An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Quantitative Measure ◽  
Simple Algorithm ◽  
Isomorphism Problem ◽  
Innovative Approach ◽  
Two Degrees Of Freedom ◽  
Kinematic Chains ◽  
Topological Characteristics ◽  
Interesting Area

Detection of isomorphism in planar and geared kinematic chains (GKCs) is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept “Net distance” is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains (PKCs) as well as GKCs. The proposed algorithm is applied on nine-link two-degrees-of-freedom (DOF) distinct kinematic chains completely and the results are presented. Algorithm is tested on examples from eight-link 1-DOF, ten-link 1-DOF, 12-link 1-DOF, and 15link 4-DOF PKCs. The algorithm is also tested on four-, six-link 1-DOF GKCs to detect isomorphism. All the results are in agreement with the existing literature.

Modified joint connectivity approach for identification of topological characteristics of planar kinematic chains

2011 ◽  
Vol 225 (11) ◽  
pp. 2700-2717 ◽  
Author(s):  
G S Bedi ◽  
S Sanyal
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Kinematic Chains ◽  
Multiple Degrees Of Freedom ◽  
Preferred Frame ◽  
Topological Characteristics ◽  
Synthesis Stage ◽  
Different Levels ◽  
Selection Of

In a kinematic chain, the links are connected to each other through joints. The connectivity of a joint indicates the number of joints to which it is connected. The connectivity level of a joint indicates the distance by which it is separated from the adjacent joints. The concept of joint connectivity and its application to detect isomorphism among kinematic chains and their inversions has been already reported by authors. The method utilizes the connectivity of joints at different levels to detect isomorphism and inversions among planar kinematic chains. The method is applied to eight-, nine-, and ten-link planar kinematic chains. The results so obtained are in agreement with those available in the literature. In this study, the method is further improved by incorporating the type of joint to make it more effective for the detection of isomorphism and distinct inversions. A joint connectivity table completely representing the kinematic chain is proposed. The application of the method is extended for the determination of additional topological characteristics of chains such as categorization of kinematic chains and selection of preferred frame, input and output links for function and path generation. The concept of ‘Motion Transfer Ability’ is introduced and utilized to develop numerical measures for comparing and categorizing the chains at the synthesis stage of mechanism design for a specific application. The method was successfully tested on planar kinematic chains with single and multiple degrees of freedom and the results for eight- and nine-link kinematic chains are appended.

Topological Representations and Characteristics of Variable Kinematic Joints

2005 ◽  
Vol 128 (2) ◽  
pp. 384-391 ◽  
Author(s):  
Hong-Sen Yan ◽  
Chin-Hsing Kuo
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Structural Synthesis ◽  
Characteristic Analysis ◽  
Push Button ◽  
Walking Machines ◽  
Operation Process ◽  
Variable Topology ◽  
Topological Characteristics ◽  
Kinematic Joint

There exist some mechanisms with variable topologies that have interesting applications, for examples, legged walking machines, mechanical push-button stopper locks, and various toys. A variable kinematic joint is a kinematic joint that is capable of topological variation in a mechanism with variable topology. This work aims at the topological representations and characteristic analysis of variable kinematic joints. During the operation process of a mechanism, the topology states of a variable kinematic joint can be expressed symbolically as the joint sequences, graphically the digraphs, and mathematically the matrices. With the applications of graph theory, it proves that the topological characteristics of variable kinematic joints appeared with the abilities of reversibility, continuity, variability of degrees of freedom, joint homomorphism, contractibility, and expansibility. Two examples are provided for illustrating how the proposed concepts can be used to analyze and synthesize the variable joints. The results of this work provide a logical foundation for the systematic structural synthesis regarding the kinematic joints and mechanisms with variable topologies.

On the Flexibility of Spatial Kinematic Chains

1986 ◽  
Vol 10 (4) ◽  
pp. 213-218
Author(s):  
A.C. Rao
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Arrangement ◽  
Kinematic Chains ◽  
Single Degree ◽  
A Chain ◽  
Space Mechanisms

A number of distinct or non-isomorphic kinematic chains exist for a specified number of links and joints. For example, sixteen distinct chains can be obtained with eight links and two hundred and thirty chains with ten links having a single degree of freedom. Similarly, many space mechanisms can be formed with four links and joints having different degrees of freedom. So far no measure is available to know which of these possesses greater mobility or flexibility. Flexibility is not to be confused with the degree of freedom. Intuitively one feels that a six-link chain has greater flexibility than a four-bar chain both having the same degrees of freedom. Though the mobility of a chain increases with the number of links one is not sure how the structural arrangement, type of links and joints, their numbers and sequence etc. influence the same. Combining graph theory with the concepts of probability, simple formulae are developed to investigate the relative merits of spatial and planar kinematic chains. The greater the flexibility or mobility of the chain, the higher is the ability to meet the motion requirements, i.e., a chain having greater entropy can be expected, say, to reproduce a given function more accurately.

Feasibility Study of a Hand Exoskeleton for Rehabilitation of Post-Stroke Patients

2012 ◽  
Author(s):  
Marco Troncossi ◽  
Mohammad Mozaffari Foumashi ◽  
Marco Carricato ◽  
Vincenzo Parenti Castelli
Keyword(s):  
Feasibility Study ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Design Issues ◽  
Stroke Patients ◽  
Two Degrees Of Freedom ◽  
Kinematic Chains ◽  
Basic Module ◽  
Post Stroke ◽  
Hand Exoskeleton

This paper illustrates the activity done by the authors for the development of a hand exoskeleton with two degrees of freedom addressed to the rehabilitation of post-stroke patients. The literature is investigated and many design issues are deeply discussed with the purpose to provide a reader who is approaching this problem with useful guidelines. The feasibility study of a one degree of freedom mechanism for one finger, intended as the basic module of the targeted hand exoskeleton, is outlined: two kinematic chains having six and eight links respectively are presented and discussed.

Dead Center Identification of Two-Degrees-of-Freedom Planar Parallel Manipulator Using Graph Theory and Transmission Angle

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Liangyi Nie ◽  
Huafeng Ding
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Fundamental Problem ◽  
Parallel Manipulators ◽  
Design Stage ◽  
Two Degrees Of Freedom ◽  
Operation Speed ◽  
Transmission Angle ◽  
The Dead ◽  
Independent Loops

Abstract Parallel manipulators are widely applied for their advantages of high stiffness, load-bearing, operation speed, and precision positioning capabilities, which are required in many industrial applications. However, dead center identification is a challenging task and fundamental problem during design stage of parallel manipulators, and becomes more intractable for two-degrees-of-freedom (DOF) complex planar parallel manipulators (PPMs) design. This paper proposes a method to identify the dead center positions of two-DOF PPMs based on graph theory and transmission angle. First, these PPMs are denoted by a set of independent loops using a topological structural analysis of the kinematic chains and structural decomposition. Then, the relationship between the mobility factor and the loop factor in the same independent loop is utilized to obtain the folded or stretched operation to form the new PPMs containing the corresponding instantaneous virtual loop. Subsequently, the dead center positions can be located since the corresponding transmission angle of the new PPMs is equal to 0 deg or 180 deg. As a result, the solved dead center positions of the two-DOF three types seven-bar, nine-bar, and 11-bar PPMs will provide guidance for the proper design of these PPMs. Finally, the Jacobian method for identifying the dead center position is then used to verify the proposed method. The proposed method is systematic and programmable and can be applied to any two-DOF PPM regardless of the number of independent loops or types of joints.

The Creation of a Multi-Link Load Balancing Mechanism for Planetary Gearing: Part 1 — Type Synthesis

1992 ◽  
Author(s):  
Zhang Hong ◽  
Ting Li Yang ◽  
Jin Kui Chu ◽  
Wei-qing Cao
Keyword(s):  
Load Balancing ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Kinematic Structure ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Topological Parameters ◽  
Topological Characteristics ◽  
The Creation

Abstract This series of papers design a multi-link load balancing mechanism for the Planetary Gearings with arbitrary number of planet gears. Based on the study of SGP load balancing mechanisms, this paper analyzed the relations between the function and kinematic structure of the multilink load balancing mechanism, and presented the topological characteristics and parameters of the kinematic chains suited for load balancing mechanism. Those topological parameters depend on the number of planet gears. In the type synthesis for the case of six planet gears, the kinematic chains with five degrees of freedom and eighteen links were enumerated according to the topological characteristics. The resulting mechanisms were 15 candidate multi-link load balancing mechanism.

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