Clocks and Clocks and WatchesWatches

Pendulum ClocksPendulum Clocks

A pendulum oscillates with a A pendulum oscillates with a frequency of:frequency of:

g is gravitational acceleration

R is the length of the pendulum (pivot to center of mass)

Frequency does not depend on weight of the Bobg = 32 ft/s2 on earth

R

How fast would a 1 ft pendulum How fast would a 1 ft pendulum swing?swing?

Freq. = 0.9 cycles/sec. = 9 cycles/10 sec.Freq. = 0.9 cycles/sec. = 9 cycles/10 sec.

= 3.14= 3.14

g = 32 ft/s2 on earth

http://electronics.howstuffworks.com/http://electronics.howstuffworks.com/clock3.htmclock3.htm The torque of the gears keep the

pendulum going.The gears get energy from the potential energy of the weight or spring in the clock.

Winding the clock raises the weight or tightens the spring.

The escapement ensures that the energy is released in small increments over a long period of time (e.g. daily or weekly).The pendulum length determines the frequency of the tick-tocks.

http://en.wikipedia.org/wiki/Escapementhttp://en.wikipedia.org/wiki/Escapement

When watching this animation, notice When watching this animation, notice that the gear’s tooth gives a little push that the gear’s tooth gives a little push to the pendulum so that the pendulum to the pendulum so that the pendulum continues to oscillates.continues to oscillates.

The escape tooth slides across the pallet, The escape tooth slides across the pallet, exerting a small force on it. This small exerting a small force on it. This small force exerted each cycle keeps the force exerted each cycle keeps the pendulum moving.pendulum moving.

Energy is allowed to “escape” Energy is allowed to “escape” each time a tooth is released.each time a tooth is released.

http://www.geocities.com/mvhw/anchor.html

Escape Wheel

Escape Tooth

Pallet

Anchor

The pendulum oscillates at two cycles/secPeriod = ½ second.Second hand is directly connected to the Escapement gear

This axle is rotating(40/16)x(40/16)x(40/16)x(40/16)x(16/120)

Or 5.2 times slower.

Every 5.2 minutesthe Weight wheel rotates once.

This is a clock with only a second hand:

Effects of TemperatureEffects of Temperature

►Pendulums expand when heated Pendulums expand when heated causing R to get longer, making the causing R to get longer, making the clock slow down and lose time.clock slow down and lose time.

► In colder temperatures lubricants In colder temperatures lubricants become thicker increasing friction. become thicker increasing friction. Some clocks might stop if not enough Some clocks might stop if not enough energy is given to the pendulum with energy is given to the pendulum with each tick.each tick.

From clock to watches From clock to watches (portable clocks)(portable clocks)

Replace pendulum with a small hair Replace pendulum with a small hair spring and balance that oscillates at a spring and balance that oscillates at a certain frequency if regularly certain frequency if regularly energized.energized.

http://elginwatches.org/help/what_is_a_watch.html

The hairspring coils and uncoils. The hairspring and balance are made to oscillate at a specificfrequency. The hair spring is made from an alloy that can take the constant coiling and uncoiling.

Watches are Energized with a main Watches are Energized with a main spring instead of weights.spring instead of weights.

1. Mainspring is the energy source.

1. Escpapement ensures that energy is released slowly and in constant increments.

1. Multiple gear trains control the hands. Hands line up in the center with slower moving hands mounted on hollow spindles.

http://img.timezone.com/img/articles

SpringsSprings

Springs store energy:Springs store energy:

F = k * xF = k * x

PE PE springspring = ½ k * x = ½ k * x22

k is spring constant (stiffness)k is spring constant (stiffness)

x is the amount of displacement or x is the amount of displacement or how tight the spring is woundhow tight the spring is wound

As the spring slowly is allowed to unwind, it does very small increments ofWork on the clock.

Self Winding WatchesSelf Winding Watches

http://www.timezone.com

An Oscillating Weight moves as the wearer’s wrist moves.

The mainspring is automatically wound.

ResourcesResources

http://electronics.howstuffworks.com/clock.htmhttp://electronics.howstuffworks.com/clock.htm

http://www.engineerguy.com/comm/3926.htmhttp://www.engineerguy.com/comm/3926.htm

http://www.engineerguy.com/comm/4340.htmhttp://www.engineerguy.com/comm/4340.htm

Videos:Videos:

►Da Vinci’s Clocks:Da Vinci’s Clocks:

http://www.youtube.com/watch?http://www.youtube.com/watch?v=QMpd811EeyEv=QMpd811EeyE

http://www.youtube.com/watch?v=e-http://www.youtube.com/watch?v=e-RR0H_4DYARR0H_4DYA

Assignment:Assignment:

►Reverse Engineer the Westclok Alarm Reverse Engineer the Westclok Alarm ClockClock

►Do not break the clock works or case. Do not break the clock works or case. ►Draw the mechanics that relate to the Draw the mechanics that relate to the

second, minute, and hours hands. second, minute, and hours hands. Label the primary parts.Label the primary parts.

►See lab handoutSee lab handout

http://www.horologist.com/escapements.htm

Plan vs. Elevation View of a clock works