Skip to main content

Design of Reactionless Linkages and Robots Equipped with Balancing Assur Groups

  • Chapter
Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots

Abstract

In the present chapter, we consider the shaking moment and shaking force balancing through the use of additional Assur groups mounted on the mechanism to be balanced. Two types of mechanisms are considered: (1) the in-line four-bar linkage and (2) the planar parallel robots with prismatic pairs. For both types of mechanisms, the proposed solution allows the reduction (or even the cancellation in the case of the four-bar linkage) of the number of counter-rotations used for obtaining the shaking moment balancing, which decreases the design complexity and the inherent problems due to the use of counter-rotations (backlash, noise, vibrations, etc.). All theoretical developments are validated via simulations carried out using ADAMS software. The simulations show that the obtained mechanisms (both in-line four-bar linkages and planar parallel robots) transmit no inertia loads to their surroundings, i.e. the sum of all ground bearing forces and their moments are eliminated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A “physical pendulum” is a link which has such a distribution of masses that it allows the dynamic substitution of link’s mass and inertia by two concentrated masses.

References

  1. Foucault, S., Gosselin, C.M.: On the development of a planar 3-dof reactionless parallel mechanism. In: Proceedings of the ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDECT/CIE 2002), Montreal, September 2002

    Google Scholar 

  2. van der Wijk, V., Demeulenaere, B., Gosselin, C.M., Herder, J.L.: Comparative analysis for low-mass and low-inertia dynamic balancing of mechanisms. ASME J. Mech. Robot. 4 (2012)

    Google Scholar 

  3. Raaijmakers, R.: Besi zoekt snelheidslimiet pakken en plaatsen op (besi attacks the speedlimit for pick and place motion). In: Mechatronica nieuws (Dutch Magazine), pp. 26–31 (2007)

    Google Scholar 

  4. Lowen, G.G., Berkof, R.S.: Survey of investigations into the balancing of linkages. ASME J. Mech. 3, 221–231 (1968)

    Google Scholar 

  5. Ishida, K., Matsuda, T.: Performance characteristics and working comfortableness of forest workers of a new non-vibrating chain saw utilizing perfectly balanced rotation-reciprocation device. In: Proceedings of the Fifth World Congress of Theory of Machines and Mechanisms, Montreal, pp. 951–954 (1979)

    Google Scholar 

  6. Arakelian, V., Briot, S.: Balancing of Linkages and Robot Manipulators – Advanced Methods with Illustrative Examples. Springer, Cham (2014)

    Google Scholar 

  7. Lowen, G.G., Tepper, F.R., Berkof, R.S.: Balancing of linkages – an update. Mech. Mach. Theory 18(3), 213–230 (1983)

    Article  Google Scholar 

  8. Arakelian, V., Dahan, M., Smith, M.R.: A historical review of the evolution of the theory on balancing of mechanisms. In: Ceccarelli, M. (ed.) Proceedings of the International Symposium on History of Machines and Mechanisms (HMM 2000), pp. 291–300. Kluwer Academic, Dordrecht (2000)

    Chapter  Google Scholar 

  9. Arakelian, V., Smith, M.R.: Shaking force and shaking moment balancing of mechanisms: A historical review with new examples. ASME J. Mech. Des. 127, 334–339 (2005)

    Article  Google Scholar 

  10. Nabat, V., Pierrot, F., Mijangos, M.R., Arteche, J.M.A., Zabalo, R.B., Company, O., Perez De Armentia, K.F.: High-speed parallel robot with four degrees of freedom, patent (2006)

    Google Scholar 

  11. van der Wijk, V., Krut, S., Pierrot, F., Herder, J.L.: Design and experimental evaluation of a dynamically balanced redundant planar 4-RRR parallel manipulator. Int. J. Robot. Res. 32, 744–759 (2013)

    Article  Google Scholar 

  12. Leinonen, T.: Terminology for the theory of machines and mechanisms. Mech. Mach. Theory 26, 435–539 (1991)

    Article  Google Scholar 

  13. Fischer, O.: über die reduzierten Systeme und die Hauptpunkte der Glieder eines Gelenkmechanismus. Zeit. für Math. Phys. 47, 429–466 (1902)

    Google Scholar 

  14. Artobolevsky, I.I., Edelshtein, B.V.: Methods of Inertia Calculation for Mechanisms of Agricultural Machines. Selkhozizdate, Moscow (1935) [in Russian]

    Google Scholar 

  15. Crossley, F.R.E.: Dynamics in Machines. Roland Press, New York (1954)

    Google Scholar 

  16. Talbourdet, G.L., Shepler, P.R.: Mathematical solution of 4-bar linkages - IV. Balancing of linkages. Mach. Des. 13, 73–77 (1941)

    Google Scholar 

  17. Smith, M.R., Maunder, L.: Inertia forces in a four-bar linkage. Mech. Eng. Sci. 9(3), 218–225 (1967)

    Article  Google Scholar 

  18. Berkof, R.S., Lowen, G.G.: A new method for completely force balancing simple linkages. ASME J. Eng. Ind. 91(1), 21–26 (1969)

    Article  Google Scholar 

  19. Hilpert, H.: Weight balancing of precision mechanical instruments. Mechanisms 3(4), 289–302 (1968)

    Article  Google Scholar 

  20. Lowen, G.G., Berkof, R.S.: Determination of force-balanced four-bar linkages with optimum shaking moment characteristics. ASME J. Eng. Ind. 93(1), 39–46 (1971)

    Article  Google Scholar 

  21. Lowen, G.G., Berkof, R.S.: Theory of shaking moment optimization of force-balanced four-bar linkages. ASME J. Mech. Des. 12, 53–60 (1970)

    Google Scholar 

  22. Berkof, R.S., Lowen, G.G.: Theory of shaking moment optimization of force-balanced four-bar linkages. ASME J. Eng. Ind. 93(1), 53–60 (1971)

    Article  Google Scholar 

  23. Wiederrich, J.L., Roth, B.: Momentum balancing of four-bar linkages. ASME J. Mech. Des. 98B(4), 1289–1295 (1976)

    Google Scholar 

  24. Elliot, J.L., Tesar, D.: The theory of torque, shaking force and shaking moment balancing of four link mechanisms. ASME J. Eng. Ind. 99(3), 715–722 (1977)

    Article  Google Scholar 

  25. Carson, W.L., Stephens, J.M.: Feasible parameter design spaces for force and root-mean-square moment balancing on in-line 4R 4-bar linkage synthesized for kinematic criteria. Mech. Mach. Theory 13(6), 649–658 (1978)

    Article  Google Scholar 

  26. Haines, R.S.: Minimum RMS shaking moment or driving torque of a force-balanced 4-bar linkage using feasible counterweights. Mech. Mach. Theory 16, 185–190 (1981)

    Article  Google Scholar 

  27. Shchepetilnikov, V.A.: The determination of the mass centers of mechanisms in connection with the problem of mechanism balancing. Mechanisms 3, 367–389 (1968)

    Article  Google Scholar 

  28. Arakelian, V., Dahan, M.: Partial shaking moment balancing of fully force balanced linkages. Mech. Mach. Theory 36(11–12), 1241–1252 (2001)

    Article  MATH  Google Scholar 

  29. Arakelian, V., Dahan, M.: Complete shaking force and partial shaking moment balancing of planar four-bar linkages. Proc. Inst. Mech. Eng. K J. Multibody Dyn. 15, 31–34 (2001)

    Google Scholar 

  30. Zhang, S.: A constitutive method of objective function for the dynamic optimum balance of shaking force in linkage. Mech. Mach. Theory 29(6), 829–835 (1994)

    Article  Google Scholar 

  31. Zhang, S., Chen, J.: The optimum balance of shaking force and shaking moment of linkages. Mech. Mach. Theory 30(4), 589–597 (1995)

    Article  Google Scholar 

  32. Qi, N.M., Pennestri, E.: Optimum balancing of four-bar linkages. Mech. Mach. Theory 26(3), 337–348 (1991)

    Article  Google Scholar 

  33. Chaudhary, H., Saha, S.K.: Balancing of four-bar linkages using maximum recursive dynamic algorithm. Mech. Mach. Theory 42(2), 216–232 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  34. Kamenski, V.A.: On the question of the balancing of planar linkages. Mechanisms 3(4), 303–322 (1968)

    Article  Google Scholar 

  35. Berkof, R.S.: Complete force and moment balancing of inline four-bar linkages. Mech. Mach. Theory 8(3), 397–410 (1973)

    Article  Google Scholar 

  36. Bagci, C.: Complete shaking force and shaking moment balancing of link mechanisms using balancing idler loops. ASME J. Mech. Des. 104, 482–493 (1982)

    Article  Google Scholar 

  37. Ye, Z., Smith, M.R.: Complete balancing of planar linkages by an equivalence method. Mech. Mach. Theory 29(5), 701–712 (1991)

    Article  Google Scholar 

  38. Arakelian, V., Smith, M.R.: Complete shaking force and shaking moment balancing of linkages. Mech. Mach. Theory 34(8), 1141–1153 (1999)

    Article  MATH  Google Scholar 

  39. Gao, F.: Complete shaking force and shaking moment balancing of 17 types of eight-bar linkages only with revolute pairs. Mech. Mach. Theory 26(2), 197–206 (1991)

    Article  Google Scholar 

  40. Berestov, L.B.: Comparative analysis of the reactions in the kinematic pairs of the four-bar linkages for the different methods of balancing. J. Mech. Mach. 61–70 (1977) [in Russian]

    Google Scholar 

  41. Dresig, H., Naake, S., Rockausen, L.: Vollständiger und harmonischer Ausgleich ebener Mechanismen. VDI, Düsseldorf (1994)

    Google Scholar 

  42. Esat, I., Bahai, H.: A theory of complete force and moment balancing of planar linkage mechanisms. Mech. Mach. Theory 34(6), 903–922 (1999)

    Article  MATH  Google Scholar 

  43. Arakelian, V., Dahan, M.: Balanced four-bar articulated mechanism has output member extended beyond axis of second pivot and meshing gears. FR, 2817008 (2002)

    Google Scholar 

  44. Kochev, I.S.: Full shaking moment balancing of planar linkages by a prescribed input speed fluctuation. Mech. Mach. Theory 25(4), 459–466 (1990)

    Article  Google Scholar 

  45. Ricard, R., Gosselin, C.M.: On the development of reactionless parallel manipulators. In: Proceedings of the ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2000), Baltimore (2000)

    Google Scholar 

  46. Wu, Y., Gosselin, C.M.: Synthesis of reactionless spatial 3-dof and 6-dof mechanisms without separate counter-rotations. Int. J. Robot. Res. 23(6), 625–642 (2004)

    Article  Google Scholar 

  47. Gosselin, C.M., Vollmer, F., Côté, G., Wu, Y.: Synthesis and design of reactionless three-degree-of-freedom parallel mechanisms. IEEE Trans. Robot. Autom. 20(2), 191–199 (2004)

    Article  Google Scholar 

  48. Gosselin, C.M., Moore, B., Schicho, J.: Dynamic balancing of planar mechanisms using toric geometry. J. Symb. Comput. 44(9), 1346–1358 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  49. Jiang, Q., Gosselin, C.M.: Dynamic optimization of reactionless 4-bar linkages. ASME J. Dyn. Syst. Meas. Control 132, 041006 (2010)

    Article  Google Scholar 

  50. Demeulenaere, B., Berkof, R.: Improving machine drive dynamics: a structured design approach towards balancing. ASME J. Mech. Des. 130(8), (2008)

    Google Scholar 

  51. Berkof, R.S.: The input torque in linkages. Mech. Mach. Theory 14(1), 61–73 (1979)

    Article  Google Scholar 

  52. Wu, Y., Gosselin, C.M.: On the dynamic balancing of multi-dof parallel mechanisms with multiple legs. ASME J. Mech. Des. 129, 234–238 (2007)

    Article  Google Scholar 

  53. Martin, G.H.: Kinematics and Dynamics of Machines, 3rd edn. McGraw-Hill, Columbus (2002)

    Google Scholar 

  54. Agrawal, S.K., Fattah, A.: Reactionless space and ground robots: Novel design and concept studies. Mech. Mach. Theory 39, 25–40 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  55. Wang, J., Gosselin, C.M.: Static balancing of spatial three-degree-of-freedom parallel mechanisms. Mech. Mach. Theory 34, 437–452 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  56. Newman, W.S., Hogan, N.: The optimal control of balanced manipulators. In: Proceedings of the ASME Winter Annual Meeting, California (1986)

    Google Scholar 

  57. Laliberté, T., Gosselin, C.M., Jean, M.: Static balancing of 3-DOF planar parallel mechanisms. IEEE/ASME Trans. Mechatron. 4(4), 363–377 (1999)

    Article  Google Scholar 

  58. Fujikoshi, K.: Balancing apparatus for jointed robot. JP, pp. 51–12 (1976)

    Google Scholar 

  59. Wang, J., Gosselin, C.M.: Static balancing of spatial four-degree-of-freedom parallel mechanisms. Mech. Mach. Theory 35(4), 563–592 (2000)

    Article  MATH  Google Scholar 

  60. Russo, A., Sinatra, R., Xi, F.: Static balancing of parallel robots. Mech. Mach. Theory 40(2), 191–202 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  61. Ouyang, P.R., Zhang, W.J.: Force balancing of robotic mechanisms based on adjustment of kinematic parameters. ASME J. Mech. Des. 127, 433–440 (2005)

    Article  Google Scholar 

  62. Herder, J.L., Gosselin, C.M.: A counter-rotary counterweight for light-weight dynamic balancing. In: Proceedings of the ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2004), Salt Lake City, pp. 659–667 (2004)

    Google Scholar 

  63. Fattah, A., Agrawal, S.K.: On the design of reactionless 3-dof planar parallel mechanisms. Mech. Mach. Theory 41(1), 70–82 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  64. Foucault, S., Gosselin, C.M.: Synthesis, design, and prototyping of a planar three degree-of-freedom reactionless parallel mechanism. ASME J. Mech. Des. 126, 992–999 (2004)

    Article  Google Scholar 

  65. Wu, Y., Gosselin, C.M.: Design of reactionless 3-dof and 6-dof parallel manipulators using parallelepiped mechanisms. IEEE Trans. Robot. 21(5), 821–833 (2005)

    Article  Google Scholar 

  66. Papadopoulos, E., Abu-Abed, A.: Design and motion planning for a zero-reaction manipulator. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 1994), San Diego, pp. 1554–1559 (1994)

    Google Scholar 

  67. Arakelian, V., Briot, S.: Dynamic balancing of the scara robot. In: Proceedings of 17th CISM-IFToMM Symposium on Robot Design, Dynamics, and Control (RoManSy 2008), Tokyo (2008)

    Google Scholar 

  68. Briot, S., Arakelian, V.: Complete shaking force and shaking moment balancing of the position-orientation decoupled PAMINSA manipulator. In: Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM2009), Singapore (2009)

    Google Scholar 

  69. Briot, S., Arakelian, V., Le Baron, J.P.: Shaking force minimization of high-speed robots via centre of mass acceleration control. Mech. Mach. Theory 57, 1–12 (2012)

    Article  Google Scholar 

  70. Frolov, K.V.: Theory of Mechanisms and Machines. Vishaya Shkola, Moscow (1987)

    Google Scholar 

  71. Doronin, V., Pospelov, A.: Balanced slider-crank mechanism. SU, 1627769 (1991)

    Google Scholar 

  72. Arakelian, V.: équilibrage dynamique complet des mécanismes. Mech. Mach. Theory 33(4), 425–436 (1998)

    Google Scholar 

  73. Baradat, C., Arakelian, V., Briot, S., Guegan, S.: Design and prototyping of a new balancing mechanism for spatial parallel manipulators. ASME J. Mech. Des. 130(7) (2008)

    Google Scholar 

  74. Leblond, M., Gosselin, C.M.: Static balancing of spatial and planar parallel manipulators with prismatic actuators. In: Proceedings of the ASME 1998 DETC Conference (1998)

    Google Scholar 

  75. Seyferth, W.: Massenersatz duch punktmassen in räumlichen getrieben. Mech. Mach. Theory 9, 49–59 (1974)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sébastien Briot .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Briot, S., Arakelian, V. (2016). Design of Reactionless Linkages and Robots Equipped with Balancing Assur Groups. In: Zhang, D., Wei, B. (eds) Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots. Springer, Cham. https://doi.org/10.1007/978-3-319-17683-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-17683-3_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17682-6

  • Online ISBN: 978-3-319-17683-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics