Absolute coordinate system adjustment and calibration by using standalone alignment metrology system

According to comprehensive theories of navigation, animals navigate by using two complementary strategies: (1) dead reckoning informs the subject in a continuous manner on its actual location with respect to an Earthbound or absolute coordinate system; while (2) long-term associations between particular landmarks and specific locations allow the animal to find its way within a familiar environment. If the subject structures familiar space as a system of interconnected places – the so-called ‘cognitive map’ – it may know through dead reckoning where it is located on its map and relate its route-based expectations to the actually perceived scenario of local cues.

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Study on Elastic Dynamic Model for the Clamping Mechanism of High-Speed Precision Injection Molding Machine

Shock and Vibration ◽

10.1155/2015/427934 ◽

2015 ◽

Vol 2015 ◽

pp. 1-13

Author(s):

Xue-feng Chen ◽

Jian-guo Hu ◽

Yan-sheng Xu ◽

Zhong-ming Xu ◽

Hong-bo Wang

Keyword(s):

Coordinate System ◽

Dynamic Model ◽

High Speed ◽

Equations Of Motion ◽

Elastic Vibration ◽

Lagrange Equations ◽

Beam Elements ◽

Model Matrix ◽

Absolute Coordinate System ◽

Plastic Injection

This work centered on the double-toggle clamping mechanism with diagonal-five points for the high-speed precise plastic injection machine. Based on Lagrange equations, the differential equations of motion for the beam elements are established, in a rotating coordinate system and an absolute coordinate system, respectively. 43 generalized coordinates and a model matrix for the mechanism are created and some coordinate matrices are derived. By coupling the coordinate transformation and matrix manipulation, a high nonlinear and strong time-variant elastic dynamic model is obtained. Based on the dynamic model, a Kineto-Elasto Dynamics (KED) analysis and a Kineto-Elasto Static (KES) analysis are carried out, respectively. By comparing and analyzing the simulation results of KED and KES, the regularity of elastic vibration of the clamping mechanism in high-speed clamping process has been revealed.

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A Relative Nodal Coordinate Formulation for Finite Element Nonlinear Analysis

Volume 6A: 18th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc2001/vib-21315 ◽

2001 ◽

Author(s):

J. H. Park ◽

J. H. Choi ◽

D. S. Bae

Keyword(s):

Coordinate System ◽

Large Deformations ◽

Small Deformation ◽

Open Loop ◽

Lagrangian Formulation ◽

Nodal Coordinates ◽

Updated Lagrangian Formulation ◽

Absolute Coordinate System ◽

Nodal Displacements ◽

Updated Lagrangian

Abstract Nodal coordinates are referred to a fixed configuration in the conventional equations of equilibrium. Nodal coordinates are referred to the initial configuration in the total Lagrangian formulation and to the last calculated configuration in the updated Lagrangian formulation. This research proposes to use the relative nodal coordinates in representing the position and orientation for a node. Since the nodal coordinates are measured relative to its adjacent nodal reference frame, they are still small for a structure undergoing large deformations if the element sizes are small. As a consequence, many element formulations developed under small deformation assumptions are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph form, respectively. Closed loops are opened to form a tree topology by cutting edges. Two computational sequences are defined in a graph. One is the forward path sequence that is used to recover the Cartesian nodal deformations from relative nodal displacements and traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large displacements are analyzed to demonstrate the efficiency and validity of the proposed method.

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Absolute Coordinate System

Van Nostrand's Scientific Encyclopedia ◽

10.1002/0471743984.vse0033 ◽

2005 ◽

Keyword(s):

Coordinate System ◽

Absolute Coordinate System

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Relative differential equations from water treatment Leukocytes with self-operating computer

10.21203/rs.3.rs-446592/v2 ◽

2021 ◽

Author(s):

Yuusuke Nonomura

Keyword(s):

Differential Equation ◽

Water Treatment ◽

Differential Equations ◽

Coordinate System ◽

Real Number ◽

Uncertainty Principle ◽

Arithmetic Operation ◽

Simultaneous Equations ◽

The World ◽

Absolute Coordinate System

Abstract Conventional differentiation has many problems, they are no smoothness, singularity, and non simultaneous.The origin of those problems is:1. Since the differentiation value of conventional differentiation has the infinitesimal real number (include the 10 problem of direction) direction), simultaneous equations are impossible rotation, vibration, and instability Moreover , it generates singularity.2. The problem concerning the existence of minus, There is no apple of a minus piece.A minus piece (a minus time and a minus space) does not exist in the macro world , although it is able to exist in the world of the uncertainty principle. Therefore , don't use the number of minuses absolutely . It is defined as an absolute arithmetic. Relatively the number of minuses should be used. It is defined as a relative arithmetic (operation).In this study, relative differential equation (RDE) by Zai Pair which elementized Nature World solves those problems. Concretely, RDE is able to obtain smoothness by Str Zai, obtain the solution from the singularity by Zai Pair, obtain Kyoku without the infinitesimal real number by Zai Pair and obtain independent from the conventional absolute coordinate system. Moreover, the RDE has self-operating computing, the RDE self-operating computer (SOC) is not model, and the RDE SOC is solution itself and the graph itself. In an example, inflammation itself is RDE SOC itself.

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Generalized algorithms for the identification of seismic ground excitations to building structures based on generalized Kalman filtering under unknown input

Advances in Structural Engineering ◽

10.1177/1369433220906225 ◽

2020 ◽

Vol 23 (10) ◽

pp. 2163-2173 ◽

Cited By ~ 1

Author(s):

Jinshan Huang ◽

Yongping Rao ◽

Hao Qiu ◽

Ying Lei

Keyword(s):

Kalman Filter ◽

Coordinate System ◽

External Force ◽

Kalman Filtering ◽

Structural State ◽

Seismic Excitation ◽

Unknown Input ◽

Building Structures ◽

Seismic Excitations ◽

Absolute Coordinate System

The exact information of seismic excitation and structural state is a prerequisite for structural seismic safety assessment and vibration control. When the seismic excitation to a structure is not measured, the seismic excitation can be identified as an inversed problem from measured structural responses. Although some relevant approaches have been developed, there are certain limitations or drawbacks in the existing approaches. To circumvent these problems, two generalized algorithms are proposed for the identification of seismic ground excitation to multi-story and tall buildings, respectively. When the seismic ground excitation to a structure is not measured, the data measured by a structural health monitoring system are structural absolute responses. So the structural motion equation in the absolute coordinate system is derived, in which the unknown seismic ground excitation is treated as unknown external force acting on the structure. First, the identification of unknown seismic excitations to multi-story building structures is studied. A generalized Kalman filtering under unknown input is proposed for the identification of structural state and unknown seismic excitation without the observation of structural absolute acceleration responses at the location of unknown external force. The derivation of the proposed generalized Kalman filtering under unknown input is based on the classical Kalman filter, but is more general than the existing identification approaches based on Kalman filter with unknown input in the deployments of accelerometers in the building structure. Then, it is extended to explore the identification of unknown seismic excitations to tall building structures. To avoid substructural identification from the top to bottom in a sequential manner, the motion equation in absolute coordinate system is reduced by modal expansion. Moreover, instead of the identification of unknown modal forces in previous approaches, the seismic excitation is directly identified without increasing the number of unknown forces. To demonstrate the proposed algorithms, numerical examples of identifying seismic excitations to a 6-story shear building and an 18-story tall building are investigated.

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A Programmable VLSI Filter Architecture for Application in Real-Time Vision Processing Systems

International Journal of Neural Systems ◽

10.1142/s0129065700000168 ◽

2000 ◽

Vol 10 (03) ◽

pp. 179-190

Author(s):

Teresa Serrano-Gotarredona ◽

Andreas G. Andreou ◽

Bernabé Linares-Barranco

Keyword(s):

Coordinate System ◽

Real Time ◽

Vision System ◽

Vertical Component ◽

Performance Degradation ◽

System Level ◽

Edge Extraction ◽

Event Representation ◽

System P ◽

Absolute Coordinate System

An architecture is proposed for the realization of real-time edge-extraction filtering operation in an Address-Event-Representation (AER) vision system. Furthermore, the approach is valid for any 2D filtering operation as long as the convolutional kernel F(p,q) is decomposable into an x-axis and a y-axis component, i.e. F(p,q)=H(p)V(q), for some rotated coordinate system {p,q}. If it is possible to find a coordinate system {p,q}, rotated with respect to the absolute coordinate system a certain angle, for which the above decomposition is possible, then the proposed architecture is able to perform the filtering operation for any angle we would like the kernel to be rotated. This is achieved by taking advantage of the AER and manipulating the addresses in real time. The proposed architecture, however, requires one approximation: the product operation between the horizontal component H(p) and vertical component V(q) should be able to be approximated by a signed minimum operation without significant performance degradation. It is shown that for edge-extraction applications this filter does not produce performance degradation. The proposed architecture is intended to be used in a complete vision system known as the Boundary-Contour-System and Feature-Contour-System Vision Model, proposed by Grossberg and collaborators. The present paper proposes the architecture, provides a circuit implementation using MOS transistors operated in weak inversion, and shows behavioral simulation results at the system level operation and electrical simulation and experimental results at the circuit level operation of some critical subcircuits.

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A Relative Method for Finite Element Nonlinear Structural Analysis

Materials Science Forum ◽

10.4028/www.scientific.net/msf.505-507.577 ◽

2006 ◽

Vol 505-507 ◽

pp. 577-582 ◽

Cited By ~ 1

Author(s):

Jin Hwan Choi ◽

Dae Sung Bae ◽

Hui Je Cho

Keyword(s):

Coordinate System ◽

Large Deformations ◽

Small Deformation ◽

Lagrangian Formulation ◽

Graph Representation ◽

Truss Structures ◽

Updated Lagrangian Formulation ◽

Absolute Coordinate System ◽

Nodal Displacements ◽

Updated Lagrangian

Nodal displacements are referred to the initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian formulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacements and traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One closed loop structure undergoing large deformations is analyzed to demonstrate the efficiency and validity of the proposed method.

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Relative differential equations from water treatment Leukocytes with self-operating computer

10.21203/rs.3.rs-446592/v1 ◽

2021 ◽

Author(s):

Yuusuke Nonomura

Keyword(s):

Differential Equation ◽

Water Treatment ◽

Differential Equations ◽

Coordinate System ◽

Real Number ◽

Uncertainty Principle ◽

Arithmetic Operation ◽

Simultaneous Equations ◽

The World ◽

Absolute Coordinate System

Abstract Conventional differentiation has many problems, they are no-smoothness, singularity, and non-simultaneous. The origin of those problems is:1. Since the differentiation value of conventional differentiation has the infinitesimal real number (include the problem of direction), simultaneous equations are impossible (rotation, vibration, and instability). Moreover, it generates singularity. 2. The problem concerning the existence of minus, There is no apple of a minus piece. A minus piece (a minus time and a minus space) does not exist in the macro world, although it is able to exist in the world of the uncertainty principle. Therefore, don't use the number of minuses absolutely. It is defined as an absolute arithmetic. Relatively, the number of minuses should be used. It is defined as a relative arithmetic (operation). In this study, relative differential equation (RDE) by Zai Pair which element-ized Nature World solves those problems. Concretely, RDE is able to obtain smoothness by Str Zai, obtain the solution from the singularity by Zai Pair, obtain Kyoku without the infinitesimal real number by Zai Pair and obtain independent from the conventional absolute coordinate system. Moreover, the RDE has self-operating computing, the RDE self-operating computer (SOC) is not model, and the RDE SOC is solution itself and the graph itself. In an example, inflammation itself is RDE SOC itself.

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Reference Coordinate System Requirements for Geophysics

International Astronomical Union Colloquium ◽

10.1017/s0252921100050946 ◽

1975 ◽

Vol 26 ◽

pp. 87-92

Author(s):

P. L. Bender

Keyword(s):

Coordinate System ◽

Polar Motion ◽

Main Part ◽

Measurement Techniques ◽

Reference Points ◽

Angular Motion ◽

Coordinate Systems ◽

Axis Of Rotation ◽

The Earth ◽

Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

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