A Vector Bond Graph Method of Kineto-Static Analysis for Spatial Multibody Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1725-1729 ◽  
Author(s):  
Zhong Shuang Wang ◽  
Yang Yang Tao ◽  
Quan Yi Wen
Keyword(s):  
Static Analysis ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Graph Model ◽  
Bond Graph ◽  
Constraint Forces ◽  
Decoupling Method ◽  
Complete Form ◽  
Three Degrees Of Freedom

In order to increase the reliability and efficiency of the kineto-static analysis of complex multibody systems, the corresponding vector bond graph procedure is proposed. By the kinematic constraint condition, spatial multibody systems can be modeled by vector bond graph. For the algebraic difficulties brought by differential causality in system automatic kineto-static analysis, the effective decoupling method is proposed, thus the differential causalities in system vector bond graph model can be eliminated. In the case of considering EJS, the unified formulae of driving moment and constraint forces at joints are derived based on vector bond graph, which are easily derived on a computer in a complete form and very suitable for spatial multibody systems. As a result, the automatic kineto-static analysis of spatial multibody system on a computer is realized, its validity is illustrated by the spatial multibody system with three degrees of freedom.

A Vector Bond Graph Method of Kineto-Static Analysis for Complex Planar Linkage

2012 ◽  
Vol 482-484 ◽  
pp. 1062-1067
Author(s):  
Zhong Shuang Wang ◽  
Jian Guo Cao ◽  
Ji Chen
Keyword(s):  
Static Analysis ◽  
Graph Model ◽  
Bond Graph ◽  
Constraint Forces ◽  
Constraint Force ◽  
Graph Method ◽  
Algebraic Problem ◽  
Complete Form ◽  
Junction Structure ◽  
Force Vectors

For the kineto-static analysis of complex planar linkage, the procedure based on vector bond graph is proposed. The constraint force vectors at joints can be considered as unknown effort source vectors and added to the corresponding 0-junctions of the system vector bond graph model, most of the differential causalities in system vector bond graph model can be eliminated . In the case of mixed causality, the unified formulae of driving moment and constraint forces at joints are derived based on vector bond graph, which are easily derived on a computer in a complete form. As a result, the very difficult algebraic problem caused by differential causality and nonlinear junction structure can be overcome, and the automatic kineto-static analysis of complex planar linkage on a computer is realized. By a practical example, the validity of this procedure is illustrated.

The Dynamic Modelling and Simulation of Spatial Multibody Systems with Prismatic Joint Based on Vector Bond Graph

2013 ◽  
Vol 756-759 ◽  
pp. 740-745 ◽  
Author(s):  
Zhong Shuang Wang ◽  
Yang Yang Tao ◽  
Shang Liu
Keyword(s):  
Multibody Systems ◽  
Dynamic Modelling ◽  
Graph Model ◽  
Bond Graph ◽  
Modelling And Simulation ◽  
System State ◽  
Constraint Forces ◽  
Kinematic Constraint ◽  
Decoupling Method ◽  
Prismatic Joint

For the modelling and simulation of complex spatial multibody systems, the vector bond graph method is proposed. By the kinematic constraint condation, spatial prismatic joint can be modeled by vector bond graph. For the algebraic difficulties brought by differential causality in system automatic modeling and simulation, the effective decoupling method is proposed and the differential causalities in system vector bond graph model can be eliminated. In the case of considering EJS, the unified formulae of system state space equations and constraint forces at joints are derived, which are easily derived on a computer and very suitable for spatial multibody systems. As a result, the unified modelling and simulation for complex spatial multibody systems are realized, its validity is illustrated by a practical example.

Orienting Body Coordinate Frames Using Karhunen-Loe`ve Expansion for More Effective Structural Simplification

2006 ◽  
Author(s):  
Tulga Ersal ◽  
Hosam K. Fathy ◽  
Jeffrey L. Stein
Keyword(s):  
Multibody Dynamics ◽  
Multibody Systems ◽  
Multibody System ◽  
Bond Graph ◽  
The Body ◽  
Coordinate Frames ◽  
Highly Sensitive ◽  
Structural Simplification

Previous work by the authors developed a junction-inactivity-based structural simplification technique for bondgraph models. The technique is highly sensitive to the orientation of the body coordinate frames in multibody systems: improper alignment of body coordinate frames may prohibit a significant simplification. This paper demonstrates how the Karhunen-Loe`ve expansion can be used to automatically detect the existence of and to find the transformation into body coordinate frames that render the bond-graph of a multibody system more conducive to simplification. The conclusion is that the Karhunen-Loe`ve expansion complements well the junction-inactivity-based structural simplification technique when multibody dynamics are involved in the system.

Dynamic Modeling of Robot Systems with Cylindrical Joint Based on Vector Bond Graph

2013 ◽  
Vol 694-697 ◽  
pp. 17-21
Author(s):  
Zhong Shuang Wang ◽  
Yang Yang Tao ◽  
Xiao Mei Xie
Keyword(s):  
Modeling And Simulation ◽  
Degrees Of Freedom ◽  
Bond Graph ◽  
Constraint Condition ◽  
Robot System ◽  
Kinematic Constraint ◽  
Decoupling Method ◽  
Unified Modeling ◽  
Cylindrical Joint ◽  
Robot Systems

In order to increase the reliability and efficiency of the dynamic analysis of complex robot systems, the corresponding vector bond graph procedure is proposed. Based on the kinematic constraint condition, the vector bond graph procedure for modeling robot systems with cylindrical joint is described. For the difficulties brought by differential causality in the system automatic modeling and simulation, the effective decoupling method is proposed. As a result, the unified modeling and simulation for robot systems are realized, its validity is illustrated by the spatial robot system with five degrees of freedom.

Approximate End-Effector Tracking Control of Flexible Multibody Systems Using Singular Perturbations

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Thomas Gorius ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Tracking Control ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Feedforward Control ◽  
Flexible Multibody Systems ◽  
Flexible Manipulator ◽  
End Effector ◽  
Nonminimum Phase ◽  
Flexible Multibody

In many cases, the design of a tracking controller can be significantly simplified by the use of a 2-degrees of freedom (DOF) control structure, including a feedforward control (i.e., the inversion of the nominal system dynamics). Unfortunately, the computation of this feedforward control is not easy if the system is nonminimum-phase. Important examples of such systems are flexible multibody systems, such as lightweight manipulators. There are several approaches to the numerical computation of the exact inversion of a flexible multibody system. In this paper, the singularly perturbed form of such mechanical systems is used to give a semianalytic solution to the tracking control design. The control makes the end-effector to even though not exactly, but approximately track a certain trajectory. Thereby, the control signal is computed as a series expansion in terms of an overall flexibility of the bodies of the multibody system. Due to the use of symbolic computations, the main calculations are independent of given parameters (e.g., the desired trajectories), such that the feedforward control can be calculated online. The effectiveness of this approach is shown by the simulation of a two-link flexible manipulator.

Inverse Dynamics of Constrained Multibody Systems

1990 ◽  
Vol 57 (3) ◽  
pp. 750-757 ◽  
Author(s):  
J. T. Wang
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Multibody System ◽  
Coefficient Matrix ◽  
Force Term ◽  
Constraint Forces ◽  
Kinematic Constraints ◽  
Constrained Multibody Systems ◽  
Orthogonal Complement Matrix ◽  
Partial Velocity

A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.

Singularly Perturbed Bond Graph Models for Simulation of Multibody Systems

1995 ◽  
Vol 117 (3) ◽  
pp. 401-410 ◽  
Author(s):  
A. A. Zeid ◽  
J. L. Overholt
Keyword(s):  
Time Scale ◽  
Multibody Systems ◽  
Graph Model ◽  
Bond Graph ◽  
Rigid Bodies ◽  
Singularly Perturbed ◽  
Bond Graphs ◽  
Graph Models ◽  
Multibody Modeling ◽  
Nonlinear Properties

This paper develops a bond graph-based formalism for modeling multibody systems in a singularly perturbed formulation. As opposed to classical multibody modeling methods, the singularly perturbed formulation is explicit, which makes it suitable for modular simulation. Kinematic joints that couple rigid bodies are described by a set of differential equations with an order of magnitude smaller time scale than that of the system. Singularly perturbed models of joints can be used to investigate nonlinear properties of joints, such as clearance and friction. The main restriction of this approach is that the simulation may need to be computed using 64 bits precision because of the two-time scale nature of the solution. The formalism is based on developing bond graph models of an elementary set of graphical velocity-based constraint functions. This set can be used to construct bond graphs of any type of mechanical joint. Here, this set is used to develop bond graphs of several joints used in multibody systems and spatial mechanisms. Complex models of multibody systems may now be built by graphically concatenating bond graphs of rigid bodies and bond graphs of joints. The dynamic equations of the system are automatically generated from the resulting bond graph model. The dynamic equation derived from the bond graph are in explicit state space form, ready for numerical integration, and exclude the computationally intensive terms that arise from acceleration analysis.

A Self-Stabilized Algorithm for Enforcing Constraints in Multibody Systems

2003 ◽  
Author(s):  
Olivier A. Bauchau
Keyword(s):  
Multibody Systems ◽  
Convergence Rates ◽  
Multibody System ◽  
Flexible Multibody System ◽  
Constraint Forces ◽  
High Frequencies ◽  
Elastic Forces ◽  
Element Approach ◽  
Index 2 ◽  
Work Done

A new algorithm is developed for the enforcement of constraints within the framework of nonlinear, flexible multibody system modeled with the finite element approach. The proposed algorithm exactly satisfies the constraints at the displacement and velocity levels, and furthermore, it achieves nonlinear unconditional stability by imposing the vanishing of the work done by the constraint forces when combined with specific discretizations of the inertial and elastic forces. Identical convergence rates are observed for the displacements, velocities, and Lagrange multipliers. The proposed algorithm is closely related to the stabilized index-2 or GGL method, although no additional multipliers are introduced in the present approach. These desirable characteristics are obtained without resorting to numerically dissipative algorithms. If high frequencies are present in the system, i.e. the system +is physically stiff, dissipative schemes become necessary; the proposed algorithm is extended to deal with this situation.

Reduction of Physical and Constraint Degrees-of-Freedom of Redundant Formulated Multibody Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Daniel Stadlmayr ◽  
Wolfgang Witteveen ◽  
Wolfgang Steiner
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
A Priori ◽  
Plane Motion ◽  
Critical Discussion ◽  
Galerkin Projection ◽  
Differential Algebraic Equation ◽  
Numerical Examples ◽  
Constraint Equations

Commercial multibody system simulation (MBS) tools commonly use a redundant coordinate formulation as part of their modeling strategy. Such multibody systems subject to holonomic constraints result in second-order d-index three differential algebraic equation (DAE) systems. Due to the redundant formulation and a priori estimation of possible flexible body coordinates, the model size increases rapidly with the number of bodies. Typically, a considerable number of constraint equations (and physical degrees-of-freedom (DOF)) are not necessary for the structure's motion but are necessary for its stability like out-of-plane constraints (and DOFs) in case of pure in-plane motion. We suggest a combination of both, physical DOF and constraint DOF reduction, based on proper orthogonal decomposition (POD) using DOF-type sensitive velocity snapshot matrices. After a brief introduction to the redundant multibody system, a modified flat Galerkin projection and its application to index-reduced systems in combination with POD are presented. The POD basis is then used as an identification tool pointing out reducible constraint equations. The methods are applied to one academic and one high-dimensional practical example. Finally, it can be reported that for the numerical examples provided in this work, more than 90% of the physical DOFs and up to 60% of the constraint equations can be omitted. Detailed results of the numerical examples and a critical discussion conclude the paper.

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