A Recursive Formulation for Constrained Mechanical System Dynamics: Part I. Open Loop Systems

Bae, Dong‐Sik; Haug, Edward J.

doi:10.1080/08905458708905124

Cited by 252 publications

(102 citation statements)

References 13 publications

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“…It is worth mentioning that, in the specialized literature, this possibility has not been considered as far as we are aware; with some works commenting that solving this kind of linear problems (or related ones) is costly (but not giving further details) [19][20][21], and some other works explicitly stating that such a computation must take O(N 3 c ) [22] or O(N 2 c ) [23,24] operations. Also, in the field of robot kinematics, many O(N c ) algorithms have been devised to deal with different aspects of constrained physical systems (robots in this case) [25][26][27], but none of them tackles the calculation of the Lagrange multipliers themselves.…”

Section: Introductionmentioning

confidence: 99%

Exact and efficient calculation of lagrange multipliers in biological polymers with constrained bond lengths and bond angles: Proteins and nucleic acids as example cases

2011

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In order to accelerate molecular dynamics simulations, it is very common to impose holonomic constraints on their hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thus allowing, in principle, to reach longer total simulation times. The imposition of such constraints results in an aditional set of N c equations (the equations of constraint) and unknowns (their associated Lagrange multipliers), that must be solved in one way or another at each time step of the dynamics. In this work it is shown that, due to the essentially linear structure of typical biological polymers, such as nucleic acids or proteins, the algebraic equations that need to be solved involve a matrix which is banded if the constraints are indexed in a clever way. This allows to obtain the Lagrange multipliers through a non-iterative procedure, which can be considered exact up to machine precision, and which takes O(N c ) operations, instead of the usual O(N 3 c ) for generic molecular systems. We develop the formalism, and describe the appropriate indexing for a number of model molecules and also for alkanes, proteins and DNA. Finally, we provide a numerical example of * Email: garcia.risueno@gmail.com the technique in a series of polyalanine peptides of different lengths using the AMBER molecular dynamics package.

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Section: Introductionmentioning

confidence: 99%

Exact and efficient calculation of lagrange multipliers in biological polymers with constrained bond lengths and bond angles: Proteins and nucleic acids as example cases

2011

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“…It is easier to specify initial conditions for position of a system. The initial conditions for momenta p n can be calculated using (6). In order to do that, one has to assume that at the initial time-step all constraint force impulses are known to be zero (σ m = 0), and no momentum is absorbed at constrained directions (see [30] for a more detailed discussion).…”

Section: Hamilton's Canonical Equationsmentioning

confidence: 99%

“…Due to the advances in the robotics field, there has been a growing attention to the development of efficient, low order algorithms for the simulation of open-loop and closed-loop kinematic chain system dynamics [5][6][7]. It is especially worth noticing the analogies between the optimal filtering theory and robot dynamics [8] that gave foundations for various mass matrix factorizations of a manipulator.…”

Section: Introductionmentioning

confidence: 99%

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

2016

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This paper presents a novel recursive divide-and-conquer formulation for the simulation of complex constrained multibody system dynamics based on Hamilton's canonical equations (HDCA). The systems under consideration are subjected to holonomic, independent constraints and may include serial chains, tree chains, or closed-loop topologies. Although Hamilton's canonical equations exhibit many advantageous features compared to their acceleration based counterparts, it appears that there is a lack of dedicated parallel algorithms for multi-rigid-body system dynamics based on the Hamiltonian formulation. The developed HDCA formulation leads to a two-stage procedure. In the first phase, the approach utilizes the divide and conquer scheme, i.e., a hierarchic assembly-disassembly process to traverse the multibody system topology in a binary tree manner. The purpose of this step is to evaluate the joint velocities and constraint force impulses. The process exhibits linear O(n) (n -number of bodies) and logarithmic O(log 2 n) numerical cost, in serial and parallel implementations, respectively. The time derivatives of the total momenta are directly evaluated in the second parallelizable step of the algorithm. Sample closed-loop test cases indicate very small constraint violation errors at the position and velocity level as well as marginal energy drift without any additional form of constraint stabilization techniques involved in the solution process. The results are comparatively set against more standard acceleration based Featherstone's DCA approach to indicate the performance of the HDCA algorithm.

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“…In the article [8], a dynamic analysis method of one-DOF PUSR spatial linkage mechanism (where P means a one-DOF prismatic joint and U-a two-DOF universal joint, in fact being a composition of two rotational joints R), presented in the work [9], has been analyzed. The authors based here on the assumptions included in the works [10][11][12]. Both characterized mechanisms, in fact being a family of the spatial linkage mechanisms, contain neither redundant DOF nor passive constraints.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Selected Spatial One-DOF Linkage Mechanism with Friction in Joints

Harlecki¹,

Urbaś²

2016

JCSE

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Abstract:The dynamic analysis of a one-DOF RSRRR spatial linkage mechanism, including four rotational joints R and one spherical joint S, is presented in the paper. It is assumed that friction occurs in the rotational joints, whereas a spherical joint can be treated as an ideal one. The mechanism in the form of a closed-loop kinematic chain was divided by cut joint technique into two open-loop kinematic chains in place of the spherical joint. Joint coordinates and homogeneous transformation matrices were used to describe the geometry of the system. Equations of the chains" motion were derived using formalism of Lagrange equations. Cut joint constraints and reaction forces, acting in the cutting place-i.e. in the spherical joint, have been introduced to complete the equations of motion. As a consequence, a set of differential-algebraic equations has been obtained. In order to solve these equations, a procedure based on differentiation twice of the formulated constraint equations with respect to time has been applied. In order to determine values of friction torques in the rotational joints in each integrating step of the equations of motion, joint forces and torques were calculated using the recursive Newton-Euler algorithm taken from robotics. For the requirements of the method, a model of a rotational joint has been developed. Some examples of results of the numerical calculations made have been presented in the conclusions of the paper.

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A Recursive Formulation for Constrained Mechanical System Dynamics: Part I. Open Loop Systems

Cited by 252 publications

References 13 publications

Exact and efficient calculation of lagrange multipliers in biological polymers with constrained bond lengths and bond angles: Proteins and nucleic acids as example cases

Exact and efficient calculation of lagrange multipliers in biological polymers with constrained bond lengths and bond angles: Proteins and nucleic acids as example cases

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

Dynamic Analysis of a Selected Spatial One-DOF Linkage Mechanism with Friction in Joints

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