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.

Lagrange’s Equations, Hamilton’s Equations, and Kane’s Equations: Interrelations, Energy Integrals, and a Variational Principle

1995 ◽  
Vol 62 (2) ◽  
pp. 505-510 ◽  
Author(s):  
D. L. Mingori
Keyword(s):  
Analytical Mechanics ◽  
Energy Integral ◽  
Governing Equations ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Lagrange’S Equations ◽  
Energy Integrals ◽  
Hamilton's Equations ◽  
Lagrange's Equations ◽  
Hamilton’S Equations

A new viewpoint is suggested for expressing the governing equations of analytical mechanics. This viewpoint establishes a convenient framework for examining the relationships among Lagrange’s equations, Hamilton’s equations, and Kane’s equations. The conditions which must be satisfied for the existence of an energy integral in the context of Kane’s equations are clarified, and a generalized form of Hamilton’s Principle is presented. Generalized speeds replace generalized velocities as the velocity variables in the formulation. The development considers holonomic systems in which the generalized forces are derivable from a potential function.

scholarly journals Finite Element Method-Based Elastic Analysis of Multibody Systems. A Review

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 257
Author(s):  
Sorin Vlase ◽  
Marin Marin ◽  
Negrean Iuliu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical System ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Methods ◽  
Engineering Applications ◽  
Lagrange’S Equations ◽  
Lagrange's Equations ◽  
Element Method

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

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.

scholarly journals A contribution to the dynamic simulation of robot manipulator with the software RobotDyn

2004 ◽  
Vol 26 (4) ◽  
pp. 215-225
Author(s):  
Nguyen Van Khang ◽  
Do Thanh Tung
Keyword(s):  
Computer Program ◽  
Dynamic Simulation ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Theoretical Background ◽  
Tree Structures ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

Robots manipulators are multibody systems with tree structures. In this paper the theoretical background of the computer program RobotDyn is presented. The program is developed using Lagrange's equations and Denavit-Hartenberg matrix. The dynamic simulation of the Robot SCARA with four degrees of freedom is considered as an example of application of the program RobotDyn.

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.

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