Title :
Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincare maps
Author :
Roup, Alexander V. ; Bernstein, Dennis S. ; Nersesov, Sergey G. ; Haddad, Wessim M. ; Chellaboina, VijaySekhar
Author_Institution :
Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA
Abstract :
The verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator. In this paper we analyze the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations and Poincare maps to model the dynamics of this closed-loop system, we determine conditions under which the system possesses a limit cycle, and we analyze the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution
Keywords :
clocks; control system analysis; differential equations; feedback; mechanical control equipment; Poincare maps; closed-loop system; colliding masses; feedback regulator; impulsive differential equations; mechanical clock; verge and foliot escapement; Aerodynamics; Aerospace engineering; Angular velocity; Clocks; Differential equations; Feedback control; Gears; Limit-cycles; Space technology; Teeth;
Conference_Titel :
American Control Conference, 2001. Proceedings of the 2001
Conference_Location :
Arlington, VA
Print_ISBN :
0-7803-6495-3
DOI :
10.1109/ACC.2001.946422
