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.

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.

Designing Statically Determinable Mechanisms of Technological Mechatronic Machines with Parallel Kinematics

2019 ◽  
Vol 20 (7) ◽  
pp. 428-436
Author(s):  
A. K. Tolstosheev ◽  
V. A. Tatarintsev
Keyword(s):  
Structural Analysis ◽  
Hierarchical Structure ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Parallel Structure ◽  
Parallel Kinematics ◽  
Output Link ◽  
Parallel Connection ◽  
Kinematic Chains ◽  
Chain Increase

The work is devoted to improving the reliability and manufacturability of mechatronic machine designs with parallel kinematics by replacing statically indeterminable manipulators with statically determinable mechanisms. A technique is proposed in which the design of statically determinable manipulators of technological mechatronic machines with parallel kinematics is performed by modifying the structure of prototypes and includes three steps: identifying and analyzing redundant links, eliminating redundant links, checking the correctness of eliminating redundant links. To determine the number of degrees of freedom of the mechanism, identify redundant links, and verify the solution, the authors use the proposed methodology for structural analysis of parallel structure mechanisms. In structural analysis, a manipulator is represented by a hierarchical structure and is considered as a parallel connection of elementary mechanisms with an open kinematic chain; as a kinematic chain consisting of leading and driven parts; as a set of links and kinematic pairs; as a kinematic connection of the output link and the rack. The article implements the following techniques for eliminating redundant links: mobility increase in kinematic pairs; introduction of unloading links and passive kinematic pairs to the kinematic chain; exclusion of extra links and pairs from the kinematic chain; increase in mobility in some kinematic pairs simultaneously with the exclusion of other kinematic pairs that have become superfluous. The authors developed several variants of structural schemes of self-aligning manipulators based on the Orthoglide mechanism, which retain the basic functional proper ties of the prototype. To increase the number of self-aligning mechanism diagrams, the redistribution of mobilities and links within the connecting kinematic chain and between connecting kinematic chains is used. The proposed methodics allow to determine the number of degrees of freedom of the mechanism, the number and type of redundant links, eliminate redundant links and, on an alternative basis, build structural diagrams of statically determinable mechanisms of technological mechatronic machines with parallel kinematics.

Structural Analysis of Mechanism with Compound Hinges in Ordinal Single Opened Chain Theory

2011 ◽  
Vol 418-420 ◽  
pp. 2050-2054
Author(s):  
Hong Bing Xin ◽  
Qiang Huang ◽  
Yue Qing Yu
Keyword(s):  
Structural Analysis ◽  
Structure Factor ◽  
Kinematic Chain ◽  
Kinematics And Dynamics ◽  
Kinematic Chains ◽  
Dual Color ◽  
Chain Theory ◽  
Topology Graph

The coupling degree and structure factor of mechanism are the important parameters for the research of principle of mechanism structure, kinematics and dynamics in the ordinal single opened chain method, This article presents the algorithm of coupling degree for the kinematic chain with compound hinges on the basis of that for the kinematic chain without compound hinges and the dual-color topology graph, through which the mechanism with compound hinges can be decomposed into basic kinematic chains, the correctness of the algorithm has been verified by the practical example.

scholarly journals Matrix Representation of Bi-Periodic Jacobsthal Sequence

2020 ◽  
pp. 1-12
Author(s):  
Sukran Uygun ◽  
Evans Owusu
Keyword(s):  
Generating Function ◽  
Initial Conditions ◽  
Matrix Representation ◽  
General Term ◽  
Identity Matrix ◽  
Summation Formulas ◽  
Matrix Sequence ◽  
Binet Formula ◽  
The Matrix ◽  
Generalized Matrix

In this paper, we bring into light the matrix representation of bi-periodic Jacobsthal sequence, which we shall call the bi-periodic Jacobsthal matrix sequence. We dene it as with initial conditions J0 = I identity matrix, . We obtained the nth general term of this new matrix sequence. By studying the properties of this new matrix sequence, the well-known Cassini or Simpson's formula was obtained. We then proceed to find its generating function as well as the Binet formula. Some new properties and two summation formulas for this new generalized matrix sequence were also given.

A More Direct Method for Structural Synthesis of Simple-Jointed Planar Kinematic Chains

1994 ◽  
Author(s):  
Varada Raju Dharanipragada ◽  
Nagaraja Kumar Yenugadhati ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Computer Program ◽  
Reliable Method ◽  
Direct Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Structural Synthesis ◽  
Indirect Methods ◽  
Kinematic Chains ◽  
A Chain

Abstract Structural synthesis of kinematic chains leans heavily on indirect methods, most of them based on Graph Theory, mainly because reliable isomorphism tests are not available. Recently however, the first and third authors have established the Secondary Hamming String of a kinematic chain as an excellent indicator of its isomorphism. In the present paper this Hamming String method was applied with slight modifications for synthesizing on a PC-386, distinct kinematic chains with given number of links and family description. The computer program, written in Pascal, generated both the six-bar and all 16 eight-bar chains as well as one sample family (2008) of ten-bar chains, verifying previously established results. Hence this paper presents a direct, quick and reliable method to synthesize planar simple-jointed chains, open or closed, with single- or multi-degree of freedom, containing any number of links. A spin-off of this paper is a simple, concise and unambiguous notation for representing a 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.

Generation and Sketching of Generalized Kinematic Chains

2008 ◽  
Author(s):  
Chiu-Fan Hsieh ◽  
Yii-Wen Hwang ◽  
Hong-Sen Yan
Keyword(s):  
Computer Program ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Kinematic Chains ◽  
A Chain

An algorithm of generalized kinematic chains and its computer program are developed in this paper. By this program, users can give the number of links and joints and then the link assortments and contracted link assortments can be calculated. The synthesis of multiple link adjacency matrix (MLAM) and the cut-link diagnosis are proposed to produce effectively the generalized kinematic chains. The algorithm can automatically determine the feature of a chain, which is connected, closed, non-isomorphism, without any cut-link (or cut-joint), and with simple joint only. Then, it can be called a generalized kinematic chain. Finally, various given number of links and joints, the nice looking atlas of generalized kinematic chains can also be generated. The developed computer program could help designers to be able to study and compare different devices in a very basic way.

Loop Based Detection of Isomorphism Among Chains, Inversions and Type of Freedom in Multi Degree of Freedom Chain

1999 ◽  
Vol 122 (1) ◽  
pp. 31-42 ◽  
Author(s):  
A. C. Rao ◽  
V. V. N. R. Prasad Raju Pathapati
Keyword(s):  
Unsolved Problem ◽  
Kinematic Chain ◽  
Computational Effort ◽  
Degree Of Freedom ◽  
Complete List ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Adjacency Matrices ◽  
The Creation ◽  
A Chain

Structural synthesis of kinematic chains usually involves the creation of a complete list of kinematic chains, followed by a isomorphism test to discard duplicate chains. A significant unsolved problem in structural synthesis is the guaranteed precise elimination of all isomorphs. Many methods are available to the kinematician to detect isomorphism among chains and inversions but each has its own shortcomings. Most of the study to detect isomorphism is based on link-adjacency matrices or their modification but the study based on loops is very scanty although it is very important part of a kinematic chain.  Using the loop concept a method is reported in this paper to reveal simultaneously chain is isomorphic, link is isomorphic, and type of freedom with no extra computational effort. A new invariant for a chain, called the chain loop string is developed for a planar kinematic chain with simple joints to detect isomorphism among chains. Another invariant called the link adjacency string is developed, which is a by-product of the same method to detect inversions of a given chain. The proposed method is also applicable to know the type of freedom of a chain in case of multi degree of freedom chains. [S1050-0472(00)70801-4]

On The Performance of Kinematic Chains

1988 ◽  
Vol 12 (2) ◽  
pp. 99-103 ◽  
Author(s):  
A.C. Rao
Keyword(s):  
Kinematic Chain ◽  
Isomorphism Type ◽  
Kinematic Chains ◽  
Output Error ◽  
A Chain

A great deal has been reported by several investigators regarding detection of isomorphism, type of freedom etc., of kinematic chains based on their structure. The work reported so far will be meaningful only if some useful conclusions can be drawn from the structure of a chain, one of these being that the designer must be able to compare the structure of say, two kinematic chains and predict before completing dimensional synyhesis which of these will meet the motion requirements more accurately, in the sense of output error. The authors feel that his earlier work [1] in this direction needs to be supplemented to provide with (i) conviction that the entropy of a kinematic chain is representative of its ability to generate motion and (ii) clarification that the expression equivalent to entropy can be developed and used without resorting to probability considerations. The same is accomplished in this paper through illustrations.

The Structure, Work Space and Direct Kinematic of the Robots with 8 Axes of Type T Normal R Parallel (PM)(OM)

2014 ◽  
Vol 658 ◽  
pp. 718-723
Author(s):  
Ionel Staretu
Keyword(s):  
Reference System ◽  
Characteristic Point ◽  
Kinematic Chain ◽  
Industrial Robots ◽  
Kinematic Chains ◽  
The Matrix ◽  
Fixed Reference ◽  
Translation Coupling ◽  
Homogeneous Operators ◽  
Direct Kinematics

The paper presents first structural synthesis aspects of serial redundant open kinematic chains for industrial robots. These chains are obtained from 3-axis positioning kinematic chains that create non-degenerate workspaces plus first a rotation or translation coupling in parallel or perpendicular position, obtaining structures with 7-axis, to which by adding in the same way one more rotation or translation coupling structures with 8 axes are obtained. Below we present the direct kinematics analysis for this kinematic chain using the homogeneous operators’ method. This method is based on the use of homogeneous translation or rotation operators and covering the kinematic chain from the base to the characteristic point at its end by a mobile reference system. Based on linear and angular dimensions expressed in matrix by corresponding homogeneous operators we obtain the matrix of the robot characteristic point coordinates in the fixed reference system attached to the robot base. Thus, direct kinematics is solved qualitatively. For a set of numerical values, ​​we obtain a quantitative solution.

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