335 research outputs found

    Computer-Aided Design and Kinematic Simulation of Huygens’s Pendulum Clock

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    This article presents both the three-dimensional modelling of the isochronous pendulum clock and the simulation of its movement, as designed by the Dutch physicist, mathematician, and astronomer Christiaan Huygens, and published in 1673. This invention was chosen for this research not only due to the major technological advance that it represented as the first reliable meter of time, but also for its historical interest, since this timepiece embodied the theory of pendular movement enunciated by Huygens, which remains in force today. This 3D modelling is based on the information provided in the only plan of assembly found as an illustration in the book Horologium Oscillatorium, whereby each of its pieces has been sized and modelled, its final assembly has been carried out, and its operation has been correctly verified by means of CATIA V5 software. Likewise, the kinematic simulation of the pendulum has been carried out, following the approximation of the string by a simple chain of seven links as a composite pendulum. The results have demonstrated the exactitude of the clock

    Measurements of Radiation Pressure on Diffractive Films

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    One of the few ways to reach distant stars is by radiation pressure, in which photon momentum is harnessed from free sunlight or extraordinarily powerful laser systems. Large but low mass light-driven sails reflect photons and transfer momentum to the sailcraft, providing large velocity from continuous acceleration. Over the past decade, demonstrative reflective light sail missions were enabled by cost-efficient small satellites and the emerging private space economy. The maneuver of these metal-coated polyimide films is mechanically cumbersome because the sail must be rapidly tilted towards and away from the sun line during navigation. Modern diffractive films such as high-efficiency single-order gratings, liquid crystal cycloidal diffractive wave-plates, and meta-material gratings may provide enhanced control schemes with radiation pressure tangential to the sail surface. The potential to replace motorized control components with all-optical components also offers a reduction in mass and the risk of mission failure. Before spending considerable resources sending a rocket to deploy a solar sail, it must be verified that the sail will behave as expected in a lab on Earth. This is challenging since Earth’s gravity, electro-static forces, thermal effects, and environment vibrations exceed the relatively weak effects of radiation pressure. In this dissertation, we designed and constructed an opto-mechanical torsional pendulum in a vacuum environment that measures radiation pressure on diffraction films with sub-nano-Newton precision. With the system, we observed a large component of force parallel to the surface of a diffraction grating owing to “grating momentum”. Furthermore, we proposed, designed, and validated Diffractive Beam-Rider structures that enable spatially varying forces to pull and align the sailcraft to the beam. We parametrically “cooled” the turbulence on the Beam-Rider, which demonstrates its potential for implementation on a laser sail. This experimental stability verification was performed on a centimeter-sized bi-grating and a diffractive axicon with one and two-dimensional restoring force, respectively

    Huygens' cycloidal pendulum: an elementary derivation

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    A pedagogical derivation of the Huygens cycloidal pendulum, suitable for high-school students, is here presented. Our derivation rests only on simple algebraic and geometrical tricks, without the need of any Calculus concept

    Thomas Young and Eighteenth-Century Tempi

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    The physician, natural philosopher, and linguist Thomas Young in 1800 provided a table of tempi gauged by a pendulum. Calibrated against Quantz’s pulse-based system (1752), Young’s observations quantitatively corroborate the generally faster contemporary tempi, while also indicating cases in which they should be moderated. His statement about the relative order of very slow and fast tempo markings contradict several contemporary English sources; as a natural philosopher, he brought special skill in observation to these controversies

    O uso de pêndulos centrífugos para controle de vibrações torcionais em trens de potência automotivos

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    Orientador: Milton Dias JuniorTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Absorvedores de Vibração Pendulares Centrífugos (ou CPVAs) são uma tecnologia criada em 1911, que trouxe excelentes resultados na redução de vibração torcional de muitos sistemas. Porém, sua aplicação em trens de potência automotivos para redução de vibração no virabrequim tornou-se inviável ao final da década de 1940 pela existência de dampers viscosos à base de silicone, uma solução mais barata e com performance similar em certas aplicações. Contudo, a vibração torcional transmitida a transmissões manuais ou automatizadas, em certas velocidades críticas, pode gerar ruído em níveis inaceitáveis, e as soluções atuais para a atenuação deste tipo de vibração, em algumas aplicações, são ou pouco efetivas, como o atrito em discos de embreagem, ou muito custosas, como volantes de dupla massa. Por isso, neste trabalho busca-se a aplicação de absorvedores de vibração pendulares em um disco de embreagem de um trem de potência automotivo equipado com uma transmissão automatizada para a redução de vibração torcional na transmissão, reduzindo possivelmente o ruído de rattle. Para este fim, primeiramente testes são realizados no veículo em estudo para o levantamento de dados torcionais do trem de potência, e em seguida, um modelo linear torcional é proposto, para que a dinâmica torcional do trem de potência seja representada. Em seguida, uma análise extensiva dos principais tipos de CPVA é realizada. São realizadas análises lineares e não lineares em modelos com parâmetros adimensionais de um e dois rotores com pêndulos centrífugos, e nas análises não lineares, o Método de Múltiplas Escalas é utilizado; um método mais robusto e preciso do que o método que vem sendo utilizado nos principais trabalhos nesta área. Além disso, as análises são feitas considerando-se que os pêndulos possuem trajetória genérica, e ênfase é dada às trajetórias clássicas: circular, cicloide e epiciclóide. Com base nestas análises, duas metodologias de projeto de pêndulos centrífugos são propostas. Além disso, um protótipo de disco de embreagem com pêndulo é proposto. Então, baseando-se nas limitações do projeto, simulações são feitas utilizando o modelo proposto para o trem de potência e o modelo não linear do pêndulo. As primeiras simulações são feitas obedecendo as limitações do projeto, que propiciam um pequeno raio de instalação do pêndulo e permitem que ele possua massa muito menor do que o valor ideal. Estas simulações mostram que, neste caso o pêndulo se torna instável e ineficaz. Nas simulações seguintes, as limitações de projeto são desprezadas e ambos os projetos de pêndulo são testados. Com maior inércia, o absorvedor pendular é capaz de reduzir substancialmente a vibração torcional na transmissão sem que seja necessário introduzir atrito no disco de embreagem. Contudo, pêndulos com maior inércia podem comprometer a vida útil dos sincronizadores da transmissão, e por isso estudos devem ser realizados para verificar este efeito colateralAbstract: Centrifugal Pendulum Vibration Absorbers (or CPVAs) are a technology which dates back to 1911, and which has brought excellent results on the reduction of torsional vibrations in many systems. Its application in automotive powertrains for the reduction of vibration on the crankshaft became impracticable by the second half of the 1940s due to the existence of silicone based viscous dampers, a cheaper solution that had similar performance in many applications. However, torsional vibration transmitted to manual or semi-automatic gearboxes may cause unacceptable noise in some critical speeds, and the current solutions for the mitigation of this kind of vibration are, in some cases, either not effective, as torsional friction in clutch disks, or too expensive, as dual mass flywheels. For this reason, in this work, the use of centrifugal pendulum vibration absorbers on a clutch disk of a vehicle powertrain equipped with a semi-automatic gearbox is studied, aiming at reducing torsional vibration at the gearbox, leading to possible reduction of rattle noise. For this means, firstly tests are performed on the vehicle under investigation in order to obtain torsional data from its powertrain, and a linear torsional model of it is proposed next, so that the torsional dynamics of the powertrain can be represented. Then, an extensive analysis of the main types of CPVA are performed. Linear and nonlinear analyses are made in models with dimensionless parameters composed by one of two rotors and centrifugal pendulums. For the nonlinear analyses, the Method of Multiple Scales is used; a more robust and precise method than the one which has been used on the main literature in this area. Besides, the analyses are performed considering general-path pendulums and emphasis is given to the classical paths: circular, cycloid and epicycloid. Based on these analyses, two design techniques for CPVAs are proposed. Furthermore, a prototype of a clutch disk with pendulum absorbers is proposed. Then, based on project limitations, simulations are performed using the powertrain model and the nonlinear model of the CPVA. The first simulations are performed taking into consideration the project limitations, which allow a small radius for pinning the pendulum and also for a small mass of the pendulum bob, much lower than the ideal value. These simulations show that, in this case, the pendulum becomes unstable and ineffective. On the forthcoming simulations, project limitations are neglected and both pendulum design techniques are tested. With higher inertia, the pendulum absorbers are capable of providing a substantial reduction on the amplitude of vibration of the gearbox without the need for adding torsional friction to the clutch disk. However, pendulum bobs with high inertia may harm the service life of the gearbox¿s synchronizers, and further studies must be performed to evaluate this side effectDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânic

    CYCLOIDAL GAIT WITH DOUBLE SUPPORT PHASE FOR THE NAO HUMANOID ROBOT

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    The commercial Nao humanoid robot has 11 DOF in legs. Even if these legs include 12 revolute joints, only 11 actuators are employed to control the walking of the robot. Under such conditions, the mobility of the pelvis and that of the oscillating foot are mutually constrained at each step. Besides, the original gait provided by the manufacturer company of the Nao employs only single support phases during the walking. Because of both issues, the reduced mobility in legs and the use of only single support phases, the stability of the walking is affected. To contribute to improving such stability, in this paper an approach is proposed that incorporates a double support phase and a gait based on cycloidal time functions for motions of the pelvis and those of the oscillating foot. To assess the stability of the walking an index is applied, which is based on the notion of zero-moment point (ZMP) of the static foot at each step. Results of experimental tests show that the proposed gait enhances the stability of the robot during the walking

    Energy Localization in Periodic Structures: Application to Centrifugal Pendulum Vibration Absorber

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    International audienceIn this paper we study the non-linear dynamic of centrifugal pendulum vibration absorbers (CPVA), and we pay a special a ention to localized state solutions. e prediction of such states of vibration, and their stability, is of particular importance because they can lead to inefficient behavior for the CPVA and/or unforeseen stress levels. Using an approximated equation for the pendulums dynamics, we derive initial conditions to put the system in localized states. Following an analytic study of the non-linear normal mode of the system, the resolution of the approximated equation is carried out in the frequency domain using the Harmonic Balance Method and the Asymptotic Numeric Method. For sufficiently low inertia ratio, we show that the system can possess stable localized states
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