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Sensitivity analysis approach to multibody systems described by natural coordinates

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Abstract

The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation. A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-α integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system. Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.

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Authors and Affiliations

  1. State Key Laboratory of Electromechanical Dynamic Control, Beijing Institute of Technology, Beijing, 100081, China

    Xiufeng Li & Yabin Wang

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  1. Xiufeng Li
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  2. Yabin Wang
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Corresponding author

Correspondence to Yabin Wang.

Additional information

This project is supported by National Defense Pre-research Foundation of China during the 12th Five-Year Plan Period(Grant No. 51036050107)

LI Xiufeng, born in 1987, is currently a doctor candidate at State Key Laboratory of Electromechanical Dynamic Control, School of Mechatronical Engineering, Beijing Institute of Technology, China. He received his master degree from Beijing Institute of Technology, China, in 2010. His research interests include virtual prototyping and computer aided engineering.

WANG Yabin, born in 1977, is currently an associate professor at Beijing Institute of Technology, China. He received his PhD degree from Beijing Institute of Technology, China, in 2006. His research interests include mechanical engineering, virtual prototyping and digital design of mechatronical systems.

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Li, X., Wang, Y. Sensitivity analysis approach to multibody systems described by natural coordinates. Chin. J. Mech. Eng. 27, 402–410 (2014). https://doi.org/10.3901/CJME.2014.02.402

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