Kinematics and Statics Including Friction in Single-Loop Mechanisms by Screw Calculus and Dual Vectors

1973 ◽  
Vol 95 (2) ◽  
pp. 471-480 ◽  
Author(s):  
M. L. Keler
Keyword(s):  
Iterative Technique ◽  
Complex Vector ◽  
Single Loop ◽  
Vector Algebra ◽  
Dual Complex

After reviewing the fundamentals of dual-complex vector algebra, a method of accounting for friction in kinematic joints is developed. The method, which is based on an iterative technique, is applicable to all single-loop mechanisms which are kinematically and statically determinate.

Burmester-Theory for Band-Mechanisms

1992 ◽  
Author(s):  
Kurt Luck ◽  
Karl-Heinz Modler
Keyword(s):  
Analytical Methods ◽  
Path Generation ◽  
Complex Vector ◽  
Vector Algebra ◽  
Flexible Application ◽  
Four Bar Linkage ◽  
Special Case ◽  
Better Than

Abstract A band-mechanism includes inter alia a flexible band and a disk-profile. Such a mechanism can excellent be used for path-generation, better than a four-bar-linkage. Also several plane-positions additionally can be realized. This paper investigates the synthesis of four-bar-band-mechanisms by using the complex vector-algebra. Several technical tasks demonstrate the flexible application of such mechanisms. This tasks are formulated analogous to the wellknown BURMESTER-THEORY, but with higher claims and the solution is done by analytical methods. Further it is demonstrated that a four-bar-linkage is a special case of a four-bar-band-mechanism.

Burmester Theory for Four-Bar-Band Mechanisms

1995 ◽  
Vol 117 (1) ◽  
pp. 129-133
Author(s):  
K. Luck ◽  
K.-H. Modler
Keyword(s):  
Analytical Methods ◽  
Path Generation ◽  
Complex Vector ◽  
Vector Algebra ◽  
Flexible Application ◽  
Four Bar Linkage ◽  
Special Case ◽  
Better Than

A band mechanism includes inter alia a flexible band and a disk profile. Such a mechanism can be used for path generation better than a four-bar linkage. Also several plane positions can be realized. This paper investigates the synthesis of four-bar-band mechanisms by using complex vector algebra. Several technical tasks demonstrate the flexible application of such mechanisms. These tasks are formulated according to the well-known Burmester Theory, but with higher claims and a solution achieved by analytical methods. Furthermore, this paper demonstrates that a four-bar linkage is a special case of a four-bar-band mechanism.

Structure Synthesis of Rank-Degenerated Serial Mechanisms and Over-Constrained Single-Loop Kinematic Chains

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Single Loop ◽  
Kinematic Chains ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Position And Orientation

Based on the Position and orientation characteristic (POC) equation of serial mechanisms proposed by the author, this paper presents a novel systematic approach for structure synthesis of rank-degenerated serial mechanisms and over-constrained single-loop kinematic chains (KCs) (excluding the Bennett mechanism etc). This approach is totally different from the approaches based on the screw theory and based on the displacement subgroup, and only simple mathematical tools (vector algebra, etc.) are used. Using this approach, the structure types of serial mechanisms with the specified ranks and the specified degree of freedom (DOF) are synthesized firstly. After that, using the structure types of the obtained serial mechanisms, structure types of over-constrained single-loop KCs with the specified ranks and the specified DOF can be generated in a straightforward way. The structure types of the obtained serial mechanisms can be used as branches of parallel mechanisms. The structure types and the ranks of the obtained over-constrained single-loop KCs can be used to calculate the DOF of multi-loop mechanisms. In fact, the systematic approach proposed in this paper is a key component of the systematic approach for structure synthesis of parallel mechanisms.

Complex Vector Algebra in Electromagnetics

1983 ◽  
Vol 20 (1) ◽  
pp. 33-47 ◽  
Author(s):  
Ismo V. Lindell
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Fields ◽  
Complex Vector ◽  
Postgraduate Teaching ◽  
Time Harmonic ◽  
Vector Algebra

The algebra of complex vectors, often applied in the analysis of time-harmonic electromagnetic fields in an incomplete manner, is introduced in a systematic way, applicable in graduate or postgraduate teaching. The examples chosen to elucidate the notation are from the field of antennas and wave propagation.

Efficient Analysis of Multiport Passive Circuits Using the Iterative Technique

2001 ◽  
Vol 21 (1) ◽  
pp. 73-84 ◽  
Author(s):  
A. Gharsallah ◽  
A. Gharbi ◽  
H. Baudrand
Keyword(s):  
Iterative Technique ◽  
Passive Circuits

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

Stress and Deformation

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Finite Strain ◽  
Stress Strain ◽  
Complex Problems ◽  
Vector Algebra ◽  
Stress And Deformation

Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. This book, based on a course taught by the author at UCLA, can provide the proper introduction. Included throughout the eight chapters are 136 complex problems, advancing from vector algebra in standard and subscript notations, to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help, students can monitor their progress, and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations.

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