General Formulation of an Efficient Recursive Algorithm Based on Canonical Momenta for Forward Dynamics of Closed-Loop Multibody Systems

2005 ◽  
Author(s):  
Joris Naudet ◽  
Dirk Lefeber
Keyword(s):  
Multibody Systems ◽  
Closed Loop ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Open Loop ◽  
Forward Dynamics ◽  
Virtual Power ◽  
Generalized Coordinates ◽  
First Order

In previous work, a method for establishing the equations of motion of open-loop multibody mechanisms was introduced. The proposed forward dynamics formulation resulted in a Hamiltonian set of 2n first order ODE’s in the generalized coordinates q and the canonical momenta p. These Hamiltonian equations were derived from a recursive Newton-Euler formulation. It was shown how an O(n) formulation could be obtained in the case of a serial structure with general joints. The amount of required arithmetical operations was considerably less than comparable acceleration based formulations. In this paper, a further step is taken: the method is extended to constrained multibody systems. Using the principle of virtual power, it is possible to obtain a recursive Hamiltonian formulation for closed-loop mechanisms as well, enabling the combination of the low amount of arithmetical operations and a better evolution of the constraints violation errors, when compared with acceleration based methods.

scholarly journals Special Coordinates Associated With Recursive Forward Dynamics Algorithm for Open Loop Rigid Multibody Systems

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
Ashitava Ghosal
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Special Property ◽  
Open Loop ◽  
Forward Dynamics ◽  
Rigid Multibody Systems ◽  
Two Stages ◽  
Rigid Multibody ◽  
General Tree

The recursive forward dynamics algorithm (RFDA) for a tree structured rigid multibody system has two stages. In the first stage, while going down the tree, certain equations are associated with each node. These equations are decoupled from the equations related to the node’s descendants. We refer them as the equations of RFDA of the node and the current paper derives them in a new way. In the new derivation, associated with each node, we recursively obtain the coordinates, which describe the system consisting of the node and all its descendants. The special property of these coordinates is that a portion of the equations of motion with respect to these coordinates is actually the equations of RFDA associated with the node. We first show the derivation for a two noded system and then extend to a general tree structure. Two examples are used to illustrate the derivation. While the derivation conclusively shows that equations of RFDA are part of equations of motion, it most importantly gives the associated coordinates and the left out portion of the equations of motion. These are significant insights into the RFDA.

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Dynamics Modeling of Elastic Multibody Systems Using Kane’s Method As Applied to a Flexible Robot

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Component Mode Synthesis ◽  
Flexible Robot ◽  
Dynamics Modeling ◽  
Generalized Coordinates ◽  
Kane’S Method ◽  
Kane's Method ◽  
Elastic Multibody Systems ◽  
Elastic Form

Abstract Generalization of Kane’s equations of motion for elastic multibody systems is considered. Initially, finite element techniques are used to generate the elastic form of generalized coordinates. Then, the number of elastic coordinates are reduced by the component mode synthesis. Finally, Kane’s method is applied to obtain the equations of motion of such systems. Using this method, dynamic model of an elastic robot with one degree of freedom is presented.

Recursive Method for the Dynamic Analysis of Open-Loop Flexible Multibody Systems

2003 ◽  
Author(s):  
Yunn-Lin Hwang
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Open Loop ◽  
Flexible Multibody Systems ◽  
Recursive Method ◽  
Flexible Bodies ◽  
System Equations ◽  
Generalized Newton ◽  
Time Invariant

The main objective of this paper is to develop a recursive method for the dynamic analysis of open-loop flexible multibody systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve for the equations of motion for open-loop systems consisting of interconnected rigid and flexible bodies is presented in this investigation. This method applies recursive method with the generalized Newton-Euler method for flexible bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the vector or digital computer systems. The algorithms presented in this investigation are illustrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The basic recursive formulations developed in this paper are demonstrated by two numerical examples.

Plans and The Structure of Target Acquisition Behavior

1981 ◽  
Vol 25 (1) ◽  
pp. 571-575
Author(s):  
R. A. Miller ◽  
R. J. Jagacinski ◽  
R. B. Nalavade ◽  
W. W. Johnson
Keyword(s):  
Closed Loop ◽  
Position Control ◽  
Open Loop ◽  
General Strategy ◽  
Velocity Control ◽  
Additional Time ◽  
First Order ◽  
Oscilloscope Screen ◽  
Activity Sequence ◽  
Event Based

Subjects manipulated a position control stick with one hand and a velocity control stick with the other hand in order to capture a moving target displayed on an oscilloscope screen. The two control sticks were additively coupled. In order to understand the coordination of the two control sticks, event-based first-order markov “activity sequence generators” were constructed for individual subjects. These discrete probabilistic structures are closely related to each subject's overall plan or general strategy for the capture task. Striking individual differences and strategic errors in performance were revealed. When combined with additional time-conditioned (open-loop) and error-conditioned (closed-loop) details, the activity sequence generators provide a basis for a hierarchic description of this perceptual-motor skill.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Efficient Parallel Computer Simulation of the Motion Behaviors of Closed-Loop Multibody Systems

2007 ◽  
Author(s):  
Shanzhong Duan ◽  
Andrew Ries
Keyword(s):  
Parallel Computing ◽  
Multibody Systems ◽  
Closed Loop ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Parallel Computer ◽  
Constraint Forces ◽  
Computing Systems ◽  
Closed Loops

This paper presents an efficient parallelizable algorithm for the computer-aided simulation and numerical analysis of motion behaviors of multibody systems with closed-loops. The method is based on cutting certain user-defined system interbody joints so that a system of independent multibody subchains is formed. These subchains interact with one another through associated unknown constraint forces fc at the cut joints. The increased parallelism is obtainable through cutting joints and the explicit determination of associated constraint forces combined with a sequential O(n) method. Consequently, the sequential O(n) procedure is carried out within each subchain to form and solve the equations of motion while parallel strategies are performed between the subchains to form and solve constraint equations concurrently. For multibody systems with closed-loops, joint separations play both a role of creation of parallelism for computing load distribution and a role of opening a closed-loop for use of the O(n) algorithm. Joint separation strategies provide the flexibility for use of the algorithm so that it can easily accommodate the available number of processors while maintaining high efficiency. The algorithm gives the best performance for the application scenarios for n>>1 and n>>m, where n and m are number of degree of freedom and number of constraints of a multibody system with closed-loops respectively. The algorithm can be applied to both distributed-memory parallel computing systems and shared-memory parallel computing systems.

scholarly journals Control-Oriented High-Frequency Turbomachinery Modeling: Single-Stage Compression System 1D Model

1993 ◽  
Author(s):  
O. O. Badmus ◽  
S. Chowdhury ◽  
K. M. Eveker ◽  
C. N. Nett
Keyword(s):  
Experimental Data ◽  
High Frequency ◽  
Closed Loop ◽  
Open Loop ◽  
Rotating Stall ◽  
Single Stage ◽  
Model Parameters ◽  
Compression System ◽  
First Order ◽  
Direct Model

In this paper, a 1D unsteady compressible viscous flow model of a generic compression system previously developed by the authors is applied to a multi-stage axial compressor experimental rig configured for single–stage operation. The required model parameters and maps are identified from experimental data. The resulting model is an explicit system of 9 first order ODE’s. The model inputs are compressor speed, nozzle area, compressor discharge bleed area, plenum bleed area, inlet total pressure and entropy, and nozzle and bleed exit static pressures. The model and experimental data are compared with respect to both open–loop uncontrolled and closed–loop controlled behaviors. These comparisons focus on i) forced transients and ii) global nonlinear dynamics and bifurcations. In all cases the comparison between the model and experimental data is excellent. Of particular interest is the ability of the model, which does not include any hysteretic maps, to predict experimentally observed hysteresis with respect to the onset and cessation of surge. This predictive capability of the model manifests itself as the coexistence of a stable equilibrium (rotating stall) and a stable periodic solution (surge) in the model at a single fixed set of system input values. Also of interest is the fact that the controllers used for closed–loop comparisons were designed directly from the model with no a posteriori tuning of controller parameters. Thus, the excellent closed–loop comparisons between the model and experimental data provide strong evidence in support of the validity of the model for use in direct model based controller design. The excellent agreement between the model and experimental data summarized above is attributed in large part to the use of effective lengths within the model, as functions of axial Mach number and nondimensional compressor rotational speed, as prescribed by the modeling technique. The use of these effective lengths proved to be far superior to the use of physical lengths. The use of these effective lengths also provided substantial improvement over the use of physical lengths coupled with fixed first order empirical lags, as proposed by other authors for the modeling of observed compressor dynamic lag. The overall success of this model is believed to represent a positive first step toward a complete experimental validation of the approach to control–oriented high–frequency turbomachinery modeling being developed by the authors.

A Novel Approach for Decoupling of Dynamical Equations of Flexible Manipulators

1999 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Flexible Manipulators ◽  
Dynamical Equations ◽  
First Order ◽  
Novel Approach ◽  
Elastic Multibody Systems ◽  
Two Degree Of Freedom ◽  
Generalized Coordinate

Abstract Recent advances in the study of dynamics of elastic multibody systems, specially the flexible manipulators, indicate the need and importance of decoupling the equations of motion. In this paper, an improved method for deriving elastic generalized coordinates is presented. In this regard, the Kane’s equations of motion for elastic multibody systems are considered. These equations are in the generalized form and may be applied to any desired holonomic system. Flexibility in choosing generalized speeds in terms of generalized coordinate derivatives in Kane’s method is used. It is shown that proper choice of a congruency transformation between generalized coordinate derivatives and generalized speeds leads to a series of first order decoupled equations of motion for holonomic elastic multibody systems. Furthermore, numerical implementation of the decoupling technique using congruency transformation is discussed and presented via simulation of a two degree of freedom flexible manipulator.

Sign in / Sign up

Export Citation Format

Share Document