Relevant bibliographies by topics / Closed-form dynamic model

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Closed-form dynamic model'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 February 2022

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Journal articles on the topic "Closed-form dynamic model"

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Bascetta, Luca, Gianni Ferretti, and Bruno Scaglioni. "Closed form Newton–Euler dynamic model of flexible manipulators." Robotica 35, no. 5 (November 17, 2015): 1006–30. http://dx.doi.org/10.1017/s0263574715000934.

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SUMMARYIn this paper, a closed-form dynamic model of flexible manipulators is developed, based on the Newton–Euler formulation of motion equations of flexible links and on the adoption of the spatial vector notation. The proposed model accounts for two main innovations with respect to the state of the art: it is obtained in closed form with respect to the joints and modal coordinates (including the quadratic velocity terms) and motion equations of the whole manipulator can be computed for any arbitrary shape of the links and any possible link cardinality starting from the output of several commercial (finite element analysis) FEA codes. The Newton–Euler formulation of motion equations in terms of the joint and elastic variables greatly improves the simulation performances and makes the model suitable for real-time control and active vibration damping. The model has been compared with literature benchmarks obtained by the classical multibody approach and further validated by comparison with experiments collected on an experimental manipulator.
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De Luca, A., and B. Siciliano. "Closed-form dynamic model of planar multilink lightweight robots." IEEE Transactions on Systems, Man, and Cybernetics 21, no. 4 (1991): 826–39. http://dx.doi.org/10.1109/21.108300.

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Hafner, Christian M., and Oliver Linton. "AN ALMOST CLOSED FORM ESTIMATOR FOR THE EGARCH MODEL." Econometric Theory 33, no. 4 (August 22, 2016): 1013–38. http://dx.doi.org/10.1017/s0266466616000256.

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The exponential GARCH (EGARCH) model introduced by Nelson (1991) is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference are usually done via maximum likelihood. Although some progress has been made recently, a complete distribution theory of MLE for EGARCH models is still missing. Furthermore, the estimation procedure itself may be highly sensitive to starting values, the choice of numerical optimization algorithm, etc. We present an alternative estimator that is available in a simple closed form and which could be used, for example, as starting values for MLE. The estimator of the dynamic parameter is independent of the innovation distribution. For the other parameters we assume that the innovation distribution belongs to the class of Generalized Error Distributions (GED), profiling out its parameter in the estimation procedure. We discuss the properties of the proposed estimator and illustrate its performance in a simulation study and an empirical example.
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Huang, Qilin, Yong Wang, Zhipu Huo, and Yudong Xie. "Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/149046.

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A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM). Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.
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Kachani, S., Y. Oumanar, and N. Raissi. "A closed-form solution for a dynamic pricing model with reference price effect." Applied Mathematical Sciences 8 (2014): 1693–701. http://dx.doi.org/10.12988/ams.2014.4119.

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Chen, I.-Ming, and Guilin Yang. "Automatic Model Generation for Modular Reconfigurable Robot Dynamics." Journal of Dynamic Systems, Measurement, and Control 120, no. 3 (September 1, 1998): 346–52. http://dx.doi.org/10.1115/1.2805408.

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In control and simulation of a modular robot system, which consists of standardized and interconnected joint and link units, manual derivation of its dynamic model needs tremendous effort because these models change all the time as the robot geometry is altered after module reconfiguration. This paper presents a method to automate the generation of the closed-form equation of motion of a modular robot with arbitrary degrees-of-freedom and geometry. The robot geometry we consider here is branching type without loops. A graph technique, termed kinematic graphs and realized through assembly incidence matrices (AIM) is introduced to represent the module assembly sequence and robot geometry. The formulation of the dynamic model is started with recursive Newton-Euler algorithm. The generalized velocity, acceleration, and forces are expressed in terms of linear operations on se(3), the Lie algebra of the Euclidean group SE(3). Based on the equivalence relationship between the recursive formulation and the closed-form Lagrangian formulation, the accessibility matrix of the kinematic graph of the robot is used to assist the construction of the closed-form equation of motion of a modular robot. This automatic model generation technique can be applied to the control of rapidly reconfigurable robotic workcells and other automation equipment built around modular components that require accurate dynamic models.
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Cheng, S. P., and N. C. Perkins. "Closed-Form Vibration Analysis of Sagged Cable/Mass Suspensions." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 923–28. http://dx.doi.org/10.1115/1.2894062.

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A theoretical model is presented which describes the three-dimensional nonlinear motion of a sagged cable that supports an array of discrete masses. An asymptotic form of this general model is derived for the linear response of a cable/mass suspension having small equilibrium curvature and horizontal supports. While the asymptotic model remains rich enough to capture dominant sagged cable effects, it is simple enough to permit closed-form analysis. A free vibration analysis is pursued that leads to closed-form solutions for problems which, heretofore, were analyzed using purely numerical methods. Among the advantages of the present method is its ability to pro vide results for: (1) complex mass arrays, (2) high-order modes, and (3) dynamic cable tension. Examples highlight the key role played by mass array symmetry and lead to new conclusions regarding free vibration.
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Hadian, Hamoon, Yasser Amooshahi, and Abbas Fattah. "Kinematics and Dynamics Modeling of a New 4-DOF Cable-Driven Parallel Manipulator." International Journal of Intelligent Mechatronics and Robotics 1, no. 4 (October 2011): 44–60. http://dx.doi.org/10.4018/ijimr.2011100103.

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This paper addresses the kinematics and dynamics modeling of a 4-DOF cable-driven parallel manipulator with new architecture and a typical Computed Torque Method (CTM) controller is developed for dynamic model in SimMechanics. The novelty of kinematic architecture and the closed loop formulation is presented. The workspace model of mechanism’s dynamic is obtained in an efficient and compact form by means of natural orthogonal complement (NOC) method which leads to the elimination of the nonworking kinematic-constraint wrenches and also to the derivation of the minimum number of equations. To verify the dynamic model and analyze the dynamical properties of novel 4-DOF cable-driven parallel manipulator, a typical CTM control scheme in joint-space is designed for dynamic model in SimMechanics.
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Siu, D. P., and G. S. Ladde. "A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution." Journal of Probability and Statistics 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/720614.

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In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the systems are obtained. Furthermore, the major part of the work is devoted to finding closed-form probability density functions of the solution processes of linear homogeneous and Ornstein-Uhlenbeck type systems with jumps.
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Akhmedov, Odiljon S., Abdulla A. Azamov, and Gafurjan I. Ibragimov. "FOUR–DIMENSIONAL BRUSSELATOR MODEL WITH PERIODICAL SOLUTION." Ural Mathematical Journal 6, no. 1 (July 29, 2020): 3. http://dx.doi.org/10.15826/umj.2020.1.001.

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In the paper, a four-dimensional model of cyclic reactions of the type Prigogine's Brusselator is considered. It is shown that the corresponding dynamical system does not have a closed trajectory in the positive orthant that will make it inadequate with the main property of chemical reactions of Brusselator type. Therefore, a new modified Brusselator model is proposed in the form of a four-dimensional dynamic system. Also, the existence of a closed trajectory is proved by the DN-tracking method for a certain value of the parameter which expresses the rate of addition one of the reagents to the reaction from an external source.
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Dissertations / Theses on the topic "Closed-form dynamic model"

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Boyle, Cameron. "A Closed-Form Dynamic Model of the Compliant Constant-Force Mechanism Using the Pseudo-Rigid-Body Model." BYU ScholarsArchive, 2003. https://scholarsarchive.byu.edu/etd/53.

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A mathematical dynamic model is derived for the compliant constant-force mechanism, based on the pseudo-rigid-body model simplification of the device. The compliant constant-force mechanism is a slider mechanism incorporating large-deflection beams, which outputs near-constant-force across the range of its designed deflection. The equation of motion is successfully validated with empirical data from five separate mechanisms, comprising two configurations of compliant constant-force mechanism. The dynamic model is cast in generalized form to represent all possible configurations of compliant constant-force mechanism. Deriving the dynamic equation from the pseudo-rigid-body model is useful because every configuration is represented by the same model, so a separate treatment is not required for each configuration. An unexpected dynamic trait of the constant-force mechanism is discovered: there exists a range of frequencies for which the output force of the mechanism accords nearer to constant-force than does the output force at static levels.
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Books on the topic "Closed-form dynamic model"

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Eigenvalues of inhomogeneous structures: Unusual closed-form solutions. Boca Raton, Fla: CRC Press, 2005.

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Elishakoff, Isaac. Eigenvalues of Inhomogeneous Structures: Unusual Closed-Form Solutions. CRC, 2004.

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Book chapters on the topic "Closed-form dynamic model"

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Vukobratović, Miomir, and Nenad Kirćanski. "Computer-Aided Method for Closed-Form Dynamic Robot Model Construction." In Real-Time Dynamics of Manipulation Robots, 53–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82198-1_3.

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Takewaki, Izuru, and Kotaro Kojima. "Closed-form dynamic collapse criterion for a bilinear hysteretic SDOF model under near-fault ground motions." In An Impulse and Earthquake Energy Balance Approach in Nonlinear Structural Dynamics, 189–217. First edition. | Boca Raton, FL : CRC Press, 2021.: CRC Press, 2021. http://dx.doi.org/10.1201/9781003134435-9.

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Takewaki, Izuru, and Kotaro Kojima. "Closed-form overturning limit of a rigid block as a SDOF model under near-fault ground motions." In An Impulse and Earthquake Energy Balance Approach in Nonlinear Structural Dynamics, 219–35. First edition. | Boca Raton, FL : CRC Press, 2021.: CRC Press, 2021. http://dx.doi.org/10.1201/9781003134435-10.

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Braak, Daniel. "What Kind of Insight Provide Analytical Solutions of Quantum Models?" In International Symposium on Mathematics, Quantum Theory, and Cryptography, 5–6. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_2.

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Abstract There are several concepts of what constitutes the analytical solution of a quantum model, as opposed to the mere “numerically exact” one. This applies even if one considers only the determination of the discrete spectrum of the corresponding Hamiltonian, setting aside such important questions as the asymptotic dynamics for long times. In the simplest case, the spectrum can be given in closed form, the eigenvalues $$E_{j}, j=0,\ldots ,N\le \infty $$ read $$E_{j} =f(j,\{p_{k}\})$$, where f is a known function of the label $$j\in \mathbb {N}_{0}$$ and the $$\{p_k\}$$ are a set of numbers parameterizing the Hamilton operator. This kind of solution exists only in cases where the classical limit of the model is Liouville-integrable. Some quantum-mechanical many-body systems allow the determination of the spectrum in terms of auxiliary parameters $$[\{k_j\},\{n_l\}]$$ as $$E(\{n_l\}) = f(\{k_{j}(\{n_{l}\})\})$$ where the $$\{k_{j}(\{n_{l}\})\}$$ satisfy a coupled set of transcendental equations, following from a certain ansatz for the eigenfunctions. These systems (integrable in the sense of Yang-Baxter (Eckle 2019)) may have a Hilbert space dimension growing exponentially with the system size L, i.e., $$N\sim e^{L}$$. The simple enumeration of the energies with the label j is replaced by the multi-index $$\{n_{l}\}$$. Although no priori knowledge about the spectrum is available, its statistical properties can be computed exactly (Berry and Tabor 1977). Other integrable and also non-integrable models exist where N depends polynomially on L and the energies $$E_j$$ are the zeroes of an analytically computable transcendental function, the so-called G-function $$G(E,\{p_k\})$$ (Braak 2013a, 2016), which is proportional to the spectral determinant. Although no closed formula for $$E_j$$ as function of the index j exists, detailed qualitative insight into the distribution of the eigenvalues can be obtained (Braak 2013b). Possible applications of these concepts to information compression and cryptography are outlined.
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Anand, Adarsh, Shakshi Singhal, and Ompal Singh. "Revisiting Dynamic Potential Adopter Diffusion Models under the Influence of Irregular Fluctuations in Adoption Rate." In Handbook of Research on Promoting Business Process Improvement Through Inventory Control Techniques, 499–519. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-3232-3.ch026.

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A pragmatic innovation diffusion model is proposed in the present chapter that interpolates stochasticity in the logistic formulation of the widely-acknowledged Bass model with dynamic market size. These irregular changes are caused due to uncertainty attached to the socioeconomic and political environment in which an innovation is positioned that affects the action of potential adopters leading to their non-uniform behavior. The aim of the current study is to find the analytical solution for the two dynamic market expansion structures, namely, linear and exponential under the influence of irregular fluctuations whose closed-form solutions were not possible in the existing literature. In addition to the changeable market size, the proposed innovation diffusion also incorporates the concept of repeat purchase. The anticipated stochastic differential equation based new product diffusion model is then expounded methodically using the Itô process and Itô's integral equation. Further, the model has been used to study the growth pattern of different consumer durable products.
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Donmez, Cem Cagri. "An Econophysics Approach to Introduction Uncertainty in Dynamics of Complex Market Structural Models." In Advances in Finance, Accounting, and Economics, 1–22. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-3767-0.ch001.

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Econophysicists have begun to make progress in answering significant questions. In particular, these collaborations have the potential to change the paradigm for understanding fluctuations. New theoretical approaches to predict complex markets may be proposed, by the captivating formulation of the stock market concerning statistical correlation to be given, where some simple (non-differential, non-fractal) expressions are also suggested as general stock price formulae in a closed form that can generate a variety of possible price movements in time. A given attribute of mechanics may be submitted as a likely option to cover the price movements regarding traditional concepts where utilising stock mechanics to grow the portfolios in real markets may be realised. The ideas prove useful in risk evaluation, extreme value statistics, critical limit theorems for sums of independent variables with power law distribution, random walks, fractals, and multfractal formalisms, etc.
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Homsy, George E., and Norman H. Margolus. "Simulating Digital Logic with the Reversible Aggregation Model of Crystal Growth." In New Constructions in Cellular Automata. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195137170.003.0012.

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We are concerned with understanding the implicit computation occurring in a physical model of crystal growth, the Reversible Aggregation (RA) model. The RA model is a lattice gas model of reversible cluster growth in a closed two-dimensional system, which captures basic properties of physics such as determinism, locality, energy conservation, and exact microscopic reversibility. There are three species of particles in the RA model: gas, heat, and crystal. A diffusing gas particle may aggregate when contacting the boundary of a crystal cluster. Latent heat is released during each aggregation event and is explicitly modeled by introducing a heat particle into a diffusing heat bath. Conversely a cluster member at the boundary of the crystal may absorb a heat particle and evaporate, becoming a diffusing gas particle. Allowing ourselves complete control over all the initial conditions of the model, we show that the RA model can simulate any logic circuit, and, hence, perform any computation. The mobile gas and heat particles are used as logic signals. The paths these particles take are the wires. Sequences of conditional crystallization events form the basis of the logic gates. We show how to embed a universal single use gate into the dynamics of the model, then show how to construct a reusable universal gate, showing the system is capable of space-efficient computation. We show how to build arbitrary logic circuits by interconnecting gates. This requires steering and routing the signals, delaying them, and letting them cross. Finally, we briefly discuss the relationship of computation in the RA model to computation in real physical systems. We examine the computational capabilities of a physical model of crystal growth, the Reversible Aggregation (RA) model [3], which captures basic properties of physics such as determinism, locality, energy conservation, and exact microscopic reversibility. The RA model is a lattice gas model of reversible cluster growth in a closed two-dimensional system. It was introduced as a microscopically reversible physical model for studying the thermodynamics of crystal growth and pattern formation. By microscopically reversible we mean that from any state in the system we can recover the previous state exactly.
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Conference papers on the topic "Closed-form dynamic model"

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Izadbakhsh, Alireza. "Closed-form dynamic model of PUMA 560 robot arm." In 2009 4th International Conference on Autonomous Robots and Agents. IEEE, 2009. http://dx.doi.org/10.1109/icara.2000.4803940.

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Maxwell, Jesse. "Thermal and Fluid Dynamic Model for Capillary-Driven Heat Pipe With Closed-Form Solution." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69441.

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A model is derived for the steady state performance of capillary-driven heat pipes on the basis treating fluid flow through miniature- and micro-channels and applied as bulk properties to a large aspect ratio quasi-one-dimensional two-phase system. Surface tension provides the driving force based on an equivalent bulk capillary radius while laminar flow through micro-channels and the vapor core are treated. Heat conduction is accounted for radially while isothermal advection is treated along the axis. A closed-form solution is derived for a steady state heat pipe with a constant heat flux boundary condition on the evaporator as well as a constant heat flux or a convective boundary condition along the condenser. Two solution methods are proposed, and the result is compared to empirical data for a copper-water heat pipe. The components of the closed-form solution are discussed as contributors to driving or frictional forces, and the existence of an optimal pore radius is demonstrated.
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Marins, Joao L., Taua M. Cabreira, Kristofer S. Kappel, and Paulo Roberto Ferreira. "A Closed-Form Energy Model for Multi-rotors Based on the Dynamic of the Movement." In 2018 VIII Brazilian Symposium on Computing Systems Engineering (SBESC). IEEE, 2018. http://dx.doi.org/10.1109/sbesc.2018.00047.

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Li, Mengtang, Ryan Foss, Kim A. Stelson, James D. Van de Ven, and Eric J. Barth. "A Design Optimization Model for an Alternating Flow (AF) Hydraulic Pump Based on First Principles." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5171.

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Although current state of the art hydraulic variable displacement pumps are highly efficiently at high displacement, they have poor efficiency at low displacement. Besides, different operating speed and load pressure conditions also strongly affect their performance. This paper proposed a novel alternating flow (AF) hydraulic variable displacement pump to 1) eliminate throttling loss by acting as a high-bandwidth pump for displacement control, 2) achieve high efficiency across a wide range of operating conditions and displacements, and 3) allow multiple units to be easily common-shaft mounted for a compact multi-actuator displacement control system from a single prime-mover. This paper presents a simple closed form model for the AF hydraulic pump and shows the model validation with a first generation prototype. The simple closed form model captures input motor energy, output fluid energy and associated energy losses. With the closed form model validated, it can then be used to drive optimal design for future generation prototypes using a dimensionless group method.
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Bastani, Yaser, and Marcio de Queiroz. "An Alternative Hydrodynamic Force Model for Finite Bearings." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2504.

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A method for determining a closed-form expression for the hydrodynamic forces in finite plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely-long (IL) or infinitely-short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. The models are shown to outperform the standard limiting approximations in the steady-state analysis of the bearing system under static loading.
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Nataraj, C., and Ramesh Thimmaraya. "Tracking Control of Unmanned Surface Vehicles With Abkowitz Steering Model." In ASME 2010 Dynamic Systems and Control Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/dscc2010-4293.

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This paper is concerned with the tracking control of unmanned surface vehicles. Steering dynamics is modeled using nonlinear equations with three degrees of freedom following Abkowitz. Tracking control of this nonlinear system leads to the need to derive a control algorithm for linear error equations which have time-varying coefficients. Next, a control algorithm has been derived for this set of linear time-varying equations. Lyapunov transformations have been applied to transform the error equation into a canonical form. A desired closed-loop PD-spectrum and the desired right PD-modal matrix have been chosen and the resulting Sylvester equation has been solved to obtain a matrix of time-varying controller gains. This leads to the closed loop equations for controlling the ship steering of an unmanned ship. The controller algorithm is applied to the motion control of ships with parametric values from published reports. Several tracking trajectories have been generated with and without obstacles, and time-varying control has been investigated and presented. The control algorithm is shown to be quite effective for tracking of unmanned surface vehicles. Stability conditions are derived to ensure convergence. Present work in experimental verification is outlined.
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Zhang, Xianmin, Wenfeng Hou, and Yisheng Guan. "Closed-Form Equations of Mass Matrix of the Single-Axis Right Circular Flexure Hinge." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86509.

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This paper presents a closed-form expression of the mass matrix of the right circular hinges which are widely used in compliant mechanism systems. The flexure hinge is treated as a two nodes element, in which there are three degrees of freedom at each node. The cosine functions with high-order terms are introduced, and the closed-form expression for each element of the mass matrix of the single-axis right circular flexure hinge is obtained. Based on the closed-form expression, the dynamic equations of motion of a piezodriven 3-DOF compliant precision micro-positioning stage are developed. The lower order modal frequencies are experimentally identified and the dynamic analysis model is proved to be feasible. Dynamic and static output comparisons show that the dynamic analysis is highly necessary for a precision micro-positioning stage. The closed-form expression of the mass matrix of the right circular hinge made it more convenient for dynamic analysis of the compliant mechanisms by using finite element approach.
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Shang, Yuchen, Nikolaos I. Xiros, James H. VanZwieten, and Cornel Sultan. "A Data Model for Turbulence Analysis Downstream of an Ocean Current Turbine Rotor for Hydrokinetic Power Generation." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5371.

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Neural networks are derived to be used as closed-form representations of mean hydrokinetic turbine performance variables. These representations can be used to obtain estimates of turbine performance when the ambient turbulence characteristics, namely in-flow velocity and turbulence intensity, are given. The neural networks were developed using a detailed hydrodynamic code, which simulates performance of a rigidly mounted hydrokinetic turbine where only rotor rotation is allowed (1-DOF). By varying the in-flow velocity (U) of the water current between 0.4m/s and 2.6m/s with a step of 0.2m/s, as well as Turbulence Intensity (TI) between 5% and 20% with a step of 2.5%, a set of variables including the output shaft power, shaft torque, force on a single blade and drag force were obtained for each case. The obtained data sets were used to train appropriately sized, feed-forward (i.e. without recirculation) neural networks. Four neural networks obtained, one for each output variable of the hydrodynamic code. Each neural net constitutes a closed-form, explicit mathematical relationship (equation) generating estimates for the corresponding dependent variable it has been trained to approximate, when presented with specific values for the independent (input) variables current velocity, U, and turbulence intensity, TI. Four output (dependent) variables of interest of the hydrodynamic code are considered: shaft power, shaft torque, force on a single blade and drag. The dependent variables are actually time-averaged steady-state values derived from each hydrodynamic code run. The results of the neural networks are validated using the background theory, as well as the data generated by the hydrodynamic code. Error of less than 1% has been achieved between the neural net output and the hydrodynamics code data values suggesting that the neural networks and the equations are usable in place of the hydrodynamic code for estimating time-averaged loadings and power production.
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Canfield, Stephen L., R. Randall Soper, and Charles F. Reinholtz. "Dynamic Force Analysis of the Carpal Wrist." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-3970.

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Abstract The Carpal Wrist is a novel, parallel-architecture device that exhibits many features desirable in a robotic wrist. Previous static analysis has verified the large, singularity-free workspace and the excellent force-bearing ability of the Carpal Wrist. Here, the parallel structure is shown to be particularly advantageous when considered dynamically due to its lightweight structure and multiple load bearing members. The dynamic equations of motion are derived in closed form by direct application of Lagrange’s equations to the kinematic model. The model assumes a relatively massive tool and includes all gravitational, inertial, and gyroscopic effects. The equations of motion provide closed-form evaluation of the actuation moments based on general tool trajectories.
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Yoo, Jin-Hyeong, and Norman M. Wereley. "Quasi-Steady Axisymmetric Bingham-Plastic Model of Magnetorheological Flow Damper Behavior." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82592.

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A typical magnetorheological (MR) flow mode damper consists of a piston attached to a shaft that travels in a tightly fitting hydraulic cylinder. The piston motion makes fluid flow through an annular valve in the MR damper. An electro-magnet applies magnetic field to the MR fluid as it flows through the MR valve, and changes its yield stress. An MR fluid, modeled as a Bingham-plastic material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Although the analysis of such an annular MR valve is well understood, a closed form solution for the damping capacity of a damper using such an MR valve has proven to be elusive. Closed form solutions for the velocity and shear stress profile across the annular gap are well known. However, the location of the plug must be computed numerically. As a result, closed form solutions for the dynamic range (ratio of field on to field off damper force) cannot be derived. Instead of this conventional theoretic procedure, an approximated closed form solution for a dampers dynamic range, damping capacity and other key performance metrics is derived. And the approximated solution is used to validate a rectangular duct simplified analysis of MR valves for small gap condition. These approximated equations are derived, and the approximation error is also provided.
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