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

Volume

4

fYear

2001

fDate

2001

Firstpage

3245

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;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2001. Proceedings of the 2001

Conference_Location

Arlington, VA

ISSN

0743-1619

Print_ISBN

0-7803-6495-3

Type

conf

DOI

10.1109/ACC.2001.946422

Filename

946422