Advancement of MSA-Technique for Stiffness Modeling of Serial and Parallel Robotic Manipulators

Conference paper
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 584)


The paper presents advancement of the matrix structural analysis technique (MSA) for stiffness modeling of robotic manipulators. In contrast to the classical MSA, it can be applied to both parallel and serial manipulators composed of flexible and rigid links connected by rigid, passive or elastic joints with multiple external loadings. The manipulator stiffness model is presented as a set of basic equations describing the link elasticities that are supplemented by a set of constraints describing connections between links. These equations are aggregated straightforwardly in a common linear system without traditional merging of the matrix rows and columns, which allows avoiding conventional manual transformations at the expense of numerical inversion of the sparse matrix of higher dimension.


Stiffness modeling Matrix structural analysis Serial robots Parallel robots 



The work presented in this paper was supported by the grant of Russian Science Foundation № 17-19-01740.


  1. 1.
    Klimchik, A., et al.: Efficiency evaluation of robots in machining applications using industrial performance measure. Rob. Comput.-Integr. Manuf. 48, 12–29 (2017)CrossRefGoogle Scholar
  2. 2.
    Pashkevich, A., Klimchik, A., Chablat, D.: Enhanced stiffness modeling of manipulators with passive joints. Mech. Mach. Theory 46(5), 662–679 (2011)CrossRefGoogle Scholar
  3. 3.
    Yan, S.J., Ong, S.K., Nee, A.Y.C.: Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method. Rob. Comput.-Integr. Manuf. 37, 13–22 (2016)CrossRefGoogle Scholar
  4. 4.
    Gonçalves, R.S., et al.: A comparison of stiffness analysis methods for robotic systems. Int. J. Mech. Control 17(2), 35–58 (2016)Google Scholar
  5. 5.
    Klimchik, A., Chablat, D., Pashkevich, A.: Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings. Mech. Mach. Theory 79, 1–28 (2014)CrossRefGoogle Scholar
  6. 6.
    Liu, H., et al.: Stiffness Modeling of Parallel Mechanisms at Limb and Joint/Link Levels. IEEE Trans. Rob. 33(3), 734–741 (2017)CrossRefGoogle Scholar
  7. 7.
    Yeo, S.H., Yang, G., Lim, W.B.: Design and analysis of cable-driven manipulators with variable stiffness. Mech. Mach. Theory 69, 230–244 (2013)CrossRefGoogle Scholar
  8. 8.
    Klimchik, A., Pashkevich, A.: Serial vs. quasi-serial manipulators: comparison analysis of elasto-static behaviors. Mech. Mach. Theory 107, 46–70 (2017)CrossRefGoogle Scholar
  9. 9.
    Cammarata, A.: Unified formulation for the stiffness analysis of spatial mechanisms. Mech. Mach. Theory 105, 272–284 (2016)CrossRefGoogle Scholar
  10. 10.
    Shi, S., et al., Static stiffness modelling of EAST articulated maintenance arm using matrix structural analysis method. Fusion Engineering and Design (2017)Google Scholar
  11. 11.
    Azulay, H., et al.: Comparative analysis of a new 3 × PPRS parallel kinematic mechanism. Rob. Comput.-Integr. Manuf. 30(4), 369–378 (2014)CrossRefGoogle Scholar
  12. 12.
    Deblaise, D., Hernot, X., Maurine, P.: A systematic analytical method for PKM stiffness matrix calculation. In: IEEE International Conference on Robotics and Automation (ICRA 2006). IEEE (2006)Google Scholar
  13. 13.
    Klimchik, A., Pashkevich, A., Chablat, D.: CAD-based approach for identification of elasto-static parameters of robotic manipulators. Finite Elem. Anal. Des. 75, 19–30 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© CISM International Centre for Mechanical Sciences 2019

Authors and Affiliations

  1. 1.Innopolis UniversityInnopolisRussia
  2. 2.Centre National de la Recherche Scientifique (CNRS)NantesFrance
  3. 3.Le Laboratoire des Sciences du Numérique de Nantes (LS2N)NantesFrance
  4. 4.IMT AtlantiqueNantesFrance

Personalised recommendations