Workspace Modelling of a Parallel Robot with Relative Manipulation Mechanisms Based on Optimization Methods

  • Dmitry MalyshevEmail author
  • Larisa Rybak
  • Laxmidhar Behera
  • Santhakumar Mohan
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 78)


The article describes the application of optimization algorithms for solving the problem of determining the workspace of a relative mechanism device, which includes a planar 3-RPS mechanism and a tripod module. Approximation sets of individual modules are used to approximate its workspace in the moving coordinate system. The considered method of approximating a solution set of nonlinear inequalities based on the concept of the non-uniform coverings, describes constraints on the robot geometric parameters. The exterior and interior approximations of the 3-RPS mechanism are obtained. Similarly, an approximation of the restrictions for the tripod module in the moving platform coordinate system is obtained. The constraints with a given accuracy are transferred to the coordinate system of the output using a three-dimensional binary array approximating the workspace. The workspace of the relative mechanism device was obtained on the basis of these results, taking into account the relative manipulation of modules and restrictions on the workpiece geometric parameters. Moving coordinate system is located in the center of the planar 3-RPS mechanism platform.


Approximation set Relative mechanism device Workspace Non-uniform coverings Optimization 



This work was supported by the Russian Science Foundation, the agreement number 16-19-00148 and Science Committee, the Ministry of Education and Science, Republic of Kazakhstan, project no. АР05133190.


  1. 1.
    Aleshin, A.K., Glazunov, V.A., Rashoyan, G.V., Shai, O.: Analysis of kinematic screws that determine the topology of singular zones of parallel-structure robots. J. Mach. Manuf. Reliab. 45(4), 291–296 (2016)CrossRefGoogle Scholar
  2. 2.
    Kong, H., Gosselin, C.M.: Type Synthesis of Parallel Mechanisms. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  3. 3.
    Merlet, J.-P.: Parallel Robots, 2nd edn. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  4. 4.
    Evtushenko, Y.: Numerical methods for finding global extreme (case of a non-uniform mesh). U.S.S.R. Comput. Maths. Math. Phys. 11, 1390–1403 (1971)CrossRefGoogle Scholar
  5. 5.
    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, El-ConRus 2017, pp. 386–389 (2017)Google Scholar
  6. 6.
    Evtushenko, Y., Posypkin, M., Rybak, L., Turkin, A.: Approximating a solution set of non-linear inequalities. J. Global Optim. 7, 129–145 (2018)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Rao, P.S., Rao, N.M.: Position analysis of spatial 3-RPS parallel manipulator. Int. J. Mech. Eng. Robot. Res. 2(2), 80–90 (2013)Google Scholar
  9. 9.
    Posypkin, M., Rybak, L., Malyshev, D., Gaponenko, E.: Approximation of the parallel robot working area using the method of nonuniform covering. In: Liu, G.R., Trovalusci, P. (eds.) Proceedings at the 9th ICCM2018, 6th–10th August 2018, Rome, Italy, pp. 949–960. ScienTech Publisher (2018)Google Scholar
  10. 10.
    Rybak, L.A., Gaponenko, E.V., Malyshev, D.I., Virabyan, L.G.: The algorithm for planning the trajectory of the 3-RPR robot, taking into account the singularity zones based on the method of non-uniform covering. In: IOP Conference on Series: Materials Science and Engineering 489, 012060 (2019)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Belgorod State Technological University Named After V.G. ShukhovBelgorodRussian Federation
  2. 2.Indian Institute of Technology KanpurKanpurIndia
  3. 3.Indian Institute of Technology PalakkadPalakkadIndia

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