Dynamics of Large Constrained Flexible Structures

1988 ◽  
Vol 110 (1) ◽  
pp. 78-83 ◽  
Author(s):  
F. M. L. Amirouche ◽  
R. L. Huston
Keyword(s):  
Structure Analysis ◽  
Flexible Structures ◽  
Orthogonal Complement ◽  
Space Structures ◽  
Governing Equations ◽  
Finite Segment ◽  
Closed Loops ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Kane's Equations

This paper presents an automated procedure useful in the study of large constrained flexible structures, undergoing large specified motions. The structure is looked upon as a “partially open tree” system, containing closed loops in some of the branches. The governing equations are developed using Kane’s equations as formulated by Huston et al. The accommodation of the constraint equations is based on the use of orthogonal complement arrays. The flexibility and oscillations of the bodies is modelled using finite segment modelling, structure analysis, and scaling techniques. The procedures developed are expected to be useful in applications including robotics, space structures, and biosystems.

Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach

1988 ◽  
Vol 55 (4) ◽  
pp. 899-904 ◽  
Author(s):  
S. K. Ider ◽  
F. M. L. Amirouche
Keyword(s):  
Null Space ◽  
Computationally Efficient ◽  
New Approach ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Linearly Independent ◽  
Kane's Equations ◽  
Constrained Dynamical Systems ◽  
Coordinate Reduction ◽  
Algebraic Constraint

In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.

Dynamics of Constrained Multibody Systems

1984 ◽  
Vol 51 (4) ◽  
pp. 899-903 ◽  
Author(s):  
J. W. Kamman ◽  
R. L. Huston
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Dynamical Equations ◽  
Closed Loops ◽  
Constrained Multibody Systems ◽  
Constraint Equations ◽  
Cable Dynamics ◽  
Hanging Chain ◽  
A Chain

A new automated procedure for obtaining and solving the governing equations of motion of constrained multibody systems is presented. The procedure is applicable when the constraints are either (a) geometrical (for example, “closed-loops”) or (b) kinematical (for example, specified motion). The procedure is based on a “zero eigenvalues theorem,” which provides an “orthogonal complement” array which in turn is used to contract the dynamical equations. This contraction, together with the constraint equations, forms a consistent set of governing equations. An advantage of this formulation is that constraining forces are automatically eliminated from the analysis. The method is applied with Kane’s equations—an especially convenient set of dynamical equations for multibody systems. Examples of a constrained hanging chain and a chain whose end has a prescribed motion are presented. Applications in robotics, cable dynamics, and biomechanics are suggested.

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.

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.

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.

A Recursive Householder Transformation for Complex Dynamical Systems With Constraints

1988 ◽  
Vol 55 (3) ◽  
pp. 729-734 ◽  
Author(s):  
F. M. L. Amirouche ◽  
Tongyi Jia ◽  
Sitki K. Ider
Keyword(s):  
Dynamical Systems ◽  
General Solution ◽  
Equations Of Motion ◽  
New Method ◽  
Systems Dynamics ◽  
Complex Dynamical Systems ◽  
Governing Equations ◽  
Householder Transformation ◽  
Constraint Equations ◽  
Computer Automation

A new method is presented by which equations of motion of complex dynamical systems are reduced when subjected to some constraints. The method developed is used when the governing equations are derived using Kane’s equations with undetermined multipliers. The solution vectors of the constraint equations are determined utilizing the recursive Householder transformation to obtain a Pseudo-Uptriangular matrix. The most general solution in terms of new independent coordinates is then formulated. Methods previously used for handling such systems are discussed and the new method advantages are illustrated. The procedures developed are suitable for computer automation and especially in developing generic programs to study a large class of systems dynamics such as robotics, biosystems, and complex mechanisms.

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.

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