Selective Generalized Coordinates Partitioning Method for Multibody Systems With Non-Holonomic Constraints

2017 ◽  
Author(s):  
Ayman A. Nada ◽  
Abdullateef H. Bashiri
Keyword(s):  
Multibody Systems ◽  
Large Scale ◽  
Research Work ◽  
Nonholonomic Constraints ◽  
Integration Step ◽  
Large Scale Systems ◽  
Holonomic Constraints ◽  
Generalized Coordinates ◽  
Holonomic And Nonholonomic Constraints ◽  
Multi Body

The goal of this research work is to extend the method of generalized coordinates partitioning to include both holonomic and nonholonomic constraints. Furthermore, the paper proposes a method for selective coordinates for integration instead of identifying a set of independent coordinates at each integration step. The effectiveness of the proposed method is presented and compared with full-coordinates integration as well as generalized co-ordinates partitioning method. The proposed method can treat large-scale systems as one of the main advantages of multi-body systems.

The Skew-Symmetric Property of the Newton-Euler Formulation for Constrained Multibody Systems

1996 ◽  
Author(s):  
Hong-Chin Lin ◽  
Tsung-Chieh Lin ◽  
KwangHae H. Yae
Keyword(s):  
Special Form ◽  
Multibody Systems ◽  
Large Scale ◽  
Computational Analysis ◽  
Necessary Condition ◽  
Large Scale Systems ◽  
Lagrange Formulation ◽  
Dynamics Simulations ◽  
And Control ◽  
Symmetric Property

Abstract This paper proposes a special form of the recursive Newton-Euler formulation that satisfies the skew-symmetric property, which is a necessary condition to ensure global convergence in a class of regressor-based identification and adaptive control (Slotine, 1987a & 1987b; Craig, 1987). For general multibody systems, such a special form has been developed in a reduced Euler-Lagrange formulation, but not in the Newton-Euler formulation, which has been very popular in the computational analysis of large scale systems. The paper successfully constructs a pair of inertia and Coriolis-centrifugal matrices for a “skew-symmetric” recursive Newton-Euler formulation, which can be used in both dynamics simulations and control applications.

scholarly journals Differential-Geometric Characteristics of Optimized Generalized Coordinates Partitioned Vectors for Holonomic and Non-Holonomic Multibody Systems

2009 ◽  
Author(s):  
Zdravko Terze ◽  
Dubravko Matijasˇevic´ ◽  
Milan Vrdoljak ◽  
Vladimir Koroman
Keyword(s):  
Multibody Systems ◽  
Gradient Analysis ◽  
Holonomic Constraints ◽  
Constrained Multibody Systems ◽  
Generalized Coordinates ◽  
Geometric Characteristics ◽  
Holonomic Systems ◽  
Dae Systems ◽  
Velocity Level ◽  
Short Presentation

Differential-geometric characteristics and structure of optimized generalized coordinates partitioned vectors for generally constrained multibody systems are discussed. Generalized coordinates partitioning is well-known procedure that can be applied in the framework of numerical integration of DAE systems. However, although the procedure proves to be a very useful tool, it is known that an optimization algorithm for coordinates partitioning is needed to obtain the best performance. After short presentation of differential-geometric background of optimized coordinates partitioning, the structure of optimally partitioned vectors is discussed on the basis of gradient analysis of separate constraint submanifolds at configuration and velocity level when holonomic and non-holonomic constraints are present in the system. While, in the case of holonomic systems, the vectors of optimally partitioned coordinates have the same structure for generalized positions and velocities, when non-holonomic constraints are present in the system, the optimally partitioned coordinates generally differ at configuration and velocity level and separate partitioned procedure has to be applied. The conclusions of the paper are illustrated within the framework of the presented numerical example.

scholarly journals Automated Linearization of Nonlinear Coupled Differential and Algebraic Equations

1991 ◽  
Author(s):  
Martin J. Vanderploeg ◽  
Jeff D. Trom
Keyword(s):  
Finite Difference ◽  
Dynamic Systems ◽  
Large Scale ◽  
Algebraic Equations ◽  
New Approach ◽  
Large Scale Systems ◽  
Equation Formulation ◽  
Equilibrium Configurations ◽  
Multi Body ◽  
Body Dynamic

Abstract This paper presents a new approach for linearization of large multi-body dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for large-scale systems that were previously impossible.

Quasi-velocities definition in Lagrangian multibody dynamics

2021 ◽  
pp. 095440622199585
Author(s):  
S Mohammad Mirtaheri ◽  
Hassan Zohoor
Keyword(s):  
Computational Efficiency ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Matrix Inversion ◽  
Lagrangian Mechanics ◽  
Holonomic Constraints ◽  
Velocity Constraints ◽  
Analytical Relations ◽  
Explicit Equations Of Motion

Based on Lagrangian mechanics, use of velocity constraints as a special set of quasi-velocities helps derive explicit equations of motion. The equations are applicable to holonomic and nonholonomic constrained multibody systems. It is proved that in proposed quasi-spaces, the Lagrange multipliers are eliminated from equations of motion; however, it is possible to compute these multipliers once the equations of motion have been solved. The novelty of this research is employing block matrix inversion to find the analytical relations between the parameters of quasi-velocities and equations of motion. In other words, this research identifies arbitrary submatrices and their effects on equations of motion. Also, the present study aimed to provide appropriate criteria to select arbitrary parameters to avoid singularity, reduce constraints violations, and improve computational efficiency. In order to illustrate the advantage of this approach, the simulation results of a 3-link snake-like robot with nonholonomic constraints and a four-bar mechanism with holonomic constraints are presented. The effectiveness of the proposed approach is demonstrated by comparing the constraints violation at the position and velocity levels, conservation of the total energy, and computational efficiency with those obtained via the traditional methods.

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