Structural and Kinematic Analysis of a Shaper Linkage with Four-Bar Assur Group

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


This study provides a structural and kinematic analysis of the shaper linkage, which includes a four-bar Assur group with three levers. The linkage structural analysis has been carried out in three cases when different driving links have been chosen. A four-bar Assur group has been separated out from the linkage’s structure in the first case, and dyads PRP, RRR, and RPR have been separated out in the second and third cases. The kinematic analysis of the shaper linkage has been carried out for the case when a four-bar Assur group forms a part of its composition. The study provides 3D modeling of the shaper linkage with reproduced trajectories and coordinates data of the distinguished points of movable links with the regard to specified dimensions. The results of the study can be used in kinetostatic and dynamic analysis of the shaper linkage. The research results can be also applied in a design of planing machines and shaper linkages as well as in structural synthesis and analysis of novel planar mechanisms.


Degree of freedom Kinematic pair Assur group Shaper linkage 



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.
    Jansen T (2007) The great pretender. 010 Publishers, RotterdamGoogle Scholar
  2. 2.
    Nansai S et al (2013) Exploration of adaptive gait patterns with a reconfigurable linkage mechanism. In: IEEE/RSJ international conference on intelligent robots and systems (IROS), Tokyo, Japan, 3–7 Nov 2013Google Scholar
  3. 3.
    Rooney T et al (2011) Artificial active whiskers for guiding underwater autonomous walking robots. In: CLAWAR 2011, Paris, France, 6–8 Sept 2011Google Scholar
  4. 4.
    Kim H et al (2016) Running robotic platform by repeated motion of six spherical footpads. IEEE/ASME Trans Mechatron 21(1):175–183Google Scholar
  5. 5.
    Acary V, Akhadkar N, Brogliato B (2017) Worst-case analysis of approximate straight-line motion mechanism with link tolerances and joint clearances. In: ENOC 2017, Budapest, Hungary, 25–30 June 2017Google Scholar
  6. 6.
    Ghassaei A (2011) The design and optimization of a crank-based leg mechanism. Thesis, Pomona CollegeGoogle Scholar
  7. 7.
    Simionescu P, Tempea I (1999) Kinematic and kinetostatic simulation of a leg mechanism. In: 10th world congress on the theory of machines and mechanisms, Oulu, Finland, 20–24 June 1999Google Scholar
  8. 8.
    Funabashi H et al (1999) Development of a walking chair with a self-attitude-adjusting mechanism for stable walking on uneven terrain. In: 10th world congress on the theory of machines and mechanisms, Oulu, Finland, 20–24 June 1999Google Scholar
  9. 9.
    Simionescu P (2016) MeKin2D: Suite for planar mechanism kinematics. In: ASME 2016 design engineering technical conferences and computers and information in engineering conference, Charlotte, USA, 21–24 Aug 2016Google Scholar
  10. 10.
    Seifabadi R, Iordachita I, Fichtinger G (2012) Design of a tele operated needle steering system for MRI-guided prostate interventions. In: 4th IEEE RAS & EMBS international conference on biomedical robotics and biomechatronics (BioRob), Rome, Italy, 24–27 June 2012Google Scholar
  11. 11.
    Ceccarelli M (2014) Distinguished figures in mechanism and machine science: their contributions and legacies. History of mechanism and machine science. Springer, LondonCrossRefGoogle Scholar
  12. 12.
    Hsieh W, Tsai C (2009) A study on a novel quick return mechanism. Trans Can Soc Mech Eng 33(3):139–152CrossRefGoogle Scholar
  13. 13.
    Lipson H (2004) How to draw a straight line using a GP: benchmarking evolutionary design against 19th century kinematic synthesis. In: Keijzer M (ed) Late breaking papers at the 2004 genetic and evolutionary computation conference, Seattle, USAGoogle Scholar
  14. 14.
    Monkova K et al (2011) Kinematic analysis of quick-return mechanism in three various approaches. Tech Gaz 18(2):295–299Google Scholar
  15. 15.
    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
  16. 16.
    Haug E (1989) Computer aided kinematics and dynamics of mechanical systems. Volume I: basic methods. Allyn & Bacon, Inc. Needham Heights, MA, USAGoogle Scholar
  17. 17.
    Pavlovic N (1989) Analysis of mechanical error in quick-return shaper mechanism. In: 12th IFToMM world congress, Besancon, France, 18–21 June 2007Google Scholar
  18. 18.
    Peisakh E (2007) An algorithmic description of the structural synthesis of planar Assur groups. J Mach Manuf Reliab 6:3–14Google Scholar
  19. 19.
    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
  20. 20.
    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
  21. 21.
    Barker C (1985) A complete classification of planar four-bar linkages. Mech Mach Theory 20(6):535–554CrossRefGoogle Scholar
  22. 22.
    Arakelian V, Smith M (2008) Design of planar 3-DOF 3-RRR reactionless parallel manipulators. Mechatronics 18(10):601–606CrossRefGoogle Scholar
  23. 23.
    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
  24. 24.
    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
  25. 25.
    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
  26. 26.
    Fomin A, Dvornikov L, Paik J (2017) Calculation of the general number of imposed constraints of kinematic chains. J Procedia Eng 206:1309–1315CrossRefGoogle Scholar
  27. 27.
    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 December 2015, 124 (1):012055Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

Personalised recommendations