Solving the Forward Kinematics Problem for a Welding Manipulator With Six Degrees of Freedom

: pp. 27 - 34
Lviv Polytechnic National University, Ukraine
Lviv Polytechnic National University, Bydgoszcz University of Science and Technology

The article proposes a solution of the forward kinematics problem for a welding manipulator with six degrees of freedom. Solving this problem is the first necessary step in creating a control system for this manipulator. This will make it possible to determine the displacement, accelerations and moments in each of the manipulator parts and will ensure accurate positioning of the welding tool.

When solving the set task, the manipulator structure was described and features of its application were specified. The kinematic scheme of the manipulator with six degrees of freedom is presented. Based on it and using the Denavit—Hartenberg method, transformation matrices were compiled, which determine the spatial positions of each of the manipulator links. Using the Denavit—Hartenberg transformation made it possible to reduce the total number of generalized coordinates from six to four without losing the accuracy of the final result.

To find the final position of the welding tool, an algorithm of sequential operations was developed, based on which gradual transitions between the joints of the welding manipulator are carried out. The created algorithm was implemented in the Matlab environment in the form of a mathematical model. In order to verify the correctness of the decisions made, an example of calculating the trajectory of movement and the final position of the welding tool of the Carl Cloos Schweisstechnik industrial manipulator is presented. The obtained results completely coincided with the predetermined position, which indicates the adequacy of the created model. In the future, based on this model, it is planned to synthesize a control system for the welding manipulator.

  1. Synthesis of robotic systems in mechanical engineering: Textbook / L. E. Pelevin, K. I, Pochka, O. M. Garkavenko, D. O. Mishchuk, I. V. Rusan. K.: NVP "Interservice", 2016. 258 p. books/2019/Pelevin_2016_258.pdf.
  2. Tsvirkun L. I., Gruler G. Robotics and mechatronics: Study guide. D. National Mining University, 2007. 216 p.
  3. Denavit J. and Hartenberg R. S. "A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices," Journal of Applied Mechanics, vol. 22, pp. 215-221, 1955. DOI:
  4. Fu K. S., Gonzalez R. C., Lee Robotics C. S. G.: Trans. from Eng. M.:Mir, 1989. 624 p. https://www.studmed. ru/fu-k-gonsales-r-li-k-robototehnika_8855f0f7adb.html.
  5. Sokol G. I. Theory of mechanisms of robotic systems. Kinematics: Study guide. / Sokol G. I. Dnipro: RVV DNU, 2002. 92 p.
  6. Marushchak Y. Y., Kushnir A. P. The mathematical model of the mechanism of electrodes movement of arc steel-melting furnaces on he basis of Denavit-Hartenberg presentation // Electrical and computer systems. 2016. No. 22 (98). pp. 20-27. DOI:
  7. Dmitrieva I. S., Levchenko D. O. Research of kinematic model of manipulative robot // System technology. 2015. No. 3 (98). pp. 57-62.
  8. Zenkevich S. L., Yushchenko A. S. Robot control. The basics of manipulating robots control: Textbook for universities - M.: Pub. BMSTU, 2000. 400 p.
  9. Burdakov S. F., Dyachenko V. A., Timofeev A. N. Design of manipulators of industrial robots and robotic complexes. M.: High school, 1986. 264 p. proektirovanie-manipulyatorov-promyshlennyh-robotov-i-robotizirovannyh-kompleksov_f9dfe59d37d.html.
  10. Lomovtseva E. I., Chelnokov Y. N., Dual matrix and biquaternion methods for solving direct and inverse problems of kinematics of robotic manipulators on the example of a Stanford manipulator // Pub. Saratov univ. new ep. Ep. Mathematics. Mechanics. Informatics. 2014. T. rel. 1. pp. 88--95. DOI:10.0000/ article/n/dualnye-matrichnye-i-bikvaternionnye-metody-resheniya-pryamoy-i-obratnoy-zadach-kinematiki-robotov- manipulyatorov-na-primere.
  11. Chelnokov Y. N. Quaternion and biquaternion models and methods of rigid body mechanics and their applications. Geometry and kinematics of motion. M.: Fizmatlit, 2016. 511 p.
  12. Funda, J.; Taylor, R. H. & Paul, R.P. On homogeneous transforms, quaternions, and computational efficiency //IEEE Trans.Robot. Automat. 1990. Vol. 6. pp. 382-388. DOI:
  13. Colomé A., Torras C. Redundant inverse kinematics: Experimental comparative review and two enhancements // Intelligent Robots and Systems (IROS). 2012. pp. 5333-5340. DOI:
  14. Duka A.V. Neural network based inverse kinematics solution for trajectory tracking of a robotic arm // Procedia Technology. 2014. Vol. 12. рр. 20-27. DOI: