Study on Structure and Kinematics of Quick-Return Mechanism with Four-Bar Assur Group

  • A. FominEmail author
  • A. Olexenko
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The presented study shows results of structural and kinematic analysis of a planar six-bar quick-return mechanism that is used in shaping and planing machines for transformation of rotational motion of a driving link into prismatic motion of an end-effector. Assur groups of the III and II classes have been separated out from a quick-return mechanism when different driving links have been chosen during a structural analysis. Kinematic analysis has been carried out by grapho-analytical method for the case when a four-bar Assur group is included. Finally, 3D model has been simulated and coordinates of distinguished points of movable links have been found in six positions of the mechanism depending on the rotation of a driving link. The obtained results can be used in kinetostatic and dynamic analysis of the quick-return mechanism. The findings of the study can also be used in a design of planning and shaping machines, in synthesis and analysis of novel planar mechanisms.


Quick-return mechanism Assur group Degree-of-freedom Kinematic pair 



The study has been carried out with the support of the Russian President Scholarship according to the research project SP-3755.2016.1.


  1. 1.
    Vasiliu A, Yannou B (2001) Dimensional synthesis of planar mechanisms using neural networks: application to path generator linkages. Mech Mach Theory 36(2):299–310CrossRefGoogle Scholar
  2. 2.
    Nielsen J, Roth B (1999) Solving the input/output problem for planar mechanisms. J Mech Des 121(2):206–211CrossRefGoogle Scholar
  3. 3.
    Glazunov V, Kheylo S (2016) Dynamics and control of planar, translational and spherical parallel manipulators. In: Zhang D, Wei B (eds) Dynamic balancing of mechanisms and synthesizing of parallel robots. Springer, Cham, pp 365–402CrossRefGoogle Scholar
  4. 4.
    Liu Y, McPhee J (2004) Automated type synthesis of planar mechanisms using numeric optimization with genetic algorithms. J Mech Des 127(5):910–916CrossRefGoogle Scholar
  5. 5.
    Glazunov V et al (2013) 3-DOF translational and rotational parallel manipulators. In: Viadero-Rueda F, Ceccarelli M (eds) EUCOMES 2012, 4th European conference on mechanism science. New trends in mechanism and machine science. Mechanisms and Machine Science, vol 7. Springer, Dordrecht, pp 199–207Google Scholar
  6. 6.
    Wu J et al (2006) Analysis and application of a 2-DOF planar parallel mechanism. J Mech Des 129(4):434–437CrossRefGoogle Scholar
  7. 7.
    Laryushkin P et al (2014) Singularity analysis of 3-DOF translational parallel manipulator. In: Ceccarelli M, Glazunov V. (eds) ROMANSY 2014 XX CISM-IFToMM symposium on theory and practice of robots and manipulators, Moscow, 23–26 June 2014. Mechanisms and Machine Science, vol 22. Springer, Cham, pp 47–54Google Scholar
  8. 8.
    Monkova K et al (2011) Kinematic analysis of quick-return mechanism in three various approaches. Tech Gazette 18(2):295–299Google Scholar
  9. 9.
    Fung F, Lee Y (1997) Dynamic analysis of the flexible rod of quick-return mechanism with time-dependent coefficients by the finite element method. J Sound Vib 202(2):187–201CrossRefGoogle Scholar
  10. 10.
    Dvornikov L (2008) K voprosu o klassifikacii ploskih grupp Assura (On the classification of planar Assur groups). Theory Mech Mach 2(6):18–25Google Scholar
  11. 11.
    Peisakh EE (2007) An algorithmic description of the structural synthesis of planar Assur groups. J Mach Manuf Reliab 6:3–14Google Scholar
  12. 12.
    Li S, Dai J (2008) Structure synthesis of single-driven metamorphic mechanisms based on the augmented Assur groups. J Mech Robot 4(3):031004CrossRefGoogle Scholar
  13. 13.
    Barker C (1985) A complete classification of planar four-bar linkages. Mech Mach Theory 20(6):535–554CrossRefGoogle Scholar
  14. 14.
    Uicker J, Pennock G Jr, Shigley J (2011) Theory of machines and mechanisms, 4th edn. Oxford University Press, New YorkGoogle Scholar
  15. 15.
    Arakelian V, Smith M (2008) Design of planar 3-DOF 3-RRR reactionless parallel manipulators. Mechatronics 18(10):601–606CrossRefGoogle Scholar
  16. 16.
    Cha S-H, Lasky T, Velinsky S (2007) Singularity avoidance for the 3-RRR mechanism using kinematic redundancy. In: Proceedings of IEEE international conference on robotics and automation, Roma, Italy, 10–14 Apr 2007Google Scholar
  17. 17.
    Arsenault M, Boudreau R (2004) The synthesis of three-degree-of-freedom planar parallel mechanisms with revolute joints (3-RRR) for an optimal singularity-free workspace. J Field Robot 21(5):259–274zbMATHGoogle Scholar
  18. 18.
    Wu J, Wang J, Wang L (2010) A comparison study of two planar 2-DOF parallel mechanisms: one with 2-RRR and the other with 3-RRR structures. Robotica 28(6):937–942MathSciNetCrossRefGoogle Scholar
  19. 19.
    Dvornikov L (2004) O kinematicheskoj razreshimosti ploskoj chetyrehzvennoj gruppy Assura chetvertogo klassa grafo-analiticheskim metodom (On the kinematic solvability of the planar Assur group of the fourth class by grapho-analytical method). Proceedings of Higher Educational Institutions. Mach Build 12:9–15Google Scholar
  20. 20.
    Fomin A, Dvornikov L, Paik J (2017) Calculation of the general number of imposed constraints of kinematic chains. J Proc Eng 206:1309–1315CrossRefGoogle Scholar
  21. 21.
    Fomin A et al (2016) To the theory of mechanisms subfamilies. In: Proceedings of MEACS2015. IOP Conference Series: Materials Science and Engineering, Tomsk Polytechnic University, Tomsk, 1–4 Dec 2015, vol 124, No 1, p 012055CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mechanical Engineering Research Institute of the RASMoscowRussia
  2. 2.Siberian State Industrial UniversityNovokuznetskRussia

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