Despite centuries of research and significant advances, the escapement mechanism used to count and maintain oscillations of mechanical time bases remains a complex mechanism and a major source of energy losses. We showed in previous work that, instead of the widely used rotational one degree-of-freedom (DOF) oscillators, 2-DOF flexure oscillators have the potential of revolutionizing mechanical watchmaking by eliminating the traditional escapement, replacing it by a simple crank driving a pin. Additionally, using flexures increases the quality factor of the time base, leading to further potential improvements in timekeeping accuracy and energy consumption. However, a significant challenge of these new time bases is their balancing such that the influence of external accelerations on their frequency is minimized, a necessary condition for accurate timekeeping in portable applications. This article presents a novel 2-DOF planar flexure oscillator called Wattwins and demonstrates how it can be made insensitive to linear accelerations such as gravity. For this purpose, a new approach to shaking force balancing is developed based on the decomposition of perturbations into effects corresponding to different orders of center of mass displacement. A full analytical model for frequency tuning and shaking force balancing of the 2-DOF oscillator is derived using a pseudo-rigid-body model and assuming that it can be decomposed into two independent 1-DOF oscillators. The results are validated by the finite element method and show that practical mechanical watch specifications can theoretically be reached. A physical prototype was also constructed and preliminary experimental results confirm the theory as well as the simulations.

尽管经过数百年的研究和取得重大进展，用于计数和维持机械时基振荡的擒纵机构仍然是一个复杂的机构，也是能量损失的主要来源。我们在之前的工作中表明，与广泛使用的旋转单自由度 (DOF) 振荡器不同，2-DOF 挠性振荡器通过消除传统的擒纵机构，代之以一个简单的曲柄驱动器，具有彻底改变机械制表业的潜力。别针。此外，使用挠性件可提高时基的品质因数，从而进一步提高计时精度和能耗。然而，这些新时基的一个重大挑战是它们的平衡，以便最大限度地减少外部加速度对其频率的影响，在便携式应用中准确计时的必要条件。本文介绍了一种名为 Wattwins 的新型 2-DOF 平面挠性振荡器，并演示了如何使其对线性加速度（如重力）不敏感。为此，基于将扰动分解为与质心位移的不同阶数相对应的效应，开发了一种新的振动力平衡方法。使用伪刚体模型并假设它可以分解为两个独立的 1-DOF 振荡器，推导出用于 2-DOF 振荡器的频率调谐和振动力平衡的完整分析模型。结果通过有限元方法验证，表明理论上可以达到实用的机械表规格。