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Generalized Coordinates (generalized + coordinate)
Selected AbstractsBrownian Dynamics Simulations of Rotational Diffusion Using the Cartesian Components of the Rotation Vector as Generalized CoordinatesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 7-8 2008Tom Richard Evensen Abstract Here, we report on the first Brownian dynamics (BD) simulations of rotational diffusion using the Cartesian components of the rotation vector as the generalized coordinates. The model system employed in this study consists of freely rotating and non-interacting rigid particles with arbitrary surface topography. The numerical BD algorithm contains no singularities and yields numerical results that are in full agreement with known theoretical results. Because of the absence of singularities, this new algorithm is several orders of magnitude more efficient than a simple BD algorithm employing the Euler angles as the generalized coordinates. The general theory for using generalized coordinates in studies of more complex systems involving both translation, rotation, and fluid dynamic interactions is well known. Consequently, the benefits reported here can readily be extended to such systems. Important examples are segmented polymer chains, with and without holonomic constraints, and liquid crystals. [source] Kinematic modeling of mobile robots by transfer method of augmented generalized coordinatesJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2004Wheekuk Kim A kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc. [source] Analytic determination of workspace and singularities in a parallel pointing systemJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 1 2002Raffaele Di Gregorio This paper studies a parallel pointing system, named U-2PUS, used in biomechanic and aerospace applications. In the literature, U-2PUS position analysis has already been solved in closed form, whereas simple and efficient tools to address workspace determination and singularity locations are still lacking. In this paper, the analytic expression of the U-2PUS workspace is derived, and a bidimensional representation of the workspace is proposed. The U-2PUS mobility analysis is addressed, and a singularity locus analytic expression, explicitly containing the manipulator geometric parameters and the end-effector orientation parameters, is derived. Moreover, it is shown that the U-2PUS singularity locus can be represented by curves (singularity curves) on a Cartesian plane having the U-2PUS generalized coordinates on the coordinate axes. Finally, the presented singularity conditions are geometrically interpreted. © 2002 John Wiley & Sons, Inc. [source] Use of the Rotation Vector in Brownian Dynamics Simulation of Transient Electro-Optical PropertiesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 1 2009Tom Richard Evensen Abstract We have recently developed a new singularity-free algorithm for Brownian dynamics simulation of free rotational diffusion. The algorithm is rigorously derived from kinetic theory and makes use of the Cartesian components of the rotation vector as the generalized coordinates describing angular orientation. Here, we report on the application of this new algorithm in Brownian dynamics simulations of transient electro-optical properties. This work serves two main purposes. Firstly, it demonstrates the integrity of the new algorithm for BD-simulations of the most common transient electro-optic experiments. Secondly, it provides new insight into the performance of the new algorithm compared to algorithms that make use of the Euler angles. We study the transient electrically induced birefringence in dilute solutions of rigid particles with anisotropic polarization tensor in response to external electric field pulses. The use of both one single electric pulse and two electric pulses with opposite polarity are being analyzed. We document that the new singularity-free algorithm performs flawlessly. We find that, for these types of systems, the new singularity-free algorithm, in general, outperforms similar algorithms based on the Euler angles. In a wider perspective, the most important aspect of this work is that it serves as an important reference for future development of efficient BD-algorithms for studies of more complex systems. These systems include polymers consisting of rigid segments with single-segment translational,rotational coupling, segment,segment fluid-dynamic interactions and holonomic constraints. [source] Brownian Dynamics Simulations of Rotational Diffusion Using the Cartesian Components of the Rotation Vector as Generalized CoordinatesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 7-8 2008Tom Richard Evensen Abstract Here, we report on the first Brownian dynamics (BD) simulations of rotational diffusion using the Cartesian components of the rotation vector as the generalized coordinates. The model system employed in this study consists of freely rotating and non-interacting rigid particles with arbitrary surface topography. The numerical BD algorithm contains no singularities and yields numerical results that are in full agreement with known theoretical results. Because of the absence of singularities, this new algorithm is several orders of magnitude more efficient than a simple BD algorithm employing the Euler angles as the generalized coordinates. The general theory for using generalized coordinates in studies of more complex systems involving both translation, rotation, and fluid dynamic interactions is well known. Consequently, the benefits reported here can readily be extended to such systems. Important examples are segmented polymer chains, with and without holonomic constraints, and liquid crystals. [source] Free Rotational Diffusion of Rigid Particles with Arbitrary Surface Topography: A Brownian Dynamics Study Using Eulerian AnglesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 2-3 2008Tom Richard Evensen Abstract Rotational diffusion of rigid bodies is an important topic that has attracted sustained interest for many decades, but most existing studies are limited to particles with simple symmetries. Here, we present a simple Brownian dynamics algorithm that can be used to study the free rotational diffusion of rigid particles with arbitrary surface topography. The main difference between the new algorithm and previous algorithms is how the numerical values of the mobility tensor are calculated. The only parameters in the numerical algorithm that depend on particle shape are the principal values of the particle rotational mobility tensor. These three scalars contain all information about the surface topography that is relevant for the particle rotational diffusion. Because these principal values only need to be pre-calculated once, the resulting general algorithm is highly efficient. The algorithm is valid for arbitrary mass density distribution throughout the rigid body. In this paper, we use Eulerian angles as the generalized coordinates describing the particle angular orientation. [source] Singularity-Free Brownian Dynamics Analyses of Rotational Dynamics: Non-Spherical Nanoparticles in SolutionMACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2005Stine Nalum Naess Abstract Summary: From kinetic theory we have rigorously derived singularity-free Brownian dynamics analyses of nanoparticle rotational dynamics. The rigid non-spherical nanoparticles incorporate all three rotational degrees of freedom. This was achieved by using the components of Cartesian rotation vectors as the generalized coordinates describing angular orientation. The new results constitute an important advance compared to the situation when Eulerian angles specify angular orientation. Our finding eliminates one of the main longstanding obstacles to detailed studies of nanoparticle rotational dynamics in the diffusion time domain. The described formalism is applicable to a wide range of nanoparticle systems including liquid crystals, biopolymers, and colloids. [source] Numerical integration of differential-algebraic equations with mixed holonomic and control constraintsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Mahmud Quasem The present work aims at the incorporation of control (or servo) constraints into finite,dimensional mechanical systems subject to holonomic constraints. In particular, we focus on underactuated systems, defined as systems in which the number of degrees of freedom exceeds the number of inputs. The corresponding equations of motion can be written in the form of differential,algebraic equations (DAEs) with a mixed set of holonomic and control constraints. Apart from closed,loop multibody systems, the present formulation accommodates the so,called rotationless formulation of multibody dynamics. To this end, we apply a specific projection method to the DAEs in terms of redundant coordinates. A similar projection approach has been previously developed in the framework of generalized coordinates by Blajer & Ko,odziejczyk [1]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Aspects Regarding the Conception, Modeling and Implementation of an Articulated Robot in Space with Noises and VibrationsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Virgil Ispas The authors want to conceive and to model a structure of a 6R serial modular industrial robot with six freedom degrees. Some specific points are followed: the direct geometric modelling of the robot using the matrix of rotation method, the given in 3D modelling of the robot, the presentation of its components having some possible applications in the processes of production in the spaces with noises and vibrations. The direct geometrical modelling will be determinate the relative orientation matrices, which express the position of each system Ti, (i=1-6), according to the system Ti,1, also expressing the vectors of relative position of origin Oi of the systems Ti. They will be expressed the orientation of each system Ti in account to the fixed system To attached to the robot base, the set of independent parameters of orientation then are obtained the final equation of the column vector of the generalized coordinates, which express the position and the orientation of the clamping device. The paper presents the two possible applications of the studied robot implementation in a flexible manufacturing cel for the manipulation operations of parts. The robot will be used on the other side for the execution of weld in a points applied to the car carcases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Energy consistent time integration of planar multibody systemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Stefan Uhlar The planar motion of rigid bodies and multibody systems can be easily described by coordinates belonging to a linear vector space. This is due to the fact that in the planar case finite rotations commute. Accordingly, using this type of generalized coordinates can be considered as canonical description of planar multibody systems. However, the extension to the three-dimensional case is not straightforward. In contrast to that, employing the elements of the direction cosine matrix as redundant coordinates makes possible a straightforward treatment of both planar and three-dimensional multibody systems. This alternative approach leads in general to differential-algebraic equations (DAEs) governing the dynamics of rigid body systems. The main purpose of the present paper is to present a comparison of the two alternative descriptions. In both cases energy-consistent time integration schemes are applied. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||