A Gyrobondgraph Method of Dynamic and Static Force Analysis for Spacial Multibody Systems

2011 ◽  
Vol 52-54 ◽  
pp. 1039-1044
Author(s):  
Zhong Shuang Wang ◽  
Ji Chen ◽  
Chang Shun Xu
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Static Force ◽  
Force Analysis ◽  
Constraint Forces ◽  
Bond Graphs ◽  
Algebraic Problem ◽  
Complete Form ◽  
Junction Structure ◽  
Efficiency And Reliability

In order to increase the efficiency and reliability of dynamic and static force analysis for spatial multibody systems containing the coupling of multi-energy domains, a method based on gyrobondgraph is introduced. The procedure of modeling spacial multibody systems by bond graphs and its dynamic principle are described. The unified formulae of driving moment and constraint forces at joints are derived based on gyrobondgraph, they are easily generated 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 dynamic analysis of multibody systems on a computer is realized. By a practical example, the validity of this procedure is illustrated.

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.

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.

Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses

1994 ◽  
Vol 116 (2) ◽  
pp. 614-621 ◽  
Author(s):  
Yong-Xian Xu ◽  
D. Kohli ◽  
Tzu-Chen Weng
Keyword(s):  
Stability Index ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Singularity ◽  
Numerical Examples ◽  
Transformation Matrices ◽  
Unstable Configuration ◽  
Direct Kinematics

A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulation leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

Efficient Dynamic Analysis Method for Multibody Systems With Constraint Violation Stabilization Method

1999 ◽  
Author(s):  
Apiwat Reungwetwattana ◽  
Shigeki Toyama
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Analysis Method ◽  
Stabilization Method ◽  
Kinematic Constraint ◽  
Constraint Violation ◽  
Closed Loops ◽  
Constraint Stabilization ◽  
Constraint Equations ◽  
Crank Mechanism

Abstract This paper presents an efficient extension of Rosenthal’s order-n algorithm for multibody systems containing closed loops. Closed topological loops are handled by cut joint technique. Violation of the kinematic constraint equations of cut joints is corrected by Baumgarte’s constraint violation stabilization method. A reliable approach for selecting the parameters used in the constraint stabilization method is proposed. Dynamic analysis of a slider crank mechanism is carried out to demonstrate efficiency of the proposed method.

On MBS Constraints and Projections

2021 ◽  
Author(s):  
Friedrich Pfeiffer
Keyword(s):  
Quadratic Form ◽  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Machine Process ◽  
Constraint Forces ◽  
Process Dynamics ◽  
Robot Tracking ◽  
Minimal Coordinates ◽  
Linear Differential

Abstract Constraints in multibody systems are usually treated by a Lagrange I - method resulting in equations of motion together with the constraint forces. Going from non-minimal coordinates to minimal ones opens the possibility to project the original equations directly to the minimal ones, thus eliminating the constraint forces. The necessary procedure is described, a general example of combined machine-process dynamics discussed and a specific example given. For a n-link robot tracking a path the equations of motion are projected onto this path resulting in quadratic form linear differential equations. They define the space of allowed motion, which is generated by a polygon-system.

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