Structural Analysis and Mobility Test of Fourteen Links Kinematic Chain Using Graph Theory

2014 ◽  
Vol 592-594 ◽  
pp. 1165-1169
Author(s):  
Preeti Gulia ◽  
V.P. Singh
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Reliable Method ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Degree Of Freedom ◽  
Mobility Test ◽  
Structural Problems ◽  
Algebraic Test

The present work is focused on the graph theory which is used for structural analysis of kinematic chain and identification of degree of freedom. A method based on graph theory is proposed in this paper to solve structural problems by using a suitable example of fourteen links kinematic chain. Purpose of this paper is to give an easy and reliable method for structural analysis of fourteen links kinematic chain. Here, a simple incidence matrix is used to represent the kinematic chain. The proposed method is applied for determining the characteristic polynomial equation of fourteen links kinematic chain. An algebraic test based on graph theory is also used for identifying degree of freedom of kinematic chain whether it is total, partial or fractionated degree of freedom.

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.

Generation of Epicyclic Gear Trains of One Degree of Freedom

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Y. V. D. Rao ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Hamming Matrix

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

scholarly journals Structural Analysis of Linkage Mechanisms of Hydraulic Manipulators

2019 ◽  
pp. 74-90
Author(s):  
M.A. Piskunov
Keyword(s):  
Structural Analysis ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Technological Processes ◽  
Hydraulic Manipulators ◽  
Assur Group ◽  
Individual Input

The structural schemes of hydraulic manipulators used in the roundwood handling operations are presented. The seventeen schemes of manipulators are considered. The characteristic technological processes are identified, the nominal motions of the attachment mounted on the manipulator are described and the structure of the manipulator used in each process is considered. The variety of structures of linkage mechanisms in manipulators is associated both with the accumulation of Assur groups and with the increase in the Assur group class. Mechanisms with the number of Assur groups up to 4 are used. Assur groups of 2nd and 3rd classes are mainly found in the mechanisms. Adding the degree of freedom to the manipulator is accompanied by emerging of an additional kinematic chain in the structure. The structures studied are divided into two groups: the first covers the structures in which the input links are attached to the column; the second consists of structures with internal inputs. Variants of additional classification features are proposed for structures with internal inputs. The known provisions of structural analysis as a whole allow the analysis to be performed if the internal input is separated out as an individual input link. Otherwise, it is necessary to correct the approaches to the structural analysis of mechanisms having internal input links.

Parallelism in Planar Manipulators: A Measure

2005 ◽  
Vol 128 (1) ◽  
pp. 66-68 ◽  
Author(s):  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Mechanical Advantage ◽  
Work Space ◽  
Planar Manipulators ◽  
Robotic Applications

Parallelism can be associated with every closed kinematic chain or its representative graph. Parallelism throws light on work space, rigidity, speed ratios (mechanical advantage), etc., and is of great help in selecting multi degree-of-freedom (dof) chains for robotic applications. Numerous distinct chains with the same number of links and dof exist. The extent of parallelism differs from chain to chain and hence a numerical measure is necessary to quantify the same so that the designer gains insight simply based on the structure without having to actually design all the distinct chains before selecting the best chain for the specified task. To the author’s knowledge, no measure is available in graph theory to quantify the extent of parallelism and the present work is an attempt in this direction.

Some Applications of Graph Theory to the Structural Analysis of Mechanisms

1967 ◽  
Vol 89 (1) ◽  
pp. 153-158 ◽  
Author(s):  
L. Dobrjanskyj ◽  
F. Freudenstein
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Mechanical Systems ◽  
Kinematic Chains ◽  
Computerized Method ◽  
Spatial Mechanisms ◽  
Structural Identity ◽  
Computer Aided ◽  
Systematic Enumeration

Concepts in graph theory, which have been described elsewhere [2, 4, 6] have been applied to the development of (a) a computerized method for determining structural identity (isomorphism) between kinematic chains, (b) a method for the automatic sketching of the graph of a mechanism defined by its incidence matrix, and (c) the systematic enumeration of general, single-loop constrained spatial mechanisms. These developments, it is believed, demonstrate the feasibility of computer-aided techniques in the initial stages of the design of mechanical systems.

Structural and Static Analysis of the Mechanisms Used in Car Mechanical Jacks

2016 ◽  
Vol 823 ◽  
pp. 277-282
Author(s):  
Viorica Velișcu ◽  
Dan Mesarici ◽  
Păun Antonescu
Keyword(s):  
Structural Analysis ◽  
Static Analysis ◽  
Kinematic Chain ◽  
Gravity Force ◽  
Complex Mechanisms

The paper presents a structural analysis of the complex mechanisms type screw-jack. The mechanism mobilityanalysis using various generally applicable formulas has been performed. A newkinematic scheme of the jack linkage has been proposed. Besides the actuatorscrew, it has a planar kinematic chain with articulated bars. With regard tothis new mechanism, an algorithm for static calculus has been developed, inwhich the automobile gravity force is the main exterior force.

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).

A Method for Detection of Distinct Mechanisms of a Planar Kinematic Chain

1988 ◽  
Vol 12 (1) ◽  
pp. 15-20 ◽  
Author(s):  
L.K. Patel ◽  
A.C. Rao
Keyword(s):  
Efficient Method ◽  
Numerical Scheme ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
A Chain

This paper presents a computationally simple and efficient method for identification of distinct mechanisms of a planar kinematic chain having a single degree of freedom. It is proposed that velocity diagrams for all the inversions of a chain be drawn and the possible isomorphism among these velocity diagrams be detected. From the velocity diagram, a motion transfer point matrix can be prepared resulting in the development of a numerical scheme to be associated with a mechanism. Identical schemes lead to detection of isomorphism between mechanisms. The main advantage of this method is that, apart form detecteing isomorphism, it indicates which of the inversions is better kinematically e.g. higher the total number of vectors, better is the mechanism.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

Structural Analysis of the Human Knee Kinematic Chain

2020 ◽  
pp. 27-34
Author(s):  
Esdras Salgado da Silva ◽  
Leonardo Mejia Rincon ◽  
Elias Renã Maletz ◽  
Daniel Martins
Keyword(s):  
Structural Analysis ◽  
Kinematic Chain ◽  
Knee Kinematic ◽  
Human Knee
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