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Relevant bibliographies by topics / Cone singularities

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Academic literature on the topic 'Cone singularities'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Cone singularities"

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Oberlin, Daniel M. "singularities on the light cone." Duke Mathematical Journal 59, no. 3 (December 1989): 747–57. http://dx.doi.org/10.1215/s0012-7094-89-05934-6.

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Soliman, Yousuf, Dejan Slepčev, and Keenan Crane. "Optimal cone singularities for conformal flattening." ACM Transactions on Graphics 37, no. 4 (August 10, 2018): 1–17. http://dx.doi.org/10.1145/3197517.3201367.

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Anan'in, Sasha, Carlos H. Grossi, Jaejeong Lee, and João dos Reis. "Hyperbolic 2-spheres with cone singularities." Topology and its Applications 272 (March 2020): 107073. http://dx.doi.org/10.1016/j.topol.2020.107073.

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Dimitrov, Nikolay. "Hyper-ideal Circle Patterns with Cone Singularities." Results in Mathematics 68, no. 3-4 (March 24, 2015): 455–99. http://dx.doi.org/10.1007/s00025-015-0453-3.

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MOORE, HELEN. "STABLE MINIMAL HYPERSURFACES AND TANGENT CONE SINGULARITIES." International Journal of Mathematics 10, no. 03 (May 1999): 407–13. http://dx.doi.org/10.1142/s0129167x9900015x.

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In this paper, I give an estimate on the dimension of the singular set of a tangent cone at infinity of a stable minimal hypersurface. Namely, let Mn ⊂ ℝn+1, n ≥ 2, be a complete orientable stable minimal immersion with bounded volume growth. Then n < 7 implies T∞(M) is smooth, and n ≥ 7 implies the singular set of T∞(M) has codimension at least seven.

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Järv, L., C. Mayer, T. Mohaupt, and F. Saueressig. "Space-time singularities and the Kähler cone." Fortschritte der Physik 52, no. 67 (June 1, 2004): 624–29. http://dx.doi.org/10.1002/prop.200310154.

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LIANG, JIANFENG. "HYPERBOLIC SMOOTHING EFFECT FOR SEMILINEAR WAVE EQUATIONS AT A FOCAL POINT." Journal of Hyperbolic Differential Equations 06, no. 01 (March 2009): 1–23. http://dx.doi.org/10.1142/s0219891609001745.

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For semi-linear dissipative wave equation □u + |ut|p - 1ut = 0, we consider finite energy solutions with singularities propagating along a focusing light cone. At the tip of cone, the singularities are focused and partially smoothed out under strong nonlinear dissipation, i.e. the solution gets up to 1/2 more L2 derivative after the focus. The smoothing phenomenon is in fact the result of simultaneous action of focusing and nonlinear dissipation.

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Wang, Weiqiang. "Resolution of Singularities of Null Cones." Canadian Mathematical Bulletin 44, no. 4 (December 1, 2001): 491–503. http://dx.doi.org/10.4153/cmb-2001-049-6.

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AbstractWe give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie algebras.

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PIMENTEL, B. M., and A. T. SUZUKI. "CAUSAL PRESCRIPTION FOR THE LIGHT-CONE GAUGE." Modern Physics Letters A 06, no. 28 (September 14, 1991): 2649–53. http://dx.doi.org/10.1142/s0217732391003080.

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GUENANCIA, HENRI. "KÄHLER–EINSTEIN METRICS WITH CONE SINGULARITIES ON KLT PAIRS." International Journal of Mathematics 24, no. 05 (May 2013): 1350035. http://dx.doi.org/10.1142/s0129167x13500353.

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Dissertations / Theses on the topic "Cone singularities"

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Fornasin, Nelvis [Verfasser], Sebastian [Akademischer Betreuer] Goette, and Katrin [Akademischer Betreuer] Wendland. "[eta] invariants under degeneration to cone-edge singularities = η invariants under degeneration to cone-edge singularities." Freiburg : Universität, 2019. http://d-nb.info/1203804326/34.

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McDonald, Patrick T. (Patrick Timothy). "The Laplacian for spaces with cone-like singularities." Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/13645.

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de, Borbon Gonzalo Martin. "Asymptotically conical Ricci-flat Kahler metrics with cone singularities." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/31373.

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The main result proved in this thesis is an existence theorem for asymptotically conical Ricci-flat Kahler metrics on C2 with cone singularities along a smooth complex curve. These metrics are expected to arise as blow-up limits of non-collapsed sequences of Kahler-Einstein metrics with cone singularities.

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JANIGRO, AGNESE. "Compact 3-dimensional Anti-de Sitter manifolds with spin-cone singularities." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. https://hdl.handle.net/10281/402356.

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In questa tesi, ci occupiamo dello studio delle varietà anti-de Sitter compatte di dimensione 3 dotate di singolarità coniche con spin generalizzate. Data una superficie chiusa con metrica iperbolica e una mappa di contrazione tra il rivestimento universale della superficie e il semipiano iperbolico, è possibile costruire una varietà anti-de Sitter compatta di dimensione 3 come fibrato vettoriale con base la superficie iperbolica. Seguendo la stessa costruzione del caso non singolare, mostriamo che, a partire da una superficie equipaggiata di metrica iperbolica con singolarità coniche, è possibile costruire varietà compatte anti-de Sitter come fibrati vettoriali sulla superficie con fibre singolari. Queste fibre singolari sono localmente isometriche al cosiddetto Modello per singolarità conica con spin generalizzata. In particolare, dalla costruzione del modello, vengono fuori due invarianti che permettono di studiare tali varietà anti-de Sitter singolari. L’ultimo risultato trattato riguarda il calcolo del volume delle varietà anti-de Sitter con singolarità di questo tipo.
In this thesis, we study compact Anti-de Sitter manifolds of dimension 3 with generalized spin-cone singularities. Given a closed surface equipped with a hyperbolic metric and a contraction map between the universal cover of the surface and the hyperbolic plane, it is possible to construct a compact Anti-de Sitter manifold of dimension 3 as fiber bundle over the surface. We show that, when the surface has hyperbolic metric with conical singular points, the same construction of the non singular case leads to compact Anti-de Sitter manifolds as fiber bundle with singular fibers over the surface. These singular fibers over the singular conical points are locally isometric to what we defined Model for generalized spin-cone singularity. In particular, from the model come out two invariants that allows us to study the compact Anti-de Sitter manifolds of dimension 3 with spin-cone singularities. The last result of this work is about the computation of the volume of these compact Anti-de Sitter manifolds with spin-cone singularities.

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Ma, L., and Bert-Wolfgang Schulze. "Operators on manifolds with conical singularities." Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2009/3660/.

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We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 − γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.

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Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2632/.

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We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.

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Giovenzana, Luca [Verfasser], Christian [Akademischer Betreuer] Lehn, Christian [Gutachter] Lehn, Klaus [Gutachter] Hulek, and Gregory [Gutachter] Sankaran. "Singularities of the Perfect Cone Compactification / Luca Giovenzana ; Gutachter: Christian Lehn, Klaus Hulek, Gregory Sankaran ; Betreuer: Christian Lehn." Chemnitz : Technische Universität Chemnitz, 2021. http://d-nb.info/1229085262/34.

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Vintescu, Ana-Maria. "Copier-coller 3D : paramétrisation cohérente de maillages triangulaires." Electronic Thesis or Diss., Paris, ENST, 2017. http://www.theses.fr/2017ENST0031.

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Nous proposons un algorithme efficace pour le paramétrisation global de surfaces triangulées. Tout d’abord, les singularités coniques sont automatiquement détectées dans des endroits visuellement significatifs ; ce processus est efficace sur le plan calculatoire et vise à détecter de tels cônes aux sommets du maillage, où des valeurs élevées de distorsion de surface peuvent être prédites avant la paramétrisation réelle. Afin d’assurer la continuité au travers des coupes coniques résultant de la découpe du maillage, des fonctions de transition affines sont utilisées ; celles-ci sont intégrées dans un système linéaire qui vise à minimiser la distorsion angulaire. Dans cette thèse, nous présentons également un nouvel algorithme de paramétrisation croisé qui, étant donné deux maillages triangulaires d’entrée et des points de correspondance fournit par l’utilisateur, effectue des paramétrisations topologiquement et géométriquement cohérentes. La paramétrisation cohérente simultanée des maillages est réalisée en seulement quelques secondes, en résolvant au plus quatre systèmes linéaires au sens des moindres carrés. Nous validons les résultats des algorithmes proposés en fournissant des résultats expérimentaux étendus, en démontrant l’efficacité en temps, ainsi que la qualité, illustrée en examinant les mesures de distorsion acceptées. L’efficacité de calcul des algorithmes présentés permet leur utilisation dans des applications interactives, où l’utilisateur peut modifier ou ajouter des singularités coniques (ou des correspondances de référence pour le pipeline de paramétrisation croisé) tout en obtenant des résultats dans des temps de fonctionnement pratiques
We propose an efficient algorithm for the global parameterization of triangulated surfaces. First, cone singularities are automatically detected in visually significant locations ; this process is computationally efficient and aims at detecting such cones at vertices of the mesh where high values of area distortion can be predicted prior to the actual parameterization. In order to ensure continuity across conic cuts resulted after cutting the mesh open through the detected cones, affine transition functions are employed ; these will be integrated into a linear system which aims at minimizing angular distortion. In this thesis we also present a new Cross-Parameterization algorithm which, given two input triangular meshes and sparse user landmark correspondences, computes topologically and geometrically consistent parameterizations. The simultaneous consistent parameterization of the meshes is achieved in a matter of only a few seconds, solving at most four linear systems in a least squares sense. We validate the results of the proposed algorithms by providing extensive experimental results, demonstrating the time efficiency, as well as the quality - illustrated by examining accepted distortion measures. The computational efficiency of the presented algorithms allows their usage in interactive applications, where the user can modify or add cone singularities (or landmark correspondences for the cross-parameterization pipeline) and still obtain results in practical running times

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Moreno, Ávila Carlos Jesús. "Global geometry of surfaces defined by non-positive and negative at infinity valuations." Doctoral thesis, Universitat Jaume I, 2021. http://hdl.handle.net/10803/672247.

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We consider plane divisorial valuations of Hirzebruch surfaces and introduce the concepts of non-positivity and negativity at infinity. We prove that the surfaces given by valuations of the last types have nice global and local geometric properties. Moreover, non-positive at infinity divisorial valuations are those divisorial valuations of Hirzebruch surfaces providing rational surfaces with minimal generated cone of curves. Non-positivity and negativity at infinity are also extended to the class of real valuations of the projective plane and the Hirzebruch surfaces. Finally, we compute the Seshadri-type constants for pairs formed by a big divisor and a divisorial valuation of a Hirzebruch surface and obtain the vertices of the Newton-Okounkov bodies of pairs as above under the non-positivity at infinity property.
Introducimos los conceptos de no positividad y negatividad en el infinito para valoraciones planas divisoriales de una superficie de Hirzebruch. Probamos que las superficies dadas por valoraciones con las características anteriores poseen interesantes propiedades globales y locales. Además, las valoraciones divisoriales no positivas en el infinito son aquellas valoraciones divisoriales de superficies de Hirzebruch que dan lugar a superficies racionales tales que su cono de curvas está generado por un número mínimo de generadores. Los conceptos de no positividad y negatividad en el infinito también se extienden a valoraciones reales del plano proyectivo y de superficies de Hirzebruch. Por último, calculamos explícitamente las constantes de tipo Seshadri para pares formados por divisores big y valoraciones divisoriales de superficies de Hirzebruch y obtenemos los vértices de los cuerpos de Newton-Okounkov para pares como los anteriores bajo la condición de no positividad en el infinito.
Programa de Doctorat en Ciències

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Imagi, Yohsuke. "Surjectivity of a Gluing for Stable T2-cones in Special Lagrangian Geometry." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/189337.

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Books on the topic "Cone singularities"

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Randell, Richard, ed. Singularities. Providence, Rhode Island: American Mathematical Society, 1989. http://dx.doi.org/10.1090/conm/090.

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Brasselet, Jean-Paul, José Luis Cisneros-Molina, David Massey, José Seade, and Bernard Teissier, eds. Singularities I. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/474.

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Brasselet, Jean-Paul, José Luis Cisneros-Molina, David Massey, José Seade, and Bernard Teissier, eds. Singularities II. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/475.

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Castro-Jiménez, Francisco-Jesús, David Massey, Bernard Teissier, and Meral Tosun, eds. A Panorama of Singularities. Providence, Rhode Island: American Mathematical Society, 2020. http://dx.doi.org/10.1090/conm/742.

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Goryunov, Victor, Kevin Houston, and Roberta Wik-Atique, eds. Real and Complex Singularities. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/conm/569.

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Nabarro, Ana, Juan Nuño-Ballesteros, Raúl Sinha, and Maria Aparecida Soares Ruas, eds. Real and Complex Singularities. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/conm/675.

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Gaffney, Terence, and Maria Aparecida Soares Ruas, eds. Real and Complex Singularities. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/conm/354.

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Saia, Marcelo J., and José Seade, eds. Real and Complex Singularities. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/459.

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Melles, Caroline Grant, and Ruth I. Michler, eds. Singularities in Algebraic and Analytic Geometry. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/conm/266.

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Cogolludo-Agustín, José Ignacio, and Eriko Hironaka, eds. Topology of Algebraic Varieties and Singularities. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/conm/538.

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Book chapters on the topic "Cone singularities"

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Przeszowski, Jerzy A., Elżbieta Dzimida-Chmielewska, and Jan Żochowski. "Light-Front Perturbation Without Spurious Singularities." In Light Cone 2015, 239–44. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50699-9_38.

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Kapanadze, D., B. W. Schulze, and I. Witt. "Coordinate Invariance of the Cone Algebra with Asymptotics." In Parabolicity, Volterra Calculus, and Conical Singularities, 307–58. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8191-3_5.

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Zheng, Kai. "Kähler Metrics with Cone Singularities and Uniqueness Problem." In Trends in Mathematics, 395–408. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_44.

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Donaldson, S. K. "Kähler Metrics with Cone Singularities Along a Divisor." In Essays in Mathematics and its Applications, 49–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28821-0_4.

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Zavialov, O. I. "Composite Fields. Singularities of the Product of Currents at Short Distances and on the Light Cone." In Renormalized Quantum Field Theory, 252–400. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-2585-4_4.

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Campillo, Antonio, and Gérard González-Sprinberg. "On Characteristic Cones, Clusters and Chains of Infinitely Near Points." In Singularities, 251–61. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8770-0_13.

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Kunz, Ernst, and Rolf Waldi. "§6. Applications to curve singularities." In Contemporary Mathematics, 123–47. Providence, Rhode Island: American Mathematical Society, 1988. http://dx.doi.org/10.1090/conm/079/06.

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Stevens, Jan. "15. Cones over curves." In Deformations of Singularities, 125–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-36464-1_16.

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Stevens, Jan. "16. The versal deformation of hyperelliptic cones." In Deformations of Singularities, 137–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-36464-1_17.

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Apablaza, Victor, and Francisco Melo. "Dynamics of conical singularities: S type d-cones." In Nonlinear Phenomena and Complex Systems, 141–48. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2149-7_7.

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Conference papers on the topic "Cone singularities"

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Grange, Pierre, Bruno Mutet, and Ernst WERNER. "Light-cone gauge singularities in the photon propagator and residual gauge transformations." In LIGHT CONE 2008 Relativistic Nuclear and Particle Physics. Trieste, Italy: Sissa Medialab, 2009. http://dx.doi.org/10.22323/1.061.0005.

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Müller, Andreas. "Higher-Order Local Analysis of Kinematic Singularities of Lower Pair Linkages." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67039.

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Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical. C-space singularities are reflected by the c-space geometry. Identifying kinematic singularities amounts to locally analyze the set of critical points. The local geometry of the set of critical points is best approximated by its tangent cone (an algebraic variety). The latter is defined in this paper in a form that allows for its computational determination using the Jacobian minors. An explicit closed form expression for the derivatives of the minors is presented in terms of Lie brackets of joint screws. A computational method is proposed to determine a polynomial system defining the tangent cone. This finally allows for identifying c-space and kinematic singularities.

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Müller, Andreas, and Zijia Li. "Identification of Singularities and Real and Complex Solution Varieties of the Loop Constraints of Linkages Using the Kinematic Tangent Cone." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-114638.

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Abstract The configuration space (c-space) of a mechanism is the real solution variety of a set of loop closure constraints. Singularities of this variety (referred to as c-space singularities) are singular configurations of the mechanism. In addition, a mechanism may exhibit other kinematic singularities that are not visible from the differential geometry of the c-space (referred to as hidden singularities). The latter is related to a drop in the rank of the constraint Jacobian while the c-space is locally a smooth manifold. Another kinematic feature that is only due to the corank of the constraint Jacobian is the shakiness of a mechanism. Such situations were analyzed by investigating the local geometry of the c-space and its corank stratification. It has been shown recently that hidden singularities and shakiness can be attributed to the fact that complex solution branches intersect with the c-space, i.e., with real solution branches. This paper employs the kinematic tangent cone to identify local solution branches. While the kinematic tangent cone is an established generally applicable concept, which gives rise to a computational (numeric and symbolic) algorithm, it has yet only been applied for analyzing the real solution set. The method is shown for several examples. Further, the algebraic aspects are briefly elaborated.

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Chirilli, Giovanni Antonio. "Sub-gauge Conditions for the Gluon Propagator Singularities in Light-Cone Gauge." In QCD Evolution 2016. Trieste, Italy: Sissa Medialab, 2017. http://dx.doi.org/10.22323/1.284.0038.

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Müller, Andreas. "Local Analysis of Closed-Loop Linkages: Mobility, Singularities, and Shakiness." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47485.

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The mobility of a linkage is determined by the constraints imposed on its members. The constraints define the configuration space (c-space) variety as the geometric entity in which the finite mobility of a linkage is encoded. The instantaneous motions are determined by the constraints, rather than by the c-space geometry. Shaky linkages are prominent examples that exhibit a higher instantaneous than finite DOF even in regular configurations. Inextricably connected to the mobility are kinematic singularities that are reflected in a change of the instantaneous DOF. The local analysis of a linkage, aiming at determining the instantaneous and finite mobility in a given configuration, hence needs to consider the c-space geometry as well as the constraint system. A method for the local analysis is presented based on a higher-order local approximation of the c-space adopting the concept of the tangent cone to a variety. The latter is the best local approximation of the c-space in a general configuration. It thus allows for investigating the mobility in regular as well as singular configurations. Therewith the c-space is locally represented as an algebraic variety whose degree is the necessary approximation order. In regular configurations the tangent cone is the tangent space. The method is generally applicable and computationally simple. It allows for a classification of linkages as overconstrained and underconstrained, and to identify singularities.

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Lerbet, Jean. "Stability of Singularities of a Kinematical Chain." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84126.

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Since few years, the geometry of singularities of kinematical chains is better known. Using both Lie group theory and concepts of differential or analytic geometry, we already classified these singularities according to the nature of the function f associated to the chain (f is a product of exponential mappings of a Lie group). In the most general case, the tangent cone at a singularity has been explicitely given. Here, a different (and more difficult) aspect of the problem is studied. The concrete realisation of a kinematical chain is never perfect. That means that the vectors of the Lie agebra defining the function f are not exactly those of the chain: they are deformed. What happens for the singularities in this case? Are they remaining or do they disappear during the deformation? First, the mechanical problem is analysed as this of the stability of the fuction f and mathematical tools concerning stable mappings are given. Stability of a mapping means that the orbit of f under the action of diffeomorphisms in the source and in the target is an open set and its infinitesimal equivalent formulation is noted the inf-stability. Then we prove that the set of singularities of first class itself is a sbmanifold and we analyse a condition of normal crossing of the restriction of f to its manifold of singularities. Applying a result of the general theory, the stability of f is analysed.

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Piipponen, Samuli, Eero Hyry, and Teijo Arponen. "Kinematic Analysis of Multi-4-Bar Mechanisms Using Algebraic Geometry." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67250.

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The configuration spaces (c-space) of mechanisms and robots can in many cases be presented as an algebraic variety. Different motion modes of mechanisms and robots are found as irreducible components of the variety. Singularities of the variety correspond usually (but not necessarily) to intersections of irreducible components/motion modes of the configuration space. A well-known method for finding the modes is the prime (and/or primary) decomposition of the constraint ideal corresponding to the mechanisms specific constraint map. However the direct computation of these decompositions is still in many cases too exhausting at least for standard computers. In this paper we present a method to speed up the decomposition significantly. If the mechanism consists or is constructed of subsystems whose c-space can be decomposed in feasible time then the whole decomposition of the c-space of the mechanism can be constructed from the decompositions of the subsystems. Here we concentrate on the 4-bar-subsystems but the approach generalizes naturally to more complicated subsystems as well. In fact the method works for all mechanisms which are constructed of subsystems whose decomposition is already known or can be computed. Further we present a way to investigate the nature of singularities which relies on the computation of the tangent cone at singular points of the c-space and the investigation of the primary decomposition of the tangent cone itself and partially its connection to intersection theory of algebraic varieties.

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Müller, Andreas, P. C. López Custodio, and J. S. Dai. "Identification of Non-Transversal Bifurcations of Linkages." 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/detc2020-22301.

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Abstract The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to separate different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

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De Donno, Mauro, and Faydor L. Litvin. "Computerized Design, Generation and Simulation of Meshing of a Spiroid Worm-Gear Drive With Double-Crowned Worm." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/ptg-5779.

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Abstract The authors propose methods of computerized design and analysis of a spiroid worm-gear drive with ground worm based on the following considerations: (1) The theoretical thread surface of the hob is generated by a cone surface. (2) The worm surface is crowned in profile and longitudinal directions in comparison with the hob thread surface. (3) The double crowning of the worm enables to localize the bearing contact and obtain a predesigned parabolic function of transmission errors of an assigned level. Computerized design of the worm-gear drive enables to discover and avoid singularities of the generated worm face-gear surface and pointing of teeth. The meshing and contact of the double-crowned worm and the worm face-gear is simulated to determine the influence of misalignment on the shift of bearing contact and transmission errors. Computer program for numerical solution is developed and applied. A numerical example that illustrates the developed theory is provided.

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Silva, Homero. "CODE VERIFICATION TEST IN CALCULATIONS AROUND JUMP SINGULARITIES." In 25th International Congress of Mechanical Engineering. ABCM, 2019. http://dx.doi.org/10.26678/abcm.cobem2019.cob2019-2274.

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