Dynamic Synthesis of a Crank-Rocker Mechanism Minimizing its Joint-Forces

  • Claudio VillegasEmail author
  • Mathias Hüsing
  • Burkhard Corves
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Dynamic Joint-Forces in a mechanism produce vibration and wear, decreasing its life span. Many studies have been carried out on optimization of mechanisms dynamic behaviour; however, few of it are focused on the reduction of Joint-Forces. Therefore, this work presents a method to obtain the link lengths of Function Generation Four-Bar Linkages, minimizing the maximum dynamic force in the joints. The study assumes that the crank rotates with constant angular velocity and the rocker moves a high amount of inertia between two positions. Hence, the mechanism mass and inertia is considered negligible. The equations of motion are set up together with Dead-Center Construction method after Alt. To analyze the behaviour of the Joint-Forces, all the equations are parametrized, finding out that the maximum Joint-Force is minimizable for every task given. The minimization of the Joint-Forces is achieved by using simple algorithms as Bisection and Regula-Falsi Illinois. The results show that this method reduces the maximal Joint-Force by a mean value of 8.5%, with respect to the Dead-Center Construction method with Transmission Angle Minimization. Moreover, for some tasks, the force reduction could reach up to 60%. Furthermore, this method solves the problem of null-length crank and rocker for centric crank-rocker mechanisms, generated by the Transmission Angle minimization.


Function Generator Four-Bar Linkage Reaction Forces 


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  1. 1.
    Rayner R, Sahinkaya MN, Hicks B (2009) Combining Inverse Dynamics With Traditional Mechanism Synthesis to Improve the Performance of High Speed Machinery. In: Proceedings of the ASME dynamic systems and control conference 2008. American Society of Mechanical Engineers, New York, N.Y., pp 599–606Google Scholar
  2. 2.
    Rayner RMC, Sahinkaya MN, Hicks B (2017) Improving the design of high speed mechanisms through multi-level kinematic synthesis, dynamic optimization and velocity profiling. Mechanism and Machine Theory 118: 100–114. doi: Scholar
  3. 3.
    Soong R-C, Yan H (2007) Simultaneous Minimization of Shaking Moment, Driving Torque, and Bearing Reactions of Complete Force Balanced Linkages. Journal of the Chinese Society of Mechanical Engineers(C 28(3)): 243–254Google Scholar
  4. 4.
    McDougall R, Nokleby S (2009) Synthesis of Grashof Four-Bar Mechanisms Using Particle Swarm Optimization. In: 28th computers and information in engineering conference. American Society of Mechanical Engineers, New York, pp 1471–1475Google Scholar
  5. 5.
    Bai S, Angeles J (2015) Coupler-curve synthesis of four-bar linkages via a novel formulation. Mechanism and Machine Theory 94: 177–187. doi: Scholar
  6. 6.
    Chanekar PV, Ghosal A (2013) Optimal synthesis of adjustable planar four-bar crank-rocker type mechanisms for approximate multi-path generation. Mechanism and Machine Theory 69: 263–277. doi: Scholar
  7. 7.
    Yuan L, Rastegar JS (2004) Kinematics Synthesis of Linkage Mechanisms With Cam Integrated Joints for Controlled Harmonic Content of the Output Motion. J. Mech. Des. 126(1): 135. doi: Scholar
  8. 8.
    Sahinkaya MN (2004) Inverse dynamic analysis of multiphysics systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 218(1): 13–26. doi: Scholar
  9. 9.
    Erkaya S (2013) Investigation of balancing problem for a planar mechanism using genetic algorithm. J Mech Sci Technol 27(7): 2153–2160. doi: Scholar
  10. 10.
    Kochev IS (2000) General theory of complete shaking moment balancing of planar linkages: a critical review. Mechanism and Machine Theory 35(11): 1501–1514. doi: Scholar
  11. 11.
    Truong QT, Nguyen QV, Park HC et al. (2011) Modification of a Four-Bar Linkage System for a Higher Optimal Flapping Frequency. Journal of Intelligent Material Systems and Structures 22(1): 59–66. doi: Scholar
  12. 12.
    Prebil I, Krašna S, Ciglarič I (2002) Synthesis of four-bar mechanism in a hydraulic support using a global optimization algorithm. Struct Multidisc Optim 24(3): 246–251. doi: Scholar
  13. 13.
    Verein Deutscher Ingenieure (1984) Crank and Rocker Mechanisms: VDI 2130(VDI 2130)Google Scholar
  14. 14.
    Han J, Qian W (2009) On the solution of region-based planar four-bar motion generation. Mechanism and Machine Theory 44(2): 457–465. doi: Scholar
  15. 15.
    Gupta KC (1977) A note on the optimum design of four bar crank-rocker mechanisms. Mechanism and Machine Theory 12(3): 247–254. doi: Scholar
  16. 16.
    Balli SS, Chand S (2002) Transmission angle in mechanisms (Triangle in mech). Mechanism and Machine Theory 37(2): 175–195. doi: Scholar
  17. 17.
    Conte FL, George GR, Mayne RW et al. (1975) Optimum Mechanism Design Combining Kinematic and Dynamic-Force Considerations. J. Eng. for Industry 97(2): 662. doi: Scholar
  18. 18.
    Schwarzfischer F, Hüsing M, Corves B (2017) The Dynamic Synthesis of an Energy-Efficient Slider-Crank-Mechanism. In: Proceedings of the Second International Symposium of Mechanism and Machine Science, Baku, pp 156–163Google Scholar
  19. 19.
    CHU J (2010) Unified Approach to Synthesis of Coupler Curves of Linkage by Fourier Series. JME 46(13): 31. doi: Scholar
  20. 20.
    Kerle H, Corves B, Hüsing M (2015) Getriebetechnik. Springer Fachmedien Wiesbaden, WiesbadenCrossRefGoogle Scholar
  21. 21.
    McCarthy JM, Soh GS (2011) Geometric Design of Linkages, vol 11. Springer New York, New York, NYCrossRefGoogle Scholar
  22. 22.
    Bedford A, Fowler WL (2008) Engineering mechanics: Dynamics / Anthony Bedford, Wallace Fowler, 5th ed. Pearson Prentice Hall, Upper Saddle River, N.J., LondonGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen UniversityAachenGermany
  2. 2.Department of Mechanical Engineering, University of Bio-BioConcepcionChile

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