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.

A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages: Part I — Modular Structural Analysis and Modular Kinemaic Analysis

1998 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao ◽  
Ming Zhang
Keyword(s):  
Structural Analysis ◽  
Comparative Study ◽  
Type Synthesis ◽  
Dynamical Equations ◽  
Kinematic Synthesis ◽  
Automated Generation ◽  
Kinematic Chains ◽  
Analysis And Synthesis ◽  
Modular Method ◽  
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 the 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 dynamics analysis, modular structural synthesis and modular kinematic synthesis. This paper is the first part.

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.

Mobility analysis and structural synthesis of a class of spatial mechanisms with coupling chains

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2467-2485 ◽  
Author(s):  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Ziming Chen ◽  
Shipei Zhao
Keyword(s):  
Structural Analysis ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Structural Synthesis ◽  
Systematic Method ◽  
General Methodology ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis

SUMMARYThis paper presents a systematic method for dealing with mobility analysis and structural synthesis of a class of important spatial mechanisms with coupling chains, which involve more complex coupling relations than spatial parallel mechanisms. First, an approach to the establishment of the motion screw equation of the class of mechanisms is derived. Then, a general methodology for mobility analysis along with detection of rigid substructures is proposed based on the motion screw equation. Third, the principle of structural synthesis of the class of mechanisms is established on the basis of the method of mobility analysis. Finally, some novel spatial mechanisms with coupling chains are synthesized, illustrating the effectiveness of the method. The study of the paper will benefit structural analysis and synthesis of more complex spatial mechanisms with coupling chains.

Kinematic Synthesis of Minimally Actuated Multi-Loop Planar Linkages With Second Order Motion Constraints for Object Grasping

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Nina Robson
Keyword(s):  
Second Order ◽  
Human Robot Interaction ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Open Problems ◽  
Kinematic Synthesis ◽  
Human Environment ◽  
Kinematic Chains ◽  
Curvature Effects ◽  
Planar Linkages

In this paper, we consider the dimensional synthesis of one degree-of-freedom multi-loop planar linkages such that they do not violate normal direction and second order curvature constraints imposed by contact with objects. Our goal is in developing minimally actuated multi-loop mechanical devices for human-robot interaction, that is, devices whose tasks will happen in a human environment. Currently no systematic method exists for the kinematic synthesis of robotic fingers that incorporate multi-loop kinematic structure with second order task constraints, related to curvature. We show how to use these contact and curvature effects to formulate the synthesis equations for the design of a planar one-degree-of-freedom six-bar linkage. An example for the design of a finger that maintains a specified contact with an object, for an anthropomorphic task, is presented at the end of the paper. It is important to note, that the theoretical foundation presented in this paper, assists in solving some of the open problems of this field, providing preliminary results on the synthesis of kinematic chains with multi-loop topology and the use of novel task specifications that incorporate curvature constraints with future applications in grasping and object manipulation.

A Quadratic Form-Based Approach to Identification of Kinematic Chains in Structural Analysis and Synthesis of Mechanisms

2001 ◽  
Author(s):  
Peiren He ◽  
Wenjun Zhang ◽  
Qing Li
Keyword(s):  
Structural Analysis ◽  
Quadratic Form ◽  
Test Cases ◽  
Eigenvalues And Eigenvectors ◽  
New Approach ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Adjacency Matrices ◽  
Analysis And Synthesis

Abstract Identification of kinematic chains is needed when studying in structural analysis and synthesis of mechanisms. Research on detection of isomorphism in graphs/kinematic chains has a long history. Many algorithms or methods have been proposed. However, these methods have only achieved success in restricted conditions. This paper proposes a new approach using the concept of quadratic form. Graphs/kinematic chains are first represented by their adjacency matrices, the eigenvalues and their eigenvectors corresponding to these adjacency matrices are then calculated. Two graphs are represented by two quadratic expressions. The comparison of two graphs reduces to the comparison of two quadratic expressions. Quadratic expressions are characterized by the eigenvalues and eigenvectors. An algorithm is developed to compare, correspondingly, eigenvalues and eigenvectors of two graphs, known test cases are used to verify the effectiveness of the approach.

A Systematic Formulation of Overconstraint Conditions in Kinematic Chains by Displacement Groups

2005 ◽  
Author(s):  
Carlo Galletti ◽  
Pietro Fanghella ◽  
Elena Giannotti
Keyword(s):  
Dynamic Analysis ◽  
Systematic Approach ◽  
Computer Code ◽  
Computer Implementation ◽  
Mobility Analysis ◽  
Kinematic Synthesis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Geometric Data ◽  
Systematic Formulation

The paper describes a systematic approach to define geometrical and dimensional overconstraint conditions for single-loop kinematic chains of both “banal” and “exceptional” types. The approach is an application of the theory of displacement groups. It presents several interesting features: it can be easily integrated with mobility analysis; it makes use of geometric data local to links and does not require a preliminary mechanism assembly nor a given initial congruent position; it is systematic and can be suitably implemented in a computer code; it suggests where geometrical and dimensional tolerances have to be located; it can be embedded in other group-based approaches, like kinematic synthesis or dynamic analysis. After a brief summary of the properties of displacement groups and their operations, the paper shows how they can be used to formulate systematically the overconstraint conditions in kinematic chains. A computer implementation of the approach is also outlined, and several examples with different complexities are given.

Detection of Isomorphism Between Planar Kinematic Chains

1987 ◽  
Author(s):  
L. K. Patel ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Efficient Method ◽  
Computational Effort ◽  
New Method ◽  
Structural Topology ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Analysis And Synthesis

Abstract Structural analysis and synthesis of linkages is a very important aspect. Detection of isomorphism (equivalent structural topology) is essential to determine structurally distinct chains. Some methods to detect distinct chains and mechanisms have already been developed. These methods besides being falliable, require enormous computational effort and as such necessitate development of an easy and efficient method. This paper presents a new method based on graph theory, for detection of isomorphism among kinematic chains. A probability scheme is attached with the chains and relative loop positions are determined for the chains having identical probability schemes. Isomorphism is detected between planar kinematic chains having single degree of freedom.

Linkage Characteristic Polynomials: Definitions, Coefficients by Inspection

1981 ◽  
Vol 103 (3) ◽  
pp. 578-584 ◽  
Author(s):  
H. S. Yan ◽  
A. S. Hall
Keyword(s):  
Structural Analysis ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Companion Paper ◽  
Characteristic Polynomials ◽  
Kinematic Chains ◽  
Analysis And Synthesis

A linkage characteristic polynomial is defined as the characteristic polynomial of the adjacency matrix of the kinematic graph of the kinematic chain. Some terminology and definitions, needed for discussions to follow in a companion paper, are stated. A rule from which all coefficients of the characteristic polynomial of a kinematic chain can be identified by inspection, based on the interpretation of a graph determinant, is derived and presented. This inspection rule interprets the topological meanings behind each characteristic coefficient, and might have some interesting possible uses in studies of the structural analysis and synthesis of kinematic chains.

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.

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