An Adaptive Constraint Violation Stabilization Method for Dynamic Analysis of Mechanical Systems

1985 ◽  
Vol 107 (4) ◽  
pp. 488-492 ◽  
Author(s):  
C. O. Chang ◽  
P. E. Nikravesh
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
General Purpose ◽  
Adaptive Mechanism ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Transient Dynamic Analysis ◽  
Constrained Mechanical Systems ◽  
Feedback Control Theory

The transient dynamic analysis of equations of motion for constrained mechanical systems requires the solution of a mixed set of algebraic and differential equations. A constraint violation stabilization method, based on feedback control theory of linear systems, has been suggested by some researchers for solving these equations. However, since the value of damping parameters for this method are uncertain, the method is to some extent unattractive for general-purpose use. This paper presents an adaptive mechanism for determining the damping parameters. The results of the simulation for two examples illustrate the improvement in reducing the constraint violations when using this method.

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Analysis and Optimal Design of Spatial Mechanical Systems

1987 ◽  
Author(s):  
H. Ashrafeiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Analysis And Design ◽  
Spatial Systems

Abstract This paper presents a new approach to optimal design of large multibody spatial mechanical systems. This approach uses symbolic computing to generate the necessary equations for dynamic analysis and design sensitivity analysis. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of velocity transformation matrix. Design sensitivity analysis is carried out using the Direct Differentiation method applied to the relative joint coordinate formulation for spatial systems. Symbolic manipulation programs are used to develop subroutines which provide information for dynamic and design sensitivity analysis. These subroutines are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization. An example is presented to demonstrate the efficiency of the approach.

Euler Parameters in Computational Kinematics and Dynamics. Part 1

1985 ◽  
Vol 107 (3) ◽  
pp. 358-365 ◽  
Author(s):  
P. E. Nikravesh ◽  
R. A. Wehage ◽  
O. K. Kwon
Keyword(s):  
Computer Program ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
General Purpose ◽  
Euler Parameters ◽  
Memory Space ◽  
Constrained Mechanical Systems ◽  
Limited Memory ◽  
General Purpose Computer ◽  
Purpose Computer

This paper presents useful and interesting identities between Euler parameters and their time derivatives. Using these identities, kinematic constraints and equations of motion for constrained mechanical systems are derived. These equations can be developed into a computer program to systematically generate all of the necessary equations to model mechanical systems. The compact form of these equations makes it possible to develop a general-purpose computer program for dynamic analysis of mechanical systems suitable for operation on small computers with limited memory space.

A Differentiable Null Space Method for Constrained Dynamic Analysis

1987 ◽  
Vol 109 (3) ◽  
pp. 405-411 ◽  
Author(s):  
C. G. Liang ◽  
George M. Lance
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Null Space ◽  
Mechanical Systems ◽  
Geometric Approach ◽  
Constraint Violation ◽  
Constrained Mechanical Systems ◽  
Tangent Hyperplane ◽  
Space Method ◽  
Constraint Surface

A geometric approach to the solution of the dynamic response of constrained mechanical systems is proposed. A continuous and differentiable basis of the constraint null space is automatically generated using the Gram-Schmidt process. The independent coordinates are obtained by transforming the physical velocity coordinates to the tangent hyperplane of the constraint surface. As a result the independent coordinates lie on the constraint surface and no constraint violation control is necessary.

Optimal Design of Mechanical Systems With Constraint Violation Stabilization Method

1985 ◽  
Vol 107 (4) ◽  
pp. 493-498 ◽  
Author(s):  
C. O. Chang ◽  
P. E. Nikravesh
Keyword(s):  
Optimal Design ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Procedure ◽  
Optimization Procedure ◽  
Design Sensitivity ◽  
System Response ◽  
Stabilization Method ◽  
Sensitivity Matrix ◽  
Constraint Violation

This paper presents a comprehensive optimal design procedure for constrained dynamic systems. The constraint violation stabilization method for dynamic analysis of mechanical systems is briefly reviewed. A direct differentiation method is used to form the equations of design sensitivity analysis based on a constraint violation stabilization method. The sensitivity equations and the equations of motion are integrated simultaneously to obtain the system response, as well as the state sensitivity matrices. All integrations are performed using a multistep predictor-corrector method. The first order design sensitivity matrix is used to calculate the gradient of cost function and the performance constraint during the optimization procedure. An optimization routine is linked to the analysis/sensitivity algorithm. Two examples are given which illustrate the effectiveness of this method for determining the optimal design of a system.

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.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

Stability and Accuracy Analysis of Baumgarte’s Constraint Violation Stabilization Method

1995 ◽  
Vol 117 (3) ◽  
pp. 446-453 ◽  
Author(s):  
S. Yoon ◽  
R. M. Howe ◽  
D. T. Greenwood
Keyword(s):  
Equations Of Motion ◽  
Integration Step ◽  
State Variables ◽  
Stabilization Method ◽  
Lagrange Equations ◽  
Step Size ◽  
Constraint Violation ◽  
Truncation Errors ◽  
Numerical Stability Analysis ◽  
Stability And Accuracy

When Baumgarte’s Constraint Violation Stabilization Method (CVSM) is used in the simulation of Lagrange equations of motion with holonomic constraints, it is shown that, with suitable assumptions on the integration step size h and the eigenvalues (λ’s) of the linearized system, the constraint variables are effectively integrated by the same algorithm as that used for the state variables. A numerical stability analysis of the constraint violations can be performed using this so-called pseudo-integration equation. A study is also made of truncation errors and their modeling in the continuous time domain. This model can be used to determine the effectiveness of various constraint controls and integration methods in reducing the errors in the solution due to truncation errors. Examples are presented to illustrate the use of a higher-order truncation error model which leads to an accurate quantitative steady-state analysis of the constraint violations.

On a Consistent Application of Newton’s Law to Constrained Mechanical Systems

2013 ◽  
Author(s):  
Elias Paraskevopoulos ◽  
Sotirios Natsiavas
Keyword(s):  
Riemannian Manifolds ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Constrained Mechanical Systems ◽  
Motion Constraints ◽  
Newton's Law ◽  
Newton’S Law ◽  
Correct Application ◽  
Practical Implications ◽  
Consistent Application

An investigation is carried out for deriving conditions on the correct application of Newton’s law of motion to mechanical systems subjected to constraints. It utilizes some fundamental concepts of differential geometry and treats both holonomic and anholonomic constraints. The focus is on establishment of conditions, so that the form of Newton’s law remains invariant when imposing an additional set of motion constraints on a system. Based on this requirement, two conditions are derived, specifying the metric and the form of the connection on the new manifold. The latter is weaker than a similar condition employed frequently in the literature, but holding on Riemannian manifolds only. This is shown to have several practical implications. First, it provides a valuable freedom for selecting the connection on the manifold describing large rigid body rotation, so that the group properties of this manifold are preserved. Moreover, it is used to state clearly the conditions for expressing Newton’s law on the tangent space (and not on the dual space) of a manifold. Finally, the Euler-Lagrange operator is examined and issues related to equations of motion for anholonomic and vakonomic systems are investigated.

Sign in / Sign up

Export Citation Format

Share Document