New Form of Kane's Equations of Motion for Constrained Systems

2003 ◽  
Vol 26 (1) ◽  
pp. 79-88 ◽  
Author(s):  
Abdulrahman H. Bajodah ◽  
Dewey H. Hodges ◽  
Ye-Hwa Chen
Keyword(s):  
Equations Of Motion ◽  
Constrained Systems ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
New Form

scholarly journals Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

2007 ◽  
Vol 30 (1) ◽  
pp. 286-288 ◽  
Author(s):  
Carlos M. Roithmayr ◽  
Abdulrahman H. Bajodah ◽  
Dewey H. Hodges ◽  
Ye-Hwa Chen
Keyword(s):  
Equations Of Motion ◽  
Constrained Systems ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
New Form

An Applied Form of Kane’s Equations of Motions

2005 ◽  
Author(s):  
Hossein Nejat Pishkenari ◽  
Amir Lotfi Gaskarimahalle ◽  
Seyed Babak Ghaemi Oskouei ◽  
Ali Meghdari
Keyword(s):  
Degrees Of Freedom ◽  
Control Unit ◽  
Generalized Coordinates ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
The Matrix ◽  
Angular Velocities ◽  
New Form ◽  
Derivatives Of ◽  
Equations Of Motions

In this paper we have presented a new form of Kane’s equations. This new form is expressed in the matrix form with the components of partial derivatives of linear and angular velocities relative to the generalized speeds and generalized coordinates. The number of obtained equations is equal to the number of degrees of freedom represented in a closed form. Also the equations can be rearranged to appear only one of the time derivatives of generalized speeds in each equation. This form is appropriate especially when one intends to derive equations recursively. Hence in addition to the simplicity, the amount of calculations is noticeably reduced and also can be used in a control unit.

Extended Kane’s Equations for Nonholonomic Variable Mass System

1982 ◽  
Vol 49 (2) ◽  
pp. 429-431 ◽  
Author(s):  
Z.-M. Ge ◽  
Y.-H. Cheng
Keyword(s):  
Equations Of Motion ◽  
Variable Mass ◽  
Mass System ◽  
Variable Mass System ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Variable Mass Systems

An extension of Kane’s equations of motion for nonholonomic variable mass systems is presented. As an illustrative example, equations of motion are formulated for a rocket car.

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 geometrical interpretation of Kane’s Equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 69-87 ◽  
Keyword(s):  
Tangent Space ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Analytical Mechanics ◽  
Kane’S Method ◽  
Kane's Method ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Spanning Set ◽  
Geometric Picture

The method for the development of the equations of motion for systems of constrained particles and rigid bodies, developed by T. R. Kane and called Kane’s Equations, is discussed from a geometric viewpoint. It is shown that what Kane calls partial velocities and partial angular velocities may be interpreted as components of tangent vectors to the system’s configuration manifold. The geometric picture, when attached to Kane’s formalism shows that Kane’s Equations are projections of the Newton-Euler equations of motion onto a spanning set of the configuration manifold’s tangent space. One advantage of Kane’s method, is that both non-holonomic and non-conservative systems are easily included in the same formalism. This easily follows from the geometry. It is also shown that by transformation to an orthogonal spanning set, the equations can be diagonalized in terms of what Kane calls the generalized speeds. A further advantage of the geometric picture lies in the treatment of constraint forces which can be expanded in terms of a spanning set for the orthogonal complement of the configuration tangent space. In all these developments, explicit use is made of a concrete realization of the multidimensional vectors which are called K -vectors for a K -component system. It is argued that the current presentation also provides a clear tutorial route to Kane’s method for those schooled in classical analytical mechanics.

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.

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