Citation: Flückiger, P.; Cosandier, F.; Schneegans, H.; Henein, S. Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy. Machines 2024, 12, 232. https://doi.org/10.3390/ machines12040232 Academic Editor: Alessandro Cammarata Received: 9 February 2024 Revised: 21 March 2024 Accepted: 26 March 2024 Published: 30 March 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). machines Article Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy Patrick Flückiger , Florent Cosandier , Hubert Schneegans * and Simon Henein Micromechanical and Horological Design Laboratory (Instant-Lab), École Polytechnique Fédérale de Lausanne (EPFL), CH-2000 Neuchâtel, Switzerland; patrick.fluckiger@epfl.ch (P.F.); florent.cosandier@epfl.ch (F.C.); simon.henein@epfl.ch (S.H.) * Correspondence: hubert.schneegans@epfl.ch Abstract: The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wear. This paper presents an alternative mechanism that is functionally equivalent to a classical flywheel while relying exclusively on limited- stroke flexure joints. This novel one-degree-of-freedom zero-force mechanism has no wear and requires no lubrication: it is thus compatible with extreme environments, such as vacuum, cryogenics, or ionizing radiation. The mechanism is composed of two coupled pivoting rigid bodies whose individual angular momenta vary during motion but whose sum is constant at all times when the pivoting rate is constant. The quantitative comparison of the flexure-based flywheel to classical ones based on a hollow cylinder as inertia shows that the former typically stores 6 times less angular momentum and kinetic energy for the same mass while typically occupying 10 times more volume. The freedom of design of the shape of the rigid bodies offers the possibility of modifying the ratio of the stored kinetic energy versus angular momentum, which is not possible with classical flywheels. For example, a flexure-based flywheel with rigid pivoting bodies in the shape of thin discs stores 100 times more kinetic energy than a classical flywheel with the same angular momentum. A proof-of- concept prototype was successfully built and characterized in terms of reaction moment generation, which validates the presented analytical model. Keywords: flexure mechanism; flywheel; energy storage; angular momentum 1. Introduction 1.1. Flywheel State-of-the-Art and Article Contributions Flywheels are mechanical components that are able to store kinetic energy (in the form of rotational energy) as well as angular momentum. We define a standard flywheel as a rigid body that rotates around an axis that coincides with its center of mass (COM) and is parallel to one of its principal axes of inertia. Flywheels have many applications, such as smoothing power output, serving as an additional source of energy, and generating reaction torques. The smoothing of power output is commonly found in reciprocating engines. Flywheels may serve in kinetic energy recovery system (KERS) applications to store and release kinetic energy harvested from the braking of a vehicle. They can be used as additional auxiliary power sources in the form of intermittent pulses (for a forging hammer, for example) or as a single impulse (for powering up a tokamak or aircraft catapult, for example). The generation of reaction torques comes from the flywheel’s ability to store angular momentum and finds its use in attitude control systems, such as the reaction wheels and control moment gyros of spacecrafts. A standard flywheel is fixed to its base by means of a rotating bearing, such as ball bearings, gas bearings, or magnetic bearings, which permits multiple complete revolutions. Even though the flywheel is a well-established technology, the use of ball bearings may Machines 2024, 12, 232. https://doi.org/10.3390/machines12040232 https://www.mdpi.com/journal/machines