Analytical Dynamics of Unrooted Multibody Systems with Symmetries

1999 ◽  
Vol 121 (3) ◽  
pp. 440-447 ◽  
Author(s):  
F. M. J. Pfister ◽  
S. K. Agrawal
Keyword(s):  
Differential Equations ◽  
Multibody Systems ◽  
70Th Birthday ◽  
Equations Of Motion ◽  
Analytical Dynamics

This paper is concerned with the theory of differential equations of motion for a class of unrooted (i.e., without kinematical constraints to a Galilean frame) mechanisms called orthotropic multibody-systems and the application of this theory to the solution of three mechanisms: the Hoberman-sphere, the Wohlhart Octoid and the Fulleroid. Dedicated to O. Univ.-Prof. Dipl.-Ing. Dr. Techn. Karl Wohlhart on his 70th birthday

New Formulations on Motion Equations in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 49-54 ◽  
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Higher Order ◽  
Analytical Dynamics ◽  
Lagrange Principle ◽  
Motion Equations ◽  
Differential Motion

Using the main author's researches on the energies of acceleration and higher order equations of motion, this paper is devoted to new formulations in analytical dynamics of mechanical multibody systems (MBS). Integral parts of these systems are the mechanical robot structures, serial, parallel or mobile on which an application will be presented in order to highlight the importance of the differential motion equations in dynamics behavior. When the components of multibody mechanical systems or in its entirety presents rapid movements or is in transitory motion, are developed higher order variations in respect to time of linear and angular accelerations. According to research of the main author, they are integrated into higher order energies and these in differential equations of motion in higher order, which will lead to variations in time of generalized forces which dominate these types of mechanical systems. The establishing of these differential equations of motion, it is based on a generalization of a principle of analytical differential mechanics, known as the D`Alembert – Lagrange Principle.

On MBS Constraints and Projections

2021 ◽  
Author(s):  
Friedrich Pfeiffer
Keyword(s):  
Quadratic Form ◽  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Machine Process ◽  
Constraint Forces ◽  
Process Dynamics ◽  
Robot Tracking ◽  
Minimal Coordinates ◽  
Linear Differential

Abstract Constraints in multibody systems are usually treated by a Lagrange I - method resulting in equations of motion together with the constraint forces. Going from non-minimal coordinates to minimal ones opens the possibility to project the original equations directly to the minimal ones, thus eliminating the constraint forces. The necessary procedure is described, a general example of combined machine-process dynamics discussed and a specific example given. For a n-link robot tracking a path the equations of motion are projected onto this path resulting in quadratic form linear differential equations. They define the space of allowed motion, which is generated by a polygon-system.

Analytical Dynamics of Unrooted Multibody-Systems With Symmetries

1998 ◽  
Author(s):  
Felix M. J. Pfister ◽  
Sunil K. Agrawal
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Analytical Dynamics ◽  
Geometric Properties

Abstract The objectives of this paper are to (i) exploit the structure of Euler-Liouville equations for multibody systems and separate the external and internal aspects of motion, (ii) specialize these equations to systems with special mass and geometric properties such as holonomoids and orthotropoids, (iii) apply the results to special orthotropoids, the spheroidal linkages of Wohlhart, and write their equations of motion in a simple and elegant manner.

SYMBOLIC TREATMENT FOR THE EQUATIONS OF MOTION FOR RIGID MULTIBODY SYSTEMS

2010 ◽  
Vol 34 (1) ◽  
pp. 37-55 ◽  
Author(s):  
Bukoko C. Ikoki ◽  
Marc J. Richard ◽  
Mohamed Bouazara ◽  
Sélim Datoussaïd
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
The World ◽  
Rigid Multibody Systems ◽  
Symbolic Approach ◽  
Rigid Multibody

The library of symbolic C++ routines is broadly used throughout the world. In this article, we consider its application in the symbolic treatment of rigid multibody systems through a new software KINDA (KINematic & Dynamic Analysis). Besides the attraction which represents the symbolic approach and the effectiveness of this algorithm, the capacities of algebraical manipulations of symbolic routines are exploited to produce concise and legible differential equations of motion for reduced size mechanisms. These equations also constitute a powerful tool for the validation of symbolic generation algorithms other than by comparing results provided by numerical methods. The appeal in the software KINDA resides in the capability to generate the differential equations of motion from the choice of the multibody formalism adopted by the analyst.

An Ordinary Differential Equation Formulation for Multibody Dynamics: Nonholonomic Constraints

2016 ◽  
Vol 17 (1) ◽  
Author(s):  
Edward J. Haug
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multibody Systems ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Nonholonomic Constraints ◽  
State Variables ◽  
Well Conditioning ◽  
Fifth Order

A method is presented for formulating and numerically integrating ordinary differential equations of motion for nonholonomically constrained multibody systems. Tangent space coordinates are defined in configuration and velocity spaces as independent generalized coordinates that serve as state variables in the formulation, yielding ordinary differential equations of motion. Orthogonal-dependent coordinates and velocities are used to enforce constraints at position, velocity, and acceleration levels. Criteria that assure accuracy of constraint satisfaction and well conditioning of the reduced mass matrix in the equations of motion are used as the basis for updating local coordinates on configuration and velocity constraint manifolds, transparent to the user and at minimal computational cost. The formulation is developed for multibody systems with nonlinear holonomic constraints and nonholonomic constraints that are linear in velocity coordinates and nonlinear in configuration coordinates. A computational algorithm for implementing the approach is presented and used in the solution of three examples: one planar and two spatial. Numerical results using a fifth-order Runge–Kutta–Fehlberg explicit integrator verify that accurate results are obtained, satisfying all the three forms of kinematic constraint, to within error tolerances that are embedded in the formulation.

Canonical Impulse-Momentum Equations for Impact Analysis of Multibody Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 180-186 ◽  
Author(s):  
H. M. Lankarani ◽  
P. E. Nikravesh
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Canonical Form ◽  
Multibody Systems ◽  
Impact Analysis ◽  
Equations Of Motion ◽  
Momentum Balance ◽  
Constraint Violation ◽  
Numerical Integration Error ◽  
Intermittent Motion

For mechanical systems that undergo intermittent motion, the usual formulation of the equations of motion is not valid over the periods of discontinuity, and a procedure for balancing the momenta of these systems is often performed. A canonical form of the equations of motion is used here as the differential equations of motion. A set of momentum balance-impulse equations is derived in terms of a system total momenta by explicitly integrating the canonical equations. The method is stable when the canonical equations are numerically integrated and it is efficient when the derived momentum balance-impulse equations are solved. The method shows that the constraint violation phenomenon, which is usually caused by the numerical integration error, can be substantially reduced as compared to the numerical integration of the standard Newtonian form of equations of motion. Examples are provided to illustrate the validity of the method.

Application of the Canonical Equations of Motion in Problems of Constrained Multibody Systems With Intermittent Motion

1988 ◽  
Author(s):  
H. M. Lankarani ◽  
P. E. Nikravesh
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Momentum Balance ◽  
Constrained Multibody Systems ◽  
Intermittent Motion

Abstract For mechanical systems that undergo intermittent motion, the usual formulation of the equations of motion is not valid over the periods of the discontinuity, and a procedure for balancing the momenta of the system is often performed. A canonical form of the equations of motion is used here as the differential equations of motion. A set of momentum balance-impulse equations are derived in terms of the system total momenta by explicitly integrating the canonical equations. The method shows to be stable while numerically integrating the canonical equations, and efficient while solving the momentum balance-impulse equations. Examples are provided to illustrate the validity of the method.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

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