Using linear graph theory and the principle of orthogonality to model multibody, multi-domain systems

Schmitke, Chad; McPhee, John

doi:10.1016/j.aei.2007.08.002

Cited by 20 publications

(21 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The symbolic formulation is based on Rayleigh beam theory and was implemented via the principle of orthogonality by Schmitke and McPhee [5]. The formulation was previously applied to model golf shaft deformation by Sandhu et al [6], who compared simulation results of the flexible beam model to motion capture data.…”

Section: Flexible Club and Swing Simulationmentioning

confidence: 99%

The Golf Shaft’s Influence on Clubhead-Ball Impact Dynamics

McNally

McPhee

Henrikson

2018

The 12th Conference of the International Sports Engineering Association

Self Cite

View full text Add to dashboard Cite

Abstract:A long-held assumption in golf research is that the driver-ball impact is accurately modelled as a collision between two free bodies, i.e., the clubhead is not attached to the shaft. The purpose of this work was to examine the validity of this assumption using multibody simulation and motion capture technology. Ten elite golfers were recruited to participate in a motion capture experiment to validate a Rayleigh beam model of a flexible club. Using the six degree-of-freedom motion of the grip as an input to the model, the simulated shaft deflections showed good agreement with the experiment. An impact model based on volumetric contact was integrated with the flexible club model and was used to compare the launch conditions of free-body and full-club impacts. Analysis of the launch conditions revealed that the shaft creates a stiffening effect that resists clubhead rotation during contact, corresponding to an increase in ball speed and suppression of the gear-effect relative to free-body impacts. The results demonstrate that shaft dynamics cannot be treated as negligible when evaluating driver impact mechanics.

show abstract

Section: Flexible Club and Swing Simulationmentioning

confidence: 99%

The Golf Shaft’s Influence on Clubhead-Ball Impact Dynamics

McNally

McPhee

Henrikson

2018

The 12th Conference of the International Sports Engineering Association

Self Cite

View full text Add to dashboard Cite

show abstract

“…Using (28) it is easy to form symbolically the coefficient matrix M, element by element, from partial derivatives of the velocity vectors. Nonlinearities have been preserved throughout the formulation as each element may contain branch coordinates and quantities which vary with time.…”

Section: Virtual Work Terminal Equationsmentioning

confidence: 99%

“…To be precise, each circuit equation alludes to a closed vector polygon respecting the geometric fit or compatibility law of rigid body dynamics. From graph theory, it can be shown that these kinematic constraint equations can be obtained from the cutset equations and are usually written in the following form: [5,28] (not well known in dynamics):…”

Section: Advances In Mechanical Engineeringmentioning

confidence: 99%

Graph-Theoretic Approach for the Dynamic Simulation of Flexible Multibody Systems

Richard

Bouazara

2012

Advances in Mechanical Engineering

View full text Add to dashboard Cite

This paper provides a general description of a variational graph-theoretic formulation for simulation of flexible multibody systems (FMSs) which includes a brief review of linear graph principles required to formulate this algorithm. The system is represented by a linear graph, in which nodes represent reference frames on flexible bodies, and edges represent components that connect these frames. The method is based on a simplistic topological approach which casts the dynamic equations of motion into a symmetrical format. To generate the equations of motion with elastic deformations, the flexible bodies are discretized using two types of finite elements. The first is a 2 node 3D beam element based on Mindlin kinematics with quadratic rotation. This element is used to discretize unidirectional bodies such as links of flexible systems. The second consists of a triangular thin shell element based on the discrete Kirchhoff criterion and can be used to discretize bidirectional bodies such as high-speed lightweight manipulators, large high precision deployable space structures, and micro/nano-electromechanical systems (MEMSs). Two flexible systems are analyzed to illustrate the performance of this new variational graph-theoretic formulation and its ability to generate directly a set of motion equations for FMS without additional user input.

show abstract

“…In order to put this method to the proof, without performing an experiment, an effective modeling method that described the dynamic behaviors needs to be studied. In view of the effect of the coupling magnetic field between the stator and the rotor of a generator on a detecting coil, a thermodynamics modeling method was proposed for analyzing the complex topology of turbo-generator systems [13], [14]. The thermodynamics model is represented in terms of a network of primitive elements which are associated with some elementary phenomena and are interconnected through edges representing the flow of energy.…”

Section: Introductionmentioning

confidence: 99%

Application of HHT for Online Detection of Inter-Area Short Circuits of Rotor Windings of Turbo-Generators Based on the Thermodynamics Modeling Method

Wang¹,

Wáng²,

Xü³

et al. 2011

Journal of Power Electronics

View full text Add to dashboard Cite

This paper focuses on monitoring and predicting the short circuit faults of the rotor windings of large turbo-generator systems. For the purpose of increasing efficiency and decreasing maintenance cost, a method that combines the HHT (Hilbert Huang Transform) with a wavelet has been studied. This method is based on analyzing a classical Albright detecting coil. Due to the Empirical Mode Decomposition (EMD) and the Intrinsic Mode Functions (IMF) of the HHT the exact location of a short circuit of rotor windings may be given. However, a part of the useful information is eliminated by the unreasonable decomposing scale of the wavelet. Based on the thermodynamics modeling method, this study was illustrated with a 50MW turbo-generator system that is installed in Northern China. The analysis results, which have very good agreement with those of a previous study, show that the method of combining the HHT with a wavelet is an effective way to analyze and predict the short circuit faults of the rotor windings of large generators, such as supercritical turbo-generator systems and wind turbo-generator systems. This work can offer a useful reference for analyzing smart grids by improving the power quality of a distribution network that is supplied by a turbo-generator system.

show abstract

Using linear graph theory and the principle of orthogonality to model multibody, multi-domain systems

Cited by 20 publications

References 19 publications

The Golf Shaft’s Influence on Clubhead-Ball Impact Dynamics

The Golf Shaft’s Influence on Clubhead-Ball Impact Dynamics

Graph-Theoretic Approach for the Dynamic Simulation of Flexible Multibody Systems

Application of HHT for Online Detection of Inter-Area Short Circuits of Rotor Windings of Turbo-Generators Based on the Thermodynamics Modeling Method

Contact Info

Product

Resources

About