Nonlinear Dynamics

, Volume 87, Issue 4, pp 2311–2324 | Cite as

Dynamic response analysis and chaos identification of 4-UPS-UPU flexible spatial parallel mechanism

  • Xiulong ChenEmail author
  • Liangkai Wu
  • Yu Deng
  • Qing Wang
Original Paper


In order to realize the dynamic response analysis and the chaos identification of flexible spatial parallel mechanism, the nonlinear elastic dynamics model of 4-UPS-UPU flexible parallel mechanism is established under the ideal situation, and the dynamic response, phase diagrams, Poincare map and largest Lyapunov exponent of the spatial parallel mechanism are investigated. Based on the finite element method, the driving limbs of spatial parallel mechanism are divided into elements. The kinetic energy equation and potential energy equation of units are built. Then the nonlinear elastic dynamics model of 4-UPS-UPU parallel mechanism is acquired by Lagrange equation. The dynamic response of kinematic error for 4-UPS-UPU flexible parallel mechanism is analyzed. In addition, the chaos phenomenon contained in the mechanism is identified by phase diagrams, Poincare map and largest Lyapunov exponent, respectively. Subsequently, the relationship between the basic parameters of parallel mechanism and largest Lyapunov exponent is discussed. The results indicate that there exists chaotic phenomena in the 4-UPS-UPU flexible parallel mechanism, and the basic parameters, including the material of driving limbs, diameter of driving limbs, mass of moving platform and the distribution radius of hinges of moving platform all have great effect on chaotic motion of 4-UPS-UPU flexible parallel mechanism. The researches can provide important theoretical for the further nonlinear dynamics behaviors research and optimal design of 4-UPS-UPU flexible spatial parallel mechanism.


Spatial parallel mechanism Elastodynamics Dynamic response Chaos identification 



This research is supported by the National Natural Science Foundation of China (Grant No. 51005138), the Shandong Young Scientists Award Fund (Grant No. BS2012ZZ008), Taishan Scholarship Project of Shandong Province (No. tshw20130956).


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.College of Mechanical and Electronic EngineeringShandong University of Science and TechnologyQingdaoChina
  2. 2.Institute of Nano EngineeringShandong University of Science and TechnologyQingdaoChina

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