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Coexisting chaotic and periodic dynamics in clock escapements.

Francis C Moon1, Preston D Stiefel

  • 1Joseph Ford Professor of Mechanical Engineering, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, NY 14853-7501, USA. fcm3@cornell.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 9, 2006
PubMed
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This study reveals that chaotic vibrations in clock escapements can reduce friction in the gear train. This noise is a natural phenomenon in mechanical systems, offering insights into machine dynamics.

Area of Science:

  • Mechanical Engineering
  • Physics
  • Dynamical Systems

Background:

  • Noise in machines is often studied to understand system degradation.
  • Clock escapements are complex mechanical systems with inherent periodic dynamics.
  • Understanding noise sources is crucial for improving machine performance and longevity.

Purpose of the Study:

  • To investigate the nature of noise in machines using clock escapements as a case study.
  • To analyze the dynamics of clock escapements from experimental, historical, and analytical perspectives.
  • To model and understand the phenomenon of self-generated chaos in mechanical oscillators.

Main Methods:

  • Experimental analysis of two escapement mechanisms from the Reuleaux kinematic collection.
  • Development of a mathematical model to simulate clock escapement dynamics.

Related Experiment Videos

  • Investigation of chaotic-like vibrations coexisting with periodic motion.
  • Analysis of the structural vibrations and feedback mechanisms within the clock.

    • Main Results:

    • Chaotic-like vibrations were observed in clock escapement mechanisms.
    • A mathematical model demonstrated how self-generated chaos can reduce dry friction in the gear train.
    • The model exhibited a strange attractor in the structural vibrations of the clock.
    • The internal feedback mechanisms were found to be analogous to anti-control of chaos.

    Conclusions:

    • Self-generated chaos in clock escapements can actively influence and potentially reduce mechanical friction.
    • The study provides a novel perspective on noise as a functional element in mechanical systems.
    • The findings have implications for understanding and designing machines with complex dynamical behaviors.