Dynamic response and chaos in planar multi-link mechanism considering revolute clearances


During actual motion, there are inevitably clearances between the motion pairs of the mechanism, and the clearances will have a large impact on stability of the mechanism. Previous studies mainly focused on the dynamic response of simple mechanisms with single clearance and less on chaos. Even if chaos is studied, it mainly focused on the chaos of mechanisms and less on the chaos of clearance joints; however, it is well known that the analysis of chaotic characteristics of clearance is the key to fault diagnosis of kinematic pairs. In order to give a computational methodology for dynamic analysis of planar multi-link mechanism considering multi-clearances and master the dynamic response of planar multi-link mechanism, the dynamic response and chaos of a planar six-bar mechanism are researched. A multiple clearances dynamic model of planar six-bar mechanism is built by Lagrange multiplier method, and the dynamic model is solved by Runge–Kutta method. The influence of different clearance positions, clearance numbers and clearance sizes on dynamic response of mechanism is analyzed. The nonlinear characteristic analysis of six-bar mechanism is conducted, and chaotic phenomena of the clearance joint are explained by Poincaré maps and phase diagrams. The bifurcation diagram at clearance of the revolute joint changes with different clearance values, friction coefficients and driving speeds is given. Those above results provide an important theoretical basis for the study of influence of multi-clearance on dynamic responses and chaotic phenomena of planar multi-link mechanism.

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Data availability

The data used to support the findings of this study are included within the article.


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This research is supported by Shandong Key Research and Development Public Welfare Program (2019GGX104011) and Natural Science Foundation of Shandong Province (Grant No. ZR2017MEE066). This manuscript has not been published, simultaneously submitted or already accepted for publication elsewhere. All authors have read and approved the manuscript. All acknowledged persons have read and given permission to be named. Xiulong CHEN has nothing to disclose.

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Chen, X., Jiang, S. Dynamic response and chaos in planar multi-link mechanism considering revolute clearances. Arch Appl Mech 90, 1919–1941 (2020). https://doi.org/10.1007/s00419-020-01704-4

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  • Planar multi-link mechanism
  • Revolute clearances
  • Dynamic response
  • Chaos