Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps

  • ALEXANDER V. ROUPy, DENNIS S. BERNSTEINy, SERGEY G. NERSESOVz, WASSIM M. HADDADz, VijaySekhar Chellaboina
  • Published 2003

Abstract

The verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator. In this paper we analyse the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations and Poincaré maps to model the dynamics of this closed-loop system, we determine conditions under which the system possesses a limit cycle, and we analyse the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution.

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Cite this paper

@inproceedings{ROUPy2003LimitCA, title={Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps}, author={ALEXANDER V. ROUPy and DENNIS S. BERNSTEINy and SERGEY G. NERSESOVz and WASSIM M. HADDADz and VijaySekhar Chellaboina}, year={2003} }