Characterizations of Fully Constrained Poses of Parallel Cable-Driven Robots: A Review

2008 ◽  
Author(s):  
Marc Gouttefarde
Keyword(s):  
Linear Algebra ◽  
Convex Cones ◽  
Mobile Platform ◽  
Polyhedral Cones ◽  
Fundamental Properties ◽  
Special Cases ◽  
Force Closure

The pose of the mobile platform of a parallel cable-driven robot is said to be fully constrained if any wrench can be created at the platform by pulling on it with the cables. A fully constrained pose is also known as a force-closure pose. In this paper, a review of three useful characterizations of a force-closure pose is proposed. These characterizations are stated in the form of theorems for which proofs are presented. Tools from linear algebra allow to derive some of these proofs while the others are more difficult and can hardly be obtained in this manner. Therefore, polyhedral cones, which are special cases of convex cones, are introduced along with some of their well-known fundamental properties. Then, it is shown how the aforementioned difficult proofs can be obtained as direct consequences of these properties.

Complementarity Problem and Duality Over Convex Cones

1974 ◽  
Vol 17 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Abraham Berman
Keyword(s):  
Complementarity Problem ◽  
Complementarity Problems ◽  
Convex Cones ◽  
Polyhedral Cones ◽  
Quadratic Programs ◽  
The Real ◽  
Special Cases

AbstractThe complementarity problem is defined and studied for cases where the constraints involve convex cones, thus extending the real and complex complementarity problems. Special cases of the problem are equivalent to dual, linear or quadratic, programs over polyhedral cones.

Critical angles between two convex cones II. Special cases

Top ◽  
2015 ◽  
Vol 24 (1) ◽  
pp. 66-87 ◽  
Author(s):  
Alberto Seeger ◽  
David Sossa
Keyword(s):  
Convex Cones ◽  
Special Cases

scholarly journals Multicriteria Decision Making Based on Archimedean Bonferroni Mean Operators of Hesitant Fermatean 2-Tuple Linguistic Terms

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Huijuan Wang ◽  
Xin Wang ◽  
Lidong Wang
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Decision Makers ◽  
Linguistic Terms ◽  
Fundamental Properties ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Geometric Bonferroni Mean ◽  
Parameter Values ◽  
Uncertainty Information

The study is concerned with the representation and aggregation of complex uncertainty information. First, the concept of hesitant Fermatean 2-tuple linguistic sets (HF2TLSs) is introduced for characterizing an individual’s imprecision preferences and assessing information by combining 2-tuple linguistic terms and Fermatean fuzzy sets. The advantage of hesitant Fermatean 2-tuple linguistic information is that it can handle higher levels of uncertainty and express the decision-makers’ hesitancy. Second, we extend Bonferroni mean (BM) operators under the background of HF2TLSs for the sake of their application in information fusion and decision making. The Archimedean t-norm and s-norm- (ATS-) based hesitant Fermatean 2-tuple linguistic weighted Bonferroni mean (A-HF2TLWBM) operator and the ATS-based hesitant Fermatean 2-tuple linguistic weighted geometric Bonferroni mean (A-HF2TLWGBM) operator are developed by considering the interrelationship between any two variables. The main benefit of the proposed operators is that these operators deliver more complete and flexible results compared to existing methods. Moreover, some fundamental properties and special cases are examined by adjusting parameter values. Finally, an approach is designed as a support for handling decision making problems, and an example regarding investment selection is provided to demonstrate the practicality of the designed method with a detailed discussion of parameter influence and comparisons with the existing methods.

scholarly journals Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions

2021 ◽  
Vol 18 (5) ◽  
pp. 6552-6580
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Pshtiwan Othman Mohammed ◽  
Muhammad Aslam Noor ◽  
Khadijah M. Abualnaja ◽  
...  
Keyword(s):  
Order Relation ◽  
Strong Relationship ◽  
Double Integral ◽  
New Class ◽  
Fundamental Properties ◽  
Starting Point ◽  
Special Cases ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>In this study, we introduce and study new fuzzy-interval integral is known as fuzzy-interval double integral, where the integrand is fuzzy-interval-valued functions (FIVFs). Also, some fundamental properties are also investigated. Moreover, we present a new class of convex fuzzy-interval-valued functions is known as coordinated convex fuzzy-interval-valued functions (coordinated convex FIVFs) through fuzzy order relation (FOR). The FOR $\left(\preccurlyeq \right)$ and fuzzy inclusion relation (⊇) are two different concepts. With the help of fuzzy-interval double integral and FOR, we have proved that coordinated convex fuzzy-IVF establish a strong relationship between Hermite-Hadamard (<italic>HH</italic>-) and Hermite-Hadamard-Fejér (<italic>HH</italic>-Fejér) inequalities. With the support of this relation, we also derive some related <italic>HH</italic>-inequalities for the product of coordinated convex FIVFs. Some special cases are also discussed. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.</p> </abstract>

Generalized Maps

2020 ◽  
pp. 157-170
Author(s):  
Daniel Canarutto
Keyword(s):  
Hilbert Space ◽  
Fourier Transforms ◽  
Tensor Products ◽  
Hermitian Structure ◽  
Quantum Geometry ◽  
Basic Notion ◽  
Rigged Hilbert Space ◽  
Fundamental Properties ◽  
Special Cases ◽  
Generalized Maps

Spaces of generalised sections (also called section-distributions) are introduced, and their fundamental properties are described. Several special cases are considered, with particular attention to the case of semi-densities; when a Hermitian structure on the underlying classical bundle is given, these determine a rigged Hilbert space, which can be regarded as a basic notion in quantum geometry. The essentials of tensor products in distributional spaces, kernels and Fourier transforms are exposed.

More Discoveries in Linear Algebra

1976 ◽  
Vol 69 (1) ◽  
pp. 56-58
Author(s):  
Darrell Wellen
Keyword(s):  
Linear Algebra ◽  
Mathematics Teacher ◽  
Recent Issue ◽  
Special Cases

In a recent issue of the Mathematics Teacher, Nicolai (1974) detailed several “discoveries” in linear algebra that were made by him and one of his classes. A look at their ideas yielded several discoveries showing that the relationships described by Nicolai are special cases of more general, interesting situations.

Linear algebra algorithms as dynamical systems

Acta Numerica ◽  
2008 ◽  
Vol 17 ◽  
pp. 1-86 ◽  
Author(s):  
Moody T. Chu
Keyword(s):  
Dynamical Systems ◽  
Linear Algebra ◽  
Iterative Procedure ◽  
Numerical Algorithms ◽  
Great Effort ◽  
Open Problems ◽  
Special Cases ◽  
Specific Rule ◽  
Discrete Methods ◽  
Realization Process

Any logical procedure that is used to reason or to infer either deductively or inductively, so as to draw conclusions or make decisions, can be called, in a broad sense, a realization process. A realization process usually assumes the recursive form that one state develops into another state by following a certain specific rule. Such an action is generally formalized as a dynamical system. In mathematics, especially for existence questions, a realization process often appears in the form of an iterative procedure or a differential equation. For years researchers have taken great effort to describe, analyse, and modify realization processes for various applications.The thrust in this exposition is to exploit the notion of dynamical systems as a special realization process for problems arising from the field of linear algebra. Several differential equations whose solutions evolve in submanifolds of matrices are cast in fairly general frameworks, of which special cases have been found to afford unified and fundamental insights into the structure and behaviour of existing discrete methods and, now and then, suggest new and improved numerical methods. In some cases, there are remarkable connections between smooth flows and discrete numerical algorithms. In other cases, the flow approach seems advantageous in tackling very difficult open problems. Various aspects of the recent development and application in this direction are discussed in this paper.

scholarly journals A Contextual Foundation for Mechanics, Thermodynamics, and Evolution

2020 ◽  
Author(s):  
Harrison Crecraft
Keyword(s):  
Classical Mechanics ◽  
Objective Measure ◽  
Positive Temperature ◽  
Spontaneous Transition ◽  
Fundamental Properties ◽  
Special Cases ◽  
Evolution Of Life ◽  
Measurable Rate ◽  
Definition Of ◽  
Evolutionary Paths

The prevailing interpretations of physics are based on deeply entrenched assumptions, rooted in classical mechanics. Logical implications include: the denial of entropy and irreversible change as fundamental properties of state; the inability to explain random quantum measurements and nonlocality without unjustifiable assumptions and untestable metaphysical implications; and the inability to explain or even define the evolution of complexity. The dissipative conceptual model (DCM) is based on empirically justified assumptions. It generalizes mechanics&rsquo; definition of state by acknowledging the contextual relationship between a physical system and its positive-temperature ambient background, and it defines the DCM entropy as a fundamental contextual property of physical states. The irreversible production of entropy establishes the thermodynamic arrow of time and a system&rsquo;s process of dissipation as fundamental. The DCM defines a system&rsquo;s utilization by the measurable rate of internal work on its components and as an objective measure of stability for a dissipative process. The spontaneous transition of dissipative processes to higher utilization and stability defines two evolutionary paths. The evolution of life proceeded by both competition for resources and cooperation to evolve and sustain higher functional complexity. The DCM accommodates classical and quantum mechanics and thermodynamics as idealized non-contextual special cases.

scholarly journals Some applications of Srivastava’s theorem involving a certain family of generalized and extended hypergeometric polynomials

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1811-1819 ◽  
Author(s):  
Shy-Der Lin ◽  
H.M. Srivastava ◽  
Mu-Ming Wong
Keyword(s):  
Generating Functions ◽  
Hypergeometric Functions ◽  
Integral Transforms ◽  
Pochhammer Symbol ◽  
Generalized Hypergeometric Functions ◽  
Fundamental Properties ◽  
Hypergeometric Polynomials ◽  
Special Cases

Recently, Srivastava et al. [H. M. Srivastava, M. A. Chaudhry and R. P. Agarwal, The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms Spec. Funct. 23 (2012), 659-683] introduced and initiated the study of many interesting fundamental properties and characteristics of a certain pair of potentially useful families of the so-called generalized incomplete hypergeometric functions. Ever since then there have appeared many closely-related works dealing essentially with notable developments involving various classes of generalized hypergeometric functions and generalized hypergeometric polynomials, which are defined by means of the corresponding incomplete and other novel extensions of the familiar Pochhammer symbol. Here, in this sequel to some of these earlier works, we derive several general families of hypergeometric generating functions by applying Srivastava?s Theorem. We also indicate various (known or new) special cases and consequences of the results presented in this paper.

Preliminary Results and Discussion

2011 ◽  
Author(s):  
Shaun M. Fallat ◽  
Charles R. Johnson
Keyword(s):  
Linear Algebra ◽  
Matrix Theory ◽  
Preliminary Results ◽  
Fundamental Properties ◽  
Core Matrix ◽  
Determinantal Identities ◽  
Further Development

This chapter lays out a number of basic and fundamental properties of TN matrices along with a compilation of facts and results from core matrix theory that are useful for further development of this topic. Along with the elementary bidiagonal factorization, the rules for manipulating determinants and special determinantal identities constitute the most useful tools for understanding TN matrices. Some of this technology is simply from elementary linear algebra, but the less well-known identities are given here for reference. In addition, other useful background facts are entered into the record, and a few elementary and frequently used facts about TN matrices are presented.

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