Determination of Generalized Coordinates and Forces for Generation of the Three Dimensional Curves with Torsion by PKM (Parallel Kinematik Machines)

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.166-167.15 ◽

2010 ◽

Vol 166-167 ◽

pp. 15-26

Author(s):

N.V. Orlandea

Keyword(s):

High Precision ◽

Reference System ◽

Three Dimensional ◽

Control Parameters ◽

Kinematic Control ◽

Generalized Coordinates ◽

Definition Of

The paper describes the definition of a set of generalized coordinates and forces (kinematic control parameters) necessary to satisfy a specific job. Specifically, the generation of a three dimensional curve with torsion described by a Frenet reference system. The method employed to accomplish this task is using the Original ADAMS program alias MCADA. The analysis results indicate that the method can be successfully applied when designing motion simulators; however, there are accuracy restrictions for high precision six axis machining.

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Geodetic reference frames in the Netherlands

10.54419/vy3c94 ◽

2005 ◽

Author(s):

Arnoud de Bruijne ◽

Joop van Buren ◽

Anton Kösters ◽

Hans van der Marel

Keyword(s):

The Netherlands ◽

Reference System ◽

Large Scale ◽

Reference Frames ◽

Three Dimensional ◽

Geodetic Reference System ◽

Geoid Model ◽

Leading Role ◽

Definition Of

Unambiguous and homogeneous geodetic reference frames are essential to the proper determination of locations and heights. The reference frames used in the Netherlands are the Rijksdriehoekmeting (RD) for locations and the Normaal Amsterdamse Peil (NAP) for heights. The RD has traditionally been managed by the Kadaster; the NAP by Rijkswaterstaat. The emergence of satellite positioning has resulted in drastic changes to these geodetic reference frames. A surveyor is now offered one instrument, GPS (the Global Positioning System), capable of the simultaneous determination of locations and heights. This is possible by virtue of one three-dimensional geodetic reference system - the European Terrestrial Reference System (ETRS89) - which in the Netherlands is maintained in a collaborative arrangement between the Kadaster and Rijkswaterstaat. GPS has been advanced as a practical measurement technique by linking the definition of the RD grid to ETRS89. Nevertheless the introduction of GPS also revealed distortions in the RD grid, which are modelled in the RDNAPTRANSTM2004 transformation. Furthermore, the use of the geoid model has become essential to the use of GPS in determining the height in comparison to NAP. Subsidence that has disrupted the backbone of the NAP gave cause to the need for a large-scale adjustment of the heights of the underground benchmarks and, in so doing, of the grid. Consequently new NAP heights have been introduced at the beginning of 2005; a new definition of the RD grid that had already been introduced in 2000 was once again modified in 2004. During the past few years two NCG subcommissions have devoted a great deal of time to these modifications. This publication lays down ETRS89, the RD and the NAP, together with their mutual relationships. In addition to reviewing the history of the reference frames and the manner in which they are maintained (including, for example, the use of AGRS.NL as the basis for the Dutch geometric infrastructure), the publication also discusses the status of the frames as at 1 January 2005. This encompasses the realisation of ETRS89 via AGRS.NL, the revision and new definition of the RD grid in 2004, and the new NAP publication in 2005. The publication also describes the mutual relationships between the frames in the modernized RDNAPTRANSTM2004 transformation consisting of the new NLGEO2004 geoid model and a model for the distortions of the RD grid. In conclusion, the publication also devotes attention to the future maintenance of the ETRS89, RD and NAP. The continuity of the link between the traditional frames and the three-dimensional frames is of great importance, and ETRS89 will continue to fulfil this linking role. The GPS base network and AGRS.NL reference stations will increasingly assume the leading role in the maintenance of the RD frame. The maintenance of the NAP will continue to be necessary, although during the coming decades the the primary heights will not need revision. In so doing the high quality of the geodetic reference frames required for their use in actual practice will continue to be guaranteed.

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Selective Fiscal Measures and the Definition of the Relevant Reference Framework in the Light of Cases C‑106/09 P, Commission v Gibraltar and C‑203/16 P, Heitkamp BauHolding v Commission

Helsinki Law Review ◽

10.33344/vol13iss2pp64-75 ◽

2020 ◽

Vol 13 (2) ◽

pp. 64-75

Author(s):

Hanna-Mari Immonen

Keyword(s):

Reference System ◽

European Court Of Justice ◽

Tax System ◽

Reference Framework ◽

Court Of Justice ◽

European Court ◽

Relevant Reference ◽

Definition Of ◽

State Aids

This article examines fiscal State aids and the selectivity condition. Assessing the selectivity is relatively complex in tax matters since it involves the analysis of the general tax system in which the regime under review applies. The focus of this article is on the selectivity analysis and the analysis of the general tax system i.e. the determination of the relevant reference framework. The definition of the relevant reference framework is still open to various interpretations despite the fact that the European Court of Justice has examined selectivity issues in several cases in the 2000s. The Gibraltar judgement has materially broadened the interpretation of the selectivity condition and the application of Article 107(1) TFEU. The Heitkamp BauHolding judgment confirms the interpretation adopted in the Gibraltar judgement, but also defines the scope of Article 107(1) TFEU in more detail. Yet the offset of the selectivity assessment i.e. the determination of the relevant reference system is still receptive to various interpretations.

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A Terrestrial Reference System Consistent with WGRS

International Astronomical Union Colloquium ◽

10.1017/s025292110006379x ◽

1991 ◽

Vol 127 ◽

pp. 211-214 ◽

Cited By ~ 2

Author(s):

C. Boucher ◽

Z. Altamimi

Keyword(s):

Reference System ◽

Terrestrial Reference Frame ◽

Reference Systems ◽

International Earth Rotation Service ◽

Earth Orientation Parameters ◽

Terrestrial Reference System ◽

Definition Of ◽

Orientation Parameters ◽

Evolution With Time

AbstractThe IAU and IUGG has jointly established in 1988 an International Earth Rotation Service (IERS) which is in charge of the realization of conventional celestial and terrestrial reference systems, together with the determination of earth orientation parameters which connect them.The theoretical definition of the terrestrial reference system which is realized by IERS through a conventional terrestrial reference frame formed by SLR, LLR, VLBI and GPS stations is presented. In particular its origin, scale, orientation and evolution with time are reviewed, taking into account relativistic and deformation effects.

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Fractal Dimensionalities

Geometry & Graphics ◽

10.12737/article_5bc45918192362.77856682 ◽

2018 ◽

Vol 6 (3) ◽

pp. 33-48 ◽

Cited By ~ 4

Author(s):

Л. Жихарев ◽

L. Zhikharev

Keyword(s):

Three Dimensional ◽

Fractal Sets ◽

Three Dimensional Modeling ◽

3D Space ◽

Wolfram Mathematica ◽

Dimensional Modeling ◽

Straight Line ◽

Fractal Parameters ◽

Definition Of

One of the most important characteristics of a fractal is its dimensionality. In general, there are several options for mathematical definition of this value, but usually under the object dimensionality is understood the degree of space filling by it. It is necessary to distinguish the dimensionality of space and the dimension of multitude. Segment, square and cube are objects with dimensionality 1, 2 and 3, which can be in respective spaces: on a straight line, plane or in a 3D space. Fractals can have a fractional dimensionality. By definition, proposed by Bernois Mandelbrot, this fractional dimensionality should be less than the fractal’s topological dimension. Abram Samoilovich Bezikovich (1891–1970) was the author of first mathematical conclusions based on Felix Hausdorff (1868–1942) arguments and allowing determine the fractional dimensionality of multitudes. Bezikovich – Hausdorff dimensionality is determined through the multitude covering by unity elements. In practice, it is more convenient to use Minkowsky dimensionality for determining the fractional dimensionalities of fractals. There are also numerical methods for Minkowsky dimensionality calculation. In this study various approaches for fractional dimensionality determining are tested, dimensionalities of new fractals are defined. A broader view on the concept of dimensionality is proposed, its dependence on fractal parameters and interpretation of fractal sets’ structure are determined. An attempt for generalization of experimental dependences and determination of general regularities for fractals structure influence on their dimensionality is realized. For visualization of three-dimensional geometrical constructions, and plain evidence of empirical hypotheses were used computer models developed in the software for three-dimensional modeling (COMPASS, Inventor and SolidWorks), calculations were carried out in mathematical packages such as Wolfram Mathematica.

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Détermination du géoïde astro-gravimétrique par la méthode de collocation par moindres carrés

The Canadian Surveyor ◽

10.1139/tcs-1974-0099 ◽

1974 ◽

Vol 28 (5) ◽

pp. 559-567

Author(s):

Gérard Lachapelle

Keyword(s):

Least Squares ◽

Satellite Data ◽

Reference System ◽

Reference Ellipsoid ◽

Geodetic Reference System ◽

Least Squares Collocation ◽

Method Of Least Squares ◽

Definition Of ◽

Optimum Solution

The method of least squares collocation is briefly outlined. Its application to the determination of the astrogravimetric geoid (in fact, satellite data can be used as well) and the difficulties encountered are discussed. By the use of this method, it is possible to combine all types of geodetic data available in order to obtain an optimum solution for the geoid. It is also possible to determine consistent geodetic parameters necessary for the definition of a geodetic reference system. These parameters include the position of the existing astrogeodetic reference ellipsoid with respect to the geocenter to which the gravimetric and satellite data are referred.

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ENGIN-X: a third-generation neutron strain scanner

Journal of Applied Crystallography ◽

10.1107/s0021889806042245 ◽

2006 ◽

Vol 39 (6) ◽

pp. 812-825 ◽

Cited By ~ 230

Author(s):

J. R. Santisteban ◽

M. R. Daymond ◽

J. A. James ◽

L. Edwards

Keyword(s):

Virtual Instrument ◽

Three Dimensional ◽

Absolute Number ◽

Simple Expression ◽

Neutron Diffractometer ◽

Accurate Definition ◽

Gauge Volume ◽

Computer Representation ◽

Definition Of

ENGIN-X, a new time-of-flight (TOF) neutron diffractometer optimized to measure elastic strains at precise locations in bulky specimens recently commissioned at the ISIS Facility in the Rutherford Laboratory, UK, is described. Fast counting times, together with a flexible and accurate definition of the instrumental gauge volume are the main requirements of neutron strain scanning and have been addressed on ENGIN-X through the design of a novel TOF diffractometer with a tuneable resolution and interchangeable radial collimators. Further, the routine operation of the instrument has been optimized by creating a virtual instrument,i.e.a three-dimensional computer representation of the diffractometer and samples, which assists in the planning and execution of experiments. On comparing ENGIN-X with its predecessor ENGIN, a 25× gain in performance is found, which has allowed the determination of stresses up to 60 mm deep in steel specimens. For comparison with constant-wavelength diffractometers, special attention has been paid to the absolute number of counts recorded during the experiments. A simple expression is presented for the estimation of counting times in TOF neutron strain scanning experiments.

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The determination of nonlinear forces of the second order during the ship’s swaying and rolling, based on the three-dimensional potential theory

MORSKIE INTELLEKTUAL`NYE TEHNOLOGII ◽

10.37220/mit.2020.48.2.021 ◽

2020 ◽

Author(s):

В.Ю. Семенова ◽

Д.А. Альбаев

Keyword(s):

Potential Theory ◽

Three Dimensional ◽

Nonlinear Boundary Conditions ◽

Second Order ◽

Deep Fluid ◽

Definition Of ◽

National Practice ◽

Limited Depth ◽

Good Agreement

В статье рассматривается определение нелинейных сил, возникающих при поперечно-горизонтальной и бортовой качке судов на основании трехмерной потенциальной теории. Для их определения необходимо вычисление потенциалов второго порядка малости. Представленное решение в отечественной практике является новым. Решение задачи осуществляется на основании методов малого параметра и интегральных уравнений с учетом нелинейных граничных условий на смоченной поверхности судна и свободной поверхностью жидкости. Нелинейные горизонтальные силы и моменты, возникающие при этих двух видах качки определяются в работе с использованием различных функций Грина: для бесконечно-глубокой жидкости и жидкости ограниченной глубины, когда . Полученные результаты практически полностью согласуются между собой. Приводятся результаты расчетов горизонтальных сил и моментов для четырех разных судов. Расчеты представлены в сравнении с расчетами по двумерной теории, выполненными также для случая бесконечно глубокой жидкости и жидкости ограниченной глубины при больших значениях отношения глубины к осадке H/T. Показано хорошее согласование результатов между собой The article deals with the definition of nonlinear forces arising in the sway and roll motions of the ships on the basis of three-dimensional potential theory. To determine them, it is necessary to calculate the potentials of the second order of smallness. The presented solution in national practice is new. The solution of the problem is carried out on the basis of small parameter methods and integral equations taking into account nonlinear boundary conditions on the wetted surface of the ship and the free surface of the liquid. Nonlinear horizontal forces and moments are determined in the work using various Green functions: for an infinitely deep fluid and a fluid of limited depth when H → ∞. The results obtained are completely consistent with each other. The results of calculations of the nonlinear horizontal forces and momenta for four different ships are presented. The calculations are presented in comparison with the calculations according to the two-dimensional theory, also performed for the case of an infinitely deep liquid and liquid of limited depth for large values of the ratio of depth to sediment H / T. Good agreement between the results is shown

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Vector Products As A Tool For The Investigation Of The Isometric Transformation Of Objects

Reports on Geodesy and Geoinformatics ◽

10.2478/rgg-2015-0006 ◽

2015 ◽

Vol 98 (1) ◽

pp. 60-71

Author(s):

Ryszard Józef Grabowski

Keyword(s):

Dimensional Space ◽

Three Dimensional ◽

Necessary Condition ◽

Vector Product ◽

Isometric Transformation ◽

Check Points ◽

Normal Vectors ◽

Definition Of ◽

Three Dimensional Space

Abstract The identification of isometric displacements of studied objects with utilization of the vector product is the aim of the analysis conducted in this paper. Isometric transformations involve translation and rotation. The behaviour of distances between check points on the object in the first and second measurements is a necessary condition for the determination of such displacements. For every three check points about the measured coordinate, one can determine the vector orthogonal to the two neighbouring sides of the triangle that are treated as vectors, using the definition of the vector product in three-dimensional space. If vectors for these points in the first and second measurements are parallel to the studied object has not changed its position or experienced translation. If the termini of vectors formed from vector products treated as the vectors are orthogonal to certain axis, then the object has experienced rotation. The determination of planes symmetric to these vectors allows the axis of rotation of the object and the angle of rotation to be found. The changes of the value of the angle between the normal vectors obtained from the first and second measurements, by exclusion of the isometric transformation, are connected to the size of the changes of the coordinates of check points, that is, deformation of the object. This paper focuses mainly on the description of the procedure for determining the translation and rotation. The main attention was paid to the rotation, due to the new and unusual way in which it is determined. Mean errors of the determined parameters are often treated briefly, and this subject requires separate consideration.

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Determination of nonlinear forces of the second order arising from the interaction of waves and certain types of ship’s motions

MORSKIE INTELLEKTUAL`NYE TEHNOLOGII ◽

10.37220/mit.2021.54.4.063 ◽

2021 ◽

pp. 21-30

Author(s):

В.Ю. Семенова ◽

Д.А. Альбаев

Keyword(s):

Free Surface ◽

Three Dimensional ◽

Second Order ◽

Complete Agreement ◽

Interaction Of Waves ◽

Diffracted Waves ◽

Definition Of ◽

Limited Depth ◽

Good Agreement

В статье рассматривается определение нелинейных сил второго порядка, обусловленных взаимодействием набегающего, дифрагированного волнения и волнения, обусловленного различными видами колебаний на основании применения трехмерной потенциальной теории. Для их определения необходимо вычисление потенциалов второго порядка малости. Представленное решение в отечественной практике является новым. Решение задачи осуществляется на основании методов малого параметра и интегральных уравнений с учетом нелинейного граничного условия на свободной поверхностью жидкости. В работе расчет интегралов по свободной поверхности проводится напрямую за счет их сходимости на бесконечном удалении от судна. Нелинейные силы и моменты определяются в работе с использованием различных функций Грина: для бесконечно-глубокой жидкости и жидкости ограниченной глубины, когда . Полученные результаты практически полностью согласуются между собой. Приводятся результаты расчетов нелинейных сил и моментов для разных судов. Расчеты представлены в сравнении с расчетами по двумерной теории, выполненными также для случая бесконечно глубокой жидкости и жидкости ограниченной глубины при больших значениях отношения глубины к осадке H/T. Показано хорошее согласование результатов между собой в большинстве случаев. Показана возможность расчета нелинейных сил, возникающих при взаимодействии волнения и отдельных видов качки на произвольных курсовых углах. The article considers the definition of nonlinear second-order forces caused by the interaction of incoming, diffracted waves and waves caused by various types of motions based on the application of three-dimensional potential theory. To determine them, it is necessary to calculate the potentials of the second order of smallness. The presented solution is new in domestic practice. The problem is solved on the basis of small parameter methods and integral equations taking into account the nonlinear boundary condition on the free surface of the liquid. The paper shows the possibility of calculating the integrals over the free surface directly due to their convergence at an infinite distance from the ship. Nonlinear forces and moments are determined in the work using various Green's functions: for an infinitely deep fluid and a fluid of limited depth when H → ∞. The results obtained are in almost complete agreement with each other. The results of calculations of nonlinear forces and moments for different ships are presented. The calculations are presented in comparison with the calculations according to the two-dimensional theory, performed also for the case of an infinitely deep liquid and a liquid of limited depth at large values of ratio H / T. A good agreement of the results is shown among themselves in most cases. The possibility of calculating nonlinear forces arising from the interaction of waves and certain types of motions at arbitrary course angles is shown.

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