A State-Time Formulation for Multibody Systems Dynamics Simulation: Part II — Parallel Implementation

2005 ◽  
Author(s):  
Mojtaba Oghbaei ◽  
Kurt S. Anderson ◽  
John A. Evans
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Dynamics Simulation ◽  
Systems Dynamics ◽  
Massively Parallel Computing ◽  
Spatial Domains ◽  
Time Formulation ◽  
Temporal And Spatial

This paper outlines the parallel implementation of a newly developed multibody system dynamics formulation. The methodology provides the means for the dynamic simulation to be parallelized temporally as well as spatially which will allow better exploitation of anticipated massively parallel computing resources. This will have three advantages: First, the system of equations may now be coarse grain parallelized to a far greater degree allowing an increased number of processors to be effectively utilized. Secondly, this will significantly reduce the fraction of serial operations and thus should increase speedup (reduced turn-around). Finally, the method allows temporal scale of each variable to be adjusted independently and as such offer considerable advantage for the efficient and accurate modeling and simulation of multiscale behaviors. These gains can be accomplished by discretizing a special form of the equations of motion in both temporal and spatial domains. Examples are provided to clarify the application of this scheme with particular attention on time domain parallelization.

Logarithmic Complexity Sensitivity Analysis of Flexible Multibody Systems

2009 ◽  
Author(s):  
Kishor D. Bhalerao ◽  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Sensitivity Analysis ◽  
Data Storage ◽  
Multibody Systems ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Divide And Conquer ◽  
Dynamics Simulation ◽  
Modal Shape ◽  
Flexible Multibody

This paper presents a recursive direct differentiation method for sensitivity analysis of flexible multibody systems. Large rotations and translations in the system are modeled as rigid body degrees of freedom while the deformation field within each body is approximated by superposition of modal shape functions. The equations of motion for the flexible members are differentiated at body level and the sensitivity information is generated via a recursive divide and conquer scheme. The number of differentiations required in this method is minimal. The method works concurrently with the forward dynamics simulation of the system and requires minimum data storage. The use of divide and conquer framework makes the method linear and logarithmic in complexity for serial and parallel implementation, respectively, and ideally suited for general topologies. The method is applied to a flexible two arm robotic manipulator to calculate sensitivity information and the results are compared with the finite difference approach.

A State-Time Formulation for Multibody Systems Dynamics Simulation: Part I — Extension to Systems With General Topology

2005 ◽  
Author(s):  
Mojtaba Oghbaei ◽  
Kurt S. Anderson
Keyword(s):  
Data Storage ◽  
Equations Of Motion ◽  
A Priori ◽  
Turnaround Time ◽  
General Topology ◽  
Dynamics Simulation ◽  
Constraint Forces ◽  
Time Dynamic ◽  
State Time ◽  
Massively Parallel Computing

This paper presents an extension of a newly developed multibody system dynamics formulation to systems with general topology. The State-Time dynamic formulation, which has been recently developed by the authors, provides the means to yield significantly reduced simulation turnaround time through its ability to better exploit massively parallel computing resources. The rules provided in this article are useful in automating the generation of system’s equations of motion and in determining the final form of the system tangent matrix arising in this formulation. A priori knowledge of this structure assists one to find a proper ordering for the rows and columns of this matrix such that the final structure is optimized from data storage and solution expense perspectives. Also, the extended formulation enables one to eliminate the constraint forces or to bring only the desirable ones into evidence and as such results in a reduced set of equations and unknowns. Examples are provided to demonstrate application of the given rules.

Dynamics Analysis of Spatial Multibody System With Spherical Joint Wear

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Gengxiang Wang ◽  
Hongzhao Liu ◽  
Peisheng Deng
Keyword(s):  
Contact Pressure ◽  
Contact Force ◽  
Contact Area ◽  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Force Model ◽  
Spherical Joint ◽  
Wear Model ◽  
Contact Force Model

The influence of the spherical joint with clearance caused by wear on the dynamics performance of spatial multibody system is predicted based on the Archard's wear model and equations of motion of multibody systems. First, the function of contact deformation and load acting on the spherical joint with clearance is derived based on the improved Winkler elastic foundation model and Hertz quadratic pressure distribution assumption. On this basis, considering the influence of clearance size and wear state on the contact stiffness between spherical joint elements, an improved contact force model is proposed by Lankarani–Nikravesh contact force model and improved stiffness coefficient that is the slope of the function of contact deformation and load. Second, due to the complexity for that wear impacts on the surface topography of contact bodies, an approximate calculation method of contact area with respect to the clearance spherical joint is provided for simplifying the computational process of contact pressure in the Archard's wear model. Subsequently, the contact pressure between contact bodies is calculated by the improved contact force model and approximate contact area (ICFM–ACA), which is verified via finite element method (FEM). Moreover, the dynamics model of spatial four bar mechanism considering spherical joint with clearance caused by wear is formulated using equations of motion of multibody systems. Finally, the wear depth of spherical joint with clearance is predicted via two different kinds of contact pressure based on the Archard's wear model (one is from the ICFM–ACA and the other is from FEM), respectively. The numerical simulation results show that the improved contact force model and proposed approximate contact area are correctness and validity for predicting wear in the spherical joint with clearance. Simultaneously, the effect of the spherical joint with clearance caused by wear on the dynamics performance of spatial four bar mechanism is analyzed.

Aspects of Symbolic Formulations in Flexible Multibody Systems

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Markus Burkhardt ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Fem Model ◽  
Local Shape ◽  
Flexible Bodies ◽  
Elastic Bodies ◽  
Flexible Multibody

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

New Approach to the Modeling of Complex Multibody Dynamical Systems

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Aaron Schutte ◽  
Firdaus Udwadia
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Multiple Time ◽  
New Approach ◽  
Constrained Mechanical Systems ◽  
Step Procedure ◽  
Highly Nonlinear ◽  
Mass Matrices ◽  
General Complex

In this paper, a general method for modeling complex multibody systems is presented. The method utilizes recent results in analytical dynamics adapted to general complex multibody systems. The term complex is employed to denote those multibody systems whose equations of motion are highly nonlinear, nonautonomous, and possibly yield motions at multiple time and distance scales. These types of problems can easily become difficult to analyze because of the complexity of the equations of motion, which may grow rapidly as the number of component bodies in the multibody system increases. The approach considered herein simplifies the effort required in modeling general multibody systems by explicitly developing closed form expressions in terms of any desirable number of generalized coordinates that may appropriately describe the configuration of the multibody system. Furthermore, the approach is simple in implementation because it poses no restrictions on the total number and nature of modeling constraints used to construct the equations of motion of the multibody system. Conceptually, the method relies on a simple three-step procedure. It utilizes the Udwadia–Phohomsiri equation, which describes the explicit equations of motion for constrained mechanical systems with singular mass matrices. The simplicity of the method and its accuracy is illustrated by modeling a multibody spacecraft system.

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.

EQUATIONS OF MOTION OF COMPLEX MULTIBODY SYSTEMS USING KINEMATICAL DIFFERENTIALS

1989 ◽  
Vol 13 (4) ◽  
pp. 113-121 ◽  
Author(s):  
M. HILLER ◽  
A. KECSKEMETHY
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Nonholonomic Systems ◽  
Automatic Generation ◽  
Minimal Order ◽  
Closed Form Solutions ◽  
Constraint Equations

In complex multibody systems the motion of the bodies may depend on only a few degrees of freedom. For these systems, the equations of motion of minimal order, although more difficult to obtain, give a very efficient formulation. The present paper describes an approach for the automatic generation of these equations, which avoids the use of LAGRANGE-multipliers. By a particular concept, designated “kinematical differentials”, the problem of determining the partial derivatives required to state the equations of motion is reduced to a simple re-evaluation of the kinematics. These cover the solution of the global position, velocity and acceleration problems, i.e. the motion of all bodies is determined for given generalized (independent) coordinates. For their formulation and solution, the multibody system is mapped to a network of nonlinear transformation elements which are connected by linear equations. Each transformation element, designated “kinematical transformer”, corresponds to an independent multibody loop. This mapping of the constraint equations makes it possible to find closed-form solutions to the kinematics for a wide variety of technical applications, and (via kinematical differentials) leads also to an efficient formulation of the dynamics. The equations are derived for holonomic, scleronomic systems, but can also be extended to general nonholonomic systems.

Linearizing the Equations of Motion for Multibody Systems Using an Orthogonal Complement Method

2005 ◽  
Vol 11 (1) ◽  
pp. 51-66 ◽  
Author(s):  
B. Minaker ◽  
P. Frise
Keyword(s):  
Stiffness Matrix ◽  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Orthogonal Complement ◽  
Computer Implementation ◽  
Constraint Forces ◽  
Coordinate Vector

The equations of motion of a multibody system are linearized and reduced to independent coordinates, using an orthogonal complement method. The orthogonal complement is used to eliminate the terms that result from a variation of the constraint forces. The resulting equations contain the derivative of the constraint Jacobian with respect to the coordinate vector in the stiffness matrix. The technique is suitable for a computer implementation. Examples are used to illustrate the process.

scholarly journals Evidence toward the potential absence of relationship between temporal and spatial heartbeats perception

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Betka Sophie ◽  
Łukowska Marta ◽  
Silva Marta ◽  
King Joshua ◽  
Garfinkel Sarah ◽  
...  
Keyword(s):  
Bayesian Statistics ◽  
State Anxiety ◽  
Discrimination Task ◽  
Spatial Perception ◽  
The Body ◽  
Temporal Perception ◽  
Heartbeat Perception ◽  
Sampling Locations ◽  
Spatial Domains ◽  
Temporal And Spatial

AbstractMany interoceptive tasks (i.e. measuring the sensitivity to bodily signals) are based upon heartbeats perception. However, the temporal perception of heartbeats—when heartbeats are felt—varies among individuals. Moreover, the spatial perception of heartbeats—where on the body heartbeats are felt—has not been characterized in relation to temporal. This study used a multi-interval heartbeat discrimination task in which participants judged the timing of their own heartbeats in relation to external tones. The perception of heartbeats in both time and spatial domains, and relationship between these domains was investigated. Heartbeat perception occurred on average ~ 250 ms after the ECG R-wave, most frequently sampled from the left part of the chest. Participants’ confidence in discriminating the timing of heartbeats from external tones was maximal at 0 ms (tone played at R-wave). Higher confidence was related to reduced dispersion of sampling locations, but Bayesian statistics indicated the absence of relationship between temporal and spatial heartbeats perception. Finally, the spatial precision of heartbeat perception was related to state-anxiety scores, yet largely independent of cardiovascular parameters. This investigation of heartbeat perception provides fresh insights concerning interoceptive signals that contribute to emotion, cognition and behaviour.

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.

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