online ISBN: 978-981-19-9398-5

  • eBook Packages: EngineeringEngineering (R0)

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