Numerical analysis of grasshopper escapement

Abstract: The dynamics of driven, damped pendulum as used in mechanical clocks is numerically investigated. In addition to the analysis of a well-known mechanisms such as chronometer escapement, the unusual properties of Harrison's grasshopper escapement are explored, giving some insights regarding the dynamics of this system. Both steady state operation and transient effects are discussed, indicating the optimal condition for stable long-term clock accuracy. Possibility of chaotic motion is investigated.