gear train no relation escapement
The verge (or crown wheel) escapement is the earliest known type of mechanical escapement, the mechanism in a mechanical clock that controls its rate by allowing the gear train to advance at regular intervals or 'ticks'. Verge escapements were used from the late 13th century until the mid 19th century in clocks and pocketwatches.   The name verge comes from the Latin virga, meaning stick or rod.Its invention is important in the history of technology, because it made possible the development of all-mechanical clocks.  This caused a shift from measuring time by continuous processes, such as the flow of liquid in water clocks, to repetitive, oscillatory processes, such as the swing of pendulums, which had the potential to be more accurate.   Oscillating timekeepers are used in all modern timepieces.How it works
The verge escapement consists of a wheel shaped like a crown, called the escape wheel, with sawtooth-shaped teeth protruding axially toward the front, and with its axis oriented horizontally.  In front of it is a vertical rod, the verge, with two metal plates, the pallets, that engage the teeth of the escape wheel at opposite sides. The pallets are not parallel, but are oriented with an angle in between them so only one catches the teeth at a time.  Attached to the verge at its top is an inertial oscillator, a balance wheel or in the earliest clocks a foliot, a horizontal beam with weights on either end.  This is the timekeeper of the clock.
As the clock's gears turn the crown wheel (see animation), one of its teeth catches on a pallet, pushing on it.  This rotates the verge and foliot in one direction, and rotates the second pallet into the path of the teeth on the opposite side of the wheel, until the tooth slides off the end of the pallet, releasing it.  Then the crown wheel rotates freely a short distance until a tooth on the wheel's opposite side contacts the second pallet, pushing on it.  This reverses the direction of the verge rod and foliot, rotating the verge back the other direction, until this tooth pushes past the second pallet.  Then the cycle repeats.  The result is to change the rotary motion of the wheel to an oscillating motion of the verge and foliot.  Each swing of the balance wheel thus allows one tooth of the escape wheel to pass, advancing the wheel train of the clock by a fixed amount, moving the hands forward at a constant rate.  The moment of inertia of the foliot or balance wheel controls the oscillation rate, determining the rate of the clock.  The escape wheel tooth, pushing against the pallet each swing, provides an impulse which replaces the energy lost by the foliot to friction, keeping it oscillating back and forth.
In a verge pendulum clock (see picture) which appeared after the pendulum was invented in 1656, the escapement was turned 90° so the verge rod was horizontal, while the escape wheel's axis was vertical, located under the verge rod.  In the first pendulum clocks the pendulum was attached to the end of the verge rod instead of the balance wheel or foliot.  In later pendulum clocks the  pendulum was suspended by a short straight spring of metal ribbon from the clock frame, and a vertical arm attached to the end of the verge rod ended in a fork which embraced the pendulum rod; this avoided the friction of suspending the pendulum directly from the pivoted verge rod.  Each swing of the pendulum released an escape wheel tooth.
The escape wheel must have an odd number of teeth for the escapement to function.  With an even number, two opposing teeth will contact the pallets at the same time, jamming the escapement.  The usual angle between the pallets was 90° to 105°, resulting in a foliot or pendulum swing of around 80° to 100°.  In order to reduce the pendulum's swing to make it more isochronous, the French used larger pallet angles, upward of 115°.  This  reduced the pendulum swing to around 50° and reduced recoil (below), but required the verge to be located so near the crown wheel that the teeth fell on the pallets very near the axis, reducing initial leverage and increasing friction, thus requiring lighter pendulums.
no relation