Impact and Bifurcation of Flexible Multibody Systems

2003 ◽  
Author(s):  
Evtim V. Zahariev
Keyword(s):  
Finite Elements ◽  
Eigenvalue Problem ◽  
Multibody Systems ◽  
Dynamic Equations ◽  
Loss Of Stability ◽  
Motion Simulation ◽  
Novel Approach ◽  
Spatial Systems ◽  
Relative Coordinates ◽  
Initial Forms

In the paper, the process of loss of stability of multibody systems and structures is analyzed. A novel approach is presented and applied as for the statically loaded spatial systems so for analysis of dynamic response of systems imposed on impact. The analysis is based on solution of the dynamic equations and eigenvalue problem of systems, and of resultant motion simulation. The flexible systems are discretized using the method of finite elements. The dynamic equations are derived with respect to the relative coordinates of the finite elements. Large flexible deflections due to loss of stability are simulated. The initial forms of the possible deformations are defined by the eigenvectors computed solving the eigenvalue problem for the system stiffness matrix. The critical forces and system deflections obtained due to percussive forces and impact are then analyzed. Examples of bifurcation of beam and beam structure imposed on compulsive motion, percussive forces and impact are presented.

Nonlinear Dynamics of Rigid and Flexible Multibody Systems

1999 ◽  
Author(s):  
Evtim V. Zakhariev
Keyword(s):  
Finite Elements ◽  
Multibody Systems ◽  
Virtual Work ◽  
Space Station ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Dynamic Equations ◽  
Dynamics Modeling ◽  
Lagrange Equations

Abstract In the present paper a unified numerical approach for dynamics modeling of multibody systems with rigid and flexible bodies is suggested. The dynamic equations are second order ordinary differential equations (without constraints) with respect to a minimal set of generalized coordinates that describe the parameters of gross relative motion of the adjacent bodies and their small elastic deformations. The numerical procedure consists of the following stages: structural decomposition of elastic links into fictitious rigid points and/or bodies connected by joints in which small force dependent relative displacements are achieved; kinematic analysis; deriving explicit form dynamic equations. The algorithm is developed in case of elastic slender beams and finite elements achieving spatial motion with three translations and three rotations of nodes. The beam elements are basic design units in many mechanical devices as space station antennae and manipulators, cranes and etc. doing three dimensional motion which large elastic deflections could not be neglected or linearised. The stiffness coefficients and inertia mass parameters of the fictitious joints and links are calculated using the numerical procedures of the finite element theory. The method is called finite elements in relative coordinates. Its equivalence with the procedures of recently developed finite segment approaches is shown, while in the treatment different results are obtained. The approach is used for solution of some nonlinear static problems and for deriving the explicit configuration space dynamic equations of spatial flexible system using the principle of virtual work and Euler-Lagrange equations.

scholarly journals The Mobile Robot HILARE: Dynamic Modeling and Motion Simulation

2015 ◽  
Vol 4 (2) ◽  
pp. 150
Author(s):  
M. Ghazal ◽  
A. Talezadeh ◽  
M. Taheri ◽  
M. Nazemi-Zade
Keyword(s):  
Mobile Robot ◽  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Kinematic Model ◽  
Dynamic Equations ◽  
Motion Simulation ◽  
Governing Equations ◽  
Kinematic Constraints ◽  
Extended Application ◽  
The Matrix

To perform mission in variant environment, several types of mobile robot has been developed an implemented. The mobile robot HILARE is a known wheeled mobile robot which has two fixed wheels and an off-entered orientable wheel. Due to extended application of this robot, its dynamic analysis has attracted a great deal of interests. This article investigates dynamic modeling and motion analysis of the mobile robot HILARE. As the wheels of the robot have kinematic constraints, the constraints of wheels are taken into consideration and the matrix form of the kinematic model of the robot is derived. Furthermore, dynamic model of the robot is developed by consideration of kinematic constraints. To derive dynamic equations of the robot, the Lagrange multiplier method is employed and the governing equations of the robot in state-pace form are presented. Then, some simulations are presented to show applicability of the proposed formulation for dynamic analysis of the mobile robot HILARE.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

A Hybrid Global-Topological Real-Time Formulation for Multibody Systems

2003 ◽  
Author(s):  
Javier Cuadrado ◽  
Daniel Dopico
Keyword(s):  
Real Time ◽  
Multibody Systems ◽  
Full Model ◽  
Motion Simulation ◽  
Time Motion ◽  
Car Suspension ◽  
Time Formulation ◽  
Improved Performance ◽  
New Formulation ◽  
High Level

The continuously improved performance of personal computers enables the real-time motion simulation of complex multibody systems, such as the whole model of an automobile, on a conventional $1,200 PC, provided the adequate formulation is applied. There exist two big families of dynamic formulations, depending on the type of coordinates they use to model the system: global and topological. The former leads to a simple and systematic programming while the latter is very efficient. In this work, a hybrid formulation is presented, obtained by combination of one of the most efficient global formulations and one of the most systematic topological formulations. In this way, it is developed a new formulation which shows, at the same time, easiness of implementation and a high level of efficiency. In order to verify the advantages that the new formulation has over its predecessors, the analysis of four examples is carried out using the three formulations and the corresponding results are compared: a planar mechanism which goes through a singular position, a car suspension with stiff behaviour, and a 6-dof robot with changing configurations, and the full model of a car vehicle. Furthermore, the last example is also analyzed by using a commercial tool, so as to provide the readers with a well-known reference for comparison.

Dynamic Analysis of a Mobile Mechanical System with Deformable Elements

2012 ◽  
Vol 463-464 ◽  
pp. 1242-1245 ◽  
Author(s):  
Nicolae Dumitru ◽  
Raluca Malciu ◽  
Madalina Calbureanu ◽  
Sorin Dumitru ◽  
Gabriel Cătălin Marinescu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
System Modeling ◽  
Rigid Motion ◽  
Elastic Solid ◽  
Constant Matrix ◽  
Lagrange Formulation

The paper presents a method for studying mechanisms with deformable elements, based on overlapping the solid rigid motion over the elastic solid one, in order to identify the dynamic response of the system. Modeling was based on finite element method, so the cinematic elements were meshed in bar type finite elements and the degrees of freedom per node were settled according to the motion character (planar or spatial). A Lagrange formulation of the finite element was adopted for the deformable elements connected in multibody systems. In order to define the joints constraints, the conditions for compatibility between elements were defined using a Boolean constant matrix. Computer processed results were verified by an experimental model.

Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 2—Velocity Transformation

1990 ◽  
Vol 112 (2) ◽  
pp. 160-167 ◽  
Author(s):  
C. W. Chang ◽  
A. A. Shabana
Keyword(s):  
Multibody Systems ◽  
Robot Manipulator ◽  
Spatial Dynamics ◽  
Dynamic Equations ◽  
Velocity Transformation ◽  
Joint Forces ◽  
Joint Coordinates ◽  
Deformable Bodies ◽  
Spatial System ◽  
Velocity Transformation Technique

In Part 1 of these two companion papers, the spatial system kinematic and dynamic equations are developed using the Cartesian and elastic coordinates in order to maintain the generality of the formulation. This allows introducing general forcing functions and adding and/or deleting kinematic constraints. In control applications, however, it is desirable to determine the joint forces associated with the joint variables. On the other hand the use of the joint coordinates to formulate the dynamic equations leads to a complex recursive formulation based on loop closure equations. In this paper a velocity transformation technique applicable to spatial multibody systems that consist of interconnected rigid and deformable bodies is developed. The Cartesian variables are expressed in terms of the joint and elastic variables. The resulting kinematic relationships are then employed to determine the joint forces associated with the joint variables. A spatial robot manipulator that manipulates an object is presented as a numerical example to exemplify the development presented in this paper.

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