Comparison of Motion in Anchor and Deadbeat
A major cause of error in clocks is changes in the drive force applied to the escapement, caused by small changes in the friction of the gears or the pallets, or the diminishing force of the mainspring as it unwinds. An escapement in which changes in drive force do not affect the rate is called isochronous. The superior performance of the deadbeat over the anchor is caused by its improved isochronism. This is due to the different ways changes in drive force affect the swing of the pendulum in the two escapements:
- In the anchor escapement, an increase of drive force causes the pendulum to swing back and forth more quickly, but does not increase the pendulum's amplitude, the length of its swing, much. The increased force of the escape wheel tooth on the pallet during the recoil part of the cycle tends to decrease the pendulum's swing, while the force of the tooth during the forward impulse part of the cycle tends to increase the pendulum's swing. These tend to cancel each other out, leaving the swing unchanged. But both these effects decrease the time of swing. In other words, increased force knocks the pendulum back and forth in a fixed arc faster.
- In the deadbeat escapement, increased drive force does not change the period of the pendulum much, resulting in better isochronism and better timekeeping, but it does increase the pendulum's swing. Since the escapement doesn't have a recoil period when the tooth's force opposes the direction of the pendulum's motion, increased force causes the pendulum to swing in a wider arc, as well as move faster. The time required to cover the extra distance exactly compensates for the increased speed of the pendulum, leaving the period of swing unchanged. Although the wider swing causes a slight increase in period due to circular error, for the small amplitudes used in clocks this effect is negligible.
When the deadbeat was invented, clockmakers initially believed it had inferior isochronism to the anchor, because of the greater effect of changes in force on the pendulum's amplitude.
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