This project has been assigned by SwePart Transmissions AB. It is about calculation and dimensioning, of the elements in a cycloid stage of a speed reducer. Their idea is to use the results from this project and go into production of such reducer to cover another segment of the market. The company is interested in supplying transmissions for robust systems and for various industrial purposes, where large ratios of speed reduction are needed. The company has given the necessary input data for the model. They have also provided a real cyclo-drive reducer for further analyses. To obtain the dimensions and forming the geometry of the gears, some parts of Professor Ognyan Alipiev’s Phd work have been used. Professor Alipiev is head of “Theory of Mechanisms and Machines” department in University of Ruse “Angel Kunchev”, Bulgaria. For the determination of forces on the elements, models and drawings has been used Solidworks (SW) CAD software and SW simulation environment. The resultant calculation process can be used for designing the geometry and determination of the properties regarding the cycloid reducer. / Design of a Planetary-Cyclo-Drive Speed Reducer

The Fundamental Theorem of Algebra is a useful tool in determining the number of zeros of complex-valued polynomials and rational functions. It does not, however, apply to complex-valued harmonic polynomials and rational functions generally. In this thesis, we determine behaviors of the family of complex-valued harmonic functions $f_{c}(z) = z^{n} + \frac{c}{\overline{z}^{k}} - 1$ that defy intuition for analytic polynomials. We first determine the sum of the orders of zeros by using the harmonic analogue of Rouch\'e's Theorem. We then determine useful geometry of the critical curve and its image in order to count winding numbers by applying the harmonic analogue of the Argument Principle. Combining these results, we fully determine the number of zeros of $f_{c}$ for $c > 0$.

When environmental laws are constricted and downsizing of engines has become the reality of the vehicle industry, there needs to be a solution for the rise in torsion vibrations in the drivetrain. These increased levels of torsion vibrations are mostly due to excitations from the firing pulses, which in turn have become increased due to higher cylinder pressures. One of the solutions for further dampening the system is to add a centrifugal pendulum absorber to the flywheel, and predicting the behaviour of such a device has become imperative.The intent of this thesis is to create a model that will accurately emulate the effectiveness and functionality of a centrifugal pendulum absorber, so that it can be used in simulations to predict vehicle behaviour with its addition. To validate the model, a comparison is made between simulated results, using the model created in Adams/Car and Matlab, and road measurements conducted using a prototype acquired by the industry.The results from the simulations show that, with existing theory on the subject and software provided by Scania, an accurate model can be created. The reduction of torsion vibrations is evident, and the model’s behaviour correlates to that of the prototype.Future work on the subject requires a larger insight into pendulums tuned to multiple orders, and an extension of the model geometry would be advantageous.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims at presenting methodological referrals able to make mathematics teaching more enjoyable and interactive. In this sense, the work that will be developed here will address the study of some special curves like the Agnesi Curve, the Epicycloid, the Hypocycloid and will focus in greater depth the study of Cycloid addressing its main properties with an emphasis on Tautochrone and Brachistochrone. All work performed in this study shows that mathematics can play an important role in the classroom, helping to develop the learning of other disciplines thanks to allied experimental practices to the development of interdisciplinary content. In the literature there is much talk on interdisciplinarity, but most texts do not show how it can be done, that is, little is done really. This paper describes the content and shows how to perform integrative activities that will improve the teaching of other sciences and allows students to develop other skills (in addition to mathematical reasoning). This work does not end here, it is the rst step to other studies that improve the teaching of mathematics, especially geometry. Introduce the content so that the curiosity of the student is instigated is a big step in the teaching of this discipline. This is the objective of this work, arouse the curiosity of those involved through experimental practices without so little put aside theoretical part. / Este trabalho tem como objetivo apresentar encaminhamentos metodológicos capazes de tornar o ensino da matemática mais prazeroso e interativo. Neste sentido o trabalho que será desenvolvido aqui abordará o estudo de algumas curvas especiais como a Curva de Agnesi, a Epiciclóide, a Hipociclóide e destacará com maior profundidade o estudo da Ciclóide abordando a suas principais propriedades com ênfase na Tautócrona e Braquistócrona. Todo trabalho realizado neste estudo mostra que a matemática pode assumir um papel importante na sala de aula, ajudando a desenvolver a aprendizagem de outras disciplinas graças às práticas experimentais aliadas ao desenvolvimento de conteúdos interdisciplinares. Na literatura fala-se muito em interdisciplinaridade, más na maioria dos textos não se mostra como é possível fazê-la, ou seja, pouco se faz realmente. Este trabalho descreve o conteúdo e mostra como realizar atividades integradoras que venham a melhorar o ensino de outras ciências e permite desenvolver outras habilidades (além do raciocínio matemático) no aluno. Este trabalho não se encerra aqui, ele é o primeiro passo para outros estudos que melhorem o ensino da matemática, em particular da geometria. Introduzir o conteúdo de forma que a curiosidade do aluno seja instigada já é um grande passo no ensino dessa disciplina. É este o objetivo deste trabalho, despertar a curiosidade dos envolvidos através das práticas experimentais sem tão pouco deixar de lado a parte teórica.