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Academic literature on the topic 'Essential singularities'

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Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Essential singularities"

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Gauld, D. B., and G. J. Martin. "Essential singularities of quasimeromorphic mappings." MATHEMATICA SCANDINAVICA 73 (December 1, 1993): 36. http://dx.doi.org/10.7146/math.scand.a-12454.

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Cosgrove, Christopher M. "Painlevé Classification Problems Featuring Essential Singularities." Studies in Applied Mathematics 98, no. 4 (May 1997): 355–433. http://dx.doi.org/10.1111/1467-9590.00053.

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Dethloff, Gerd-E. "On essential singularities of meromorphic mappings." Mathematische Annalen 283, no. 3 (September 1989): 499–509. http://dx.doi.org/10.1007/bf01442742.

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Qadir, Asghar. "Essential singularities of spherically symmetric space‐times." Journal of Mathematical Physics 33, no. 6 (June 1992): 2262–64. http://dx.doi.org/10.1063/1.529597.

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Ashley, Michael J. S. L. "The Stability of Abstract Boundary Essential Singularities." General Relativity and Gravitation 34, no. 10 (October 2002): 1625–35. http://dx.doi.org/10.1023/a:1020168106488.

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González Pérez, P. D., and F. Hernando. "Quasi-ordinary singularities, essential divisors and Poincaré series." Journal of the London Mathematical Society 79, no. 3 (April 30, 2009): 780–802. http://dx.doi.org/10.1112/jlms/jdp014.

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Alameer, Amerah. "Numerically stable conditions on rational and essential singularities." Complex Variables and Elliptic Equations 63, no. 5 (June 28, 2017): 640–51. http://dx.doi.org/10.1080/17476933.2017.1332049.

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Sinclair, GB. "Stress singularities in classical elasticity–I: Removal, interpretation, and analysis." Applied Mechanics Reviews 57, no. 4 (July 1, 2004): 251–98. http://dx.doi.org/10.1115/1.1762503.

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This review article has two parts, published in separate issues of this journal, which consider the stress singularities that occur in linear elastostatics. In the present Part I, after a brief review of the singularities that attend concentrated loads, attention is focused on the singularities that occur away from such loading, and primarily on 2D configurations. A number of examples of these singularities are given in the Introduction. For all of these examples, it is absolutely essential that the presence of singularities at least be recognized if the stress fields are to be used in attempts to ensure structural integrity. Given an appreciation of a stress singularity’s occurrence, there are two options open to the stress analyst if the stress analysis is to actually be used. First, to try and improve the modeling so that the singularity is removed and physically sensible stresses result. Second, to try and interpret singularities that persist in a physically meaningful way. Section 2 of the paper reviews avenues available for the removal of stress singularities. At this time, further research is needed to effect the removal of all singularities. Section 3 of the paper reviews possible interpretations of singularities. At this time, interpretations using the singularity coefficient, or stress intensity factor, would appear to be the best available. To implement an approach using stress intensity factors in a general context, two types of companion analysis are usually required: analytical asymptotics to characterize local singular fields; and numerical analysis to capture participation in global configurations. Section 4 of the paper reviews both types of analysis. At this time, methods for both are fairly well developed. Studies in the literature which actually effect asymptotic analyses of specific singular configurations will be considered in Part II of this review article. The present Part I has 182 references.
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Okuyama, Yûsuke, and Pekka Pankka. "Rescaling principle for isolated essential singularities of quasiregular mappings." Proceedings of the American Mathematical Society 143, no. 5 (December 3, 2014): 2043–50. http://dx.doi.org/10.1090/s0002-9939-2014-12378-1.

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OLDE DAALHUIS, A. B. "MIXED GEVREY ASYMPTOTICS." Analysis and Applications 06, no. 02 (April 2008): 151–68. http://dx.doi.org/10.1142/s0219530508001109.

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In this paper, we illustrate with two examples that the computation of Stokes multipliers in problems in which the asymptotic expansions are not of Gevrey order one, is much more complicated and that the singularities in the corresponding Borel plane can be essential singularities.
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Dissertations / Theses on the topic "Essential singularities"

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Ashley, Michael John Siew Leung, and ashley@gravity psu edu. "Singularity theorems and the abstract boundary construction." The Australian National University. Faculty of Science, 2002. http://thesis.anu.edu.au./public/adt-ANU20050209.165310.

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The abstract boundary construction of Scott and Szekeres has proven a practical classification scheme for boundary points of pseudo-Riemannian manifolds. It has also proved its utility in problems associated with the re-embedding of exact solutions containing directional singularities in space-time. Moreover it provides a model for singularities in space-time - essential singularities. However the literature has been devoid of abstract boundary results which have results of direct physical applicability.¶ This thesis presents several theorems on the existence of essential singularities in space-time and on how the abstract boundary allows definition of optimal em- beddings for depicting space-time. Firstly, a review of other boundary constructions for space-time is made with particular emphasis on the deficiencies they possess for describing singularities. The abstract boundary construction is then pedagogically defined and an overview of previous research provided.¶ We prove that strongly causal, maximally extended space-times possess essential singularities if and only if they possess incomplete causal geodesics. This result creates a link between the Hawking-Penrose incompleteness theorems and the existence of essential singularities. Using this result again together with the work of Beem on the stability of geodesic incompleteness it is possible to prove the stability of existence for essential singularities.¶ Invariant topological contact properties of abstract boundary points are presented for the first time and used to define partial cross sections, which are an generalization of the notion of embedding for boundary points. Partial cross sections are then used to define a model for an optimal embedding of space-time.¶ Finally we end with a presentation of the current research into the relationship between curvature singularities and the abstract boundary. This work proposes that the abstract boundary may provide the correct framework to prove curvature singularity theorems for General Relativity. This exciting development would culminate over 30 years of research into the physical conditions required for curvature singularities in space-time.
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Bouvier-Joly, Catherine. "Une approche des diviseurs essentiels des singularités algébriques." Grenoble 1, 1993. http://www.theses.fr/1993GRE10027.

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Pour une variete algebrique v, on cherche ici a caracteriser ceux parmi les diviseurs exceptionnels d'une desingularisation de v qui apparaissent aussi sur toutes les autres. Ils sont dits essentiels relativement a v. On se pose egalement le probleme de l'existence d'une desingularisation essentielle de v, dont les diviseurs exceptionnels sont les diviseurs exceptionnels sont tous essentiels. Une variete v torique et affine est associee a un semi-groupe dans un reseau; on en etudie le systeme generateur minimal g. On montre que les diviseurs essentiels pour les desingularisations equivariantes de v sont les orbites de codimension 1 du tore determinees par les elements de g. Si v est de dimension 3, on construit une desingularisation essentielle equivariante, ou g desingularisation, a partir d'un modele terminal minimal quelconque de v. En fait, une g-desingularisation se factorise toujours par un modele terminal minimal et elle est unique lorsque v est elle-meme terminale et q-factorielle. Les demonstrations portent sur la combinatoire des eventails. Dans le cas ou le corps de base est c, on utilise des resultats dus a mori pour etablir que les diviseurs essentiels equivariants restent essentiels pour les desingularisations non equivariantes. On donne aussi les exemples d'une variete torique de dimension 4, puis d'une variete de dimension 3 terminale d'indice 1, qui ne possedent pas de desingularisation essentielle
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Su, Yu-Cheng, and 蘇昱丞. "On Essential Components of Singularities." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/65717065044682698203.

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碩士
國立臺灣大學
數學研究所
99
The main purpose of this paper is to describe the correspondence between the　irreducible components of arc space of singularities and the essential components. In recent years, the development of motivic integration proposed by Kontsevich which was worked out by Denef and Loeser draws a lot of attention to the study of jet schemes and arc spaces. The study of arc spaces and jet schemes has become a very important and interesting tool in algebraic geometry, especially in the theory of singularities. Some important works are made by Denef-Loeser, Mustaţă, and Ein. In the milestone work of Nash, he proved the injectivity of the map mapping from the set of irreducible components of the space of arcs through singular points to the set of essential component of a resolution of singularities. We call this map the Nash map. He also asked whether this map is always bijective. In order to understand the Nash map explicitly, we consider many singularities in dimension two and three, and try to work out the correspondence explicitly. There are some potential difficulties. The first one is that in dimension three or higher, there is no “minimal resolution" in general. Therefore it is not easy to determine whether an exceptional divisor is essential or not. We can only see that those exceptional divisors with discrepancy not greater than one are essential. On the other hand, it is not clear how to determine irreducible components of arc space through singularities. We try to compute this explicitly in the straightforward manner. In this paper, we first introduce some notations and definitions to help us dealing with the problem. After that in section four, we try to find those essential components over a 2-dimensional singularity via the minimal resolution of surface. We also make some discussion on discrepancy of exceptional divisors for 3-dimensional terminal cases to obtain the essential components. Next, we try to determine the irreducible components of the space of arcs through the singularities. At the end, we consider a 3-dimensional terminal singularity and use Hayakawa''s method to construct a resolution then try to find out the essential components. We conclude that an exceptional divisor is essential if it appears in the minimal resolution for surface singularities or is of discrepancy less than or equal to one in the higher dimensional cases. And after enough many jet scheme computed without finding new components, we know the number of the components of arc space and how they looks like. Finally we know that if a 3-dimensional terminal singularity satisfies some extra condition, then it is enough to consider the vector in the toric language to decide whether a divisor is essential.
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Books on the topic "Essential singularities"

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Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.
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Book chapters on the topic "Essential singularities"

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"Essential Singularities, Roots, and Periods." In Complex Analysis with Applications to Flows and Fields, 893–936. CRC Press, 2010. http://dx.doi.org/10.1201/b13580-51.

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Phong, D. H., and Jacob Sturm. "On the Singularities of the Pluricomplex Green’s Function." In Advances in Analysis, edited by Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691159416.003.0016.

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This chapter seeks to establish the existence of pluricomplex Green's functions with singularities at certain multi poles, given by arbitrary local analytic functions. The Green's function plays a central role in the study of functions of one complex variable or of two real variables. This chapter also attempts to develop a geometric/analytic approach to Monge-Ampère equations with measures on the right-hand side, where the singularities of the solution arise from blow-up constructions. Since blow-ups typically lead to degenerate Kähler forms, an essential tool in this chapter's approach is the recent existence theorems for the Dirichlet problem for complex Monge-Ampère equations with degenerate background form.
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Gos, Maciej. "Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime." In The Paideia Archive: Twentieth World Congress of Philosophy, 1–5. Philosophy Documentation Center, 1998. http://dx.doi.org/10.5840/wcp20-paideia199834564.

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The general theory of relativity and field theory of matter generate an interesting ontology of space-time and, generally, of nature. It is a monistic, anti-atomistic and geometrized ontology — in which the substance is the metric field — to which all physical events are reducible. Such ontology refers to the Cartesian definition of corporeality and to Plato's ontology of nature presented in the Timaeus. This ontology provides a solution to the dispute between Clark and Leibniz on the issue of the ontological independence of space-time from distribution of events. However, mathematical models of space-time in physics do not solve the problem of the difference between time and space dimensions (invariance of equations with regard to the inversion of time arrow). Recent research on space-time singularities and asymmetrical in time quantum theory of gravitation will perhaps allow for the solution of this problem based on the structure of space-time and not merely on thermodynamics.
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Pukhlikov, Aleksandr V. "Essentials of the method of maximal singularities." In Explicit Birational Geometry of 3-folds, 73–100. Cambridge University Press, 2000. http://dx.doi.org/10.1017/cbo9780511758942.004.

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Bulatov, Vasily, and Wei Cai. "Introduction To Crystal Dislocations." In Computer Simulations of Dislocations. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198526148.003.0004.

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Dislocations first appeared as an abstract mathematical concept. In the late 19th century, Italian mathematician Vito Volterra examined mathematical properties of singularities produced by cutting and shifting matter in a continuous solid body [1]. As happened to some other mathematical concepts, dislocations could have remained a curious product of mathematical imagination known only to a handful of devoted mathematicians. In 1934, however, three scientists, Taylor, Polanyi and Orowan, independently proposed that dislocations may be responsible for a crystal’s ability to deform plastically [2, 3, 4]. While successfully explaining most of the puzzling phenomenology of crystal plasticity, crystal dislocations still remained mostly a beautiful hypothesis until the late 1950s when first sightings of them were reported in transmission electron microscopy (TEM) experiments [5]. Since then, the ubiquity and importance of dislocations for crystal plasticity and numerous other aspects of material behavior have been regarded as firmly established as, say, the role of DNA in promulgating life. Dislocations define a great many properties of crystalline materials. In addition to a crystal’s ability to yield and flow under stress, dislocations also control other mechanical behaviors such as creep and fatigue, ductility and brittleness, indentation hardness and friction. Furthermore, dislocations affect how a crystal grows from solution, how a nuclear reactor wall material is damaged by radiation, and whether or not a semiconductor chip in an electronic device will function properly. It can take an entire book just to describe the various roles dislocations play in materials behavior. However, the focus of this book is on the various computational models that have been developed to study dislocations. This chapter is an introduction to the basics of dislocations, setting the stage for subsequent discussions of computational models and associated numerical issues. Like any other crystal defect, dislocations are best defined with respect to the host crystal structure. We begin our discussion by presenting in Section 1.1 the basic elements and common terminology used to describe perfect crystal structures. Section 1.2 introduces the dislocation as a defect in the crystal lattice and discusses some of its essential properties. Section 1.3 discusses forces on dislocations and atomistic mechanisms for dislocation motion.
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Gutfreund, Hanoch, and Jürgen Renn. "Introduction." In The Formative Years of Relativity. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174631.003.0001.

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This introductory chapter provides a brief background into the development of Albert Einstein's special and general theories of relativity. As a characteristic stage in the development of the theory, the chapter focuses on the formative years which have, remarkably, received less attention from historians than subsequent periods. It argues that a “renaissance” of general relativity had begun essentially as the result of a community-building effort turning the theory into a universally applicable framework. This revival was followed by what has been called the “golden age” of relativity, which witnessed new conceptual insights, such as those into the nature of spacetime singularities, and turned the theory into the foundation of modern astrophysics and observational cosmology.
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Conference papers on the topic "Essential singularities"

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Barkatou, Moulay A., Thomas Cluzeau, and Achref Jalouli. "Formal Solutions of Linear Differential Systems with Essential Singularities in their Coefficients." In ISSAC'15: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2755996.2756669.

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Holzinger, Stefan, and Johannes Gerstmayr. "Explicit Time Integration of Multibody Systems Modelled With Three Rotation Parameters." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22261.

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Abstract Rigid bodies are an essential part of multibody systems. As there are six degrees of freedom in rigid bodies, it is natural but also precarious to use three parameters for the displacement and three parameters for the rotation parameters — since there is no singularity-free description of spatial rotations based on three rotation parameters. Standard formulations based on three rotation parameters avoid singularities, e.g. by applying reparameterization strategies during the time integration of the rotational kinematic equations. Alternatively, Euler parameters are commonly used to avoid singularities. State of the art approaches use Lie group methods, specifically integrators, to model rigid body motion without the need for the above mentioned solutions. However, the methods so far have been based on additional information, e.g., the rotation matrix, which has to been computed in each step. The latter procedure is thus difficult to be implemented in existing codes that are based on three rotation parameters. In this paper, we use the rotation vector to model large rotations. Whereby Lie group integration methods are used to compute consistent updates for the rotation vector in every time step. The resulting rotation vector update is finite, while the derivative of the rotation vector in the singularity becomes unbounded. The advantages of this method are shown in an example of a gyro. Additionally, the method is applied to a multibody system and the effects of crossing singularities are presented.
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De Floriani, Leila, Annie Hui, and Franca Giannini. "Identification of Form Features in Non-Manifold Shapes Through a Decomposition Approach." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59566.

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In Computer-Aided Design (CAD), the idealization process reduces the complexity of the model of a solid object, thus resulting in a simplified representation which captures only the essential elements of its shape. Form features extraction is a relevant issue in order to recover semantic information from an idealized object model, since such information is typically lost during the idealization process. An idealized model is usually composed of non-manifold parts, whose topology carries significant structural information about the object shape. To this aim, we define form features for non-manifold object by extending the taxonomy of form features provided by STEP [19]. We describe an approach for the identification of features, which interact with non-manifold singularities in the object, based on a decomposition of a non-manifold object into nearly manifold components and on the properties of the graph representing such decomposition.
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Yazigi, N., M. H. Charlier, G. A. Gerolymos, and J. Chauvin. "Performance Prediction of Subsonic Separated Cascades." In ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/90-gt-065.

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During the design process of fans and compressors, rapid computation of performance characteristics at various operating points is essential. In view of estimating off-design performance, the prediction of compressible separated flow is needed. A method has been developed for predicting such flows in 2-D cascades, with varying blade-height, based on an iterative viscous-inviscid interaction approach. Inviscid flow is simulated using a panel method. The effects of compressibility and streamsheet convergence or divergence are taken into account by singularities distributed in the interior of the flowfield. Viscous flow is simulated using an integral boundary-layer method, till the point of separation. Laminar and transitory separation bubbles are modelled semi-empirically. Separated-flow regions are simulated using a free streamline model. The method has been systematically compared with available experimental data and has shown very good agreement concerning the prediction of pressure distribution, deviation angle and loss coefficient, from negative to positive stall and for a wide range of Reynolds number and subsonic Mach number. The method is an interesting performance analysis tool due to its rapidity and reliability.
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Giorelli, Michele, Federico Renda, Gabriele Ferri, and Cecilia Laschi. "A Feed Forward Neural Network for Solving the Inverse Kinetics of Non-Constant Curvature Soft Manipulators Driven by Cables." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3740.

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The solution of the inverse kinetics problem of soft manipulators is essential to generate paths in the task space to perform grasping operations. To address this issue, researchers have proposed different iterative methods based on Jacobian matrix. However, although these methods guarantee a good degree of accuracy, they suffer from singularities, long-term convergence, parametric uncertainties and high computational cost. To overcome intrinsic problems of iterative algorithms, we propose here a neural network learning of the inverse kinetics of a soft manipulator. To our best knowledge, this represents the first attempt in this direction. A preliminary work on the feasibility of the neural network solution has been proposed for a conical shape manipulator driven by cables. After the training, a feed-forward neural network (FNN) is able to represent the relation between the manipulator tip position and the forces applied to the cables. The results show that a desired tip position can be achieved quickly with a degree of accuracy of 0.73% relative average error with respect to total length of arm.
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Gonzalez, M., A. Dahi Taleghani, and J. E. Olson. "A Cohesive Model for Modeling Hydraulic Fractures in Naturally Fractured Formations." In SPE Hydraulic Fracturing Technology Conference. SPE, 2015. http://dx.doi.org/10.2118/spe-173384-ms.

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Abstract A cohesive zone model (CZM) has been developed to couple fluid flow with elastic, plastic and damage behavior of rock during hydraulic fracturing in naturally fractured formations. In addition to inelastic deformations, this model incorporates rock anisotropies. Fracture mechanics of microcrack and micro-void nucleation and their coalescence are incorporated into the formulation of the CZM models to accurately capture different failure modes of rocks. The performance of the developed elastoplastic and CZM models are compared with the available data of a shale play, and then the models are introduced into a commercial finite element package through user-defined subroutines. A workflow to derive the required model parameters for both intact rock and cemented natural fractures is presented through inverse modeling of field data. The hydraulic fractures' growth in the reservoir scale is then simulated, in which the effect of fluid viscosity, natural fracture characteristics and differential stresses on induced fracture network is studied. The simulation results are compared with the available solutions in the literature. The developed CZM model outperforms the traditional fracture mechanics approaches by removing stress singularities at the fracture tips, and simulation of progressive fractures without any essential need for remeshing. This model would provide a robust tool for modeling hydraulic fracture growth using conventional elements of FEA.
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Liu, Haowen, and Bingen Yang. "Quaternion-Based Control of Acrobatic Quadrotor With Trajectory Following." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23064.

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Abstract For an unmanned aerial vehicle (UAV), its navigation in terrains can be quite challenging. To reach the destination within the required time, the maneuver of the quadrotor must behave aggressively. During this aggressive maneuvering, the quadrotor can experience singularities in the yaw-direction rotation. Thus, it is essentially important to develop a mathematical model and control method that can avoid singularities while enabling such an aggressive maneuver. In our previous effort, we demonstrated a vertical loop aggressive maneuver performed by a quadrotor UAV, which utilizes the controlled loop path following (CLPF) method. As found in this work, conventional modeling and tracking control method may not be good enough if specific requirements, such as fast coasting speed and sharp turns, are imposed. The numerical simulation by singularity-free modeling and the CLPF method enables a quadrotor to be operated in aggressive maneuverability with features like automatic flipping and precise trajectory following. The current research extends the maneuverability of a quadrotor by using a different and more capable control approach. More complex trajectories are used to test this new control method. In this paper, a quadrotor is used to demonstrate the capability of the proposed control method in delivering an aggressive and singularity-free maneuver. A quaternion-based mathematical model of the quadrotor is derived to avoid the singularities of rotation during the aggressive maneuvers. At the same time, a new control method, namely the full quaternion differential flatness (FQDF) method, is developed for quadrotors to combat the requirement of a fast maneuver in three-dimensional space. The FQDF method, which makes use of full quaternion modeling and differential flatness, enables the quadrotor to react to the reference trajectory timely and to exhibit aggressive rotation without any singularity. Also, the singularities resulting from the heading direction can be resolved by a new algorithm. The FQDF method is compared with the reference literature’s methods and is tested in different trajectories from the ones in the previous studies. The numerical simulation demonstrates the aggressive maneuverability and computational efficiency of the proposed control method.
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Stepanenko, Oleksandr, and Ilian A. Bonev. "Novel 4-DOF SCARA Parallel Robot With Cylindrical Workspace." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-86113.

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In this paper, we present a novel 4-DOF SCARA parallel robot. The 2-DOF portion of the novel robot has been proposed before and consists of an end-effector connected to the base through two legs of type RRR and one passive constraining leg of type RP, where all the base-mounted revolute joints are coaxial. Contrary to SCARA robots based on the four-bar mechanism (RRRRR), the novel robot has a fully cylindrical workspace with no voids or parallel singularities in it. The novel robot has essentially the same workspace as that of a similarly sized ceiling-mounted SCARA serial robot (RR) with links of equal length. However, the proposed robot has the advantage of having all motors mounted on the base. We present the 2-DOF portion of the robot, its kinematic analysis, and its optimal design, and finally propose a mechanism design for the 4-DOF SCARA parallel robot.
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Liu, Hanwei, Clément Gosselin, and Thierry Laliberté. "Two-Degree-of-Freedom Decoupled Non-Redundant Cable-Loop-Driven Parallel Mechanism." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70442.

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A novel two-degree-of-freedom cable-loop slider-driven parallel mechanism is introduced in this paper. The two degrees of freedom of the mechanism are decoupled and only two actuators are needed to control the motion. There are two cable loops for each direction of motion: one acts as the actuating loop while the other is the constraint loop. Due to the simple geometric design, the kinematic and static equations of the mechanism are very compact. The stiffness of the mechanism is also analyzed in the paper. It can be observed that the mechanism’s stiffness is much higher than the stiffness of the cables. Finally, the dynamic equations of the mechanism, including the compliance and the damping of the cables are obtained. The proposed mechanism’s workspace is essentially equal to its footprint and there are no singularities. The mechanism does not require the use of a rigid-link passive bridge and trolley (only cables are connected to the end-effector). Sliders located on the edges of the workspace are used and actuation redundancy is eliminated while providing force closure everywhere in the workspace.
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