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Sensitivity Analysis Approach to multibody systems Described by Natural Coordinates

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Chinese Journal of Mechanical Engineering 2014年第2期27卷 402-410页

作者： LI Xiufeng WANG Yabin State Key Laboratory of Electromechanical Dynamic Control Beijing Institute of Technology

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-ct 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.

关键词： sensitivity analysis direct differentiation method natural coordinates multibody systems

DYNAMICS OF FLEXIBLE multibody systems WITH TREE TOPOLOGIES

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Acta Mechanica Sinica 1992年第3期8卷 271-278页

作者：洪嘉振潘振宽 Shanghai Jiao Tong University Shanghai 200030China

The dynamic equations of flexible multibody systems with tree topological configuration are de- rived by using the Jourdain's *** independent joint coordinates are introduced to describe the large displacements of the bodies,and the modal coordinates are used to describe small deformations of flexible bodies based on the consistent mass finite element method and normal vibration mode *** mini- mum differential equations are developed,which are compatible with the equations of multi-rigid body sys- tems or structural *** stiff problem in the numerical integration is thus alleviated *** method used in this paper can be extended to deal with systems with other topological configurations. Finally,the validity and feasibility of the presented mathematical model are demonstrated by a numerical ex- ample of a manipulator with two elastic links.

关键词： multibody systems flexible bodies the finite element method the modal analysis method

Modeling of multibody systems with redundant joints

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Theoretical & Applied Mechanics Letters 2012年第6期2卷 22-26页

作者： Zhaohui Qi,a) and Huitao Song b) Department of Engineering Mechanics Dalian University of Technology,Dalian 116023,China Department of Engineering Mechanics Dalian University of Technology Dalian 116023 China

This paper deals with the modeling of a multibody system in which some pairs of bodies are connected by more than one joints with the same kinematic *** such system,the redundant joints must be removed out artificially to ensure the solvable condition of the equations of motion being *** is believed but not obvious that the redundant joints have no effect on the system *** give a strict positive proof of this argument and present a method to avoid the ambiguity in the reaction forces of redundant joints through contact analysis of joints.

关键词： multibody systems redundant constraints joints contact analysis

The dynamic analysis of multibody systems with uncertain parameters using interval method

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The dynamic analysis of multibody systems with uncertain par...

A NEW ALGORITHM FOR SOLVING DIFFERENTIAL/ALGEBRAIC EQUATIONS OF multibody SYSTEM DYNAMICS

2012 International Conference on Mechanical Engineering and Materials(ICMEM 2012)

作者： Wu Jinglai Zhang Yunqing Center for Computer-Aided Design School of Mechanical Science ＆ Engineering Huazhong University of Science ＆ Technology

The theoretical and computational aspects of interval methodology based on Chebyshev polynomials for modeling multibody dynamic systems in the presence of parametric uncertainties are proposed, where the uncertain parameters are modeled by uncertain-but-bounded interval variables which only need the bounds of uncertain parameters, not necessarily knowing the probabilistic distribution. The Chebyshev inclusion function which employs the truncated Chevbyshev series expansion to approximate the original function is proposed. Based on Chebyshev inclusion function, the algorithm for solving the nonlinear equations with interval parameters is proposed. Combining the HHT-I3 method, this algorithm is used to calculate the multibody systems dynamic response which is governed by differential algebraic equations（DAEs）. A numerical example that is a slider-crank with uncertain parameters is presented, which shows that the novel methodology can control the overestimation effectively and is computationally faster than the scanning method.

关键词： multibody systems interval method Chebyshev polynomials DAEs

来源： cnki会议评论

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Applied Mathematics and Mechanics(English Edition) 1997年第9期18卷 905-912页

作者：王艺兵赵维加潘振宽 Department of Automation Qingdao University Qingdao P. R. China

The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding discretization method is presented, and the results can be used to implementation of various numerical integration methods. A numerical example is presented finally.

关键词： multibody systems differential/algebraic equations numerical analysis

Recursive dynamics simulator(ReDySim):A multibody dynamics solver

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Theoretical & Applied Mechanics Letters 2012年第6期2卷 71-76页

作者： Suril V.Shah Paramanand V.Nandihal Subir K.Saha Department of Mechanical Engineering McGill University QC H3A0C3Canada Department of Mechanical Engineering Indian Institute of Technology New Delhi 110016India

Recursive formulations have significantly helped in achieving real-time computations and model-based control laws. The recursive dynamics simulator （ReDySim） is a MATLAB-based recur- sive solver for dynamic analysis of multibody systems. ReDySim delves upon the decoupled natural orthogonal complement approach originally developed for serial-chain manipulators. In comparison to the commercially available software, dynamic analyses in ReDySim can be performed without creating solid model. The input parameters are specified in MATLAB environment. ReDySim has capability to incorporate any control algorithm with utmost ease. In this work, the capabilities of ReDySim for solving open-loop and closed-loop systems are shown by examples of robotic gripper, KUKA KR5 industrial manipulator and four-bar mechanism. ReDySim can be downloaded for free from http：//*** and can be used almost instantly.

关键词： ReDySim multibody systems dynamic modeling recursive dynamics DeNOC