Coexisting chaotic and periodic dynamics in clock escapements.
This paper addresses the nature of noise in machines. As a concrete example, we examine the dynamics of clock escapements from experimental, historical and analytical points of view. Experiments on two escapement mechanisms from the Reuleaux kinematic collection at Cornell University are used to illustrate chaotic-like noise in clocks. These vibrations coexist with the periodic dynamics of the balance wheel or pendulum. A mathematical model is presented that shows how self-generated chaos in clocks can break the dry friction in the gear train. This model is shown to exhibit a strange attractor in the structural vibration of the clock. The internal feedback between the oscillator and the escapement structure is similar to anti-control of chaos models.
Moon
Francis C
FC
Joseph Ford Professor of Mechanical Engineering, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, NY 14853-7501, USA. fcm3@cornell.edu
Stiefel
Preston D
PD
D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback; D007700:Kinetics; D019563:Mechanics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D013598:Systems Theory