A Generalized Recursive Formulation for Constrained Mechanical System Dynamics∗

Bae, Dong‐Sik; Han, Jae-Il; Yoo, Hongki

doi:10.1080/08905459908915700

Cited by 47 publications

(37 citation statements)

References 3 publications

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“…This trend can be observed in early works in this field, e.g., [14][15][16]. In 1999, Featherstone [17] developed truly optimal-time, logarithmic order divide-and-conquer algorithm (DCA) for the dynamics of tree-like topologies as well as closed-loop multibody systems.…”

Section: Introductionmentioning

confidence: 90%

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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Section: Introductionmentioning

confidence: 90%

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

2016

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“…In many systems driven by electrostatic forces, the dynamic responses are mainly determined by their mechanical parts, which usually have highly nonlinear characteristics. Since efficient solving techniques have been implemented in the dynamic simulation package for highly nonlinear mechanical systems with many rigid and flexible bodies, the electrostatic forces are accounted for in a multibody dynamic simulation package so that nonlinear effects due to finite strains or large displacements are included from the start [12,13].…”

Section: Overviewmentioning

confidence: 99%

A multibody-based dynamic simulation method for electrostatic actuators

et al. 2007

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A numerical simulation method is developed to analyze the dynamic responses of electrostatic actuators, which are electromechanically-coupled systems. The developed method can be used to determine the dynamic responses of cantilever-type switches, which are an example of typical MEMS (Micro-Electro-Mechanical System) devices driven by an electrostatic force. We propose the approach that adopts a point charge to deal with electric field effects between electrodes. This approach may be considered as a lumped parameter model for the electrostatic interactions. An advantage of this model may be the easy incorporation of the electrostatic effects between electrodes into a multibody dynamics analysis algorithm. The resulting equations contain the variables for position, velocity, and electric charge to describe the motion of the masses and the charges on the electrodes in a system. By solving these equations simultaneously, the dynamic response of an electrostatically-driven system can be correctly simulated. In order to realize this approach, we implement the procedures into RecurDyn, the multibody dynamics software developed by the authors. The developed numerical simulation tool was evaluated by applying it to cantilever-type electrostatic switches in many different driving conditions. The results suggest that the developed tool may be useful for predicting behaviors of electrostatic actuators in testing as well as in design.

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“…On the other hand, recursive generalized coordinate formulation can dramatically reduce the number of constraint equations and variables, but the form of the equations varies with the topological structure of assembly systems. In both cases, to compute the Jacobian coefficients of constraint equations, a variationalvector calculus approach is widely adopted in literature, which is originally presented for deriving the equations of motions in dynamics [12][13][14][15][16]. The approach introduces a concept called virtual rotation, with which, it is convenient to derive the Jacobian coefficients of primitive constraints with respect to the state variables.…”

Section: Introductionmentioning

confidence: 99%

Calculating Jacobian coefficients of primitive constraints with respect to Euler parameters

Liu

Huang

Yong

2012

Int J Adv Manuf Technol

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It is a fundamental problem to calculate Jacobian coefficients of constraint equations in assembly constraint solving because most approaches to solving an assembly constraint system will finally resort to a numerical iterative method that requires the first-order derivatives of the constraint equations. The most-used method of deriving the Jacobian coefficients is to use virtual rotation which is originally presented to derive the equations of motion of constrained mechanical systems. However, when Euler parameters are adopted as the state variables to represent the transformation matrix, using the virtual rotation will yield erroneous formulae of Jacobian coefficients. The reason is that Euler parameters are incompatible with virtual rotation. In this paper, correct formulae of Jacobian coefficients of geometric constraints with respect to Euler parameters are presented in both Cartesian coordinates and relative generalized coordinates. Experimental results show that our proposed formulae make Newton-Raphson iterative method converge faster and more stable.

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A Generalized Recursive Formulation for Constrained Mechanical System Dynamics∗

Cited by 47 publications

References 3 publications

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

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

A multibody-based dynamic simulation method for electrostatic actuators

Calculating Jacobian coefficients of primitive constraints with respect to Euler parameters

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