| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 106 === Synchronization is a common phenomenon and has important applications in many different fields such as biology, physics, communication, medicine, engineering, etc. Huygens was the first one who observed the synchronization of two pendulum clocks hung on the wall. Stimulated by Huygens’ observation, many researchers started to study the synchronization of pendulum clocks. The key part of a pendulum clock is the escapement mechanism, which has been either modeled as a Van der Pol oscillator or as two constant pulses acting on the pendulum in the literature. To the best of our knowledge, no one has derived the governing equations of a pendulum clock taking into the account the geometric shape of the escapement mechanism. In this thesis, we studied the synchronization of pendulum clocks with the deadbeat escapement mechanism. With the help of Lagrange’s equations, we derived the governing equations according to the shapes and dimensions of the parts composing the deadbeat escapement mechanism.
We first placed a deadbeat escapement clock on the ground to study the relation between the driving moment and the period of the pendulum. Then we put a deadbeat escapement clock on a plate, which can move freely in the horizontal direction, to investigate the influence of the movement of the plate on the motion of the pendulum clock.
After that, we put several pendulum clocks on a plate and use numerical integration to study possible synchronization patterns of the pendulum clocks. We investigated the effects of system parameters, e.g., length of the pendulum, mass of the plate, initial angles, on the synchronization patterns. We examined the domains of attraction of different synchronization patterns. Finally, we employed the method of harmonic balance to determine approximately the amplitude and frequency of different synchronization patterns.
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