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.

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.

Mobile manipulator modeling with Kane's approach

Robotica ◽  
2001 ◽  
Vol 19 (6) ◽  
pp. 675-690 ◽  
Author(s):  
Herbert G. Tanner ◽  
Kostas J. Kyriakopoulos
Keyword(s):  
Control Strategies ◽  
Nonholonomic Constraints ◽  
Dynamic Equations ◽  
Mobile Manipulator ◽  
Constraint Equations ◽  
Motion Constraints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Physical Insight ◽  
Complete Framework

A wheeled mobile manipulator system is modeled using Kane's dynamic equations. Kane's equations are constructed with minimum effort, are control oriented and provide both physical insight and fast simulations. The powerful tools of Kane's approach for incorporating nonholonomic motion constraints and bringing noncontributing forces into evidence are exploited. Both nonholonomic constraints associated with slipping and skidding as well as conditions for avoiding tipping over are included. The resulting equations, along with the set of constraint equations provide a safe and complete framework for developing control strategies for mobile manipulator systems.

A fresh insight into Kane's equations of motion

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 498-510 ◽  
Author(s):  
H. Nejat Pishkenari ◽  
S. A. Yousefsani ◽  
A. L. Gaskarimahalle ◽  
S. B. G. Oskouei
Keyword(s):  
Dynamic Systems ◽  
Rapid Development ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
The Matrix ◽  
Impulsive Forces ◽  
Multi Body ◽  
Fresh Insight

SUMMARYWith rapid development of methods for dynamic systems modeling, those with less computation effort are becoming increasingly attractive for different applications. This paper introduces a new form of Kane's equations expressed in the matrix notation. The proposed form can efficiently lead to equations of motion of multi-body dynamic systems particularly those exposed to large number of nonholonomic constraints. This approach can be used in a recursive manner resulting in governing equations with considerably less computational operations. In addition to classic equations of motion, an efficient matrix form of impulse Kane formulations is derived for systems exposed to impulsive forces.

A recursive approach for the analysis of snake robots using Kane's equations

Robotica ◽  
2006 ◽  
Vol 24 (2) ◽  
pp. 251-256 ◽  
Author(s):  
H. Tavakoli Nia ◽  
H. N. Pishkenari ◽  
A. Meghdari
Keyword(s):  
Nonholonomic Constraints ◽  
Dynamic Problems ◽  
Snake Robot ◽  
Euler’S Method ◽  
Cpu Time ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Link Model ◽  
Computational Procedures ◽  
Snake Robots

This paper presents a recursive approach for solving kinematic and dynamic problems in snake-like robots using Kane's equations. An n-link model with n-nonholonomic constraints is used as the snake robot model in our analysis. The proposed algorithm which is used to derive kinematic and dynamic equations recursively, enhances the computational efficiency of our analysis. Using this method we can determine the number of additions and multiplications as a function of n. The proposed method is compared with the Lagrange and Newton-Euler's method in three different aspects: Number of operations, CPU time and error in the computational procedures.

A Recursive Approach for Analysis of Snake Robots Using Kane’s Equations

2005 ◽  
Author(s):  
Hadi Tavakoli Nia ◽  
Hossein Nejat Pishkenari ◽  
Ali Meghdari
Keyword(s):  
Nonholonomic Constraints ◽  
Dynamic Equations ◽  
Snake Robot ◽  
Euler’S Method ◽  
Cpu Time ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Link Model ◽  
Computational Procedures ◽  
Snake Robots

This paper presents a recursive approach for solving kinematic and dynamic problem in snake-like robots using Kane’s equations. An n-link model with n-nonholonomic constraints is used as the snake robot model in our analysis. The proposed algorithm which is used to derive kinematic and dynamic equations recursively enhances the computational efficiency of our analysis. Using this method we can determine the number of additions and multiplications as a function of n. The proposed method is compared with the Lagrange and Newton-Euler’s method in three different aspects: Number of operations, CPU time and error in the computational procedures.

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