Critical Review of Existing Degeneracy Testing and Mobility Type Identification Algorithms for Kinematic Chains

2005 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Critical Review ◽  
Kinematic Chain ◽  
Structural Studies ◽  
Mobility Analysis ◽  
Structural Synthesis ◽  
Common Error ◽  
Kinematic Chains ◽  
The Individual ◽  
Almost All ◽  
Mathematical Justification

Mobility analysis is one of the fundamental problems of structural studies of kinematic chains. Degeneracy testing, an important step in structural synthesis, can be considered as a part of the mobility analysis due to the similarity of the two problems. One common error in the algorithms for these two problems is the assumption that the graph of a planar kinematic chain is a planar graph. This work shows that almost all the mobility analysis algorithms, except that of Lee and Yoon, have this error. This work also critically reviews the two most efficient algorithms on degeneracy testing, those by Hwang and Hwang, and Lee and Yoon. It is shown that due to the errors in the Hwang and Hwang’s algorithm, it failed to identify some of the degenerate chains. Furthermore, the accuracy of the Lee and Yoon’s algorithms for mobility analysis and degeneracy testing is proved by providing the mathematical justification of the individual steps of the algorithms.

Structure Based Grading of Kinematic Chains

2014 ◽  
Vol 575 ◽  
pp. 501-506 ◽  
Author(s):  
Shubhashis Sanyal ◽  
G.S. Bedi
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Structural Differences ◽  
The Individual ◽  
Independent Loops

Kinematic chains differ due to the structural differences between them. The location of links, joints and loops differ in each kinematic chain to make it unique. Two similar kinematic chains will produce similar motion properties and hence are avoided. The performance of these kinematic chains also depends on the individual topology, i.e. the placement of its entities. In the present work an attempt has been made to compare a family of kinematic chains based on its structural properties. The method is based on identifying the chains structural property by using its JOINT LOOP connectivity table. Nomenclature J - Number of joints, F - Degree of freedom of the chain, N - Number of links, L - Number of basic loops (independent loops plus one peripheral loop).

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

Topological Characteristics and Automatic Generation of Structural Synthesis of Spatial Mechanisms: Part II — Automatic Generation of Structural Types of Kinematic Chains

1992 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Automatic Program ◽  
Spatial Mechanisms ◽  
Structural Types ◽  
Topological Characteristics ◽  
Linear Graphs ◽  
Independent Loops

Abstract Based on the single-opened chain constraints and the network topological characteristics of mechanisms, a powerful new method for structural synthesis of spatial kinematic chain with plane and nonplane linear graphs has been developed. This permits the development of a highly efficient and completely automatic program for the computer-generated enumeration of structural types of mechanisms. The method is illustrated by applying to the case of kinematic chains with up to six independent loops on a personal computer.

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.

scholarly journals Mobility Analysis of Kinematic Chains

1970 ◽  
Vol 6 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Ashok Dargar ◽  
Ali Hasan ◽  
RA Khan
Keyword(s):  
Efficient Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
View Point ◽  
Mobility Analysis ◽  
Kinematic Chains ◽  
Engineering And Technology ◽  
The Given ◽  
Flow Matrix

In the present work a simple and efficient method is proposed to identify whether a kinematicchain posses total, partial or fractionated mobility. The proposed method uses the chain flowvalues (CFV) derived from the flow matrix of the given kinematic chain and successfullyapplied to all known cases of 2 and 3 degree of freedom planar kinematic chains. Since themethod is systematic and efficient, it can be applied to the more complex chains which nothave been reported in the literature yet. This study will be helpful in dividing the frame andinput links from the view point of mobility. Some examples are provided to demonstrate theeffectiveness of this method.Keywords: Degree of freedom (DOF); Contour; Chain flow value (CFV).DOI: 10.3126/kuset.v6i1.3307Kathmandu University Journal of Science, Engineering and Technology Vol.6(1) 2010, pp25-32

Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain

2005 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Second Step ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Serial Chain ◽  
Parallel Kinematic

This paper presents a systematic approach for the mobility analysis of parallel mechanisms. The method is based on screw theory and the concept of equivalent serial chain. An equivalent serial kinematic chain of a k-legged PKC (parallel kinematic chain) is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. Using the proposed approach, the mobility analysis of a PKC is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step is dealt with based on screw theory. The second step is performed with the aid of the concept of equivalent serial chain and the types of multi-DOF overconstrained single-loop kinematic chains. The proposed approach is illustrated with several examples.

scholarly journals STRUCTURAL SYNTHESIS OF PARALLEL MECHANISMS THAT PROVIDE PLANE-PARALLEL MOTION OF THE OUTPUT LINK BASED ON THE THEORY OF SCREWS AND VIRTUAL KINEMATIC CHAINS

2016 ◽  
Vol 2 (1) ◽  
pp. 185-194
Author(s):  
Гапоненко ◽  
Elena Gaponenko ◽  
Рыбак ◽  
Larisa Rybak ◽  
Малышев ◽  
...  
Keyword(s):  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Structural Synthesis ◽  
Output Link ◽  
Kinematic Chains ◽  
Plane Parallel ◽  
Parallel Movement ◽  
Parallel Motion ◽  
Movable Platform ◽  
Virtual Circuits

This article describes the method of structural synthesis of a class of parallel mechanisms that provide plane-parallel movement of the movable platform. The considered method is based on the theory of screws and the concept of virtual circuits. We obtain the structure of parallel mechanisms, containing three connecting kinematic chain.

Topological Characteristics and Automatic Generation of Structural Synthesis of Planar Mechanisms Based on the Ordered Single-Opened-Chains

1994 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Regular Sequence ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Kinematic Chains ◽  
Topological Characteristics ◽  
Basic Link ◽  
Linear Graphs ◽  
Independent Loops

Abstract This paper presents a new viewpoint about structural composition of planar kinematic chains: single-opened-chains, which is composed of binary links, are regarded as basic structural units of mechanisms. The constraint characteristics (the constraint factors, Δj) of single opened chains and the constraint characteristics (the coupled degree κ and the κ-algorithm) of mechanical networks are presented. Thus a kinematic chain with v independent loops is regarded to be composed of one basic link and v single-opened-chains in regular sequence. Based on the ordered single-opened-chains and the topological constraints characteristics of mechanisms, a powerful new method for structural synthesis of planar kinematic chains with plane and nonplane linear graphs has been developed. This permits the development of a highly efficient and completely automatic program for the computer-generated enumeration of structural types of mechanisms. The method is illustrated by applying to the case of kinematic chains with up to six independent loops on a personal computer. The ordered single-opened-chains and the topological characteristics are used for setting up a new unified model for structics, kinematics and dynamics of planar mechanisms.

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]

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