Nonlinear Dynamics

, Volume 98, Issue 3, pp 1999–2018 | Cite as

Frictional impact analysis of an elastoplastic multi-link robotic system using a multi-timescale modelling approach

  • Yunian ShenEmail author
  • Ye Kuang
  • Wei Wang
  • Yuhang Zhao
  • Jiongcan Yang
  • Ali Tian
Original paper


Considering tangential contact compliance, material nonlinearity and contact nonlinearity, an efficient multi-timescale computational approach (MCA) is presented to analyse the contact forces and transient wave propagation generated by the frictional impact of an elastoplastic multi-link robotic system. In the formulation of the MCA, a rigid multibody dynamic equation is derived to calculate the large overall motion without a unilateral contact constraint (large timescale) and the nonlinear finite element dynamic equation, including the penalty function algorithm, is given to calculate the contact force and stress wave propagation (small timescale). An experimental test for a manipulator’s oblique impact against a rough moving plate is also introduced. The accuracy, convergence and efficiency of the MCA are validated by a comparison with the pure finite element method (FEM) solution and experimental data. The error between the MCA and pure FEM solutions for the first peak value of the normal contact force \(F_{\mathrm{n}}\) is less than 1.5%. The total time cost of the MCA is only 0.705% of the pure FEM. The numerical results also show that the presented MCA can effectively depict the transmission and reflection of the impact-induced waves at the middle hinge. In addition, the influences of the structural compliance, the velocity of plate \(v_{\mathrm{plate}}\) and the coefficient of friction \(\mu \) on the transient responses are investigated. The peak value of \(F_{\mathrm{n}}\) will increase as \(v_{\mathrm{plate}}\) increases, which has a strong relationship with the so-called dynamic self-locking phenomenon. Due to the large structural compliance of the rod, the “succession collisions” phenomenon (i.e. multiple contacts in a very short time) can be captured during an oblique impact event, and the normal relative motion at the local contact zone may experience two transitions between compression and restitution during a single contact process. The tangential stick-slip motion occurs as a reverse phenomenon. All investigations show that the MCA has sufficient accuracy to analyse the frictional impact of flexible robotic manipulators.


Frictional impact Stick-slip Wave propagation Elastic–plastic Transient responses 



The authors would like to thank the Robotics and Intelligent Machine Lab, NUST. This work was supported by the National Natural Science Foundation of China (Grant No. 11572157). This support is gratefully acknowledged.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Yunian Shen
    • 1
    Email author
  • Ye Kuang
    • 1
  • Wei Wang
    • 1
  • Yuhang Zhao
    • 1
  • Jiongcan Yang
    • 1
  • Ali Tian
    • 2
  1. 1.Department of Mechanics and Engineering Science, School of ScienceNanjing University of Science and TechnologyNanjingChina
  2. 2.School of Naval Architecture and Ocean EngineeringJiangsu University of Science and TechnologyZhenjiangChina

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