Title :
On the dynamics of the escapement mechanism of a mechanical clock
Author :
Roup, Alexander V. ; Bernstein, Dennis S.
Author_Institution :
Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA
Abstract :
The escapement mechanism of a mechanical clock is a classical example of a feedback regulator. We analyze the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations to model the dynamics of this closed-loop system, we show that the system possesses a periodic orbit, and we analyze the period and amplitude of this orbit in terms of the inertias of the colliding masses and their coefficient of restitution
Keywords :
closed loop systems; continuous time systems; differential equations; discrete systems; dynamics; feedback; matrix algebra; coefficient of restitution; colliding masses; escapement mechanism; feedback regulator; impulsive differential equations; inertias; mechanical clock; periodic orbit; Aerodynamics; Angular velocity; Clocks; Differential equations; Feedback control; Force feedback; Gears; History; Teeth; Torque;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.831320
