Analysis on Degree of Freedom and Singularity of Mechanism Based on Topological Graph Theory

Topological Graph ◽

Topological Graph Theory ◽

Hybrid Mechanism ◽

Definition Of ◽

Case Number

Based on the analysis of current developing state of graph theory, define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the new description method in topological graph theory. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented, as well as the necessary and sufficient condition of singularity of mechanism deduced , in-phase and assimilation condition and in-phase and dissimilarity condition and asynchronism condition of limitation of input base of branch adopted, case number of position singularity and pose singularity and position and pose singularity obtained then, still the way of founding the combination and case number of common serial mechanism and parallel mechanism and hybrid mechanism mentioned.

New Machine for Complex Structure Decoration Materials

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.178-181.262 ◽

2012 ◽

Vol 178-181 ◽

pp. 262-266

Author(s):

Jian Guo Luo ◽

Mao Yan He

Keyword(s):

Complex Structure ◽

Three Dimensional ◽

Influential Factors ◽

Degree Of Freedom ◽

Topological Graph ◽

Working Space ◽

Hybrid Mechanism ◽

Definition Of ◽

Six Degree Of Freedom ◽

A new type of machine for complex structure decoration materials based on hybrid cubic manipulator with six degree of freedom(DOF) suggested in view of traditional serial manipulator and parallel manipulator, three dimensional translation and rotation of output shaft obtained through lineal driving. Define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the fact of mechanism consists of components, a new description method by topological graph theory of components relationship suggested, new description of serial mechanism and parallel mechanism and hybrid mechanism obtained with this method, description elements include component pane and constrained component pane and component relationship line and constrained component relationship line and spacial relative moving capability between adjacent components. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented. Method of analytic geometry used to find the regular cuboid of the reachable working space shape of mechanism, the volume of the reachable working space rest with the limit of translation of couplers, its influential factors obtained, limit length of guideway etc. are the primary influential factors.

A generalized inversion formula for the continuous Jacobi transform

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171287000796 ◽

1987 ◽

Vol 10 (4) ◽

pp. 671-692 ◽

Cited By ~ 4

Author(s):

Ahmed I. Zayed

Keyword(s):

Analytic Function ◽

Inversion Formula ◽

Generalized Functions ◽

Generalized Function ◽

Sufficient Condition ◽

Generalized Inversion ◽

Definition Of ◽

Jacobi Transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.

On the Indispensability of Intentionality

Canadian Journal of Philosophy ◽

10.1080/00455091.1972.10716869 ◽

1972 ◽

Vol 2 (1) ◽

pp. 127-133

Author(s):

Harold Morick

Keyword(s):

Recent Literature ◽

Essential Property ◽

Sufficient Condition ◽

Conceptual Scheme ◽

Definition Of ◽

In the last two decades, there has been a great deal of interest in providing an intentional criterion of the psychological. Of the various ones proferred, it seems to me that the best was the earliest, which was Chisholm’s initial criterion in his 1955 essay “Sentences about Believing.” In this present paper I first single out a basic misconception pervading the recent literature on intentionality and suggest that a consequence of this misconception has been the futile attempt to use the notion of intentionality to provide a kind of definition of “mind”; that is, to use intentionality to provide a necessary and sufficient condition for the psychological. Secondly, I point out how intentionality as captured by my own criterion is indispensable in that it is an essential property of certain particulars (persons) which are basic to our conceptual scheme and apparently basic to any conceptual scheme whatsoever.

Some results concerning frames in Banach spaces

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.38.2007.80 ◽

2007 ◽

Vol 38 (3) ◽

pp. 267-276 ◽

Cited By ~ 3

Author(s):

S. K. Kaushik

Keyword(s):

Finite Number ◽

Banach Spaces ◽

Necessary Condition ◽

Sufficient Condition ◽

Linearly Independent ◽

Banach Frame ◽

Minimal Sequence ◽

Definition Of ◽

A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.

A necessary and sufficient condition for the total unimodularity of a matrix in terms of graph theory

Optimization ◽

10.1080/02331938908843511 ◽

1989 ◽

Vol 20 (6) ◽

pp. 901-914 ◽

Cited By ~ 1

Author(s):

L. Hempel ◽

U. Herrmann ◽

W. Hölzer ◽

R. Wetzel

Keyword(s):

Graph Theory ◽

Sufficient Condition ◽

Total Unimodularity ◽

The competition number of a generalized line graph is at most two

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.575 ◽

2012 ◽

Vol Vol. 14 no. 2 (Graph Theory) ◽

Author(s):

Boram Park ◽

Yoshio Sano

Keyword(s):

Graph Theory ◽

Necessary Conditions ◽

Line Graph ◽

Sufficient Conditions ◽

Line Graphs ◽

Sufficient Condition ◽

International Audience ◽

Competition Number

Graph Theory International audience In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this paper, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient conditions for the competition number of a generalized line graph being one.

Detection of Improper General Spatial Kinematic Chains With Different Types of Pairs

23rd Biennial Mechanisms Conference: Mechanism Synthesis and Analysis ◽

10.1115/detc1994-0210 ◽

1994 ◽

Author(s):

Xian-Wen Kong ◽

Ting-Li Yang

Keyword(s):

Unsolved Problem ◽

Degree Of Freedom ◽

Sufficient Condition ◽

Single Degree Of Freedom ◽

Kinematic Chains ◽

Single Degree ◽

Different Types ◽

Topological Synthesis

Abstract Improper general spatial kinematic chains (GSKCs) due to the effect of pair types may be generated during the process of topological synthesis of GSKCs with different types of pairs. Thus, detection of improper GSKCs is necessary in topological synthesis of GSKCs with different types of pairs. Unfortunately, it is still an unsolved problem. In this paper, a method for detecting improper GSKCs is presented. Both a necessary and sufficient condition and a sufficient condition for proper GSKCs with R, P, H, T and C pairs are introduced at first. Based on these two conditions, an algorithm to detect improper GSKCs is then developed which is very efficient and suitable for topological synthesis of GSKCs with R, P, H, T and C pairs. The proposed algorithm has been applied to topological synthesis of 1- and 2-loop, single degree of freedom GSKCs with R, P, H, T and C pairs and the corresponding atlas is obtained.

Rational valued and real valued projective characters of finite groups

Glasgow Mathematical Journal ◽

10.1017/s0017089500003943 ◽

1980 ◽

Vol 21 (1) ◽

pp. 23-28 ◽

Cited By ~ 6

Author(s):

J. F. Humphreys

Keyword(s):

Symmetric Group ◽

Finite Groups ◽

General Information ◽

Sufficient Condition ◽

Complex Character ◽

Definition Of ◽

A Finite Group ◽

Spin Characters

It is well-known [3; V.13.7] that each irreducible complex character of a finite group G is rational valued if and only if for each integer m coprime to the order of G and each g ∈ G, g is conjugate to gm. In particular, for each positive integer n, the symmetric group on n symbols, S(n), has all its irreducible characters rational valued. The situation for projective characters is quite different. In [5], Morris gives tables of the spin characters of S(n) for n ≤ 13 as well as general information about the values of these characters for any symmetric group. It can be seen from these results that in no case are all the spin characters of S(n) rational valued and, indeed, for n ≥ 6 these characters are not even all real valued. In section 2 of this note, we obtain a necessary and sufficient condition for each irreducible character of a group G associated with a 2-cocycle α to be rational valued. A corresponding result for real valued projective characters is discussed in section 3. Section 1 contains preliminary definitions and notation, including the definition of projective characters given in [2].

Normal Modal Vibrations for Some Damped n-Degree-of-Freedom Nonlinear Systems

Journal of Applied Mechanics ◽

10.1115/1.3625196 ◽

1966 ◽

Vol 33 (4) ◽

pp. 877-880 ◽

Cited By ~ 4

Author(s):

George W. Morgenthaler

Keyword(s):

Nonlinear Systems ◽

Normal Mode ◽

Nonlinear Vibrations ◽

Normal Modes ◽

Degree Of Freedom ◽

Sufficient Condition ◽

Damping Matrix ◽

Do So

T. K. Caughey1 has shown that a necessary and sufficient condition that a damped, linear, n-degree-of-freedom system possess classical linear normal modes is that the damping matrix be diagonalized by the same transformation which uncouples the undamped system. Rosenberg2 has defined normal modes for nonlinear n-degree-of-freedom undamped systems and has shown the existence of such modes for various classes of nonlinear systems. In linear systems, the frequency is independent of the amplitude and, if a set of masses is vibrating in unison, it is not surprising that in some cases they continue to do so as the motion damps out. In nonlinear vibrations, however, frequency depends upon amplitude so that a series of masses vibrating at different amplitudes in a Rosenberg normal mode might generally be expected to lose synchronization as their amplitudes damp out. Two classes of systems are discussed here in which normal modes are preserved under damping, and several examples are given.