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Determination of the Workspace of the System Based on the 3-PRRR Mechanism for the Lower Limb Rehabilitation

Part of the Mechanisms and Machine Science book series (Mechan. Machine Science,volume 85)


The article proposes a lower limb rehabilitation system based on a passive orthosis and an active parallel robot 3-PRRR. Numerical algorithms have been developed to determine the workspace of the parallel mechanism, taking into account the interference of the links. The optimization of the geometrical parameters of the mechanism has been carried out, and the configuration of the robot has been selected based on the criterion of maximizing the workspace. The analysis of the workspace and the influence of various geometric parameters on it is carried out. The simulation results of the workspaces, as well as the positions of the robot at which interference occur, are rendered using the transformation of a set of 3D boxes to an STL file.


  • Approximation set
  • Parallel robot
  • Workspace
  • Non-uniform covering
  • Optimization
  • Link interference

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  • DOI: 10.1007/978-3-030-83594-1_20
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  1. Vashisht, N., Puliyel, J.: Polio programme: let us declare victory and move. Indian J. Med. Ethics 9(2), 114–117 (2012)

    Google Scholar 

  2. Bouri M., Stauffer Y., Schmitt C., Allemand Y., Gnemmi S., Clavel R.: The Walk Trainer TM: A Robotic System for Walking Rehabilitation. In: IEEE International Conference on Robotics and Biomimetics, pp. 1616–1621. IEEE, USA (2006)

    Google Scholar 

  3. Rios, A., Hernandez, E., Moreno, J.A., Keshtkar, S., Garza, R.: Kinematics analysis of a new 3DOF parallel manipulator as walking rehabilitation device. In: 15th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), pp. 1–6. IEEE, USA (2018)

    Google Scholar 

  4. Almaghout, K., Tarvirdizadeh, B., Alipour, K., Hadi, A.: Design and control of a lower limb rehabilitation robot considering undesirable torques of the patient’s limb. J. Eng. Med. 234, 1457 (2020)

    CrossRef  Google Scholar 

  5. Bouri, M., Gall, B., Clavel, R.: A new concept of parallel robot for rehabilitation and tness: the Lambda. In: Proceedings of the 2009 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 2503–2508. IEEE, USA (2009)

    Google Scholar 

  6. Kong, X., Gosselin, C.M.: Kinematics and singularity analysis of a novel type of 3-CRR 3 DOF translational parallel manipulator. Int. J. Robot. Res. 21(9), 791–798 (2002)

    CrossRef  Google Scholar 

  7. Evtushenko, Y., Posypkin, M., Rybak, L., Turkin, A.: Approximating a solution set of nonlinear inequalities. J. Global Optim. 71(1), 129–145 (2017).

    MathSciNet  CrossRef  MATH  Google Scholar 

  8. Evtushenko, Y., Posypkin, M., Turkin, A., Rybak, L.: The non-uniform covering approach to manipulator workspace assessment. In: Proceedings of the 2017 IEEE Russia Section Young Researchers in Electrical and Electronic Engineering Conference (ElConRus 2017), pp. 386–389. IEEE, USA (2017)

    Google Scholar 

  9. Rybak, L.A., Posypkin, M.A., Turkin, A.V.: Method for approximating the workspace of the parallel robot. Int. J. Pharm. Technol. 8(4), 25045–25055 (2016)

    Google Scholar 

  10. Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics. Springer, New York (2001).

    CrossRef  MATH  Google Scholar 

  11. Merlet, J.P.: Determination of 6D workspace of gough-type parallel manipulator and comparison between different geometries. Int. J. Robot. Res 18(9), 902–916 (1999)

    CrossRef  Google Scholar 

  12. Anvari, Z., Ataei, P., Masouleh, M.T.: The collision-free workspace of the tripteron parallel robot based on a geometrical approach. In: Computational Kinematics, pp. 357–364 (2018)

    Google Scholar 

  13. Behera, L., Rybak, L., Malyshev, D., Gaponenko, E.: Determination of workspaces and intersections of robot links in a multi-robotic system for trajectory planning. Appl. Sci. 11, 4961 (2021)

    CrossRef  Google Scholar 

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This work was supported by the Russian Science Foundation, the agreement number 19-19-00692, the Ministry of Education and Science, Republic of Kazakhstan, project no. AP05133190.

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Ahmetzhanov, M., Rybak, L., Malyshev, D., Mohan, S. (2022). Determination of the Workspace of the System Based on the 3-PRRR Mechanism for the Lower Limb Rehabilitation. In: Beran, J., Bílek, M., Václavík, M., Žabka, P. (eds) Advances in Mechanism Design III. TMM 2020. Mechanisms and Machine Science, vol 85. Springer, Cham.

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