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Relevant bibliographies by topics / Jacobi's identity

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Academic literature on the topic 'Jacobi's identity'

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Published: 24 April 2022

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Journal articles on the topic "Jacobi's identity"

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Joichi, J. T., and Dennis Stanton. "An involution for Jacobi's identity." Discrete Mathematics 73, no. 3 (1989): 261–71. http://dx.doi.org/10.1016/0012-365x(89)90269-0.

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DUVERNEY, DANIEL. "Some arithmetical consequences of Jacobi's triple product identity." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 3 (November 1997): 393–99. http://dx.doi.org/10.1017/s0305004197001916.

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KIM, SUN. "A BIJECTIVE PROOF OF THE QUINTUPLE PRODUCT IDENTITY." International Journal of Number Theory 06, no. 02 (March 2010): 247–56. http://dx.doi.org/10.1142/s1793042110002909.

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ADIGA, C. "JACOBI'S TWO-SQUARE AND FOUR-SQUARE THEOREMS VIA ROGER'S IDENTITY." Tamkang Journal of Mathematics 25, no. 1 (June 6, 2021): 37–40. http://dx.doi.org/10.5556/j.tkjm.25.1994.4423.

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Borwein, J. M., and P. B. Borwein. "A Cubic Counterpart of Jacobi's Identity and the AGM." Transactions of the American Mathematical Society 323, no. 2 (February 1991): 691. http://dx.doi.org/10.2307/2001551.

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Srivastava, Bhaskar. "Identities for Analogous Ramanujan's Functions by Jacobi's Triple Product Identity." American Journal of Mathematics and Statistics 2, no. 1 (August 31, 2012): 25–28. http://dx.doi.org/10.5923/j.ajms.20120201.06.

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Adiga, Chandrashekar, and P. S. Guruprasad. "A Note on Four-Variable Reciprocity Theorem." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–9. http://dx.doi.org/10.1155/2009/370390.

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We give new proof of a four-variable reciprocity theorem using Heine's transformation, Watson's transformation, and Ramanujan's -summation formula. We also obtain a generalization of Jacobi's triple product identity.

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Chaudhary, M. P., and Sangeeta Chaudhary. "On relationships between q-products identities, Ralpha, Rbeta and Rm functions related to Jacobi's triple-product identity." Mathematica Moravica 24, no. 2 (2020): 133–44. http://dx.doi.org/10.5937/matmor2002133c.

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The authors establish a set of two new relationships involving q-product identities, Ralpha, Rbeta, and Rm (m = 1, 2, 3, . . .) functions; and answer a open question of Srivastava et al. [18]. The present work is motivated and based upon recent findings of Chaudhary et al. [8].

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Srivastava, Hari M., M. P. Chaudhary, and Sangeeta Chaudhary. "Some Theta-Function Identities Related to Jacobi’s Triple-Product Identity." European Journal of Pure and Applied Mathematics 11, no. 1 (January 30, 2018): 1. http://dx.doi.org/10.29020/nybg.ejpam.v11i1.3222.

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The main object of this paper is to present some q-identities involving some of the theta functions of Jacobi and Ramanujan. These q-identities reveal certain relationships among three of the theta-type functions which arise from the celebrated Jacobi’s triple-product identity in a remarkably simple way. The results presented in this paper are motivated by some recent works by Chaudhary et al. (see [4] and [5]) and others (see, for example, [1] and [13]).

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He, Thomas Y., Kathy Q. Ji, and Wenston J. T. Zang. "Bilateral truncated Jacobi’s identity." European Journal of Combinatorics 51 (January 2016): 255–67. http://dx.doi.org/10.1016/j.ejc.2015.05.014.

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Dissertations / Theses on the topic "Jacobi's identity"

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Robinson, Nicole A. "“Here’s Tae Us! Wha’s Like Us?” Jacobitism and the Creation of a Scottish National Identity." Wittenberg University Honors Theses / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1242322517.

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Sarnosky, Yolonda P. "Black female authors document a loss of sexual identity Jacobs, Morrison, Walker, Naylor, and Moody /." Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1999. http://www.kutztown.edu/library/services/remote_access.asp.

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Thesis (M.A.)--Kutztown University of Pennsylvania, 1999.
Source: Masters Abstracts International, Volume: 45-06, page: 2836. Typescript. Abstract appears on leaf [ii]. Includes bibliographical references (leaves 65-67).

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Chaves, Fernando Miguel Pacheco. "Identidades de Jacobi generalizadas em teorias de gauge." Universidade de São Paulo, 1990. http://www.teses.usp.br/teses/disponiveis/43/43132/tde-26022014-154659/.

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Estudando o processo q q BARRA W Brown, Mikaelian, Sahdev, Samuel descobriram um zero na distribuição angular do W quando seu momento magnético tem o valor característico de uma partícula de gauge. Goebel, Halzen e Leveille mostraram que este zero é uma consequência da fatorização da amplitude em um termo que contém a dependência da carga ou outros índices de simetria interna, e outro que contém a dependência dos spins ou índices de polarização. Esta fatorização existe em geral para amplitudes de processos envolvendo quatro partículas na aproximação árvore, quando uma ou mais destas partículas é um campo de gauge. Portanto a existência de um zero na seção de choque é uma prova direta da estrutura de gauge da teoria. A fatorização baseia-se em uma identidade, identidade de Jacobi espacial generalizada, cuja demonstração ou significado físico ainda não fora elucidado. O objetivo do presente trabalho é estudar esta identidade de Jacobi espacial generalizada. Para tanto calculamos, no capítulo I, a amplitude de um processo de espalhamento gluon-gluon envolvendo cinco partículas e reorganizando esta amplitude por analogia com um processo de interação fóton-pion, mostramos que não existe, no caso de cinco partículas, a identidade de Jacobi espacial generalizada, mas sim uma série de identidades espaciais parciais, que se compõe, no processo de quatro partículas, em uma única identidade. No capítulo II estudamos um processo envolvendo quatro partículas, das quais três campos escalares, porém agora aproximação de um loop, e mostramos que também não existe identidade de Jacobi espacial generalizada.
Brown, Mikaelian, Sahdev, and Samuel discovered that the angular distribution of the process q q BARRA W in lowest order has a zero, if the magnetic moment f the W has the characteristic value of a gauge field. Goebel, Halzen and Leveille showed that this zero is a consequence of a factorizability of the amplitude into one factor which contains the dependence on the charge or other internal, symmetry indices, and another which contains the dependence on the spin or polarization indices. This factorization is found to hold for any four particle tree-approximation amplitude, when one or more of the four particles is a gauge-field. Therefore, the study of the angular distribution of the process q q BARRA W, directly probes the gauge structure of the theory. The factorization hinges on a spatial generalized Jacobi identity obeyed by the polarization-dependent factors of the vertices, whose physical significance or general demonstration was not known. The purpose of the present work is to study this identity. With this in mind we work out, in chapter I, the amplitude of a scattering gluon-gloun with five particles. Reorganizing this amplitude by analogy with an interaction process photon-pion, we show that does not exist, in this case, the spatial generalized Jacobi identity, but instead many spatial partial identities that compose themselves, in the case of a four particle process, in one single identity. In chapter II, we study a process with four particles, three of them scalar fields, but in the one loop approximation, and show that, in this case too, does not exist the spatial generalized Jacobi identity.

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Hill, Tamara D. "Race, Identity and the Narrative of Self in the Autobiographies of Frederick Douglass, Harriet Jacobs and Malcolm X." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 2019. http://digitalcommons.auctr.edu/cauetds/159.

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Prophet Muhammad stated, “A white has no superiority over black nor a black has any superiority over white except by piety and good action.” Because of the continual idea of race as a social construct, this study examines the memoirs of Douglass, Jacobs and Malcolm X, as it relates to the narrative of self and identity. They have written their personal autobiographies utilizing diction as a tool that develops their art of storytelling about their distinct life journeys. These protagonists utilize their autobiographical experiences to construct a generational transference of race and identity from when Douglass was born in 1818, to Jacob’s escape to freedom in 1838 to the assassination of Malcolm X in 1965. Historically, the texts are written from where slavery was still an institution until it was abolished in 1865, proceeding through to the Civil Rights movement. Frederick Douglass, Harriet Jacobs and Malcolm X will experience racial trauma throughout their personal narratives that were life-altering events that severely influenced them as they matured from adolescence to adulthood. The writer has determined that, “Racial trauma can be chracterized as being physically and or psychologically damaged because of one’s race or skin color that permanently has long lasting negative effects on an individual’s thoughts, behavior or emotions,” i.e., African American victims of police brutality are racially traumatized because they suffer with behavioral problems and stress, after their encounters. This case study is based on the definition of race as a social construct for Douglass, Jacobs and Malcolm X’s narratives that learn to self-identify beyond the restrictions of racial discrimination which eventually manifests into white oppression in a world that does not readily embrace them. Their autobiographies provide self-reflection and a broad comprehension about how and why they were entrenched by race. Douglass, Jacobs and Malcolm X were stereotyped, socially segregated, and internalized awareness of despair because of their race. Conclusions drawn from Frederick Douglass-Narrative of the Life of Frederick Douglass: American Slave, Harriet Jacobs-Incidences of a Slave Girl, and Malcolm X’s- Autobiography of Malcolm X will exemplify the subject of African American narrators countering racism and maneuvering in society.

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Vieira, Filho Raphael Rodrigues. "Os negros em Jacobina (Bahia) no século XIX." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/12946.

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Made available in DSpace on 2016-04-27T19:31:22Z (GMT). No. of bitstreams: 1 Raphael Rodrigues Vieira Filho.pdf: 1563556 bytes, checksum: 0f582f6db3a826559c210dc8d06ec2d1 (MD5) Previous issue date: 2006-06-26
Programa de Apoio a Capacitação - Universidade do Estado da Bahia
This study aims the black populations of the region of Jacobina, Bahia, in the 19TH century. There is a bibliography, widely spread in the countryside of Bahia, which states the nonexistence of blacks men in the countryside. These authors are based on the principles of incompatibility between cattle breeding and slavery and also on the strong indigenous presence, which mixed with the white settlers. Based on several documents collection, such as: Correspondences sent to the President of Province by Judges and City Congress, Speeches of the Presidents of the Provinces, digitalized documents by Resgate Project, Books of Registration containing Registrations of Purchases, Sales and Donations, Procurations and the recordings of Letters of Freedom, Crime and Civl Lawsuits, besides the documents published at the end of the 19TH century and beginning of the 20TH century in the Annals of National Library and Historic Documents of the National Library and authors of the 19TH century and beginning of the 20TH century. Were raised data about the black populations and their insertion in the region, contrary to the bibliography mentioned above. Features of the general population composition of the region of Jacobina were studied, based on information taken from the census of the population in the 18TH and 19TH century. The specific regional configuration of the slave population, such as: sex, color/ethnicity, age, using as source the Registrations of Purchases, Sales and Donations and Procurations. The ways freedom was conquered were expressed in the recordings of Letters of Freedom of Jacobina and Morro do Chapéu, consulted. These documents brought besides prices, sex, age, color/ethnicity, the ways of these types of conquers, and other features involved beyond the monetary value of these transactions. In the Crime and Civil Lawsuits it was possible to verify how the conquers of a little more autonomy were traded and expressed in moments and diverse situations
O presente trabalho tem como objeto as populações negras da região de Jacobina, Bahia, no século XIX. Existe uma bibliografia, bastante difundida no sertão baiano, afirmando a não existência de negros no interior. Esses autores apóiam-se nos preceitos de incompatibilidade entre pecuária e escravidão e também na forte presença indígena, que se miscigenou com os colonizadores brancos. Partindo de diversos corpos documentais, tais como: Correspondências enviadas ao Presidente de Província por Juízes e Câmara Municipal, Falas dos Presidentes de Província, Documentos Digitalizados pelo Projeto Resgate, Livros de Registro contendo Registros de Compras, Vendas e Doações, Procurações e Registros de Cartas de Liberdade, Processos Crimes e Cíveis, além de documentos publicados no final do século XIX e início do século XX nos Annaes da Arquivo Publico da Bahia, Annaes da Bibliotheca Nacional e Documentos Historicos da Bibliotheca Nacional e autores do século XIX e início do século XX, foram levantados dados sobre as populações negras e sua inserção na região, contrariando a bibliografia citada acima. Foram trabalhados, a partir de informações colhidas nos recenseamentos da população do século XVIII e XIX, aspectos da composição populacional geral da região de Jacobina. Foi também trabalhado a configuração específica regional da população de escravizados, tais como: sexo, cor/etnia, idade, utilizando como fonte os Registros de Compras, Vendas e Doações e Procurações. As formas de conquista da liberdade ficaram expressas nos Registros de Cartas de Liberdade de Jacobina e Morro do Chapéu, consultados. Esses documentos nos legaram além de preços, sexo, idade, cor/etnia, as formas desse tipo conquistas, estando envolvidos outros aspectos que somente o valor monetário nessas transações. Nos Processos Crimes e Cíveis foi possível verificar como as conquistas de um pouco mais de autonomia eram negociadas e expressaram-se em momentos e situações diversas

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Moffler, Kirsten A. ""A Plea for Color:" The Construction of a Feminine Identity in African American Women's Novels." Fogler Library, University of Maine, 2001. http://www.library.umaine.edu/theses/pdf/MofflerKA2001.pdf.

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Ferguson, Matthew R. ""Baseball as Community Identity: Cleveland, Ohio -- 1891-2012"." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1363301386.

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Savoldi, Andrea. "On Poisson structures of hydrodynamic type and their deformations." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/20769.

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Systems of quasilinear partial differential equations of the first order, known as hydrodynamic type systems, are one of the most important classes of nonlinear partial differential equations in the modern theory of integrable systems. They naturally arise in continuum mechanics and in a wide range of applications, both in pure and applied mathematics. Deep connections between the mathematical theory of hydrodynamic type systems with differential geometry, firstly revealed by Riemann in the nineteenth century, have been thoroughly investigated in the eighties by Dubrovin and Novikov. They introduced and studied a class of Poisson structures generated by a flat pseudo-Riemannian metric, called first-order Poisson brackets of hydrodynamic type. Subsequently, these structures have been generalised in a whole variety of different ways: degenerate, non-homogeneous, higher order, multi-dimensional, and non-local. The first part of this thesis is devoted to the classification of such structures in two dimensions, both non-degenerate and degenerate. Complete lists of such structures are provided for a small number of components, as well as partial results in the multi-component non-degenerate case. In the second part of the thesis we deal with deformations of Poisson structures of hydrodynamic type. The deformation theory of Poisson structures is of great interest in the theory of integrable systems, and also plays a key role in the theory of Frobenius manifolds. In particular, we investigate deformations of two classes of structures of hydrodynamic type: degenerate one-dimensional Poisson brackets and non-semisimple bi-Hamiltonian structures associated with Balinskii-Novikov algebras. Complete classification of second-order deformations are presented for two-component structures.

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Fabre, Bruno. "Nouvelles variations sur les théorèmes d'Abel et de Lie." Paris 6, 2000. https://tel.archives-ouvertes.fr/tel-00008886.

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Hall, Jack Kingsbury Mathematics &amp Statistics Faculty of Science UNSW. "Some branching rules for GL(N,C)." Awarded by:University of New South Wales. Mathematics and Statistics, 2007. http://handle.unsw.edu.au/1959.4/29473.

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This thesis considers symmetric functions and algebraic combinatorics via the polynomial representation theory of GL(N,C). In particular, we utilise the theory of Jacobi-Trudi determinants to prove some new results pertaining to the Littlewood-Richardson coefficients. Our results imply, under some hypotheses on the strictness of the partition an equality between Littlewood-Richardson coefficients and Kostka numbers. For the case that a suitable partition has two rows, an explicit formula is then obtained for the Littlewood-Richardson coefficient using the Hook Length formula. All these results are then applied to compute branching laws for GL(m+n,C) restricting to GL(m,C) x GL(n,C). The technique also implies the well-known Racah formula.

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Books on the topic "Jacobi's identity"

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An invitation to q-series: From Jacobi's triple product identity to Ramanujan's "most beautiful identity". Singapore: World Scientific Pub Co., 2011.

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The Jacobite song: Political myth and national identity. Aberdeen: Aberdeen University Press, 1988.

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Jacob's voices: Reflections of a wandering American Jew. Carbondale: Southern Illinois University Press, 1996.

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Husu, Cristiano. Extensions of the Jacobi identity for vertex operators and standard Aı⁽¹⁾-modules. Providence, RI: American Mathematical Society, 1993.

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Identity and Christian-Muslim interaction: Medieval art of the Syrian Orthodox from the Mosul area. Leuven: Peeters, 2010.

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The invention of Scotland: The Stuart myth and the Scottish identity, 1638 to the present. London: Routledge, 1991.

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1923-, Şimşek Mehmet, ed. Naum Faik ve Süryani rönesansı: 1968 Diyarbakır/1930 New York. Sultanahmet, İstanbul: Belge Yayınları, 2004.

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Pluralism and the idea of the republic in France. Houndmills, Basingstoke, Hampshire: Palgrave Macmillan, 2012.

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Freedland, Jonathan. Jacob's Gift. Penguin, 2006.

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Hoffman, Ian, Sarah Hoffman, and Chris Case. Jacob's New Dress. Albert Whitman & Company, 2020.

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Book chapters on the topic "Jacobi's identity"

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Gavrilik, Alexander. "Jacobi Identity." In Concise Encyclopedia of Supersymmetry, 210. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_275.

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Kac, Victor, and Pokman Cheung. "Jacobi’s Triple Product Identity." In Quantum Calculus, 35–36. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0071-7_11.

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Schimmrigk, Rolf, Steven Duplij, Antoine Van Proeyen, Władysław Marcinek, and Gert Roepstorff. "Generalized Jacobi Identity." In Concise Encyclopedia of Supersymmetry, 164. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_212.

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Murata, Maki. "Jacobi’s Identity and Two K3-Surfaces." In Developments in Mathematics, 189–98. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0257-5_11.

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Bump, Daniel. "The Jacobi-Trudi Identity." In Lie Groups, 297–307. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4094-3_37.

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Bump, Daniel. "The Jacobi–Trudi Identity." In Lie Groups, 365–77. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8024-2_35.

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German, Kieran. "Jacobite Politics in Aberdeen and the’ 15." In Loyalty and Identity, 82–97. London: Palgrave Macmillan UK, 2010. http://dx.doi.org/10.1057/9780230248571_4.

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Hirschhorn, Michael D. "Jacobi’s “aequatio identica satis abstrusa”." In The Power of q, 169–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57762-3_19.

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Genet-Rouffiac, Nathalie. "The Irish Jacobite Regiments and the French Army: A Way to Integration." In Loyalty and Identity, 206–28. London: Palgrave Macmillan UK, 2010. http://dx.doi.org/10.1057/9780230248571_11.

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Murdoch, Steve. "Tilting at Windmills: The Order del Toboso as a Jacobite Social Network." In Loyalty and Identity, 243–64. London: Palgrave Macmillan UK, 2010. http://dx.doi.org/10.1057/9780230248571_13.

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Conference papers on the topic "Jacobi's identity"

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Koh, Sung K., Gregory S. Chirikjian, and G. K. Ananthasuresh. "A Jacobian-Based Algorithm for the Attitude Control of a Rigid Body Undergoing Fully-Reversed Sequences of Rotations." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34927.

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Jacobian-based control algorithms for the attitude control of a rigid body undergoing a series of forward and reverse rotations are proposed in this paper. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is singular as well as a null matrix at the identity that makes the conventional Jacobian formulation break down. In order to handle the singularities involved in FR rotations, the Jacobian algorithm is reformulated and implemented so as to synthesize the FR rotation for a desired orientation change. We introduce the single-step and multiple-step Jacobian methods in this paper. The single-step Jacobian method synthesizes a specific FR rotation that enables the rigid body to reach a given desired orientation through a single step. The multiple-step Jacobian method synthesizes physically feasible FR rotations on an incremental optimal path to a desired orientation. A comparison with existing control algorithms for FR motions verifies the fast convergence property of the Jacobian-based algorithm and the accuracy of the solutions.

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Notash, Leila. "Analytical Methods for Solution Sets of Interval Wrench." 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/detc2015-47575.

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Methodologies for calculating the solution set of actuator inputs, in the presence of uncertainty/error in parameters/data, are investigated. The enclosure for the vector of actuator torques is formulated utilizing the interval forms of the Jacobian matrix and external wrench. Two analytical methods are utilized to identify the solution set; one method generates the rays that bound the solution set in each orthant, and the other one is based on parameterizing the interval entries of the Jacobian matrix and wrench. For the parametric method, the existence of dominant parameter groups to produce the whole solution set (or a subset of solution set) is examined. Implementation of these methods on example parallel manipulators are presented to identify the solution set for the actuator torques, and the results are verified with the discrete method.

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Brown, Brandon, Tarunraj Singh, and Rahul Rai. "Pareto Front Identification via Objective Vector Jacobian Matrix Singularity." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12271.

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This paper presents a method to identify the exact Pareto front for a multi-objective optimization problem. The developed technique addresses the identification of the Pareto frontier in the cost space and the Pareto set in the design space for both constrained and unconstrained optimization problems. The proposed approach identifies a n – 1 dimensional hypersurface for a multi-objective problem with n cost functions, a subset of which constitute the Pareto front. The n – 1 dimensional hypersurface is identified by enforcing a singularity constraint on the Jacobian of the cost vector with respect to the optimization parameters. Since the boundary is identified in the design space, the relation of design points to the exact Pareto front in the cost space is known. The proposed method is proven effective in the Pareto identification for a set of previously released challenge problems. Six of these examples are included in this paper; 3 unconstrained and 3 constrained.

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Kim, Yoonik, Chansoo Kim, Moosung Jae, Chang Hyun Chung, and Ji Hwan Jung. "A Method to Identify Dependencies Between Organizational Factors Using Statistical Independence Test." In 12th International Conference on Nuclear Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/icone12-49125.

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A considerable number of studies on organizational factors in nuclear power plants have been made especially in recent years, most of which have assumed organizational factors to be independent. However, since organizational factors characterize the organization in terms of safety and efficiency etc. and there would be some factors that have close relations between them. Therefore, from whatever point of view, if we want to identify the characteristics of an organization, the dependence relationships should be considered to get an accurate result. In this study the organization of a reference nuclear power plant in Korea was analyzed for the trip cases of that plant using 20 organizational factors that Jacobs and Haber had suggested. By utilizing the results of the analysis, a method to identify the dependence relationships between organizational factors is presented. The statistical independence test for the analysis result of the trip cases is adopted to reveal dependencies. This method is geared to the needs to utilize many kinds of data that has been obtained as the operating years of nuclear power plants increase, and more reliable dependence relations may be obtained by using these abundant data.

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Mirman, C. R., and K. C. Gupta. "Compensation of Robot Joint Variables Using Special Jacobian Matrices." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0059.

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Abstract In dealing with an industrial manipulator, the end-effector accuracy is a major concern. The positioning of the end-effector is determined by the controller which utilizes the data from a closed-form kinematic inversion. The closed-form inversion uses nominal, i.e. manufacturer specified, values of link lengths, twists, and offsets. Due to manufacturing tolerances, set-up, and usage, these nominal parameters may be inaccurate. If the nominal parameters contain built-in error values, the closed-form kinematic inversion will yield incorrect joint values, and the actual end-effector position will deviate from its desired position. One may use a parameter identification method to identify the position-independent error parameter values. This paper assumes that this has been done and it presents an Iterative Compensation Algorithm (ICA) through which the identified position-independent parameter error values may be used to correct the joint values which are obtained through the closed-form kinematic inversion. The Denavit and Hartenberg (D-H) parameters (θ s α a) are used to model the given M-jointed manipulator, and a set of four special Jacobian matrices (Jθ, Js, Jα, and Ja) are formulated. The iterative compensation algorithm allows one to determine the M unknown position-dependent joint error values, by using these four special Jacobian matrices. The improvements obtained through the use of the compensation algorithm will be presented for regular trajectories, as well as when the robot nears certain singularity conditions. Since it is important to know a priori a definite number of iterations which must be performed, the level of compensation after a fixed number of iterations is also studied. Through the presentation of numerous examples, it is shown that the proposed compensation algorithm is simple and straightforward to implement, and it increases the end-effector accuracy.

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Abdel-Malek, Karim, Harn-Jou Yeh, and Rabeeh Ruwady. "A Unified Formulation for Swept Volume and Robot Workspace Analyses." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-3761.

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Abstract This paper presents a unified formulation for the generation of mechanical manipulator workspaces, and the representation of the volume of an entity swept along another. A constraint function is developed and its Jacobian is studied. The analysis is based upon a row-rank deficiency criteria of the non-square constraint Jacobian. Singular geometric entities inside the resulting volume are identified and parametrized. These entities are characterized by a set of singular generalized coordinates (parameters), when substituted into the constraint vector function yield parametric equations. Singular geometric entities are assembled and intersected to identify sub-entities that are boundary to the volume. A local perturbation method is applied to determine which sub-entities are boundary to the workspace. Several examples are presented to verify the formulation.

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Gogu, Grigore. "Fully-Isotropic Redundantly-Actuated Parallel Wrists With Three Degrees of Freedom." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34237.

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The paper presents fully-isotropic redundantly-actuated parallel wrists (RaPWs) with three degrees of freedom. The mobile platform has three independent rotations. A method is proposed for structural synthesis of fully-isotropic RaPWs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian mapping the two vector spaces of fully-isotropic RaPWs presented in this paper is 3×3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Redundant actuation is used to obtain fully-isotropic parallel wrists with three degrees of freedom. As far as we are aware, this paper presents for the first time in the literature the use of redundancy to design fully-isotropic parallel wrists as well as solutions of fullyisotropic RaPWs with three degrees of freedom.

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Gogu, Grigore. "Fully-Isotropic T1R2-Type Parallel Robots With Three Degrees of Freedom." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84313.

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The paper presents singularity-free fully-isotropic T1R2-type parallel manipulators (PMs) with three degrees of freedom. The mobile platform has one independent translation (T1) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T1R2-type PMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T1R2-type PMs presented in this paper is the 3x3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, this paper presents for the first time in the literature solutions of singularity-free T1R2-type PMs with decoupled an uncoupled motions, along with the fully-isotropic solutions.

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Notash, Leila. "Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators." 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/detc2017-67091.

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For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized and implemented to identify the solution set, as well as the minimum 2-norm least square solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least square solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

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Lee, Chung-Ching, and Po-Chih Lee. "Kinematics of a Prism-Type Translational Robot." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86714.

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From the viewpoint of kinematics, a three-dof Prism-type pure translational parallel robot is presented for the development of automatic assembly devices and a regional structure of a six-dof hybrid parallel platform. First, we describe the structural properties of the robot and analyze its kinematic mobility. A pure translational motion is verified to exist through the well-known D-H symbolic notations and the coordinate-transformation-matrix technique. What follows are the forward, inverse kinematics analysis, and their closed-form solutions by the matrix algebra approach. For further confirmation of the correctness of derived equations, some numerical examples are also given. With the help of the analytical displacement kinematics, we identify the volume of workspace. At last, taking account of the 3×3 reduced Jacobian matrix provides the condition number and the identification of singularity of configuration is explored based on the direct and inverse kinematics Jacobian matrix.

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