Illustrated Physics
physics, drawn
Concept

Escapement — where it appears

The mechanism in a clock that pushes its pendulum or balance a little each swing, replacing lost energy while releasing the gear train one tooth at a time. Where in the swing it pushes decides how much it disturbs the timing: a push at the bottom of the swing changes only the amplitude.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Four beads, four heights, one arrival time. One arch of a cycloid of radius 1, drawn with four beads on it at heights 0.061, 0.235, 0.592, 2.000 — a range of 33.0 to one. Each bead's time to slide, from rest and without friction, to the bottom of the arch is computed as a quadrature of ds/v along the curve as drawn, and the four answers are 1.003205 s, 1.003205 s, 1.003205 s, 1.003205 s: identical to 6.9e-13 of themselves. The closed form for this curve is π√(a/g) = 1.003205 s, which the quadrature reproduces without being told it. A bead let go at the cusp travels 5.7 times as far as the lowest one and arrives with it, because the extra distance is exactly paid for by the extra speed the extra height buys.

The curve that does not ask where it started

A pendulum's period depends on how far it swings, and the dependence is small but never zero. There is exactly one curve for which it is zero, and the reason has nothing to do with pendulums: on that curve the height above the bottom is proportional to the square of the distance travelled along it, which makes the motion harmonic by construction rather than by approximation.

mechanics · Pendulum Where a kick lands decides whether the clock gains. A pendulum's state as a point on a circle: horizontally its angle, vertically its angular speed, both scaled by the swing, so that undisturbed it goes round the grey circle clockwise once a period and its phase is the angle round the circle from the top. An escapement's kick raises its speed: an upward jump. Kicked at the bottom of the swing (top of the circle), the point jumps straight outward — a bigger swing, phase unchanged. Kicked 42° of phase before the bottom, the jump also carries it forward round the circle, by 9.8°, and the pendulum arrives early; kicked the same amount after the bottom, it is set back by 9.8° and arrives late. The kick is exaggerated here to 0.32 of the top speed to make the angles visible.

The kick that does not change the beat

A pendulum clock has to push its pendulum, or friction would stop it within minutes, and every push risks disturbing the very period the clock exists to keep. In 1826 George Airy worked out exactly when a push does no harm: at the bottom of the swing, where the pendulum is moving fastest, an impulse changes how far it swings and leaves the timing untouched. A push before the bottom makes the clock gain; after it, lose. Three centuries of escapement design are a search for a mechanism that pushes where Airy said — or that pushes in the wrong place in a way that cancels some other error.

mechanics · Pendulum

Named alongside it

The objects these essays reach for when they reach for this one.

IsochronismPendulumAmplitude dependenceArc lengthBrachistochroneCircular errorClockConstraintCycloidEvoluteImpulsePhase

All concepts