無幌擒縱器擺鐘的同步

Synchronization of Deadbeat Escapement Pendulum Clock

簡伯丞(Po-Cheng Chien) ； 盧中仁(Chung-Jen Lu)

《中華民國振動與噪音工程學會論文集》 2018 (2018/06) Pp. 98-105

摘要

同步是常見的現象，涵蓋的範圍也相當廣泛，在生物、物理、通訊、醫療、工程等領域皆有重要的應用。本論文以無幌擒縱器為計時機構的擺鐘來探討同步現象。利用Lagrange方程式及無幌擒縱器的幾何特性推導其運動方程式。首先將無幌擒縱器擺鐘放置於地面上，探討擺錘振幅和自發性週期運動的關係。接著將數個無幌擒縱器擺鐘放置於可自由運動的水平基座上，探討其間的交互作用。最後利用數值方法探討不同數目的無幌擒縱器擺鐘最終所呈現的同步運動的可能形式。

關鍵字

同步 ； 無幌擒縱器

並列摘要

Synchronization is a common phenomenon in fields of biology, physics, communication, medicine, engineering, etc. This paper studies synchronization between several deadbeat escapement clocks on a plate which can move freely in the horizontal direction. The geometric properties and motion characteristics of the deadbeat escapement are examined in detail. Lagrange's equations are then employed to derive the governing equations of this system. We first place the deadbeat escapement clock on the ground to study the relation between the driving moment and the period of the pendulum. Then several deadbeat escapement clocks are put on the plate to study possible synchronization motions. We find that, for the case of 5 clocks, the steady state motion can be classified into 1, 3, 4, and 5 groups in different kinds of synchronization motions.

並列關鍵字

Synchronization ； Deadbeat escapement