scholarly journals Application of linear and nonlinear graphs in structural synthesis of kinematic chains

1974 ◽  
Vol 6 (3) ◽  
pp. 198
Author(s):  
M. Huang ◽  
A.H. Soni
Keyword(s):  
Structural Synthesis ◽  
Kinematic Chains ◽  
Linear And Nonlinear

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

scholarly journals A New Algorithm for Unique Representation and Isomorphism Detection of Planar Kinematic Chains with Simple and Multiple Joints

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 601
Author(s):  
Mahmoud Helal ◽  
Jong Wan Hu ◽  
Hasan Eleashy
Keyword(s):  
Degree Of Freedom ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Joint Configuration ◽  
Unique Representation ◽  
Kinematic Chains

In this work, a new algorithm is proposed for a unique representation for simple and multiple joint planar kinematic chains (KCs) having any degree of freedom (DOF). This unique representation of KCs enhances the isomorphism detection during the structural synthesis process of KCs. First, a new concept of joint degree is generated for all joints of a given KC based on joint configuration. Then, a unified loop array (ULA) is obtained for each independent loop. Finally, a unified chain matrix (UCM) is established as a unique representation for a KC. Three examples are presented to illustrate the proposed algorithm procedures and to test its validity. The algorithm is applied to get a UCM for planar KCs having 7–10 links. As a result, a complete atlas database is introduced for 7–10-link non-isomorphic KCs with simple or/and multiple joints and their corresponding unified chain matrix.

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.

Synthesis of planar kinematic chains with prismatic pairs based on a similarity recognition algorithm

2021 ◽  
pp. 1-13
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Shifu Xu ◽  
Chuan-yu Wu ◽  
Liang Sun
Keyword(s):  
Recognition Algorithm ◽  
Synthesis Process ◽  
Synthesis Methods ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract The structural synthesis of planar kinematic chains (KCs) with prismatic pairs (P-pairs) is the basis of innovating mechanisms containing P-pairs. In literature, only a little research has been carried out to synthesize planar KCs with P-pairs. Moreover, these synthesis methods for KCs with P-pairs involve all possible combinations of edges, resulting in a large number of isomorphic KCs and a low synthesis efficiency. In this study, our previous similarity recognition algorithm is improved and applied to synthesize planar KCs with P-pairs. Only a small number of isomorphic KCs are generated in the synthesis process, and the synthesis efficiency is greatly enhanced. Our method is applied to synthesize 9-link 2-DOF, 10-link 1-DOF, and 11-link 2-DOF KCs with one and two P-pairs. Our synthesis results are consistent with those of the existing literature. The present work is helpful to design mechanisms with P-pairs and can be extended to mechanisms with other types of kinematic pairs.

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.

scholarly journals Structural Synthesis of a Family of Planar 8-Link Kinematic Chains for Linkages with Multiple Joints and the Most Complex Ternary Link

2020 ◽  
pp. 21-31
Author(s):  
V.I. Pozhbelko ◽  
E.N. Kuts
Keyword(s):  
Mathematical Model ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Modern Engineering ◽  
Integer Solutions ◽  
Synthesis Procedure ◽  
P Matrix ◽  
Structural Solutions

Structural synthesis of closed kinematic chains to create various mechanisms is the first and most difficult stage of creative design of complex machines due to the large variance of possible structural solutions. In this paper, the authors examine the problem of structural synthesis of a family of eight-link kinematic chains with multiple joints of various types and the most complex three-joint link in order to create multi-loop multiple-joint mechanisms with one degree of freedom. To solve this problem, a synthesis technique is proposed based on the search for all integer solutions of a generalized structural mathematical model of plane linkage mechanisms and the identification of all structurally nonisomorphic kinematic chains using a two-column P-matrix. As the result of the structural synthesis, a family of eight-link multiple joint kinematic chains is obtained, which contains seven new kinematic structures. Examples of creating 1-DOF mechanisms with multiple joints based on the obtained new structures are presented. They confirm the effectiveness of using the structural synthesis procedure and analysis of complex mechanisms with multiple joints in various areas of modern engineering (precise guiding mechanisms, automatic lines, technological machines, robots, manipulators, etc.).

Compound Topological Invariant Based Method for Detecting Isomorphism in Planar Kinematic Chains

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Rongjiang Cui ◽  
Wenjian Yang ◽  
Chuanyu Wu
Keyword(s):  
Detection Method ◽  
Planetary Gear ◽  
Topological Invariant ◽  
Detection Methods ◽  
Fourth Power ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
Simple Detection ◽  
Gear Trains

Abstract An important step in the structural synthesis of kinematic chains (KCs) or mechanisms is the detection of isomorphic structures. Although many detection methods have been proposed, most of them require complex computations and have poor versatility. In this study, a simple detection method is proposed based on a compound topological invariant (CTI), which comprises the fourth power of adjacency matrix and eigenvalues. Besides two complex 15- and 28-link planar simple-joint KCs (PSKCs), the method is tested on the complete atlas of contracted graphs with up to six independent loops, PSKCs with up to 13 links, 8-link 1-degree-of-freedom (DOF) planar multiple-joint KCs (PMKCs), and 6-link 1-DOF planetary gear trains (PGTs). All the results are in agreement with the reported results in the literature. Our method possesses good versatility and has been verified as being reliable and efficient.

A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages: Part II — Modular Dynamic Analysis, Modular Structural Synthesis and Modular Kinematic Synthesis

1998 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao ◽  
Ming Zhang
Keyword(s):  
Structural Analysis ◽  
Comparative Study ◽  
Dynamic Analysis ◽  
Structural Synthesis ◽  
Dynamical Equations ◽  
Kinematic Synthesis ◽  
Automated Generation ◽  
Kinematic Chains ◽  
Analysis And Synthesis ◽  
Planar Linkages

Abstract This paper presents a systematical comparative study of various modular methods based on the different module types: basic kinematic chains (BKCs), single opened chains (SOCs), loops (or a tree and co-tree), links-joints, etc. for analysis and synthesis of structure, kinematics and dynamics of planar linkages. The basic idea is that any linkage can be divided into (or built up by) some modular components in sequence, and based on the component constraints and network entirty constraints of the linkage, the unified modular approaches have been used for analysis and synthesis. In systematical comparative study, the main issues of a modular method have been discussed, such as: the topological characteristics revealed via different module types; the dimension of a set of kinematic equations; the automated generation and solution of kinematic equations; the dimension and automated generation of dynamical equations, and computation complexity for generating and solving dynamical equation; the automated generation of structural analysis and type synthesis; the generation of kinematic synthesis equations etc.. This paper gives a summary of the use of modular techniques for analyzing and synthesizing planar linkages in the recently thirty years. This comparative study includes two parts: Part I-modular structural analysis and modular kinematic analysis; Part II-modular dynamic analysis, modular structural synthesis and modular kinematic synthesis. This paper is the second part.

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.

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