THE NONLINEAR DYNAMICS OF ESCAPEMENT MECHANISMS

Branislav POPKONSTANTINOVIC, Alina DUTA, Gabriel MARINESCU, Misa STOJICEVIC, Aleksandar DJORDJEVIC

Abstract


Clock mechanisms belong to the field of precision mechanics, which measure the passage of time by a high degree of uniformity of their movements. The key sub-assembly of the clock mechanism is an oscillator coupled with an escapement mechanism which introduces disturbances into the oscillatory process so that the oscillations are no longer free, but forced and nonlinear with a frequency that is subjected to change. This work is dedicated to the analysis of the clock mechanism dynamics using the theory of perturbation calculus. The approximate solution of the nonlinear differential equations that describe the motion of the clock's oscillator are determined by the method of two-time scale perturbation and represent universally applicable formulas for escapement errors. These formulas are verified by the computer simulations of the escapement mechanism operation.

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References


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