Clock Escapements

Introduction

The intent of this animation is to show how the escapement of a mechanical clock works. I have chosen to use a pendulum as the source of the time unit. Also, the escapement mechanism design does not have the refinements that have been discovered over the years[1]. Because of this simplicity of design, I can let the viewer make changes to the escapement parameters to see how improvements might be made.

Time Unit Design

The frequency, f, of oscillation of a pendulum with fairly small amplitude (say, less than 10 degrees) is given by the following equation:

where g is the acceleration of gravity, 9.8 m-sec^-2 on the earth’s surface, and L is the length from the rotation axis of the pendulum to the concentrated mass on the other end of the pendulum. For a length, L, of 0.248 meters, f is 1 Hz or 1 cycle per second. The length of 0.248 meters (or 9.76 inches) happens to be convenient for a mantle clock. Obviously, we can halve the frequency (to ½ cycle per second) by increasing the length, L, by a factor of 4. That makes L almost 1 meter and that would be a good length for a standing “grandfather” clock.

It is the pendulum that regulates the advancement of the escapement device. Both the pendulum drive and the drive for the escapement gear are derived from a spiral spring that one winds up once per week or so.

The advancement of the spring-loaded escapement gear is controlled by two tines of a fork that rotates with the pendulum. The goal of these tines is to allow one and only one gear tooth advancement for each cycle of the pendulum. One can think of the “upstream” tine as the release unit and the “downstream” tine as the catcher unit. The tips of these tines both have to swing within their respective tooth notches. This action will be obvious when you run the animation.