Pseudouptriangular decomposition method for constrained multibody systems using Kane's equations

1988 ◽  
Vol 11 (1) ◽  
pp. 39-46 ◽  
Author(s):  
F. M. L. Amirouche ◽  
T. Jia
Keyword(s):  
Multibody Systems ◽  
Decomposition Method ◽  
Constrained Multibody Systems ◽  
Kane’S Equations ◽  
Kane's Equations

Kane’s Equations With Undetermined Multipliers—Application to Constrained Multibody Systems

1987 ◽  
Vol 54 (2) ◽  
pp. 424-429 ◽  
Author(s):  
J. T. Wang ◽  
R. L. Huston
Keyword(s):  
Multibody Systems ◽  
Automated Analysis ◽  
Numerical Analyses ◽  
Constrained Multibody Systems ◽  
Controlled Systems ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

A procedure for automated analysis of constrained multibody systems is presented. The procedure is based upon Kane’s equations and the concept of undetermined multipliers. It is applicable with both free and controlled systems. As with Lagrange’s equations, the multipliers are identified as scalar components of constraining forces and moments. The advantage of using Kane’s equations is that they are ideally suited for development of algorithms for numerical analyses. Also, generalized speeds and quasi-coordinates are readily accommodated. A simple example illustrating the concepts is presented.

On the Constraint Violations in the Dynamic Simulations of Multibody Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 238-243 ◽  
Author(s):  
S. K. Ider ◽  
F. M. L. Amirouche
Keyword(s):  
Mathematical Model ◽  
Large Class ◽  
Multibody Systems ◽  
Transformation Matrix ◽  
Computational Time ◽  
Dynamic Simulations ◽  
Constrained Multibody Systems ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Dynamics Of Multibody Systems

This paper presents an automated and efficient mathematical model for checking the violations of the constraints in the dynamics of multibody systems. The superfluous generalized independent speeds are obtained through a new transformation matrix called a pseudo-uptriangular decomposition (PUTD). The violation of the constraints is checked using a test condition between the generalized speeds and the independent speeds. A decision is then made to whether the transformation matrix needs to be regenerated. The method presented has a number of advantages over previously developed methods, since it requires less computational time and is suited for a large class of problems. It is believed that the use of Kane’s equations as presented in this paper make the analysis of constrained multibody systems even more tractable. Some examples used for the verification of the procedure are presented.

Modeling a Robot With Flexible Joints and Decoupling its Equations of Motion

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Flexible Joints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Recent Advances ◽  
Dynamics Of Multibody Systems ◽  
Two Degree Of Freedom

Abstract Recent advances in the study of dynamics of multibody systems indicate the need for decoupling of the equations of motion. In this paper, our efforts are focused on this issue, and we have tried to expand the existing methods for multi-rigid body systems to include systems with some kind of flexibility. In this regard, the equations of motion for a planar two-degree-of-freedom robot with flexible joints is carried out using Lagrange’s equations and Kane’s equations with congruency transformations. The method of decoupling the equations of motion using Kane’s equations with congruency transformations is presented. Finally, the results obtained from both methods are compared.

A Conservation Theorem for Constrained Multibody Systems

1993 ◽  
Vol 60 (4) ◽  
pp. 962-969
Author(s):  
J. T. Wang
Keyword(s):  
Multibody Systems ◽  
Nonholonomic Constraints ◽  
First Integral ◽  
Integral Of Motion ◽  
Power Equation ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Power And Energy ◽  
Conservation Theorem ◽  
General Conservation

This paper presents a general conservation theorem for multibody systems subject to simple nonholonomic constraints. It is applicable to both conservative and nonconservative systems. The derivation of this theorem is based on Kane’s equations with undetermined multipliers. A power equation and a first integral of motion have been derived. They emerge in physically meaningful forms and include expressions for evaluating the power and energy flowing into the system. Like Kane’s equations, the power equation and the first integral of motion are derived in matrix form. This makes them particularly useful for the computer formulation and solution of multibody system dynamics.

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.

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