Multibody graph transformations and analysis

Jain, Abhinandan

doi:10.1007/s11071-011-0188-y

Cited by 13 publications

(4 citation statements)

References 23 publications

(21 reference statements)

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“…Vector-network models have been introduced in 2D MBS [13,14] and, together with the linear graph theory, efficiently applied to extend the dynamic analysis to a 3D single body [15], and more complex particle systems [16][17][18] as well as 3D MBS formed by rigid bodies in one closed-loop [19][20][21] or multiple closure-loops [22][23][24][25], modeled with relative and absolute coordinates [26], also in MBS including flexible bodies [27,28] and in control [29] or optimization problems [30]. Vector-network models represent multibody systems by means of a detailed graph exploited by linear graph theory to generate the equations of motion of multibody systems.…”

Section: Global and Topological Approachesmentioning

confidence: 99%

Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Saura

Segado

Dopico

2019

Mechanism and Machine Theory

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Section: Global and Topological Approachesmentioning

confidence: 99%

Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Saura

Segado

Dopico

2019

Mechanism and Machine Theory

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“…In order to be able to solve the equation of motion, the kinematic relations from (20), the constraint equations from (21), and the system dynamic equation (29) are rearranged in matrix form as follows:…”

Section: Dynamic Equations Of Motionmentioning

confidence: 99%

“…where T a ℓℓ is the topological assembly matrix and it could be easily constructed using the connectivity graph and the parent child list, the superscript ℓ refers to local matrices, the superscript a refers to the system assembly matrix, and Haℓ is the influence coefficient matrices grouped by joint block [6, 21]. Similarly, the acceleration could be calculated as follows:…”

Section: Kinematic and Dynamic Equations Of Motionmentioning

confidence: 99%

Chain Drive Simulation Using Spatial Multibody Dynamics

Omar

2014

Advances in Mechanical Engineering

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This paper presents an efficient approach for modeling chain derives using multibody dynamics formulation based on the spatial algebra. The recursive nonlinear dynamic equations of motion are formulated using spatial Cartesian coordinates and joint variables to form an augmented set of differential-algebraic equations. The spatial algebra is used to express the kinematic and dynamic equations leading to consistent and compact set of equations. The connectivity graph is used to derive the system connectivity matrix based on the system topological relations. The connectivity matrix is used to eliminate the Cartesian quantities and to project the forces and inertia into the joint subspace. This approach will result in a minimum set of equation and can avoid iteratively solving the system of differential and algebraic equations to satisfy the constraint equations. In order to accurately capture the full dynamics of the chain links, each link in the chain is modeled as rigid body with full 6 degrees of freedom. To avoid singularities in closed loop configurations, the chain drive is considered a kinematically decoupled subsystem and the interaction between the links and other system components is modeled using force elements. The out-of-plane misalignment between the sprockets can be easily modeled using a compliant force element to model the joints between each two adjacent links. The nonlinear three dimensional contact forces between the chain links and the sprockets are modeled using elastic spring-damper element and accounts for the sliding friction. The proposed approach can be used to model complex drive chain, bicycle chain as well as conveyance systems. Results show that realistic behavior of the chain as well as out-of-plane vibration can be easily captured using the presented approach. The proposed approach for chain drive subsystem could be easily appended to any other multibody simulation system.

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“…This low cost algorithm has been adopted by other groups to implement torsional MD capability . The GNEIMO method also includes extensions to the SOA dynamics theory and algorithms based on graph theory ideas that generalize the mass matrix factorization results for the low‐cost recursive solution of the ICMD equations of motion GNEIMO uses a new equipartition principle that generalizes the classical equipartition principle to ICMD models.…”

Section: Introductionmentioning

confidence: 99%

GneimoSim: A modular internal coordinates molecular dynamics simulation package

et al. 2014

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The Generalized Newton Euler Inverse Mass Operator (GNEIMO) method is an advanced method for internal coordinates molecular dynamics (ICMD). GNEIMO includes several theoretical and algorithmic advancements that address longstanding challenges with ICMD simulations. In this paper we describe the GneimoSim ICMD software package that implements the GNEIMO method. We believe that GneimoSim is the first software package to include advanced features such as the equipartition principle derived for internal coordinates, and a method for including the Fixman potential to eliminate systematic statistical biases introduced by the use of hard constraints. Moreover, by design, GneimoSim is extensible and can be easily interfaced with third party force field packages for ICMD simulations. Currently, GneimoSim includes interfaces to LAMMPS, OpenMM, Rosetta force field calculation packages. The availability of a comprehensive Python interface to the underlying C++ classes and their methods provides a powerful and versatile mechanism for users to develop simulation scripts to configure the simulation and control the simulation flow. GneimoSim has been used extensively for studying the dynamics of protein structures, refinement of protein homology models, and for simulating large scale protein conformational changes with enhanced sampling methods. GneimoSim is not limited to proteins and can also be used for the simulation of polymeric materials.

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Multibody graph transformations and analysis

Cited by 13 publications

References 23 publications

Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Chain Drive Simulation Using Spatial Multibody Dynamics

GneimoSim: A modular internal coordinates molecular dynamics simulation package

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