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Thorgeirsson, Sverrir. "Hyperbolic geometry: history, models, and axioms." Thesis, Uppsala universitet, Algebra och geometri, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-227503.
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Ward, Peter James. "Euclid's Elements, from Hilbert's Axioms." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1354311965.
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Toniolo, Luciano Santos. "Cônicas em modelos físicos." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-24102018-151118/.
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Este trabalho é um estudo realizado em torno das principais curvas cônicas estudadas por alunos do ensino básico: parábola, elipse e hipérbole. A ideia central do trabalho é a autosuficiência, pois apresentamos todas as ferramentas matemáticas necessárias para o entedimento desses entes e suas aplicações, desde os axiomas iniciais da geometria plana até as definições formais das cônicas e demonstrações de suas propriedades. Espera-se que uma pessoa não especializada em matemática, ao ler o trabalho, entenda toda a matemática no entorno das aplicações dessas cônicas.This work is a study carried out around the main conic curves studied by elementary school students: parabola, ellipse and hyperbola. The main idea of this work is to be self-contained, starting from the basic axioms from the geometry and after we present formal definitions, properties and applications of conics in the everyday life. It is expected that a person that is not a specialist in mathematics, are able to read and understand all the mathematics in the surroundings of the applications of these conics.
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Portela, Antonio Edilson Cardoso. "Noções de geometria projetiva." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25586.
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PORTELA, Antonio Edilson Cardoso. Noções de geometria projetiva. 2017. 58 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.Submitted by Jessyca Silva (jessyca@mat.ufc.br) on 2017-09-06T17:17:00Z No. of bitstreams: 1 2017_dis_aecportela.pdf: 1065928 bytes, checksum: 468c05aa35745f3fd2761f13aa26eff1 (MD5)
Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, Estou devolvendo a Dissertação de ANTONIO EDILSON CARDOSO PORTELA, para que o mesmo realize algumas correções na formatação do trabalho. 1- SUMÁRIO ( A formatação do sumário está incorreta, primeiro, retire o último ponto final que aparece após a numeração dos capítulos e seções (Ex.: 3.1. Axioma....; deve ser corrigido para: 3.1 Axioma.....), o alinhamento dos títulos deve seguir o modelo abaixo 1 INTRODUÇÃO.....................00 2 O ESPAÇO...........................00 3 GEOMETRIA........................00 3.1 Axiomas...............................00 REFERÊNCIAS...................00 (OBS.: não altere a formatação do negrito, pois já estava correta) 2- TITULO DOS CAPÍTULOS E SEÇÕES ( retire o ponto final que aparece após o último dígito da numeração dos capítulos e seções, seguindo o modelo do sumário. Retire o recuo de parágrafo dos títulos das seções. Ex.: 3.1 Axioma.......) 3- REFERÊNCIAS ( substitua o termo REFERÊNCIAS BIBLIOGRÁFICAS apenas por REFERÊNCIAS, com fonte n 12, negrito e centralizado. Retire a numeração progressiva que aparece nos itens da referência. Atenciosamente, on 2017-09-06T17:56:50Z (GMT)
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In this work, initially, some results of Linear Algebra are presented, in particular the study of the Vector Space R^n, which becomes, together with Analytical Geometry, the language used in the chapters that follow. We present a study from an axiomatic point of view, from the perspectives of Hilbert's axioms and we elaborate models of planes for the Euclidean, Elliptic and Projective Geometries. The validity of the Incidence and Order axioms for Euclidean Geometry is verified. In R^3, an approach is made to the study of the plane and the unitary sphere, highlighting the elliptical line obtained by the intersection of these sets, thus making an approach to the Elliptic Geometry. With the concepts and definitions studied in the Vector Space R^n, Three-dimensional Space and in the Euclidean and Elliptic Geometries we will approach the study of Projective Geometry, demonstrating propositions and verifying its axioms.
Neste trabalho, inicialmente, apresenta-se alguns resultados da Álgebra Linear, em especial o estudo do Espaço Vetorial R^n, que passa a ser, juntamente com a Geometria Analítica, a linguagem empregada nos capítulos que se seguem. Apresentamos um estudo de um ponto de vista axiomático, sob a ótica dos axiomas de Hilbert e elaboramos modelos de planos para as Geometrias Euclidiana, Elíptica e Projetiva. É verificada a validade dos axiomas de Incidência e Ordem para a Geometria Euclidiana. No R^3, é feita uma abordagem do estudo de plano e da esfera unitária, destacando a reta elíptica obtida pela interseção destes conjuntos, passando assim a fazer uma abordagem da Geometria Elíptica. Com os conceitos e definições estudadas no Espaço Vetorial R^n, Espaço tridimensional e nas Geometrias Euclidiana e Elíptica, abordaremos o estudo da Geometria Projetiva, demonstrando proposições e verificando os seus axiomas.
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Pejlare, Johanna. "On Axioms and Images in the History of Mathematics." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8345.
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This dissertation deals with aspects of axiomatization, intuition and visualization in the history of mathematics. Particular focus is put on the end of the 19th century, before David Hilbert's (1862–1943) work on the axiomatization of Euclidean geometry. The thesis consists of three papers. In the first paper the Swedish mathematician Torsten Brodén (1857–1931) and his work on the foundations of Euclidean geometry from 1890 and 1912, is studied. A thorough analysis of his foundational work is made as well as an investigation into his general view on science and mathematics. Furthermore, his thoughts on geometry and its nature and what consequences his view has for how he proceeds in developing the axiomatic system, is studied. In the second paper different aspects of visualizations in mathematics are investigated. In particular, it is argued that the meaning of a visualization is not revealed by the visualization and that a visualization can be problematic to a person if this person, due to a limited knowledge or limited experience, has a simplified view of what the picture represents. A historical study considers the discussion on the role of intuition in mathematics which followed in the wake of Karl Weierstrass' (1815–1897) construction of a nowhere differentiable function in 1872. In the third paper certain aspects of the thinking of the two scientists Felix Klein (1849–1925) and Heinrich Hertz (1857–1894) are studied. It is investigated how Klein and Hertz related to the idea of naïve images and visual thinking shortly before the development of modern axiomatics. Klein in several of his writings emphasized his belief that intuition plays an important part in mathematics. Hertz argued that we form images in our mind when we experience the world, but these images may contain elements that do not exist in nature.
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Freitas, Brasilio Alves. "Introdução à geometria euclidiana axiomática com o geogebra." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1188.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Por conhecer a grande dificuldade dos alunos de Ensino Médio, da rede pública Estadual de Minas Gerais, em relação aos conceitos, demostrações e deduções básicas da Geometria Euclidiana plana, foi elaborado um pequeno roteiro de estudo dos axiomas que regem esses conteúdos e também uma introdução às construções geométricas básicas, utilizando os instrumentos euclidianos e o software gratuito GeoGebra. O desenvolvimento do trabalho trouxe como objetivo dotar os alunos do Ensino Fundamental, cursando oitavo ano (antiga sétima série), de uma compreensão gradual e intuitiva da geometria euclidiana plana, buscando, de forma fundamentada fixar os aspectos conceituais básicos que são extremamente necessários para estudos mais aprofundados em cursos posteriores. As atividades propostas no capítulo 4 foram criadas com o intuito de que o aluno, percorrendo os conceitos mostrados no capítulo 2, tenha oportunidade de abstrair-se literalmente e ou com recursos algébricos em um processo de demonstração das propriedades de diversas figuras geométricas.
Knowing the great hardship high school students of Minas Gerais public school system have concerning the basic concepts, demonstrations and deductions of the Euclidean Geometry, a small study guide of the axioms that rule these contents was made, and also an introduction to the basic geometry constructions using the Euclidean instruments and the free software GeoGebra. The work’s development brought as a goal to endow the middle school students, attending the eight year (the old seventh grade), a gradual and intuitive understanding of the Euclidian Geometry, trying to fix the basic conceptual aspects that are deeply necessary for further studies. The proposed activities on chapter four intend to give the student, going trough the concepts shown on chapter two, the opportunity to abstract on a descriptive way and/or use algebraic resources in a process of demonstration of many geometrical forms.
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SOUZA, Carlos Bino de. "Geometria hiperbólica : consistência do modelo de disco de Poincaré." Universidade Federal Rural de Pernambuco, 2015. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6695.
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Euclid wrote a book in 13 volumes called Elements where systematized all the mathematical knowledge of his time. In this work, the 5 postulates of Euclidean geometry were presented. For several years, the 5th Postulate was frequently asked, this inquiries it was discovered that there are several other possible geometries, including hyperbolic geometry. Beltrimi proved that hyperbolic geometry is consistent if Euclidean geometry is consistent. Hilbert showed that Euclidean geometry is consistent if the arithmetic is consistent and presented an axiomatic system that capped the gaps in Euclid’s axiomatic system. Poincaré created a model, called the Poincaré disk, to represent the plan of hyperbolic geometry. The objective of this work is to show that the Poincaré disk model is consistent with reference Axioms Hilbert, replacing only the Axioms of Parallel to "On a point outside a line passes through the two parallel straight lines given", by constructions of Euclidean geometry.
Euclides escreveu uma obra em 13 volumes chamada de Elementos onde sistematizava todo o conhecimento matemático do seu tempo. Nesta obra, foram apresentados os 5 postulados da Geometria Euclidiana. Durante vários anos, o 5o Postulado foi muito questionado, desses questionamentos descobriu-se a existência de várias outras Geometrias possíveis, entre elas a Geometria Hiperbólica. Beltrimi provou que a Geometria Hiperbólica é consistente se a Geometria Euclidiana é consistente. Hilbert mostrou que a Geometria Euclidiana é consistente se a Aritmética é consistente e apresentou um sistema axiomático que preencheu as lacunas do sistema axiomático de Euclides. Poincaré criou um Modelo, chamado de Disco de Poincaré, para representar o plano da Geometria Hiperbólica. O objetivo deste trabalho é mostrar que o Modelo de Disco de poincaré é consistente, tomando como referência os Axiomas de Hilbert, substituindo apenas os Axiomas das Paralelas para "Por um ponto fora de uma reta passam duas retas paralelas à reta dada", através de construções da Geometria Euclidiana.
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Barreto, Carlos Alberto. "A geometria do origami como ferramenta para o ensino da geometria euclidiana na educação básica." Mestrado Profissional em Matemática, 2013. https://ri.ufs.br/handle/riufs/6503.
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The purpose of this monograph is to study the geometry of origami and its applications in Euclidean Geometry as a tool that contributes to the teaching of Geometry in Basic Education. Provide a brief history of origami and its arrival in Brazil and as a result we present the axioms that define the simple movements that can be performed using points and straight lines in a plane. We also study
the classic problems of doubling the cube and the trisection of the angle, showing that they are possible to be solved through the Geometry of Origami. We show then the Origami applications for studies of flat Euclidean space, emphasizing the study of Plato polyhedra. We finished the job by showing how we developed the Origami Project - Mathematics and Art in the State College John XXIII .O objetivo desta monografia é fazer o estudo da Geometria do Origami e de suas aplicações na Geometria Euclidiana como instrumento que contribua para o ensino da Geometria na Educação Básica. Fornecemos um pequeno histórico do Origami e de sua chegada ao Brasil e na sequência apresentamos os axiomas que definem os movimentos simples que podem ser realizados utilizando pontos e retas num plano. Estudamos também os problemas clássicos da duplicação do cubo e da trissecção do ângulo, mostrando que são possíveis de ser resolvidos por meio da Geometria do Origami. Mostramos, então, aplicações do Origami para estudos de Geometria Euclidiana plana e espacial, dando ênfase ao estudo dos poliedros de Platão. Encerramos o trabalho, mostrando como foi desenvolvido o Projeto Origami - Matemática e Arte no Colégio Estadual João XXIII .
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Bassan, André Roberto. "Observações sobre geometria sintética /." Rio Claro, 2015. http://hdl.handle.net/11449/132066.
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Orientador: Alice Kimie Miwa LibardiBanca: Sérgio Roberto Nobre
Banca: Edson de Oliveira
Resumo: O objetivo deste trabalho é apresentar alguns resultados da Geometria Euclidiana no plano, que são vistos no ensino fundamental e médio sob ponto de vista sintético, ou seja, não serão assumidos os axiomas métricos. Como aplicação faremos algumas construções, usando as ferramentas desenvolvidas
Abstract: The objective of this work is to present some results of Euclidean geometry which are given in elementary and high school from the synthetic point of view, that is we will not assume the metric axioms. As an application we will make some constructions using the developed tools
Mestre
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Freitas, Aline Claro de [UNESP]. "Origami: o uso como instrumento alternativo no ensino da geometria." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/134280.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Frente à realidade do ensino contemporâneo que demanda a necessidade de diversificar o uso de estratégias de ensino, pretendemos propor uma abordagem, por meio de material concreto e que pode tornar-se bastante significativa no ensino da matemática. Este trabalho discute sobre a história, aplicações clássicas e utilização do origami em sala de aula. Após uma breve apresentação histórica sobre o origami, apresentamos uma abordagem axiomática deste instrumento. Dois dos três famosos problemas matemáticos gregos da antiguidade que não podem ser solucionados através da régua e compasso: trissecção do ângulo e duplicação do cubo encontram uma solução por meio das técnicas de origami. Além disso, apresentamos sugestões de roteiros de aulas e a atividade aplicada em sala de aula que obteve resultado satisfatório.
Faced with the reality of contemporary teaching that demands the need to diversify the use of teaching strategies, we intend to propose an approach through concrete material and can become quite significant in mathematics education. This monograph discusses about the history, classic applications and use origami in the classroom. After a brief historical introduction about origami, we present an axiomatic approach of this instrument. Two of the three famous Greek mathematical problems of antiquity that can’t be solved by ruler and compass: trisection angle and doubling the cube find a solution through of origami techniques. In addition, we present suggestions classes scripts and the activitie applied in the classroom that obtained satisfactory result.
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Bassan, André Roberto [UNESP]. "Observações sobre geometria sintética." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/132066.
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000853537.pdf: 917761 bytes, checksum: 77a62888ce2e85ced4a5b4ac963cd4f5 (MD5)O objetivo deste trabalho é apresentar alguns resultados da Geometria Euclidiana no plano, que são vistos no ensino fundamental e médio sob ponto de vista sintético, ou seja, não serão assumidos os axiomas métricos. Como aplicação faremos algumas construções, usando as ferramentas desenvolvidas
The objective of this work is to present some results of Euclidean geometry which are given in elementary and high school from the synthetic point of view, that is we will not assume the metric axioms. As an application we will make some constructions using the developed tools
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Castro, Renata Brandão de [UNESP]. "Tópicos da geometria projetiva." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/94354.
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castro_rb_me_rcla.pdf: 774630 bytes, checksum: b9499068a589a33827880e026c206fd9 (MD5)Neste projeto tratamos da Geometria Projetiva advinda da generalização da Geometria Afim do Plano Euclidiano. Estabelecemos um Sistema Axiomático para a Geometria Projetiva e provamos resultados de sustentabilidade para esta geometria, sobretudo resultados sobre Perspectivas e Projeções. Também exploramos Cônicas dentro deste contexto. O principal livro usado como referência deste trabalho foi [1] de Judith Cederberg e como textos auxiliares consultaremos [2] e [3]
This project dealt with the Projective Geometry arising from the generalization of the Affine Geometry of the Euclidean Plane. Established an Axiomatic System for Projective Geometry and prove sustainability outcomes for this geometry, particularly on results Prospects and Projections. We also explored conics within this context
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Castro, Renata Brandão de. "Tópicos da geometria projetiva /." Rio Claro : [s.n.], 2012. http://hdl.handle.net/11449/94354.
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Orientador: Elíris Cristina RizziolliBanca: Grazielle Feliciani Barbosa
Banca: Carina Alves
Resumo: Neste projeto tratamos da Geometria Projetiva advinda da generalização da Geometria Afim do Plano Euclidiano. Estabelecemos um Sistema Axiomático para a Geometria Projetiva e provamos resultados de sustentabilidade para esta geometria, sobretudo resultados sobre Perspectivas e Projeções. Também exploramos Cônicas dentro deste contexto. O principal livro usado como referência deste trabalho foi [1] de Judith Cederberg e como textos auxiliares consultaremos [2] e [3]
Abstract: This project dealt with the Projective Geometry arising from the generalization of the Affine Geometry of the Euclidean Plane. Established an Axiomatic System for Projective Geometry and prove sustainability outcomes for this geometry, particularly on results Prospects and Projections. We also explored conics within this context
Mestre
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Rodrigues, Douglas Alexandre [UNESP]. "Investigações sobre sistemas axiomáticos na geometria euclidiana." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/110484.
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000790270.pdf: 586851 bytes, checksum: a0198a8e85a2177bac5159890b67523b (MD5)O objetivo desta pesquisa é analisar o desenvolvimento histórico da obra clássica de geometria, Os Elementos, de Euclides e os fundamentos da geometria proposto por David Hilbert em seu livro Grundlangen der Geometrie (Fundamentos da Geometria), estudando a estrutura axiomática da geometria abordada por cada autor. O rigor dedutivo utilizado por Euclides, apoiado na lógica clássica de Aristóteles, recebeu diversas críticas de matemáticos modernos no que tange a lacunas no seu sistema dedutivo. As diversas incertezas em relação ao sistema axiomático ameaçavam seu desenvolvimento lógico e especificamente, tratando-se da geometria, surgiram muitas discussões sobre a aceitação do quinto postulado de Euclides. Somente no final do século XIX os sistemas axiomáticos alcançavam níveis profundos nos fundamentos da geometria e, na tentativa de completar a axiomática da geometria, Hilbert publica os Grundlangen der Geometrie, abordagem axiomática mais amplamente adotada na geometria euclidiana. Neste contexto, discutimos as diferentes concepções dos sistemas axiomáticos clássicos e modernos, estudando seus significados lógicos e suas relações com os objetos da geometria. Como parte das reflexões finais, o presente trabalho destaca algumas considerações sobre o conceito de movimento em geometria e uma possível abordagem axiomática da mesma
The objective of this research is to analyze the historical development of the classical work of geometry named The Elements and written by Euclid and the foundations of geometry Grundlangen der Geometrie (Foundations of Geometry) written by David Hilbert by studying the axiomatic structure of geometry dealt with by each author. The deductive rigor used by Euclid, which is based on the classical logic of Aristotle, has received several criticisms from modern mathematicians with regard to the gaps in its mathematical deductive system. The various uncertainties regarding the axiomatic system threatened its logical development and in the specific case of geometry, many discussions arose on the acceptance of the Euclid's fifth postulate. Only in the late nineteenth century, axiomatic systems reached deeper levels in the foundations of geometry and, in an attempt to complete the axiomatic geometry, Hilbert publishes “Grundlangen der Geometrie”, which is the axiomatic approach more widely adopted in the Euclidean geometry. In this context, we discuss the different concepts of classical and modern axiomatic systems , studying their logical meanings and its relations with the objects of geometry . As part of the final thoughts , this paper highlights some considerations on the concept of motion in geometry and a possible axiomatic approach to it
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Rodrigues, Douglas Alexandre. "Investigações sobre sistemas axiomáticos na geometria euclidiana /." Rio Claro, 2014. http://hdl.handle.net/11449/110484.
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Orientador: Irineu BicudoBanca: Henrique Lazari
Banca: Carlos Roberto de Moraes
Resumo: O objetivo desta pesquisa é analisar o desenvolvimento histórico da obra clássica de geometria, Os Elementos, de Euclides e os fundamentos da geometria proposto por David Hilbert em seu livro Grundlangen der Geometrie (Fundamentos da Geometria), estudando a estrutura axiomática da geometria abordada por cada autor. O rigor dedutivo utilizado por Euclides, apoiado na lógica clássica de Aristóteles, recebeu diversas críticas de matemáticos modernos no que tange a lacunas no seu sistema dedutivo. As diversas incertezas em relação ao sistema axiomático ameaçavam seu desenvolvimento lógico e especificamente, tratando-se da geometria, surgiram muitas discussões sobre a aceitação do quinto postulado de Euclides. Somente no final do século XIX os sistemas axiomáticos alcançavam níveis profundos nos fundamentos da geometria e, na tentativa de completar a axiomática da geometria, Hilbert publica os Grundlangen der Geometrie, abordagem axiomática mais amplamente adotada na geometria euclidiana. Neste contexto, discutimos as diferentes concepções dos sistemas axiomáticos clássicos e modernos, estudando seus significados lógicos e suas relações com os objetos da geometria. Como parte das reflexões finais, o presente trabalho destaca algumas considerações sobre o conceito de movimento em geometria e uma possível abordagem axiomática da mesma
Abstract: The objective of this research is to analyze the historical development of the classical work of geometry named The Elements and written by Euclid and the foundations of geometry Grundlangen der Geometrie (Foundations of Geometry) written by David Hilbert by studying the axiomatic structure of geometry dealt with by each author. The deductive rigor used by Euclid, which is based on the classical logic of Aristotle, has received several criticisms from modern mathematicians with regard to the gaps in its mathematical deductive system. The various uncertainties regarding the axiomatic system threatened its logical development and in the specific case of geometry, many discussions arose on the acceptance of the Euclid's fifth postulate. Only in the late nineteenth century, axiomatic systems reached deeper levels in the foundations of geometry and, in an attempt to complete the axiomatic geometry, Hilbert publishes "Grundlangen der Geometrie", which is the axiomatic approach more widely adopted in the Euclidean geometry. In this context, we discuss the different concepts of classical and modern axiomatic systems , studying their logical meanings and its relations with the objects of geometry . As part of the final thoughts , this paper highlights some considerations on the concept of motion in geometry and a possible axiomatic approach to it
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Magalhães, José Messias. "Um estuo dos modelos da geometria hiperbólica /." Rio Claro, 2015. http://hdl.handle.net/11449/134147.
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Orientador: Wladimir SeixasBanca: Yuriko Yamomoto Baldin
Banca: João Peres Vieira
Resumo: Esta dissertação tem como objetivo introduzir os conceitos e os principais resultados da Geometria Hiperbólica, entre eles a não existência de retângulos. Verifica-se assim que as diferenças entre as geometrias euclidiana e hiperbólica se dá pela negação do Quinto Axioma de Euclides ou, como é conhecido, o Axioma das paralelas de Euclides. Na parte final deste trabalho abordaremos três principais modelos da Geometria Hiperb ólica: o Disco de Beltrami-Klein, o Disco de Poincaré e o Semiplano de Poincaré. Demonstraremos também que estes modelos são isomorfos
Abstract: The aim of this dissertation is to introduce the main concepts and results of hyperbolic geometry including the non-existence of rectangles. This statement is one of the many di erences between Euclidean geometry and Hyperbolic geometry from the negation of the Fifth Axiom of Euclid or as it is known, the Axiom of parallel of Euclid. In the nal part of this work we shall cover three main models of Hyperbolic Geometry: Beltrami-Klein, Poincaré Disk and the Poincaré Half Plane. We also demonstrate that these models are isomorphic
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Magalhães, José Messias [UNESP]. "Um estuo dos modelos da geometria hiperbólica." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/134147.
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000857257.pdf: 615187 bytes, checksum: 3d19160162d4d08d6c6276d0a0299491 (MD5)Esta dissertação tem como objetivo introduzir os conceitos e os principais resultados da Geometria Hiperbólica, entre eles a não existência de retângulos. Verifica-se assim que as diferenças entre as geometrias euclidiana e hiperbólica se dá pela negação do Quinto Axioma de Euclides ou, como é conhecido, o Axioma das paralelas de Euclides. Na parte final deste trabalho abordaremos três principais modelos da Geometria Hiperb ólica: o Disco de Beltrami-Klein, o Disco de Poincaré e o Semiplano de Poincaré. Demonstraremos também que estes modelos são isomorfos
The aim of this dissertation is to introduce the main concepts and results of hyperbolic geometry including the non-existence of rectangles. This statement is one of the many di erences between Euclidean geometry and Hyperbolic geometry from the negation of the Fifth Axiom of Euclid or as it is known, the Axiom of parallel of Euclid. In the nal part of this work we shall cover three main models of Hyperbolic Geometry: Beltrami-Klein, Poincaré Disk and the Poincaré Half Plane. We also demonstrate that these models are isomorphic
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Moro, Ana Cecilia Del. "Geometria das dobraduras e aplicações no Ensino Médio." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-03102017-172103/.
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Este trabalho tem como foco a dobradura em sala de aula, auxiliando o professor em sua prática docente. Com dobras simples de serem realizadas a dobradura pode auxiliar o aluno a desenvolver a concentração, estimular a criatividade, concretizar uma ideia ou pensamento no momento em que surge a foma no papel e, consequentemente, o aluno interioriza o aprendizado desejado. Os tópicos estudados versam sobre a construção dos principais polígonos regulares e de um sólido espacial, o tetraedro. São também estudadas algumas aplicações aritméticas, como divisão de segmentos e raízes quadradas e cúbicas.This work aims to study the activity of paper folding in the classroom as an auxiliary resource for the teacher. The folders are quite simple and will improve the students skills on concentration, creativity, and the ability to realize on paper his/her thoughts and ideas. The covered topics range from the construction of the main regular poligons, a spatial solid (tetrahedron), through some arithmetic applications, like division of a segment and square and cubic roots.
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Silva, Dênis Aparecido da [UNESP]. "Sobre problemas de máximo e mínimo na Geometria Euclidiana." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/99835.
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oliveira_jm_me_rcla.pdf: 445828 bytes, checksum: 63763d24a09accecdc86bcfa4315e12d (MD5)Neste trabalho estudamos alguns problemas clássicos envolvendo máximos e míni- mos na Geometria Euclidiana como, por exemplo, o conhecido Problema de Dido e sua relação com a Desigualdade Isoperimétrica
In this work we study some classical problems envolving maximum and minimum in the Euclidean Geometry. For example, the well known Dido’s Problem and its relation with the Isoperimetric Inequality
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Silva, Dênis Aparecido da. "Sobre problemas de máximo e mínimo na Geometria Euclidiana /." Rio Claro, 2013. http://hdl.handle.net/11449/99835.
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Orientador: Thaís Fernanda Mendes MonisBanca: Vanderlei Marcos do Nascimento
Banca: Edvaldo Lopes dos Santos
O PROFMAT - Programa de Mestrado Profissional em Matemática em Rede Nacional é coordenado pela Sociedade Brasileira de Matemática e realizado por uma rede de Instituições de Ensino Superior
Resumo: Neste trabalho estudamos alguns problemas clássicos envolvendo máximos e míni- mos na Geometria Euclidiana como, por exemplo, o conhecido Problema de Dido e sua relação com a Desigualdade Isoperimétrica
Abstract: In this work we study some classical problems envolving maximum and minimum in the Euclidean Geometry. For example, the well known Dido's Problem and its relation with the Isoperimetric Inequality
Mestre
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Boutry, Pierre. "On the formalization of foundations of geometry." Thesis, Strasbourg, 2018. http://www.theses.fr/2018STRAD042/document.
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Dans cette thèse, nous examinons comment un assistant de preuve peut être utilise pour étudier les fondements de la géométrie. Nous débutons en nous concentrant sur les façons d’axiomatiser la géométrie euclidienne et leurs relations. Ensuite, nous exposons une nouvelle preuve de l’indépendance de l’axiome des parallèles des autres axiomes de la géométrie euclidienne du premier ordre. Cela nous amène à affiner la classification des plans de Hilbert de Pejas en considérant les propriétés de décidabilité. Mais, notre intuition nous amène souvent à négliger leur utilisation. Un assistant de preuve nous permet d’utiliser un outil parfait qui ne possède aucune intuition : un ordinateur. De plus, les assistants de preuve nous laissent exploiter les capacités de calcul des ordinateurs. Nous démontrons comment utiliser de méthodes algébriques de déduction automatique en géométrie synthétique. Enfin, nous présentons une procédure spécifique destinée à automatiser des preuves d’incidenceIn this thesis, we investigate how a proof assistant can be used to study the foundations of geometry. We start by focusing on ways to axiomatize Euclidean geometry and their relationship to each other. Then, we expose a new proof that Euclid’s parallel postulate is not derivable from the other axioms of first-order Euclidean geometry. This leads us to refine Pejas’ classification of parallel postulates. We do so by considering decidability properties when classifying the postulates. However, our intuition often guides us to overlook uses of such properties. A proof assistant allows us to use a perfect tool which possesses no intuition: a computer. Moreover, proof assistants let us leverage the computational capabilities of computers. We demonstrate how we enable the use of algebraic automated deduction methods thanks to the arithmetization of geometry. Finally, we present a specific procedure designed to automate proofs of incidence properties
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Costa, Iêda Maria de Araújo Câmara. "Da geometria euclidiana para a álgebra geométrica do plano." Universidade Federal do Amazonas, 2009. http://tede.ufam.edu.br/handle/tede/3666.
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Previous issue date: 2009-02-27This work will present the Plane Geometric Algebra, according Grassmann postulate, starting the axioms of plane euclidean geometry.
Este trabalho apresenta a Álgebra Geométrica do Plano, de acordo com a proposta de Grassmann, a partir dos axiomas da geometria euclidiana plana.
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Wood, David W. ""Mathesis of the Mind" : a Study of Fichte’s Wissenschaftslehre and Geometry." Paris 4, 2009. http://www.theses.fr/2009PA040135.
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Cette thèse est une étude du rôle de la géométrie dans la philosophie du penseur idéaliste allemand Johann Gottlieb Fichte (1762-1814) dans son œuvre majeure : la Doctrine de la science, en ses différentes versions de 1794 à 1814. Nous proposons une reconstruction de sa philosophie des mathématiques fondée sur le texte fragmentaire de l’Erlanger Logik (1805). La philosophie fichtéenne des mathématiques repose sur neuf éléments principaux. Elle a pour fondement un modèle de géométrie synthétique et transcendantale ; pour point de départ, des éléments archétypaux (Ur) ou idéaux ; et elle est platonicienne quant à son statut ontologique. Elle tente également de résoudre le problème des lignes parallèles et de déduire les dimensions de l’espace. En outre, la théorie fichtéenne de la connaissance mathématique repose sur l’intuition et la construction qui sont interprétées comme des paradigmes pour l’intuition et la construction philosophiques. Toutefois, Fichte montre que toutes les intuitions et constructions spécifiques de la géométrie sont fondées dans les intuitions et constructions plus universelles de sa philosophie. Par ailleurs, les éléments fondamentaux de la géométrie, tels que le point, la ligne et le tracer d’une ligne fournissent chacun une image (Bild) philosophique des divers actes et activités du moi. Enfin, le premier principe ou Grundsatz de sa Doctrine de la science possède, selon Fichte, les mêmes caractéristiques que les premiers postulats de la géométrie : évidence, certitude et irréfutabilité. C’est pourquoi il considère l’étude de la géométrie et des mathématiques pures comme une parfaite propédeutique à l’étude de son système de philosophieThis is a study of the role of geometry in the philosophy of the German idealistic thinker Johann Gottlieb Fichte (1762-1814) in his main life’s work the Wissenschaftslehre (1794-1814). I propose a reconstruction of his philosophy of mathematics based on his fragmentary text the Erlanger Logik 1805. The Fichtean philosophy of mathematics is based on nine principal elements. It includes a synthetic and transcendental model of geometry as its foundation, has a number of archetypal (Ur) or ideal elements as its starting point, and is Platonistic in an ontological sense. It also seeks to solve the problem of parallel lines and the deduction of the dimensions of space. In addition, Fichte’s theory of mathematical cognition is grounded in intuition and construction, which are interpreted as paradigms for philosophical intuition and construction. However, Fichte shows that all the specific intuitions and constructions of geometry are grounded in the more universal intuitions and construction of his philosophy. Moreover, the fundamental elements of geometry, such as the point, line and drawing of the line, all furnish philosophical images (Bilder) for the acts and activities of the I or self. Finally, the first postulates of geometry possess the characteristics of self-evidence, certitude and irrefutability. According to Fichte, the first principle or Grundsatz of his Wissenschaftslehre possesses the same characteristics, thus for him the study of geometry and pure mathematics serves as a perfect propedeutic to the study of his system of philosophy
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Freitas, Aline Claro de. "ORIGAMI : o uso como instrumento alternativo no ensino da geometria /." São José do Rio Preto, 2016. http://hdl.handle.net/11449/134280.
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Orientador: José Roberto NogueiraBanca: Enio Garbelini
Banca: Suetônio de Almeida Meira
Resumo: Frente à realidade do ensino contemporâneo que demanda a necessidade de diversificar o uso de estratégias de ensino, pretendemos propor uma abordagem, por meio de material concreto e que pode tornar-se bastante significativa no ensino da matemática. Este trabalho discute sobre a história, aplicações clássicas e utilização do origami em sala de aula. Após uma breve apresentação histórica sobre o origami, apresentamos uma abordagem axiomática deste instrumento. Dois dos três famosos problemas matemáticos gregos da antiguidade que não podem ser solucionados através da régua e compasso: trissecção do ângulo e duplicação do cubo encontram uma solução por meio das técnicas de origami. Além disso, apresentamos sugestões de roteiros de aulas e a atividade aplicada em sala de aula que obteve resultado satisfatório
Abstract: Faced with the reality of contemporary teaching that demands the need to diversify the use of teaching strategies, we intend to propose an approach through concrete material and can become quite significant in mathematics education. This monograph discusses about the history, classic applications and use origami in the classroom. After a brief historical introduction about origami, we present an axiomatic approach of this instrument. Two of the three famous Greek mathematical problems of antiquity that can't be solved by ruler and compass: trisection angle and doubling the cube find a solution through of origami techniques. In addition, we present suggestions classes scripts and the activitie applied in the classroom that obtained satisfactory result
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Joy, Jimin. "Efficient and accurate geometric simulation of multi-axis milling operations." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/63088.
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The full abstract for this thesis is available in the body of the thesis, and will be available when the embargo expires.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Uddin, Mohammad Sharif. "Tool Path Modification Approaches to Enhance Machining Geometric Accuracy in 3-Axis and 5-Axis Machining." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/49142.
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学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2861号 ; 請求記号: 新制/工/1420 ; 整理番号: 25546Introduction Precision manufacture of components has become a necessity in the present day manufacturing sectors. The ever-increasing demands of humankind have forced researchers to come up with more improved innovations in technology; achieving higher levels of integration in microprocessors, and creating more versatile and precision multitasking systems being just a few of the major drivers in this area. All these, however, have one rudimentary requirement, namely, the need to use very high precision components. Hence, it can be very safely concluded that the success of each of these industries hinges on the ability to produce such components. Recently, as the tremendous demands for mechanical parts with high geometric and dimensional accuracy increase, an exigency to produce those parts with such accuracy is greatly comprehended by today’s manufacturing industries. To this end, CNC machine tools are the most important means of production for the manufacturing industries. CNC machine tools have been widely applied to a range of applications, for example, in the aerospace industries. With the recent advancement of the machine tools manufacturing technologies including high speed feed drives and high speed spindles, high speed end milling on the CNC machine tools has become constantly popular, and is being performed to manufacture the components with the required contour geometry and dimensional accuracy. However, the geometric accuracy of the machined surface is greatly affected by the numerous errors sources ranging from errors existing in the machine tool system itself to the errors due to the cutting process. Figure 1-1 shows the general error sources that influence the machining geometric accuracy [Kakino et al., 1993]. Broadly, machining geometric errors are caused by two major error sources: motion errors of the machine tool system and errors due to the machining process. The key factors among error sources in the machine tool system that cause deviation of tool tip position relative to workpiece, and hence machining geometric errors are positioning errors and volumetric errors. Here, positioning errors are defined as the linear errors of the positioning mechanism, whose directions are in parallel with the direction of axis movement required for desired positioning. On the other hand, volumetric errors are here defined as error components whose directions are perpendicular to the direction of axis movement.
Kyoto University (京都大学)
0048
新制・課程博士
博士(工学)
甲第13390号
工博第2861号
新制||工||1420(附属図書館)
25546
UT51-2007-Q791
京都大学大学院工学研究科精密工学専攻
(主査)教授 松原 厚, 教授 吉村 允孝, 教授 松久 寛
学位規則第4条第1項該当
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Jiang, Xiaogeng. "Characterising geometric errors in rotary axes of 5-axis machine tools." Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5871/.
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It is critical to ensure that a 5-axis machine tool is operating within its geometric tolerance. However, there are various sources of errors influencing its accuracy; testing them with current methods requires expensive equipment and long machine down time. This motivates the development of a simple and fast way to identify and characterise geometric errors of 5-axis machine tools. A method using a Double Ball Bar (DBB) is proposed to characterise rotary axes Position Independent Geometric Errors (PIGEs), which are caused by imperfections during assembly of machine components. An established method is used to test the same PIGEs, and the results are used to validate the developed method. The Homogeneous Transformation Matrices (HTMs) are used to build up a machine tool model and generate DBB error plots due to different PIGEs based on the given testing scheme. The simulated DBB trace patterns can be used to evaluate individual error impacts for known faults and diagnose machine tool conditions. The main contribution is the development of the fast and simple characterisation of the PIGEs of rotary axes. The results show the effectiveness and improved efficiency of the new methods, which can be considered for 5-axis machine tool maintenance and checking.
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Ho, Stephen 1974. "Real-time detection of geometric interference : application to full-body 5-axis haptics." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/80505.
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Postolski, Michal. "Discrete topology and geometry algorithms for quantitative human airway trees analysis based on computed tomography images." Phd thesis, Université Paris-Est, 2013. http://pastel.archives-ouvertes.fr/pastel-00977514.
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Computed tomography is a very useful technic which allow non-invasive diagnosis in many applications for example is used with success in industry and medicine. However, manual analysis of the interesting structures can be tedious and extremely time consuming, or even impossible due its complexity. Therefore in this thesis we study and develop discrete geometry and topology algorithms suitable for use in many practical applications, especially, in the problem of automatic quantitative analysis of the human airway trees based on computed tomography images. In the first part, we define basic notions used in discrete topology and geometry then we showed that several class of discrete methods like skeletonisation algorithms, medial axes, tunnels closing algorithms and tangent estimators, are widely used in several different practical application. The second part consist of a proposition and theory of a new methods for solving particular problems. We introduced two new medial axis filtering method. The hierarchical scale medial axis which is based on previously proposed scale axis transform, however, is free of drawbacks introduced in the previously proposed method and the discrete adaptive medial axis where the filtering parameter is dynamically adapted to the local size of the object. In this part we also introduced an efficient and parameter less new tangent estimators along three-dimensional discrete curves, called 3D maximal segment tangent direction. Finally, we showed that discrete geometry and topology algorithms can be useful in the problem of quantitative analysis of the human airway trees based on computed tomography images. According to proposed in the literature design of such system we applied discrete topology and geometry algorithms to solve particular problems at each step of the quantitative analysis process. First, we propose a robust method for segmenting airway tree from CT datasets. The method is based on the tunnel closing algorithm and is used as a tool to repair, damaged by acquisition errors, CT images. We also proposed an algorithm for creation of an artificial model of the bronchial tree and we used such model to validate algorithms presented in this work. Then, we compare the quality of different algorithms using set of experiments conducted on computer phantoms and real CT dataset. We show that recently proposed methods which works in cubical complex framework, together with methods introduced in this work can overcome problems reported in the literature and can be a good basis for the further implementation of the system for automatic quantification of bronchial tree properties
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Bringmann, Bernhard. "Improving geometric calibration methods for multi-axis machining centers by examining error interdependencies effects /." Düsseldorf : VDI-Verl, 2007. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015962642&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Flynn, Joseph. "The identification of geometric errors in five-axis machine tools using the telescoping magnetic ballbar." Thesis, University of Bath, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.698982.
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To maximise productivity and reduce scrap in high-value, low-volume production, five-axis machine tool (5A-MT) motion accuracy must be verified quickly and reliably. Numerous metrology instruments have been developed to measure errors arising from geometric imperfections within and between machine tool axes (amongst other sources). One example is the TMBB, which is becoming an increasingly popular instrument to measure both linear and rotary axis errors. This research proposes new TMBB measurement technique to rapidly, accurately and reliably measure all position-independent rotary axis errors in a 5A-MT. In this research two literature reviews have been conducted. The findings informed the subsequent development of a virtual machine tool (VMT). This VMT was used to capture the effects of rotary and linear axis position-independent geometric errors, and apparatus set-up errors on a variety of candidate measurement routines. This new knowledge then informed the design of an experimental methodology to capture specific phenomena that were observed within the VMT on a commercial 5A-MT. Finally, statistical analysis of experimental measurements facilitated a quantification of the repeatability, strengths and limitations of the final testing method concept. The major contribution of this research is the development of a single set-up testing procedure to identify all 5A-MT rotary axis location errors, whilst remaining robust in the presence of set-up and linear axis location errors. Additionally, a novel variance-based sensitivity analysis approach was used to design testing procedures. By considering the effects of extraneous error sources (set-up and linear location) in the design and validation phases, an added robustness was introduced. Furthermore, this research marks the first usage of Monte Carlo uncertainty analysis in conjunction with rotary axis TMBB testing. Experimental evidence has shown that the proposed corrections for set-up and linear axis errors are highly effective and completely indispensable in rotary axis testing of this kind. However, further development of the single set-up method is necessary, as geometric errors cannot always be measured identically at different testing locations. This has highlighted the importance of considering the influences on 5A-MT component errors on testing results, as the machine tool axes cannot necessarily be modelled as straight lines.
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Silva, Lucilene Moraes da. "Cálculo do escoamento em uma turbina axial de alta pressão com diferentes configurações na geometria do topo do rotor utilizando técnicas de CFD." Instituto Tecnológico de Aeronáutica, 2012. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2032.
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Os motores do tipo turbinas a gás são utilizados em aplicação onde altas potências são requeridas. Para ambas as aplicações, industrial ou aeronáutica, a busca por alta eficiência e desempenho é constante, procurando melhorar o processo de transferência de energia. Nesse ponto, torna-se importante a pesquisa e o estudo de componentes mais sofisticados. É nesse contexto, que o presente trabalho foi desenvolvido para avaliar um dos itens de grande influência no desempenho de turbomáquinas, conhecido como perdas de alto desempenho devido ao escoamento interno sobre o topo do rotor. O escoamento que passa do lado de pressão para o lado de sucção da pá através do topo do rotor é chamado de escoamento de vazamento, este não participa do processo de transferência de energia, sendo uma fonte de perda interna que causa queda na eficiência da turbomáquina. Neste estudo, diferentes tecnologias para a geometria do topo das pás do rotor são utilizadas para analisar a influência destas geometrias em uma turbina axial de alta pressão (HPT) de único estágio. O estudo dessas diferentes configurações no topo do rotor da turbina foi baseado nos cálculos do escoamento utilizando a dinâmica dos fluidos computacional (CFD) com equações de Navier-Stokes com média de Reynolds (RANS), utilizando o programa comercial ANSYS CFX v. 13.0. A configuração de topo padrão (topo plano) foi modificada e as seguintes configurações foram utilizadas: sem folga, com topo plano, com squealer, com winglet e com squealer-winglet. Os resultados mostraram que os métodos de dessensibilização aplicados no topo do rotor possuem melhor desempenho que o caso com topo plano. A configuração winglet apresentou melhor resultados que as outras configurações para a turbina na rotação de projeto. E a configuração squealer-winglet apresentou melhor resultados que as outras configurações para 80% da rotação de projeto. As três configurações de dessensibilização estudadas comprovaram serem superiores ao rotor de topo plano, justificando seu uso para aplicações em turbina de alta pressão.
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Zhao, Wulue. "Shape and medial axis approximation from samples." Columbus, Ohio : Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1059593634.
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Thesis (Ph. D.)--Ohio State University, 2003.Title from first page of PDF file. Document formatted into pages; contains xvi, 131 p.; also includes graphics (some col.). Includes abstract and vita. Advisor: Tamal K. Dey, Dept. of Computer and Information Science. Includes bibliographical references (p. 126-131).
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Pádua, Eduardo de Melo. "Controle de ressonância de base de máquinas rotativas por meio de forças axiais." reponame:Repositório Institucional da UFABC, 2017.
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Orientador: Prof. Dr. Reyolando M. L. R. F. BrasilDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2017.
Neste trabalho realiza-se um estudo do efeito causado pela alteracao da rigidez geometrica, por meio de forcas axiais, na frequencia natural de bases de maquinas rotativas, na forma de viga e portico plano, todos metalicos, no intuito de tira-las na ressonancia ou proximo dessa regiao. Essa regiao proxima da ressonancia e chamada de regiao fora de seguranca e compreende o intervalo que comeca em 20% abaixo da frequencia da maquina ate 25% acima dela. Duas ferramentas foram utilizadas para realizar o estudo, Metodo de Rayleigh e Metodo dos Elementos Finitos (MEF). Na viga estuda-se um perfil estrutural de um tubo retangular em aco estrutural, utilizando o Metodo de Rayleigh e o MEF. Ja o portico e estudado somente pelo MEF, so que mais perfis foram analisados desse mesmo tubo. No caso da base como viga, sem carregamento algum, ela se mostrou dentro na zona perigosa, tanto por Rayleigh como por MEF. Uma intervencao com forcas axiais foi realizada para estabilizar as bases. No portico tanto portico, o perfil 60x60 nao ficou dentro da zona perigosa, ja os demais, 80x80 e perfil ¿§, ficaram dentro da regiao { 0,8¿¶, 1,25¿¶ }. O estudo mostrou que a rigidez geometrica
In this work a study of the effect caused by the alteration of the geometric stiffness, by means of axial forces, in the natural frequency of bases of rotating machines, in the form of beam and plan portico, all metallic, in order to take them out in the resonance or near this region. This region near the resonance is called unsafe region, and comprises the range starting at 20% below the frequency of the machine and to 25% above it. Two tools were used to carry out the study, Rayleigh Method and Finite Element Method (FEM). In the beam, a structural profile of a rectangular tube in structural steel is studied, using the Rayleigh Method and MEF. Already the portico is studied only by MEF, except that more profiles were analyze in this same tube. In the case of the base as beam, without any loading, it showed itself inside the dangerous zone, by both Rayleigh and MEF. An axial force intervention was performed to stabilize the bases. In the planar portal frame, the 60x60 profile was not inside the dangerous zone, while the others, 80x80 and profile É, were within the region {0.8Ù, 1.25Ù}. The study showed that the geometric stiffness has a close relation with the natural frequencies in solid structures.
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Ding, Ke. "A study on a new geometric modeling for off-line and on-line multi-axis machining simulation system /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2004. http://uclibs.org/PID/11984.
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Lai, Guanyu. "Distributed actuation and control for morphing structures." Thesis, University of Bath, 2017. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760934.
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It is believed that structures and actuation systems should be tightly integrated together in the future to create fast moving, efficient, lightweight dynamic machines. Such actuated structures could be used for morphing aircraft wings, lightweight actuated space structures, or in robotics. This requires actuators to be distributed through the structure. A tensegrity structure is a very promising candidate for this future integration due to its potentially excellent stiffness and strength-to-weight ratio, and the inherent advantage of being a multi-element structure into which actuators can be embedded. Development of these machines will utilise expertise in several fields, involving kinematics, dynamics, actuation and multi-axis motion control. The research presented in this thesis concerns the study of multi-axis actuated tensegrity structures. A form-finding method has been developed to find stable geometries and determine stiffness properties of the type of tensegrity structure proposed. It has been shown that a tensegrity structure, with practical nodes of finite size, can be designed with actuated members to give shape-changing properties while potentially allowing a good stiffness to mass ratio. An antagonistic multi-axis control scheme has been developed for the tensegrity structure. The describing function technique has been used to analyse the dead band controller in the control scheme, giving a stability criterion. An experimental actuated tensegrity system has been designed and built incorporating pneumatic muscles controlled by switching valves. Mathematical models for the experimental actuated tensegrity system have been developed in detail, including the pneumatic actuation system and the structure geometry. The dynamic behaviour of the tensegrity system has been investigated via several simulation studies, using the developed models and the proposed control scheme. Experimental validation has been successfully conducted. The multi-axis control scheme can accurately control the tensegrity structure to achieve shape changes while maintaining a desired level of internal pre-load. The mathematical models can be used as a basis for further development.
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Hong, Cefu. "Error Calibration on Five-axis Machine Tools by Relative Displacement Measurement between Spindle and Work Table." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157572.
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Nguyen, Tuong. "Unions finies de boules avec marges interne et externe." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAT022/document.
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Représenter un objet géométrique complexe par un ensemble de primitives simples est une tâche souvent fondamentale, que ce soit pour la reconstruction et la réparation de données, ou encore pour faciliter la visualisation ou la manipulation des données. Le choix de la ou les primitives, ainsi que celui de la méthode d'approximation, impactent fortement les propriétés de la représentation de forme qui sera obtenue.Dans cette thèse, nous utilisons les boules comme seule primitive. Nous prenons ainsi un grand soin à décrire les unions finies de boules et leur structure. Pour cela, nous nous reposons sur les faisceaux de boules. En particulier, nous aboutissons à une description valide en toute dimension, sans hypothèse de position générale. En chemin, nous obtenons également plusieurs résultats portant sur les tests d'inclusion locale et globale dans une union de boules.Nous proposons également une nouvelle méthode d'approximation par union finie de boules, l'approximation par boules à (delta,epsilon)-près. Cette approche contraint l'union de boules à couvrir un sous-ensemble de la forme d'origine (précisément, un epsilon-érodé), tout en étant contenu dans un sur-ensemble de la forme (un delta-dilaté). En nous appuyant sur nos précédents résultats portant sur les unions de boules, nous démontrons plusieurs propriétés de ces approximations. Nous verrons ainsi que calculer une approximation par boules à (delta,epsilon)-près qui soit de cardinal minimum est un problème NP-complet. Pour des formes simples dans le plan, nous présentons un algorithme polynomial en temps et en espace qui permet de calculer ces approximations de cardinal minimum. Nous concluons par une généralisation de notre méthode d'approximation pour une plus large variété de sous-ensembles et sur-ensemblesDescribing a complex geometric shape with a set of simple primitives is often a fundamental task for shape reconstruction, visualization, analysis and manipulation. The type of primitives, as well as the choice of approximation scheme, both greatly impact the properties of the resulting shape representation.In this PhD, we focus on balls as primitives. Using pencils of balls, we carefully describe finite unions of balls and their structure. In particular, our description holds in all dimension without assuming general position. On our way, we also establish various results and tools to test local and global inclusions within these unions.We also propose a new approximation scheme by union of balls, the (delta,epsilon)-ball approximation. This scheme constrains the approximation to cover a core subset of the original shape (specifically, an epsilon-erosion), while being contained within a superset of the shape (a delta-dilation). Using our earlier results regarding finite unions of balls, we prove several properties of these approximations. We show that computing a cardinal minimum (delta,epsilon)-ball approximation is an NP-complete problem. For simple planar shapes however, we present a polynomial time and space algorithm that outputs a cardinal minimum approximation. We then conclude by generalizing the approximation scheme to a wider range of core subsets and bounding supersets
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Sickmann, Jan. "Ortsaufgelöste Messung der Gitterverspannungen in Halbleitern mittels Dunkelfeld off-axis Elektronenholographie." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-160646.
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Die Dunkelfeld off-axis Elektronenholographie (DFH) im Transmissionselektronenmikroskop ist eine nanoskalige Interferometriemethode, die es erlaubt, eine ausgewählte Beugungswelle eines Kristalls aufzuzeichnen und anschließend als zweidimensionale Amplituden- und Phasenverteilung zu rekonstruieren. Da sich aus dem Gradientenfeld der Phasenverteilung geometrische Verzerrungen des Kristallgitters bestimmen lassen, ermöglicht die DFH, Deformationsfelder in Kristallen zu vermessen. Damit eröffnen sich der Halbleiterindustrie vielversprechende Analysemöglichkeiten von lokalen mechanischen Verspannungen in Halbleiterkristallen insbesondere im Kanalbereich von Transistoren. Dabei verspricht die DFH eine höhere Ortsauflösung als rasternde, auf Elektronenbeugung mit möglichst fein fokussierten Elektronensonden basierende Methoden wie Nanobeugung. Jedoch steht die DFH als Analysemethode für mechanische Verspannungen bisher noch nicht standardmäßig zur Verfügung. Forschungs- und Entwicklungsbedarf besteht insbesondere hinsichtlich der Anpassung der Methodik auf kompliziertere Halbleiterstrukturen. Am Beispiel des Elementargitters wird demonstriert, wie einerseits die Gitterverzerrung die Phase der Beugungswelle moduliert, und wie andererseits aus dem Gradient der Phase diese Deformation wieder rekonstruiert werden kann. Zusätzlich wird die Modulation der Beugungswelle mit Hilfe eines erst kürzlich veröffentlichten analytischen Modells für den Zweistrahlfall erläutert. Spezielle Anpassungen der DFH im TEM erlauben, die geometrische Phase entweder mit 3...5 nm Lateralauflösung bei 200 nm breitem Gesichtsfeld oder mit 8...10 nm Lateralauflösung bei 800 nm breitem Gesichtsfeld aufzuzeichnen. Da die Deformationskarte durch numerische Ableitung der geometrischen Phase bestimmt wird, hängt die Signalauflösung der Deformationsmessung direkt von der Signalqualität in der rekonstruierten geometrischen Phase ab. Da die Ableitung das Rauschen verstärkt, werden verschiedene Strategien zur Rauschminderung und Signalverbesserung untersucht, u.a. werden Methoden zur Rauschfilterung eines DF-Hologramms oder zur Glättung der Deformationskarte vorgestellt. Durch Rekonstruktion einer gemittelten geometrischen Phase aus einer Dunkelfeldhologrammserie lassen sich Deformationen E mit einer Messabweichung von lediglich Delta_E=+/-0,05% bestimmen. Bei Aufzeichnung und Rekonstruktion der geometrischen Phase treten eine Reihe von Artefakten auf, die durch Fresnelsche Beugungssäume, defekte Detektorpixel sowie Verzeichnungen durch Projektivlinsen und Detektoroptik hervorgerufen werden. Da sie die Bestimmung der Deformationskarte erschweren, werden geeignete Methoden zur Vermeidung oder Korrektur vorgestellt. Die Präparation von TEM-Lamellen mit fokussiertem Ionenstrahl (FIB) verursacht Schädigungen der Probenoberfläche. Durch Vergleiche von DFH-Messungen mit Finite-Elemente-Simulationen wird gezeigt, dass die auf Oberflächenrelaxation zurückzuführenden Abweichungen vom simulierten Deformationszustand bei 120...160 nm Lamellendicke bis zu 10% betragen können. Präparationsbedingte lokale Dickenvariationen (Curtaining) können zu ähnlich großen Abweichungen führen. Anwendbarkeit und Funktionalität der DFH werden an modernen Halbleiterstrukturen untersucht. Die Vermessung einer verspannten SiGe-Schicht auf Si-Substrat zeigt eine sehr gute Übereinstimmung mit einem analytischen Modell. Die Abweichung beträgt ca. 10% und kann durch Oberflächenrelaxation an der SiGe/Si-Grenzfläche erklärt werden. Mittels SiGe an Source und Drain verspannte Transistoren dienen als Testobjekte für einen Vergleich von DFH und Nanobeugung. Beide Methoden liefern identische Ergebnisse. Der Vorteil der DFH besteht jedoch darin, das Deformationsfeld vollständig in Form einer zweidimensionalen Karte abzubilden, anstatt wie die Nanobeugung lediglich einzelne Profilschnitte zu messen. Die Deformationsmessung an SOI-Strukturen wird durch die leicht unterschiedliche Kristallorientierung (Miscut) zwischen SOI und Si-Substrat, das als Referenzbereich dient, erschwert. Die Deformationswerte im SOI zeigen ein Offset von 0,2% Dehnung gegenüber dem Si-Substrat. Der Miscut zwischen SOI und Si-Substrat kann zu 0,3°bestimmt werden. Für Transistoren mit tensiler Deckschicht gelingt es, Dehnungen von +0,3% in perfekter Übereinstimmung mit FE-Simulationen zu messen. Bei Transistoren, bei denen gleichzeitig eine kompressive Deckschicht und SiGe an Source und Drain eingesetzt werden, gelingt es mittels DFH, Stauchungen von -(0,1+/-0,05)% im Transistorkanal 5 nm unterhalb des Gateoxids nachzuweisenDark-field off-axis electron holography (DFH) in a transmission electron microscope is based on the interference of a diffracted wave emanating from adjacent strained and unstrained sample areas to form a dark-field hologram, from which the phase of the diffracted wave can be reconstructed. Since the gradient of the phase parallel to the diffraction vector yields the lattice strain in this direction, a two-dimensional strain map can be derived. Therefore, DFH is considered to be a promising technique for strain metrology by semiconductor industry, especially for local strain measurements in the transistor channel. In particular, DFH offers better lateral resolution than scanning TEM-techniques based on electron diffraction with small focused electron probe like nano-beam diffraction. However, DFH is not yet available as a standard technique for strain metrology. Research is still needed to apply the method to complex devices. Using the example of a strained cosine lattice the phase modulation due to lattice distortions is discussed. In addition, modulation of the diffracted wave is approximated in two-beam diffraction condition. Adjustments of DFH in the TEM provide strain measurements with 3...5 nm lateral resolution at 200 nm field of view or 8...10 nm lateral resolution at 800 nm field of view. During recording and reconstruction of dark-field holograms several artifacts appear, for instance Fresnel diffraction, defective detector pixels, distortions of projective lenses or detector optics. Since they limit strain evaluation, suitable methods to either avoid or correct these artifacts are discussed. Sample preparation with focused ion beam (FIB) causes surface damage. Comparing DFH results with finite-element simulations reveals a deviation of 10% between simulation and experiment at 120...160 nm sample thickness due to surface relaxation. FIB-induced thickness variations (curtaining) lead to comparable deviations. Applicability of DFH for strain metrology is analyzed on several modern device structures. Strain measurements of SiGe-layers on Si-substrate correspond quite well with an analytic model. A residual deviation of 10% can be explained by surface relaxation close to the SiGe/Si-interface. Transistors strained by SiGe-source/drain serve as test objects for a comparison of DFH with nano-beam diffraction. Though both techniques reveal identical results, DFH is able to map the complete two-dimensional strain field, whereas nano-beam diffraction can only provide single line-scans. Strain mapping in silicon-on-insulator (SOI) is limited by the different crystal orientation (miscut) between the SOI layer and the Si-substrate, which serves as reference. Strain values in the SOI show an off-set of 0.2% in comparison to the unstrained Si-substrate. The miscut between SOI and Si-substrate is estimated to 0.3°. In transistor devices with tensile stress overlayers DFH is able to measure +0.3% tensile strain in excellent agreement with finite-element simulations. In devices with compressive overlayers and SiGe-source/drain a strain value of only -(0.1+/-0.05)% can be determined in the transistor channel 5nm beneath the gate oxide
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Silva, Janderson Ribeiro da. "Pontos axiumbílicos de superfícies imersas em R4." Universidade Federal de Sergipe, 2016. https://ri.ufs.br/handle/riufs/5821.
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The notion of umbilic points and principal curvature lines are traditionally studied in surfaces of R3. Our goal is to extend these notions to surfaces immersed in R4. For this, we will analyze the image of the second fundamental form, restricted to the unit circle in the normal plane of the surface. We show that this image is an ellipse, called ellipse of curvature. The points where the ellipse of curvature becomes a circle are called axiumbilics points and lines corresponding to large and small axes of the ellipse are called, respectively, of principal and mean axial lines. In this work we describe the structure of the principal axial lines on surfaces immersed in R4 in the neighborhood of generic axiumbilics points.As noções de pontos umbílicos e linhas de curvatura principal são tradicionalmente estudadas em superfícies do R3. Nosso objetivo é estender essas noções para superfícies imersas em R4. Para isto, analisaremos a imagem da segunda forma fundamental, restrita ao círculo unitário, no plano normal da superfície. Mostraremos que tal imagem é uma elipse, chamada elipse de curvatura. Os pontos onde a elipse de curvatura se torna um círculo são chamados pontos axiumbílicos e as linhas correspondentes ao eixo maior e menor da elipse são chamadas, respectivamente, de linhas axiais principais e médias. Neste trabalho descreveremos a estrutura das linhas axiais principais de imersões de superfícies em R4 na vizinhança de pontos axiumbílicos genéricos.
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Viprey, Fabien. "Modélisation et caractérisation des défauts de structure de machine-outil 5 axes pour la mesure in-process." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLN071/document.
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Le principe de la métrologie en cours d’usinage est d'obtenir des données de mesure directement dans le flot de production. Ce principe fait suite au besoin croissant des industriels de réaliser des mesures en ligne durant une opération ou entre deux opérations d'usinage en employant le moyen de production pour mesurer la pièce usinée. La maîtrise des sources d’erreur de mesure telles que les erreurs géométriques est une condition sine qua non pour garantir la métrologie dimensionnelle traçable directement sur les machines-outils. Ces travaux portent sur la modélisation géométrique de machine-outil 5 axes, basée sur une paramétrisation normalisée des erreurs géométriques. Ce modèle est simulé et simplifié par l’utilisation d’une machine virtuelle développée comme un outil d’aide à la compréhension et à la visualisation des effets des erreurs géométriques sur l’erreur volumétrique. Un nouvel étalon matériel thermo-invariant a été développé : la Multi-Feature Bar. Raccordé à la définition internationale du mètre par un étalonnage et une intercomparaison européenne, il permet d’envisager des mesures traçables sur machine-outil dans un environnement hostile. L’identification de trois paramètres intrinsèques à cet étalon, couplée à une procédure de mesure, assure une identification complète et traçable des erreurs de mouvement d’axes linéaires. Suite à cela, l’identification des erreurs entre axes est quant à elle basée sur une analyse de combinaisons de paramètres suffisants pour caractériser au mieux l’erreur volumétrique. Une procédure d’identification des paramètres du modèle est proposée en minimisant la dérive temporelle de la structure ainsi que les effets des erreurs de mouvement précédemment identifiées. Une analyse de sensibilité des paramètres de réglages de la procédure de mesure ainsi que des effets de bruits permet de garantir la qualité de l’identification proposéeIn-process metrology consists in obtaining measurement data directly into the manufacturing process. This method results from an increasing need of manufacturers to carry out on-line measurements during one manufacturing task or between two manufacturing tasks by using the mean of production to measure the machined part. Monitoring the sources of errors like geometric errors is one of the prerequisites to ensure the traceable dimensional metrology directly on the machine tool.This thesis deals with the geometric modeling of 5-axis machine tool based on a standardized parameterization of geometric errors. This model is simulated and simplified by the use of a virtual machine developed in order to help understand and visualize the effects of geometric errors on the volumetric error.A new standard thermo-invariant material namely Multi-Feature Bar has been developed.After its calibration and after a European intercomparison, it provides a direct metrological traceability to the SI meter for dimensional measurement on machine tool in a hostile environment. The identification of three intrinsic parameters of this standard, coupled with a measurement procedure ensures complete and traceable identification of motion errors of linear axes. The identification of position and orientation errors of axis is based on an analysis of combinations of necessary parameters to characterize volumetric error and at best. A model parameter identification procedure is proposed by minimizing the time drift of the structural loop and the effects of previously identified motion errors. Asensitivity analysis of the measurement procedure settings and of the noise effects ensures the quality of this proposed identification
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De, Notariis Kevin. "Light hyperweak new gauge bosons from kinetic mixing in string models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19491/.
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String theory is at the moment our best candidate for a unified quantum theory of gravity, aiming to reconcile all the known (and unknown) interactions with gravity as well as provide insights for currently mysterious phenomena that the Standard Model and the modern Cosmology are not able to explain. In fact, it is believed that most of the problems associated to the Standard Model can indeed be resolved in string theory. Supersymmetry is supposed to be an elegant solution to the Hierarchy problem (even though more and more stringent bounds in this direction are being placed by the fact that we have been unable to experimentally find supersymmetry yet), while all the axions that compactifications bring into play can be used to resolve the strong CP problem as well as provide good candidates for Dark Matter. Inflationary models can also be constructed in string theory, providing, then, the most diffused solution to the Horizon problem. This work, in particular, is formulated in type IIB string theory compactified on an orientifolded Calabi-Yau three-fold in LARGE Volume Scenario (LVS) and focuses on the stabilisation of all the moduli in play compatible with the construction of a hidden gauge sector whose gauge boson kinetically mixes to the visible sector U(1), acquiring a mass via a completely stringy process resulting in the St{\"u}ckelberg mechanism. The "compatibility" regards the fact that certain experimental bounds should be respected combined with recent data extrapolated by Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) events at the Spallation Neutron Source at Oak Ridge National Laboratory. We are going to see that in this context we will be able to fix all the moduli as well as present a brane and fluxes set-up reproducing the correct mass and coupling of the hidden gauge boson. We also get a TeV scale supersymmetry, since the gravitino in this model will be of order O(TeV), with an uplifted vacuum to reproduce a de Sitter universe as well.
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Dvořáček, Jan. "Analýza silového zatížení řezného nástroje při pětiosém frézování." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228829.
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The diploma thesis is focused on machining using the ball-end shank mill. Content of the preliminary part of the work is a shank mill characteristic and a consequent part shows a splitting of ball-end milling cutters, its application, the cutting tool geometry and a characteristic signs of machining. The cutting force model of the ball-end mill is presented as well. A part of proposed model is the conversion of the resultant force too. Practical part is aimed at cutting force analysis of the ball-end mill and the main purpose of this part is a quantification of the cutting force for different work piece tilt angles while milling is performed.
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Cheng, Chien-Hua, and 鄭鈐華. "The Performance of Sixth Graders on Geometry Problems that are Conducive to the Use of the Equality Axioms." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/67563062112467161399.
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碩士國立臺灣師範大學
科學教育研究所
91
The Equality Axioms in this study mean “If equals be added to equals, the wholes are equal.” and “If equals be subtracted from equals, the remainders are equal.”; the former is an additional type, and the latter is a subtractive type. There are two main purposes for this study. The first one is to understand sixth graders’ performance of using the Equality Axioms in solving different addional and subtractive geometry problems. The second is to understand how students recognize to solve problems with Equality Axioms, and what problem solving strategies the other students use and why they do. This study was a investigation through the written test designed by the researcher, and the way of case study matched with interview. The structure of the instrument was based on Equality Axioms’ three components by Tam & Lien (2002). There were 29 students in this study. They were chosen from a sixth class of an elementary school in Taipei County. And eight different achievers were chosen for the interview. To understand students’ performance in using Equality Axioms, this study took the way of descriptive statistic in the quantitative analysis, and also adopted the protocol analysis in qualitative analysis. To get the realistic data, we also used the data triangulation. By these methods, we could understand sixth graders’ performance of using Equality Axioms in different geometry problems. The results in the study were: (a)The performance of different backgrounds’ sixth graders of using Equality Axioms was different. (b)High achievers used Equality Axiom better in area and length problems in 「a=b,c=d」type, and they usually used.other strategies to solve area problems in 「a=a,c=d」type. (c)High achiever used Equality Axioms in additional geometry problems better than subtractive ones. (d)No matter in what geometry problems, low achievers tended to use other strategies to solve problems.(e)Students thought of using Equality Axioms by paying attention to equal conditions, recognizing out the equal parts in the sketch, or trying to use numbers to calculate, use symbles, or write algebra equations. (f)Most of students who didn’t use Equality Axioms usually followed intuitive rules to solve problems.
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Kosina, Jan. "Modely Lobačevského geometrie a možnosti jejich využití na střední škole." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-346123.
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This thesis Models of Lobachevskij's geometry and the possibilities of their use at secondary school focuses on one kind of non-Euclidean geometries, the Bolyai - Lobachevskij's geometry. The first chapter describes the history of non-Euclidean geometry, shows difficulties of understanding of one publication dedicated to these problems by current students of secondary schools and shows some chosen methods in the didactics of mathematics, especialy the constructivist method. The second chapter is dedicated to elemental concepts of projective geometry, Bolyai - Lobachevskij's geometry and it shows its basic models. It further analyses the specific features of this kind of geometry in Beltrami - Klein's model, especially mutual positions of straight lines. This theses further contains a set of gradual tasks. The third chapter is dedicated to the description of a didactical experiment. In this experiment were students of secondary school acquainted with this theory and tasks, which they solved. Student's solution were writen down and than analysed in the constructivist methodology term in the didactics of mathematics.
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LIEN, HSIN CHIN, and 連信欽. "On understanding the use of the Equality Axiom in solving geometry problems by junior high school students." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/73230693992762275343.
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碩士國立臺灣師範大學
科學教育研究所
90
There are two main purposes for this study. The first one is to understand junior high school students’ performance of using the Equality Axiom in solving different geometry problems. The second is to understand whether students’ performance of using the Equality Axiom in solving different geometry problems are related with field independent/field dependent or formal/informal in learning geometry. There were eight students involved in this research. They were chosen form two junior high schools in Taipei city. In each school, we chose 2 grade three students, 1 grade two student and 1 grade one student. So there are 4 grade three students, 2 grade two students and 2 grade one students. This study were an qualitative research and designed by the way of case study, matched with interview, and requested students try to speak out or write down their viewpoints during they solved the geometry problems. We also took all the process with a video recorder. In the part of data analysis, we adopted the way of descriptive statistic in quantitative analysis and the protocol analysis in qualitative analysis and used the data triangulation to get more objective viewpoints. In general the manifestation of the result in the research are: (a)Students’ performance of using Equality Axiom in solving different geometry problems is different. (b)Students’ performance between field independent or field dependent and formal or informal in learning geometry is different. (c)Students were easy influenced by the presentation of the color of the sketch. (d)Some recognized the equal parts in the sketch by drawing or observing the sketch from different angle of views to control the relation between the element and element in the sketch. (e) After students recognized out the equal parts in the sketch, they thought of using Equality Axiom by two ways. The first is arithmetic, the second is trying to deducts the not related part in the sketch. According to the result of the research and the detection of the above, we suggest teachers should emphasize the Equality Axiom under all kind of suitable situations, and educated students to cultivate ability and habits of drawing a sketch. And educated students to observe the sketch from different angle, direction, or distance, to help them control the relation between elements and elements in the sketch and reduce the possibility of the influence of the sketch. And suggest the designer of teaching material should thinking of the presentation of the colors in sketch carefully.
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Kuan, Ming-Yang, and 官明陽. "Geometry Design and Multi-Axis Machining of Distal Radius Volar Plate." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/23495911724175935022.
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碩士正修科技大學
機電工程研究所
100
Wrist is an important joint of high activity rate. A distal radius fracture is a common bone fracture of the radius in the forearm. Because of its proximity to the wrist joint, this injury is often called a wrist fracture. Improper treatment of wrist fracture will cause stiffness, pain, and affect the quality of life seriously. The key of success surgery is to create nice joint restoration. Precise radial bone plate can help doctors to conduct accurate and effective reduction surgery. According to different type of radial cracking for each patient, radius bone plate shape with a fixed position is planned in order to shorten the operation time and increase the success rate of surgery. The main objective of this paper is the geometry design and machining of a radius bone plate. First, reverse engineering equipment is used to capture the important parameters of the geometric shape and curvature of the wrist bones. Those parameters are employed to design the radius bone plate geometry and locking. Three-dimensional model of the radius bone plate is constructed by CAD, the radius bone plate holder fixture is manufactured, and the 3D model of the radius bone plate is imported into Unigraphics NX software. After drawing a reference plane, projection curve, establishing of appropriate tool path, and verifying the correct tool path, the NX processor will export NC codes, the solid cutting simulation software VERICUT will verify that it is the correct cutting tool path. Then, multi-axis NC machine is used to process the work piece, and non-contact 3D optical scanner and contact 3D coordinate measuring machine are employed to verify machining results.
48
Fatalini, Azul Lihuen. "Geometría del plano hiperbólico." Bachelor's thesis, 2019. http://hdl.handle.net/11086/11748.
Full textAbstract:
Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.En este trabajo estudiamos la geometría del plano hiperbólico siguiendo un esquema axiomático similar al de la geometría euclídea. Ambas geometrías coinciden en sus bases, salvo por reemplazar el Axioma de las paralelas o Postulado V de Euclides. Este cambio genera una geometría muy rica, que abre un nuevo mundo en donde los triángulos tienen suma de ángulos interiores menor que 180°, existen rectas paralelas asintóticas y hay pentágonos con todos sus ángulos rectos. Usamos el modelo del semiplano superior para desarrollar los elementos básicos: distancia, trigonometría, área y circunferencias. A lo largo del trabajo, estuvimos guiados por las siguientes preguntas: ¿Cuáles teoremas conocidos se siguen cumpliendo? ¿Hay resultados completamente diferentes a los de la geometría euclídea? Para concluir, haremos una breve mención a los hexaframes, que son una generalización de los hexágonos rectangulares en el espacio hiperbólico.
In the present work we study the hyperbolic plane geometry. We follow an axiomatic approach, similar to the one used in euclidean geometry. Both geometries share their bases with the exception of the parallel postulate, also called Euclid’s fifth postulate. This change generates a really rich geometry. It opens up a world of possibilities, where the sum of the angles of a triangle is always strictly less than 180°, there exist asymptotic parallel lines, and there are right-angled pentagons. We use the Poincaré half-plane model to develop the basic elements in geometry: distance, trigonometry, area and circles. Throughout this work, the following questions have been guiding us: Which well known theorems are still true? Is there any result completely different from the ones in euclidean geometry? To conclude, we will briefly mention the hexaframes, a generalization of the right-angled hexagons in the hyperbolic space.
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Yeh, Chun-Liang, and 葉俊良. "Planning of Tool Attitude for 5-Axis NC Machining of Complex Geometry." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/49490000589604952569.
Full textAbstract:
碩士國立臺灣科技大學
機械工程系
90
Abstract This study proposes the methodology to solve the gouging and collision problems typically found in 5-axis NC machining. A two-stage approach is proposed which finds an initial orientation at the first place, and then uses interference checking to obtain the final tool orientation. The procedures are set as follows: (1)Convert the to-be-machined surface into discrete data points based on the allowable scallop height and chordal deviation. (2)For each point to be machined, find an initial tool orientation by comparing the angles formed by tangent vectors of the cutter-contact points with those formed by vectors among cutter-location points. (3)Check the occurrence of gouging and collision for a specific initial orientation. If gouging takes place, the cutting tool is moved along the tool axis. For the case of collision, the concept of vector fields and the method of configuration space are applied to adjust the tool orientation until all obstacles generated from collision cease to happen. In addition to proposing the methodology, this research adopts ACIS as the geometric kernel to develop a Windows-based prototype system, verifying the feasibility of the proposed approach to solving the problems encountered in five-axis NC machining.
50
Rigsby, James. "Machining Speed Gains in a 3-Axis CNC Lathe Mill." Thesis, 2010. http://hdl.handle.net/10012/5325.
Full textAbstract:
The intent of this work is to improve the machining speed of an existing 3 axis CNC
wood working lathe. This lathe is unique in that it is a modi ed manual lathe that is
capable of machining complex sculptured surfaces. The current machining is too slow for the lathe to be considered useful in an industrial setting. To improve the machining speed of the lathe, several modi cations are made to the mechanical, electrical and software aspects of the system.
It was found that the x-axis of the system, the axis that controls the depth of cut of
the tool, is the limiting axis. A servo motor is used to replace the existing stepper motor, providing the x-axis with more torque and faster response times, which should improve the performance of the system. To control the servo motor, a 1st-order linear transfer function model is selected and identi ed. Then, an adaptive sliding mode controller is applied to make the x-axis a robust and accurate positioning system. A new trajectory generator is implemented to create a smooth motion for all three axes of the lathe. This trajectory uses a 5th-order polynomial to describe the position curve of the feed pro le, giving the system continuous jerk motion. This type of pro le is much easier for motors to follow, as
discontinuous motion will always result in errors. These modi cations to the lathe system
are then evaluated experimentally using a test case. Three test pieces are designed to
represent three of the common shapes that are typically machined on the wood turning
lathe. These test cases indicated a minimum reduction in machining time of 52:91% over
the previous lathe system.
An algorithm is also developed that attempts to sacri ce work piece model geometry to achieve speed gains. The algorithm is used when a certain feedrate is desired for a
model, but machining at that speed will cause toolpath following errors, leaving surface
defects in the work piece. The algorithm will attempt to solve this problem by sacri cing
model geometry. A simulation tool is used to detect where surface defects will occur
during machining and a then the work piece model is modi ed in the corresponding area.
This will create a smoother part, which allows each axis of the system to follow the new toolpath more easily, as the dynamic requirements are reduced. The potential of this algorithm is demonstrated in an experimental test case. A test piece is created that has features of varying di culty to machine. When the algorithm is run, Matlab/Simulink is used simulate the output of the lathe and locate the areas in the part geometry that will cause defects. Once located, the geometry features are smoothed in SolidWorks using the fi llet feature. The algorithm produces a work piece with smoothed geometry that can be machined at a feedrate approximately 42:8% faster than before. Although it is only the first implementation of the algorithm, the experimental results con rm the potential of the
method. Machining speed gains are successfully achieved through the sacrifice of model geometry.