**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# Design of a Flexure Based Low Frequency Foucault Pendulum

Abstract

The Foucault pendulum is a well-known mechanism used to demonstrate the rotation of the Earth. It consists in a pendulum launched on linear orbits and, following Mach’s Principle, this line of oscillation will remain fixed with respect to absolute space but appear to slowly precess for a terrestrial observer due to the turning of the Earth. The theoretical proof of this phenomenon uses the fact that, to first approximation, the Foucault pendulum is a harmonic isotropic two degree of freedom (2-DOF) oscillator. Our interest in this mechanism follows from our research on flexure-based implementations of 2-DOF oscillators for their application as time bases for mechanical timekeeping. The concept of the Foucault pendulum therefore applies directly to 2-DOF flexure based harmonic oscillators. In the Foucault pendulum experiment, the rotation of the Earth is not the only source of precession. The unavoidable defects in the isotropy of the pendulum along with its well-known intrinsic isochronism defect induce additional precession which can easily mask the precession due to Earth rotation. These effects become more prominent as the frequency increases, that is, when the length of the pendulum decreases. For this reason, short Foucault pendulums are difficult to implement, museum Foucault pendulum are typically at least 7 meters long. These effects are also present in our flexure based oscillators and reducing these parasitic effects, requires decreasing their frequency. This paper discusses the design and dimensioning of a new flexure based 2-DOF oscillator which can reach low frequencies of the order of 0.1[Hz]. The motion of this oscillator is approximatelyplanar, like the classical Foucault pendulum, and will have the same Foucault precession rate. The construction of a low frequency demonstrator is underway and will be followed by quantitative measurements which will examine both the Foucault effect as well as parasitic precession.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts

Loading

Related publications

Loading

Related publications (8)

Loading

Loading

Loading

Related concepts (18)

Oscillation

Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar example

Pendulum

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gra

Precession

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Eul

Patrick Robert Flückiger, Simon Nessim Henein, Ilan Vardi

In 1851 Léon Foucault created a sensation with his pendulum providing a direct demonstration of the turning of the Earth. This simple device consists of a pendulum which is launched in a purely planar orbit. Following Mach's principle of inertia, the mass will continue to oscillate in the same planar orbit with respect to absolute space. For an observer on Earth, however, the plane of oscillation will turn. Conceptually speaking, Foucault constructed a very precise demonstrator showing that, when put on a rotating table, planar oscillations of an isotropic two degree of freedom oscillator remain planar with respect to an inertial frame of reference. These oscillators have currently been under study in order to construct new horological time bases. A novel concept was a spherical isotropic two degree of freedom oscillator. Theoretical computations indicate that when put on a rotating table, planar oscillations of the spherical oscillator neither remain planar in the inertial frame nor in the rotating frame of reference, but in a frame of reference rotating at exactly half the rotational speed of the rotating table. This intriguing result led to the design, construction and experimental validation of a proof of concept demonstrator placed on a motorized rotating table. The demonstrator consists of a spherical isotropic oscillator, a launcher to place the oscillator on planar orbits, a motorized rotating table and a measurement setup. The experimental data recorded by the lasers validates the physical phenomenon.

Patrick Robert Flückiger, Simon Nessim Henein, Ilan Vardi

The Foucault pendulum provides a demonstration of the turning of the Earth. The principle at work is that linear oscillations of a two-degree-of-freedom isotropic harmonic oscillator remain unchanged in an inertial frame of reference, so appear to precess in a rotating frame of reference. In recent work, we applied two-degree-of-freedom isotropic oscillators to mechanical timekeeping. In this paper, we note that the spherical oscillators we considered have qualitatively different behavior in a non-inertial frame. We show that when in a rotating frame, linear oscillations precess at one half the rotational speed of the rotating frame. We validate this result experimentally by designing and constructing a proof of concept demonstrator placed on a motorized rotating table. The demonstrator consists of a spherical isotropic oscillator, a launcher to place the oscillator on planar orbits, a motorized rotating table, video recording for qualitative observation, and a laser measurement setup for quantitative results. The experimental data recorded by the lasers strongly validate the physical phenomenon.

2020In this thesis we describe a strategy to control robotic knees and ankles. A dynamical system is used to generate a position trajectory to control a servo motor replacing the missing joint. The dynamical system consists in a pool of coupled oscillators modeling a central pattern generator (CPG). As a first step, anthropometric trajectories of the knee and ankle are learned by the system through the convergence of the oscillators to the specific frequencies, corresponding amplitudes and phase relations. The same system is then used to play back these trajectories. As a sensory feedback to trigger the playback we use one adaptive frequency oscillator to synchronized with the acceleration from the thigh. We use a bipedal model in a physics-based robot simulation environment to test the proposed system. Finally we present a simple hardware implementation of this system on the Agonist-Antagonist Active Knee prototype.

2010