scholarly journals A joint–joint matrix representation of planar kinematic chains with multiple joints and isomorphism identification

2018 ◽  
Vol 10 (6) ◽  
pp. 168781401877840 ◽  
Author(s):  
Wei Sun ◽  
Jianyi Kong ◽  
Liangbo Sun
Keyword(s):  
Matrix Representation ◽  
Kinematic Chain ◽  
Chain Structure ◽  
Kinematic Chains ◽  
Essential Step ◽  
Matrix Description ◽  
The Matrix ◽  
Chain Synthesis ◽  
The Relationship ◽  
Isomorphism Identification

The synthesis of the kinematic chain needs to obtain the information of the kinematic chain accurately and comprehensively. Isomorphism identification is an essential step in kinematic chain synthesis. In this article, a novel isomorphism determination method of planar kinematic chains with multiple joints based on joint–joint matrix description was proposed. First, a joint–joint matrix is presented to describe the kinematic chain, which can uniquely represent the kinematic chain structure. Then links and joints information were extracted from the matrix. And the link code and joint code were introduced to represent the link attributes and joint attributes, respectively. Furthermore, the standardization rules of joint–joint matrix are proposed. Isomorphism of kinematic chain is identified by comparing links, joints, and matrices. And the relationship between the links and the joints corresponding to the isomorphic kinematic chain is determined. Finally, the examples demonstrate that the method is novel and efficient.

Structural Analysis of Kinematic Chains and Mechanisms Based on Matrix Representation

1979 ◽  
Vol 101 (3) ◽  
pp. 488-494 ◽  
Author(s):  
T. S. Mruthyunjaya ◽  
M. R. Raghavan
Keyword(s):  
Structural Analysis ◽  
Physical Meaning ◽  
Matrix Representation ◽  
Kinematic Chain ◽  
Kinematic Chains ◽  
Matrix Notation ◽  
The Matrix ◽  
Generalized Matrix ◽  
A Chain ◽  
Insight Into

A method based on Bocher’s formulae has been presented for determining the characteristic coefficients (which have recently been suggested [19] as an index of isomorphism) of the matrix associated with the kinematic chain. The method provides an insight into the physical meaning of these coefficients and leads to a possible way of arriving at the coefficients by an inspection of the chain. A modification to the matrix notation is proposed with a view to permit derivation of all possible mechanisms from a kinematic chain and distinguishing the structurally distinct ones. Algebraic tests are presented for determining whether a chain possesses total, partial or fractionated freedom. Finally a generalized matrix notation is proposed to facilitate representation and analysis of multiple-jointed chains.

The Systemic Research on Loop Characteristics of Planar Kinematic Chains and Its Applications

2005 ◽  
Author(s):  
H. F. Ding ◽  
Z. Huang ◽  
Y. Cao
Keyword(s):  
Degree Sequence ◽  
Kinematic Chain ◽  
Loop Analysis ◽  
Topological Graph ◽  
Type Analysis ◽  
Kinematic Chains ◽  
Relationship Of ◽  
The Relationship ◽  
Basic Loop ◽  
Isomorphism Identification

Based on the array representation of loop in topological graph of kinematic chains, this paper proposes two basic loop operations. Their existent conditions and properties of the two operations are also researched. In further loop analysis we discuss the important concepts including the independent loop, canonical degree-sequence and perimeter topological graph. Two Theorems deal with the relationship of loops. Based on above basic theory some important applications are given, such as the isomorphism identification based on the loop set concept, the detection of the rigid sub-chains in a kinematic chain and the type analysis of freedom of kinematic chains.

scholarly journals Influence of lower leg myofascial kinematic chains on flat feet development of children 7-14 years old

2019 ◽  
Vol 5 (2) ◽  
pp. 28 ◽  
Author(s):  
A. Danyschuk
Keyword(s):  
Experimental Studies ◽  
Kinematic Chain ◽  
Motor Units ◽  
Biomechanical Properties ◽  
Flat Foot ◽  
Kinematic Chains ◽  
Flat Feet ◽  
The Relationship ◽  
Possible Cause ◽  
Anthropometric Study

<p><strong>The aim of the work </strong>is to study the biomechanical properties of the myo-fascial kinematic chain "foot-shin" of children of 7-14 years old with non-fixed and clinically expressed flat-footedness.</p><p><strong>Material and methods</strong>. The study involved 14 children with flat-footedness of grades I-II and 6 children with flat-foot deformity of the foot and 20 children who only had functional disorders of the foot. An anthropometric study of the foot was carried out, electrophysiological indicators of the muscles of the leg were determined, and plantograms were analyzed.</p><p><strong>Results</strong>. The study found a correlation between the indicators of the anatomical and functional state of the foot and the imbalance of the frequency-amplitude indices of the ipsi and contralateral muscles within one link of the myofacial kinematic chain, may be important as one of the factors that contribute to the development of flatfoot. This is confirmed by other indicators and indicate a decrease in the height of the longitudinal arch, a decrease in the metatarsal and heel angles of the arch of the foot. Such changes have a pronounced relationship with age. The results of the work indicate that a possible cause of flattening of the vaulted apparatus of the foot is not only the weakness of its joint-ligament-muscular system, but also above the located kinematic segment - the tibia. The correlation analysis revealed the relationship between the indicators of the development of the anatomical and biomechanical components of the foot and the characteristics of the electromyographic indicators of the muscles of the leg in children 7-14 years old. As a result of a comprehensive study, it was found that during this period of ontogenesis in the formation of flatfoot such electromyographic indicators as frequency-amplitude characteristics of action potentials of motor units of the long and posterior tibial muscles, as well as their tone imbalance, take on major importance.</p><p><strong>Conclutions</strong>. Experimental studies have established that the registered changes in the articular components of the foot of children 7-14 years old lead to a change in the electromyographic parameters of the muscles of the leg, which are involved in the formation of the initial sections of myo-fascial kinematic chains.</p>

THE MODELLING OF HOLONOMIC MECHANICAL SYSTEMS USING A NATURAL ORTHOGONAL COMPLEMENT

1989 ◽  
Vol 13 (4) ◽  
pp. 81-89 ◽  
Author(s):  
J. ANGELES ◽  
SANGKOO LEE
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Kinematic Chain ◽  
Chain Structure ◽  
Rigid Bodies ◽  
Orthogonal Complement ◽  
Constraint Forces ◽  
Constrained Mechanical Systems ◽  
Constraint Equations ◽  
The Matrix

A computationally efficient and systematic algorithm for the modelling of constrained mechanical systems is developed and implemented in this paper. With this algorithm, the governing equations of mechanical systems comprised of rigid bodies coupled by holonomic constraints are derived by means of an orthogonal complement of the matrix of the velocity-constraint equations. The procedure is applicable to all types of holonomic mechanical systems, and it can be extended to cases including simple nonholonomic constraints. Holonomic mechanical systems having a simple Kinematic-chain structure, such as single-loop linkages and serial-type robotic manipulators, are analysed regarding the derivation of the matrix of the constraint equations and its orthogonal complement, and the computation of the constraint forces.

Topological invariant and definition method for detecting isomorphism in planar kinematic chains

2020 ◽  
pp. 095440622096078
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Liang Sun ◽  
Chuanyu Wu
Keyword(s):  
Planetary Gear ◽  
Topological Invariant ◽  
Detection Methods ◽  
Kinematic Chains ◽  
Essential Step ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Configuration Synthesis ◽  
Definition Of ◽  
Isomorphism Identification

Isomorphism identification is an essential step in mechanism configuration synthesis. Although various detection methods have been proposed, some of them can only effectively identify kinematic chains (KCs) within 10 links or complex programs that are needed to identify multilink KCs. In this study, a new isomorphism identification method is proposed based on the distance concept of graphs and the graph theory definition of isomorphism. In addition to two complex 21- and 28-link planar simple-joint KCs (PSKCs), the proposed algorithm is tested on the complete atlas of 8-link 1-DOF, 9-link 2-DOF, 10-link 1-DOF, 12-link 1-DOF, and 13-link 2-DOF PSKCs. The algorithm is also tested on 6-link 1-DOF and 7-link 1-DOF planetary gear trains (PGTs) to detect isomorphism. All results are in agreement with those of the existing literature. The method is fully automated via a computer program and has been verified to be reliable and efficient.

Identification of Isomorphism in Kinematic Chains Using Hamming Method

2014 ◽  
Vol 592-594 ◽  
pp. 2723-2727
Author(s):  
Indu Saini ◽  
Vijay Pal Singh
Keyword(s):  
Reliable Method ◽  
Kinematic Chain ◽  
Difficult Problem ◽  
Satisfactory Solution ◽  
Sewing Machine ◽  
Kinematic Chains ◽  
Straight Line ◽  
And Inversion ◽  
Isomorphism Identification

Isomorphism identification is a difficult problem in kinematic chains. There is number of method given by many researchers to detect the isomorphism and inversion of kinematic chain but each has its own shortcomings. Purpose of this paper is to give an efficient and reliable method. An attempt has been made to provide satisfactory solution to detection of isomorphism by using hamming method. The method is implemented on sewing machine, break drum; straight line motion mechanisms have six links kinematic chain.

A Matrix Representation and Motion Space Exchange Metamorphic Operation

2011 ◽  
Vol 308-310 ◽  
pp. 2058-2061
Author(s):  
Shu Jun Li ◽  
Jian Sheng Dai
Keyword(s):  
Adjacency Matrix ◽  
Matrix Representation ◽  
Matrix Operation ◽  
Planar Mechanism ◽  
Kinematic Chains ◽  
Orientation Change ◽  
Joint Axis ◽  
The Matrix

The paper presents a matrix representation of mechanical chains based on proposed joint-axis matrix, and a matrix operation of joints orientation change metamorphic processes. A four elements joint-axis matrix with joints types and orientations is developed first, and an augmented adjacency matrix of kinematic chains is formed by adding the elements of joint-axis matrix into the corresponding positions of general adjacency matrix of kinematic chains. Then the matrix operation of metamorphic process is performed through changing the orientation of metamorphic joint of augmented planar mechanism to transform the configuration of the mechanism from planar to spatial one.

A Strategy for Geometric Error Characterization in Multi-Axis Machine Tool by Use of a Laser Tracker

2014 ◽  
Vol 615 ◽  
pp. 22-31 ◽  
Author(s):  
Sergio Aguado ◽  
Jorge Santolaria ◽  
David Samper ◽  
Juan Jose Aguilar Martín
Keyword(s):  
Machine Tool ◽  
Kinematic Model ◽  
Kinematic Chain ◽  
Geometric Error ◽  
Laser Tracker ◽  
Geometric Errors ◽  
Kinematic Chains ◽  
Error Characterization ◽  
Machine Tool Accuracy ◽  
The Relationship

This paper aims to present different methods of volumetric verification in long range machine toll with lineal and rotary axes using a commercial laser tracker as measurement system. This method allows characterizing machine tool geometric errors depending on the kinematic of the machine and the work space available during the measurement time. The kinematic of the machine toll is affected by their geometric errors, which are different depending on the number and type of movement axes. The relationship between the various geometrical errors is different from relationship obtained in machine tool whit only lineal axes. Therefore, the identification strategy should be different. In the same way, the kinematic chain of the machine tool determines determines the position of the laser tracker and available space for data capture. This paper presents the kinematic model of several machine tools with different kinematic chains use to improve the machine tool accuracy of each one by volumetric verification. Likewise, the paper thus presents a study of: the adequacy of different nonlinear optimization strategies depending on the type of axis and the usable space available.

Research on Kinematic Chain Isomorphism Identification Method Based on the Standardization Adjacent Matrix

2010 ◽  
Vol 43 ◽  
pp. 514-518 ◽  
Author(s):  
Mao Zhong Ge ◽  
Jian Yun Xiang ◽  
Yong Kang Zhang
Keyword(s):  
Graph Theory ◽  
Kinematic Chain ◽  
New Method ◽  
Kinematic Chains ◽  
Identification Method ◽  
Isomorphism Identification

In order to solve a baffling problem of kinematic chain isomorphism identification, proceeded from the isomorphism’s principles of graph theory, a new method for detecting isomorphism among planar kinematic chains using the standardization adjacent matrix is presented in this paper. The general course of adjacent matrix standardization processing and numbering principle of node are introduced, the implementation of this new method is illustrated with an example, it is showed that this new method can be accurately and effectively performed.

A simple and efficient method for isomorphism identification of planar kinematic chains

2021 ◽  
Author(s):  
Luchuan Yu ◽  
Chenxu Cai ◽  
Jianhua Zhang ◽  
Qinhe Zhang
Keyword(s):  
Structural Design ◽  
Kinematic Chain ◽  
Structural Synthesis ◽  
Topological Graphs ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Solid Foundation ◽  
Programming Software ◽  
Chain Links ◽  
Isomorphism Identification

Abstract Isomorphism identification plays an important role in structural design and innovative design. Based on the adjacency matrix and loop theory, a new method is proposed in this paper to identify the isomorphic kinematic chains. It enriches the application of loop-based theory for isomorphism identification. In the kinematic chain, links and joints are connected alternatively and every link corresponds to a fixed link degree. Due to the inherent characteristics, the labeled sequence of links can be random, which does not affect the result of isomorphism identification. By the programming software MATLAB, some examples with 6-, 8-, 10-, 11-, 12-link kinematic chains, and 15-vertex topological graphs are presented. Results show that the proposed method applies to topology graphs and kinematic chains with one or multiple joints. Compared with other methods, the proposed method is confirmed correctly. And there is no counterexample. It lays a solid foundation for structural synthesis in the future.

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