scholarly journals MULTIBODY SYSTEMS AND SIMULATION IN MATLAB

2018 ◽  
pp. 84-94
Author(s):  
Darina Hroncová
Keyword(s):  
Kinematic Analysis ◽  
Graphical Representation ◽  
Industrial Robot ◽  
Mathematical Representation ◽  
Teaching Methodology ◽  
Transformation Matrices ◽  
The Matrix ◽  
Virtual Prototypes ◽  
Internal Properties ◽  
Kinematic Properties

Urgency of the research. Computer modeling changes the teaching methodology, the way of thinking and the possibilities of applications. It helps to move from external to internal properties and from individual to related properties. The development of the product is accelerated by experimenting with a computer model. Target setting. Kinematic analysis in Matlab and MSC Adams View. The aim is to investigate the rotation of individual members of the robotic system and to determine the spatial movement of the end effector. Actual scientific researches and issues analysis. MSC Adams represents dynamic simulators of virtual prototypes of mechanical systems. Virtual prototypes allow to model, analyze and optimize the future products and to examine their properties before building a real prototype. This approach is suitable for developing miniature mechatronic elements as well as complex systems. Uninvestigated parts of general matters defining. Virtual prototypes represent a suitable resource for testing of control and regulation procedures. The research objective. Compilation of a virtual prototype of a mechanical system that has all the decisive features and is computationally stable. The statement of basic materials. Virtual model is a mathematical representation of real-world structures, simulating all its physical properties virtually. Conclusions. The aim was to determine the kinematic properties and also to evaluate the influence of the parameters of the mechanism which influence these kinematic properties. The matrix method was used. The process of the solution consisted of determining the transformation matrices of the coordinate systems, the kinematic analysis of the industrial robot and the graphical representation of the effector handling space.

Kinematic Transformation Matrices for 3D Surface Contact Joints

1992 ◽  
Author(s):  
L. J. Gutkowski ◽  
Gary L. Kinzel
Keyword(s):  
Kinematic Analysis ◽  
Three Dimensional ◽  
Analysis Procedure ◽  
Transformation Matrices ◽  
3D Surface ◽  
Surface Contact ◽  
The Matrix ◽  
Kinematic Transformation

Abstract A generalized procedure is presented for the development of a pair matrix that describes kinematic joints formed by contact between three-dimensional surfaces. The pair matrix is useful in the matrix-based kinematic analysis procedure put forth by Sheth and Uicker (1971) previously. Any two surfaces may make up the joint as long as the surfaces can be described parametrically, and contact takes place at one point. The corresponding pair matrix is a function of five pair variables.

Kinematic Transformation Matrices for 3D Surface Contact Joints

1995 ◽  
Vol 117 (2A) ◽  
pp. 278-285 ◽  
Author(s):  
L. J. Gutkowski ◽  
G. L. Kinzel
Keyword(s):  
Kinematic Analysis ◽  
Three Dimensional ◽  
Analysis Procedure ◽  
Transformation Matrices ◽  
3D Surface ◽  
Surface Contact ◽  
The Matrix ◽  
Kinematic Transformation

A generalized procedure is presented for the development of a pair matrix that describes kinematic joints formed by contact between three-dimensional surfaces. The pair matrix is useful in the matrix-based kinematic analysis procedure put forth by Sheth and Uicker (1971) previously. Any two surfaces may make up the joint as long as the surfaces can be described parametrically, and contact takes place at one point. The corresponding pair matrix is a function of five pair variables.

A UNIFIED FORMALISM OF THERMAL QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (14) ◽  
pp. 2363-2409 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Polarization ◽  
Time Dependent ◽  
Quantum Field ◽  
Bogoliubov Transformation ◽  
Transformation Matrices ◽  
Thermo Field Dynamics ◽  
The Matrix ◽  
Recent Developments

We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.

scholarly journals THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES

2019 ◽  
pp. 71-78
Author(s):  
Elena Zaitseva ◽  
Peter Sedlacek ◽  
Andrej Forgac
Keyword(s):  
Structure Function ◽  
System Reliability ◽  
Boolean Logic ◽  
Mathematical Representation ◽  
Complex Concept ◽  
System Components ◽  
The Matrix ◽  
Importance Analysis ◽  
The Impact ◽  
Fixed System

System reliability/availability is a complex concept that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures in reliability analysis. Some of the most used indices are important measures. These measures allow us to evaluate the influence of fixed system components or set of components to the system reliability/availability. Importance measures are used today to allow for various aspects of the impact of system elements on its failure or operability. Analysis of element importance is used in the system design, diagnosis, and optimization. In this paper new algorithms for the calculation, some of the important measures are developed based on the matrix procedures. This paper's goal is the development of a new algorithm to calculate importance measures of the system based on the matrix procedures that can be transformed in the parallel procedures/algorithms. These algorithms are developed based on the application of Logical Differential Calculus of Boolean logic for the important analysis of the system. The application of parallel algorithms in importance analysis allows the evaluation of the system of large dimensions. Importance specific of the proposed matrix procedures for calculation of importance measures is the application of structure-function for the mathematical representation of the investigated system. This function defined the correlation of the system components states and system reliability/ availability. The structure-function, in this case, is defined as a truth vector to be used in the matrix transformation. The truth vector of a Boolean function is a column of the truth table of function if the values of the variables are lexicographically ordered. Therefore, the structure-function of any system can be represented by the truth vector of 2n elements un-ambiguously.

scholarly journals IMAGES CONVERTER OF GEOLOGIC- LITHOLOGICAL PROFILES

2021 ◽  
Vol 445 (1) ◽  
pp. 121-126
Author(s):  
D. B. Nurseitov ◽  
N. A. Toiganbayeva ◽  
M. O. Kenzhebayeva
Keyword(s):  
Image Segmentation ◽  
Distribution Density ◽  
Graphical Representation ◽  
Oil Field ◽  
Object Oriented Programming ◽  
Two Dimensional ◽  
Dimensional Array ◽  
Digital Format ◽  
The Matrix ◽  
Oriented Programming Language

The article is devoted to the program "Converter", which allows you to translate the geologic-lithological profile of a mineral field into a digital format in the form of a two-dimensional array. The object-oriented programming language Python was used to write the program. The NumPy, OpenCV, and MatPlotlib libraries are actively used. The implementation of this program is based on image segmentation and finding the prevailing colors in the OpenCV library. Image segmentation is a preliminary step in image processing. The obtained values allow you to find out the density distribution in the area under consideration. The program "Converter" has a good graphical representation of the results obtained using the MatPlotlib library. The program writes the final converted result as a two-dimensional array to a text file along the desired path. Thus, the matrix is easy to read for further use in conjunction with other programs. The purpose of this work was to create a program that converts the geologic-lithological profile of the field into a digital format in the form of a two-dimensional array, for further use of this matrix as the distribution density of the oil field. The "Converter" program converts any geologic-lithological profile into a two-dimensional array in a matter of minutes.

Strain History and Polar Decomposition

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Polar Decomposition ◽  
Transformation Matrix ◽  
Strain History ◽  
Transformation Matrices ◽  
Before And After ◽  
The Matrix ◽  
Principal Stretches ◽  
Principal Directions ◽  
The Right ◽  
Asymmetric Transformation

The effect of two consecutive strains (only two states enter into the calculation of a strain, the states before and after, independently of the actual strain path) can be calculated by premultiplying the transformation matrix of the first strain (its stretch tensor) with that of the second. Unless the two strains are coaxial (their principal directions coincide), however, the resulting cumulative transformation matrix represents not only a strain but also a rigid-body rotation; in that case the matrix is asymmetric. The method of polar decomposition allows one to interpret the combined transformation as if it had come about either by a strain followed by a rotation (right polar decomposition) or by a rotation followed by a strain (left polar decomposition). Let 𝔸 and 𝔹 be two stretch tensors, or transformation matrices, representing each a strain without rotation; and let the strain 𝔹 follow the strain 𝔸. Then the combined transformation matrix 𝔽 is: . . . 𝔹𝔸 = 𝔽 = ℝ𝕌= 𝕍ℝ, (8.1) . . . where 𝔽 results from premultiplication of the earlier stretch 𝔸 with the later 𝔹, where ℝ𝕌 is the “right” and 𝕍ℝ the “left” decomposition of 𝔽, where 𝕌 and 𝕍 are two distinct stretch tensors, and where ℝ is the transformation matrix for a rotation (elements of rotation matrices are indicated by the symbol aij elsewhere in this book). 𝔽 is asymmetric and ℝ differs from the identity matrix (δij) except when 𝔸 and 𝔹 are coaxial. 𝕌 and 𝕍 have the same principal stretches and differ by orientation only. In Problems 120 to 122, false approaches in the search for an appropriate decomposition of an asymmetric transformation were recognized by yielding impossible values for a rotation. Application of eq. (8.1) makes such a trial-and-error approach unnecessary.

Kinematic Analysis and Digital Mock-up Based Hybrid Verification about the Industrial Robot with Symmetric Dual Planar Four-Bar Mechanism

2012 ◽  
Vol 251 ◽  
pp. 191-195
Author(s):  
Xiao Xi Chen ◽  
Ping He ◽  
Liu Han
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Industrial Robot ◽  
Forward Kinematics ◽  
Kinematic Modeling ◽  
Inverse Kinematics Problem

In this paper, the context of relative kinematic modeling, and the analysis of symmetric dual four-bar mechanism industrial robot are introduced. For such mechanism, its designation of the representative algorithm, and its simplification, simulation, verification and alternately analysis in Forward Kinematics Problems (FKP) and Inverse Kinematics Problem (IKP) were studied. Via such method, it’s possible to efficiently analyze and solve the both of FKP and IKP of symmetric dual planar four-bar mechanism. Thus this method can be applied for the design, simulation and verification for the robot with similar structure.

Kinematic Analysis of Robotic Bevel-Gear Trains

1984 ◽  
Vol 106 (3) ◽  
pp. 371-375 ◽  
Author(s):  
F. Freudenstein ◽  
R. W. Longman ◽  
C.-K. Chen
Keyword(s):  
Kinematic Analysis ◽  
Industrial Robot ◽  
General Procedure ◽  
Bevel Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
End Effector ◽  
Gear Trains ◽  
Three Degree Of Freedom

A general procedure has been developed for the kinematic analysis of complex bevel-gear trains in which the motion of the arm can be of mobility two or greater (i.e. the arm can rotate about two or more nonparallel, intersecting axes). The analysis of a three-degree-of-freedom gear train used in guiding the motion of the end effector of a recently developed industrial robot is described in detail.

scholarly journals Tensor Decomposition of KUKA Industrial Robot (KR16-2) in Rotational System

2020 ◽  
Vol 9 (2) ◽  
pp. 688-690
Keyword(s):  
Rotational Motion ◽  
Industrial Robot ◽  
Matrix Decomposition ◽  
Tensor Decomposition ◽  
Tensor Model ◽  
Third Order ◽  
Order Tensor ◽  
The Third ◽  
Decomposition Model ◽  
The Matrix

This paper refers to study of industrial robot (KUKA KR16-2), in which we have considered the matrix decomposition and tensor decomposition model in rotational motion. We have considered robotic matrix & Tensor and defined a modal product between robot rotation matrix and a tensor Further we have proposed the third order tensor for the motion of Industrial robot and tried to find out the useful result. At last we have shown that the tensor model is providing alternate way to find the solution.

Novel Methods in the Displacement Analysis of Spatial Mechanisms

1994 ◽  
Author(s):  
Ian S. Fischer
Keyword(s):  
Iterative Methods ◽  
Coordinate Transformation ◽  
Kinematic Analysis ◽  
Displacement Analysis ◽  
Dual Number ◽  
Transformation Matrices ◽  
Spatial Mechanisms ◽  
Novel Methods

Abstract An aspect of dual-number coordinate-transformation matrices is used to establish iterative methods for determining the rotational and translational displacements in the kinematic analysis of complex spatial mechanisms.

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